Ben-Yakar, Adela (2000). - The Hanson Group

Transcription

EXPERIMENTAL INVESTIGATION OF MIXING AND
IGNITION OF TRANSVERSE JETS IN SUPERSONIC
CROSSFLOWS
a dissertation
submitted to the department of mechanical engineering
and the committee on graduate studies
of stanford university
in partial fulfillment of the requirements
for the degree of
doctor of philosophy
Adela Ben-Yakar
December, 2000
c Copyright 2001 by Adela Ben-Yakar
°
All Rights Reserved
ii
Abstract
Ignition, flame-holding, and mixing enhancement are fundamental aspects of supersonic combustion and are critical to the development of hypersonic airbreathing
propulsion engines. High velocities associated with supersonic/hypersonic flight speeds
constrain the performance of propulsion systems because of the limited flow residence
time inside the combustor. A useful hypervelocity propulsion system therefore requires
enhanced mixing of fuel and air, injection with very low drag penalty, and effective
distribution of fuel over the burner cross-section. One of the simplest approaches is
the transverse injection of fuel from wall orifices. The interesting but rather complicated flow-field dynamics of transverse jets injected into a supersonic crossflow has been
studied by many supersonic combustion researchers since 1960’s, but with limited freestream flow conditions. Most of the previous research was performed in conventional
wind tunnels by accelerating cold air into supersonic conditions, namely in low velocity
and low total enthalpy flow conditions. However, a real supersonic combustor environment at flight speeds beyond Mach 8 can only be simulated using impulse facilities due
to the required high total enthalpies. Among various impulse facilities, expansion tubes
are especially useful in providing high total enthalpy flows with the proper chemical
composition, namely the absence of dissociated species.
This research is focused on studying the near-field mixing and ignition properties of
transverse fuel jets injected into realistic supersonic combustor flows. We use advanced
flow visualization techniques, namely planar laser-induced fluorescence (PLIF) imaging of the hydroxyl radical (OH) and ultra-fast-framing-rate schlieren imaging. While
schlieren indicates the location of shock waves, jet penetration and large scale flow
features, OH-PLIF is used to map the regions of ignition.
The first objective of the present work is to characterize the expansion tube facility
iii
for three operating points, simulating flight Mach 8, 10 and 13 total enthalpy conditions.
The ability of the expansion tube to provide a steady-flow test time of adequate duration
and a core flow of sufficient size for 2 mm diameter jet-in-crossflow studies is verified.
The second objective is to study the flow-field properties of hydrogen and ethylene
jets, owing to their relevance to supersonic combustion. Visual observations of image
data, supported by the results for the convection velocity and jet penetration, reveal
significant differences between the hydrogen and ethylene injection cases with similar
momentum flux ratio. Previously the momentum flux ratio was found to be the main
controlling parameter of the jet penetration but the results here demonstrate the existence of an additional mechanism which alters the vortical structure, the penetration
and the mixing properties of the jet shear layer. The thickness of the penetration band,
used as the representation of the jet-shear-layer thickness is considerable in the ethylene injection case, due to the “tilting-stretching-tearing” mechanism and also due to
the larger growth rate of the jet shear layer. Furthermore autoignition of an ethylene
transverse jet is achieved at flight Mach 10 conditions despite the relatively long ignition delay times of ethylene (hydrocarbons), a key limitation for hydrocarbon-fueled
scramjets. These results of higher penetration, larger jet shear layer growth rate and
autoignition capability indicate that hydrocarbons might be a useful fuel in scramjets
flying at Mach 10 conditions.
The third objective is to investigate the stability of the jet shear layer at various
speed ratios and density ratios via schlieren. The high shear stresses induced by the
large velocity difference across the jet shear layer have a large effect on the structure of
the layer. For the unstable case, we notice: 1) breakdown of Kelvin-Helmholtz structures
with the tilting-stretching-tearing mechanism; 2) increased growth rates with decreasing
values of jet-to-free-stream velocity ratio; 3) large intrusions of crossflow in between the
eddies, and 4) additional shock waves and distortion of the bow shock around the large
eddies. Stable layers show well-defined Kelvin-Helmholtz spanwise rollers. The results
plotted in a density-effective velocity ratio (s − λ) diagram demonstrate two separate
regions of “stable”and “unstable”jet shear layers with a separation line at a critical
“effective velocity ratio”.
The final objective is to study the ignition and flame-holding capabilities of a hydrogen transverse jet injected into flight Mach 8, 10 and 13 total enthalpy conditions.
The results demonstrate self-ignition in the near-field of the hydrogen jet for the high
iv
total enthalpy conditions (flight Mach 10 and 13). OH-fluorescence is detected along
the jet shear layer periphery in a continuous and very thin filament. For the low total
enthalpy Mach 8 condition, however, the ignition is limited to a small region behind the
bow shock and no OH fluorescence can be observed farther downstream.
It is evident from the results that improved injection schemes for better flame-holding
would be required for practical applications in scramjet engines, especially in the flight
Mach 8 range. During the last few years, cavities have gained the attention of the
scramjet community as a promising flame-holding device, owing to results obtained in
flight tests and to feasibility demonstrations in laboratory scale supersonic combustors.
In this thesis, we summarize the flowfield characteristics of cavities and research efforts
related to cavities employed in low- and high-speed flows. Open questions impacting
the effectiveness of the cavities as flame-holders in supersonic combustors are discussed.
Preliminary studies on cavities with upstream injection are presented indicating selfignition inside and around the cavity.
v
Contents
Abstract
iii
1 Introduction
1.1
1.2
1
Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1
Typical Scramjet Burner Entry Conditions . . . . . . . . . . . .
1
1.1.2
Flow-Field Features of Jets in Supersonic Crossflows . . . . . . .
4
1.1.3
Ignition and Flame-Holding Strategies in Supersonic Combustion
8
Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
2 Experimental Aspects
14
2.1
Critical Parameters in Supersonic Combustion Simulation . . . . . . . .
14
2.2
Experimental Facility
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.2.1
Expansion Tube . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.2.2
Injection System and its Calibration . . . . . . . . . . . . . . . .
20
2.2.3
Cavity/Injection Plate . . . . . . . . . . . . . . . . . . . . . . . .
23
Test Flow Characterization in the Flight Mach 8 - 13 Range . . . . . . .
23
2.3.1
Flow Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2.3.2
Measurement of Flow Properties . . . . . . . . . . . . . . . . . .
27
2.3.3
Boundary Layer Effects on Test Time . . . . . . . . . . . . . . .
32
2.3.4
Core-Flow Size . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.3.5
Flow Establishment Time . . . . . . . . . . . . . . . . . . . . . .
37
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
2.3
2.4
3 Flow Visualization Techniques
3.1
41
Ultra-Fast Framing Rate Schlieren . . . . . . . . . . . . . . . . . . . . .
vi
41
3.2
3.3
3.1.1
Previous and Current High Speed Imaging Efforts . . . . . . . .
43
3.1.2
High-Speed Schlieren Imaging Components . . . . . . . . . . . .
45
3.1.3
Timing and Synchronization
. . . . . . . . . . . . . . . . . . . .
47
3.1.4
Resolution Considerations . . . . . . . . . . . . . . . . . . . . . .
49
3.1.5
Image Processing and Analysis . . . . . . . . . . . . . . . . . . .
52
OH-PLIF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
3.2.1
Excitation and Detection Strategy . . . . . . . . . . . . . . . . .
54
3.2.2
OH-PLIF Laser Source and Tuning . . . . . . . . . . . . . . . . .
54
3.2.3
OH-PLIF Imaging System and Its Spatial Resolution . . . . . . .
55
3.2.4
Interpretation of OH-PLIF . . . . . . . . . . . . . . . . . . . . .
56
Simultaneous Schlieren and OH-PLIF . . . . . . . . . . . . . . . . . . .
56
4 Time Evolution and Mixing Characteristics of Hydrogen and Ethylene
Transverse Jets
59
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
4.2
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
4.2.1
General Flow-Field Features
. . . . . . . . . . . . . . . . . . . .
61
4.2.2
Large Scale Coherent Structures . . . . . . . . . . . . . . . . . .
64
4.2.3
Convection Characteristics . . . . . . . . . . . . . . . . . . . . .
74
4.2.4
Penetration and Shear Layer Properties . . . . . . . . . . . . . .
81
4.2.5
OH-PLIF Results
. . . . . . . . . . . . . . . . . . . . . . . . . .
84
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
4.3
5 The Effect of Velocity and Density Ratio on Transverse Jets
5.1
Effect of Jet Molecular Weight . . . . . . . . . . . . . . . . . . . . . . .
89
5.1.1
Flow Visualization Results
. . . . . . . . . . . . . . . . . . . . .
89
5.1.2
Penetration and Shear Layer Thickness . . . . . . . . . . . . . .
90
5.1.3
Convection Characteristics . . . . . . . . . . . . . . . . . . . . .
95
5.1.4
Characteristic Large Eddy Frequencies (Possible Transverse Jet
Modes) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.5
5.2
88
Jet Compressibility Analysis . . . . . . . . . . . . . . . . . . . . 100
Effect of Density and Velocity Ratios
5.2.1
95
vii
. . . . . . . . . . . . . . . . . . . 104
. . . . . . . . . . . . . . . . . . . . . 104
5.2.2
Definition of an “Effective Velocity Ratio, λ” . . . . . . . . . . . 106
5.2.3
Discussion on the Effect of the Curvature - Centrifugal Instability
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6 Autoignition and Flame-Holding Capability of a Hydrogen Transverse
Jet
114
6.1
Ignition and Flame-Holding Considerations . . . . . . . . . . . . . . . . 114
6.2
Ignition and Flame-Holding Results . . . . . . . . . . . . . . . . . . . . 117
6.3
6.2.1
Simultaneous OH-PLIF/Schlieren Results . . . . . . . . . . . . . 117
6.2.2
Top View OH-PLIF Images . . . . . . . . . . . . . . . . . . . . . 117
6.2.3
Comparison of Ignition in Flight Mach 8-13 Total Enthalpy Range 120
Discussion of the Ignition Process . . . . . . . . . . . . . . . . . . . . . . 123
6.3.1
Ignition Characteristics of Hydrogen . . . . . . . . . . . . . . . . 123
6.3.2
Ignition in Supersonic Combustors . . . . . . . . . . . . . . . . . 126
6.3.3
Ignition of a Hydrogen Transverse Jet . . . . . . . . . . . . . . . 127
6.3.4
Ignition of Ethylene Transverse Jet . . . . . . . . . . . . . . . . . 128
7 Cavity Flame-Holders
7.1
7.2
132
Review of Previous Research . . . . . . . . . . . . . . . . . . . . . . . . 132
7.1.1
Cavity Flow-Field Characteristics . . . . . . . . . . . . . . . . . . 132
7.1.2
Cavity in Reacting Flows . . . . . . . . . . . . . . . . . . . . . . 141
7.1.3
Outstanding Questions . . . . . . . . . . . . . . . . . . . . . . . . 148
Preliminary Cavity Results . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.2.1
Visual Observation of Cavities Using Ultra-Fast Schlieren . . . . 153
7.2.2
Preliminary Ignition Results of Injection/Cavity Schemes . . . . 157
8 Concluding Remarks
8.1
161
Summary of Major Results and Conclusions . . . . . . . . . . . . . . . . 161
8.1.1
Experimental Aspects . . . . . . . . . . . . . . . . . . . . . . . . 161
8.1.2
Flow Visualization Techniques . . . . . . . . . . . . . . . . . . . 163
8.1.3
Characteristics of Hydrogen and Ethylene Transverse Jets . . . . 165
8.1.4
Density and Velocity Ratio Effects . . . . . . . . . . . . . . . . . 166
8.1.5
Ignition and Flame-Holding Capability of a Hydrogen Transverse
Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
viii
8.1.6
8.2
Cavity Flame-Holders . . . . . . . . . . . . . . . . . . . . . . . . 167
Recommendation For Future Work . . . . . . . . . . . . . . . . . . . . . 169
A Expansion Tube Equations
175
B Maps of Estimated Expansion Tube Test Conditions
178
Bibliography
184
ix
List of Tables
1.1
Advantages and disadvantages of expansion tubes relative to shock tunnels for hypervelocity combustion simulations. . . . . . . . . . . . . . . .
2.1
5
Test gas (free-stream) flow properties simulating the burner entry conditions of three flight Mach numbers. The corresponding values are from
Fig. 1.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
17
Summary of measured, ideal (inviscid 1-D) and predicted (based on
Mirels solution) properties of test gas for Mach 10 and 13 flow conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
4.1
Jet exit flow properties. . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
5.1
The general flow exit properties of gaseous jets with different molecular
weights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2
90
The specific flow exit properties of gaseous jets used in the study of the
jet molecular weight effect. The free-stream used in these experiments
simulates the flight Mach 10 flow condition. . . . . . . . . . . . . . . . .
5.3
90
Summary of the different conditions used in the study of jet instability
analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.1
Summary of cavity oscillation frequencies, fm , for different cavity length
to depth ratios, L/D. The table includes the expected values based on
Rossiter’s formula and the ones measured in our experiments. . . . . . . 153
8.1
Recommended free-stream flow conditions for further ignition studies. . 170
x
List of Figures
1.1
Typical scramjet burner entry conditions as a function of flight Mach
number, calculated assuming adiabatic compression. a) The burner entry Mach number, M3 , for different temperature ratios, T3 /T0 . b) The
burner entry pressure, p3 , and the flight trajectories of constant dynamic
pressure, q0 , of 50 and 100 kPa. In our experiments, total enthalpy flows
(Mach number, M3 , and static temperature, T3 ) simulating three nominal
flight conditions (Mach 8, 10 and 13) were generated. . . . . . . . . . . .
1.2
2
Schematic of an underexpanded transverse injection into a supersonic
cross-flow, (a) instantaneous side view at the center-line axis of the jet;
(b) 3-D perspective of the averaged features of the flow-field (Gruber et
al. 1995). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3
7
Flow-field schematics of traditional injection/flame-holding schemes for
supersonic combustors. a) underexpanded fuel injection normal to the
crossflow, b) fuel injection at angle, c) injection behind a sudden expansion produced by a step. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
Expansion tube facility (12 m in length and 89 mm inner diameter) and
imaging system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
10
18
Expansion tube distance-time (x-t) diagram calculated for flight Mach
13 condition. Method of characteristics was used to solve the flow gasdynamics properties assuming one-dimensional inviscid theory. Test time
is defined as the time that the test gas has uniform flow quantities and
determined by the time arrival of the contact surface to the tube exit,
and that of the first subsequent rarefaction wave (reflected rarefaction
head in our case of high total enthalpy simulations). . . . . . . . . . . .
xi
19
2.3
Schematic of the test section (27 x 27 cm cross section) where a rake of 4
pitot probes, instrumented with pressure transducers, was located 2.5 cm
downstream of the tube exit. The flow history during the expansion tube
operation was detected via pitot pressure information. Note that the
inner diameter of the tube is 8.9 cm. . . . . . . . . . . . . . . . . . . . .
2.4
21
Optical set-up to measure the test gas velocity, assumed to be equal to
the CS - contact surface velocity. IR emission from 5% CO2 seeded in the
test gas nitrogen is collected by an InSb IR detector at the viewing port
located at 101.6 cm from the end of the tube. The test gas velocity can
then be calculated by considering its time of arrival at the viewing port
and at the pitot rake.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.5
Schematic of a) Injection system, b) cavity/injection plate system. . . . .
23
2.6
Schlieren visualization of an underexpanded gaseous injection into still
air. (a)-(c) hydrogen (d)-(e) ethylene jets. The exposure time of the
images was 3 musec. Mach disk height, y1 , was measured for different
pressure ratios, Pj /Peb , to calibrate the injection system. . . . . . . . . .
2.7
24
Maps of estimated test gas (nitrogen) conditions (state 5) at the exit of an
expansion tube: a) pressure and temperature, b) total enthalpy and velocity of the test gas are plotted for different initial driven and expansion
section pressures. Calculations are performed using the inviscid 1D equations for a given driver pressure of P4 = 600 psig (helium). Note that the
effective filling pressure of the driver section is taken as P4,eff = 686 psig,
as its inner diameter (10.2 cm) is larger than that of the driven and expansion sections (8.9 cm). This area difference is accounted for in the
curves presented above. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8
26
Example of IR emission, pitot pressure, wall pressure records and the
Mach number variation based on the pitot-to-static pressure ratios, as
a function of time for the Mach 10 flow condition. t = 0 represents
incident shock arrival at the pitot probe, placed 2.5 cm downstream of
the tube exit, while the wall pressure transducer and IR detector are
positioned 40.6 cm and 101.6 cm upstream of the tube exit, respectively
(see Fig. 2.4). Note that the time scale of the static pressure trace is
shifted by 235 µs to match the shock arrival at the pitot probe. . . . . .
xii
29
2.9
Example of IR emission, pitot pressure and wall pressure traces as a
function of time for the Mach 13 flow condition. . . . . . . . . . . . . . .
31
2.10 Example of IR emission, pitot pressure and wall pressure traces as a
function of time for the Mach 8 flow condition. . . . . . . . . . . . . . .
32
2.11 Comparison of the measured contact-surface velocity (test gas velocity)
with the shock-induced gas velocity estimated using the measured shock
speeds in the expansion section. . . . . . . . . . . . . . . . . . . . . . . .
33
2.12 X-t diagrams for the expansion section only. 1-D inviscid calculations
are plotted in straight lines and results applying Mirels’ model to include
the boundary layer effects are plotted in dashed lines. One can see the
improved test time as a result of the contact surface (CS) acceleration
due to the developing boundary layer behind the incident shock in the
low pressure expansion section helium flow. The incident shock velocity
was measured and assumed to be constant along the expansion section.
34
2.13 Useful core-flow size in flight Mach 13, 10 and 8 conditions, (a), (b) and
(c), respectively, determined by measuring the radial variation of pitot
pressure at different distances from the tube exit. . . . . . . . . . . . . .
38
3.1
Schlieren imaging set-up.
46
3.2
Examples of schlieren images of jet issuing into quiescent air as obtained
. . . . . . . . . . . . . . . . . . . . . . . . . .
for different positions of the knife edge (razor blade) at the focal point.
We use the set-up demonstrated in (d) where the knife edge cuts the
focused light at an angle to enhance both the vertical and the horizontal
density gradient effects. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
Timing diagram of the high-speed rate imaging system and its synchronization with the expansion tube test flow time. . . . . . . . . . . . . . .
3.4
47
48
Examples of schlieren images with different integration/exposure times:
a) 100 ns exposure time, resolving the instantaneous features of the flowfield, b) 200 ns exposure time, resulting in blurring of the image, c) 3 µs
exposure time, averaging the general features while enhancing the weak
shocks such as upstream separation shock wave and downstream recompression wave. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
51
3.5
Timing diagram of the high-speed rate imaging system and its synchronization with the expansion tube test flow time. . . . . . . . . . . . . . .
3.6
52
a) Triggering diagram and timing connections of the imaging, the injection and the data acquisition systems. b) Timing diagram of simultaneous OH-PLIF and schlieren and their synchronization with the expansion
tube test flow time.
4.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
Examples of hydrogen (a) and ethylene (b) injections into a supersonic
crossflow (nitrogen). Exposure time of each image was 200 ns. The x-axis
is normalized by the jet diameter d.
4.2
. . . . . . . . . . . . . . . . . . . .
62
An example of schlieren image with 3 µs exposure time for hydrogen
injection case. While the unsteady features (coherent structures) are
averaged to zero, some of the weak shocks such as upstream separation
shock wave and downstream recompression wave are emphasized. . . . .
4.3
63
(a) Bow shock position and its angle at the center-line of the jet as measured from the long exposure schlieren image shown in Fig. 4.2. (b) The
free-stream velocity behind the bow shock and the flow turning angle
based on the measured bow shock shape. For the calculations a calorically perfect gas has been assumed. . . . . . . . . . . . . . . . . . . . . .
4.4
65
An example of 8 consecutive schlieren images of underexpanded hydrogen
injection (d=2 mm) into a supersonic crossflow (nitrogen) obtained by
high-speed-framing camera. Exposure time of each image is 100 ns and
interframing time is 1 µs. Free-stream conditions are: U∞ =2360 m/s,
M∞ =3.38, T∞ =1290 K, p∞ =32.4 kPa; and jet-to-free-stream momentum
ratio is: J=1.4±0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5
69
The second example of 4 of 8 consecutive schlieren images of hydrogen
injection into flight Mach 10 condition. Exposure time of each image is
100 ns and interframing time is 1 µs. . . . . . . . . . . . . . . . . . . . .
4.6
70
Time evolution of an ethylene jet in a supersonic crossflow (nitrogen)
as observed from 8 consecutive schlieren images. Exposure time of each
image is 100 ns and interframing time is 1.5 µs. Free-stream conditions
are: U∞ =2360 m/s, M∞ =3.38, T∞ =1290 K, p∞ =32.4 kPa; and jet-tofree-stream momentum ratio is: J=1.4±0.1. . . . . . . . . . . . . . . . .
xiv
71
4.7
The second example of an ethylene transverse jet flow-field in a supersonic
crossflow as observed from 8 time correlated schlieren images. Exposure
time of each image is 200 ns and interframing time is 1.2 µs. . . . . . . .
4.8
Schematic of the three-dimensional shape (Ω shape) of the unsteady vortical structures formed intermittently (Brizzi et al. 1995). . . . . . . . .
4.9
72
73
Development of a large-scale ethylene structure (eddy number “-1” in
Fig. 4.7) as it goes through the tilting and stretching processes. Four
different parts of the eddy structure were independently tracked in the
duration of the 8.6 µs flow visualization time. . . . . . . . . . . . . . . .
74
4.10 Space-time trajectories of large-scale eddies present in the hydrogen jet
shear layer. The center of the eddies are tracked from the 8 successive
schlieren images shown (a) in Fig. 4.4 and (b) in Fig. 4.5. . . . . . . . . .
75
4.11 Space-time trajectories of ethylene large scale eddies as tracked from 8
time-correlated schlieren images: (a) x-t diagram of the example shown
in Fig. 4.6, (b) x-t diagram of the example shown in Fig. 4.7. . . . . . .
76
4.12 Convection features of coherent large scale structures present in the hydrogen jet/free-stream shear layer. The data were subtracted by analyzing the eddy displacement in 8 consecutive schlieren images of 2 experiments (images shown in Figs. 4.4 and 4.5). (a) the convection velocity
of eddies in streamwise and transverse directions, Uc,x and Uc,y , respectively; (b) the convection angle of eddies. . . . . . . . . . . . . . . . . . .
77
4.13 Convection features of eddies present in the ethylene jet/free-stream shear
layer. The data were subtracted by analyzing the eddy displacement in 8
consecutive schlieren images of 2 experiments (images shown in Figs. 4.6
and 4.7). (a) the convection velocity of eddies in streamwise and transverse directions, Uc,x and Uc,y , respectively; (b) the convection angle of
eddies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
4.14 Measured convection velocity of large eddy structures in the hydrogen and
ethylene jet shear layers. The results are compared with the estimated
values of the free-stream velocity immediately behind the bow shock. . .
79
4.15 Schematic showing the low- and high-speed regions of the bow shockinduced free-stream velocity around the large-scale ethylene eddies. . . .
xv
81
4.16 Transverse penetration data of (a) hydrogen jet and (b) ethylene jet. The
data points were obtained by manually tracking the visually observable
outer edge of the jet from 8 consecutive schlieren images for J = 1.4±0.1.
Both of the figures include analysis of 2 experiments namely 16 images.
For comparison, also shown in the figures is the penetration correlation
given by other studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
4.17 OH-PLIF results mapping the ignition regions at the jet center-line of:
a) hydrogen injection into air, b) ethylene injection into air, c) ethylene
injection into pure oxygen. . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1
Examples of instantaneous schlieren images of jets with different molecular weights.
Free-stream conditions are: U∞ =2360 m/s, M∞ =3.38,
T∞ =1290 K, p∞ =32.4 kPa. . . . . . . . . . . . . . . . . . . . . . . . . .
5.2
86
91
Jet transverse penetration along the axial distance, x/d. Data for four
gases with different molecular weights are presented: a) Mw = 2, J =
1.84, b) Mw = 4, J = 1.72, c) Mw = 8, J = 1.85, d) Mw = 16, J = 1.67.
For comparison, empirical correlations suggested by Gruber et al. (1995)
and Rothstein and Wantuck (1992) are also included for J = 1.75. . . .
5.3
93
Convection velocity of large scale structures in the streamwise (Mc,x )
and transverse (Mc,y ) directions as a function of axial distance x/d. The
results for each case (for each molecular weight of jet) are obtained from
4-5 experiments each including 8 consecutive schlieren images. . . . . . .
5.4
96
Formation frequency of the large scale structures and the corresponding
“preferred mode Strouhal number”, Std = fj d/Uj , as a function of the jet
exit velocity. The data were collected from the time evolution observation
of the jet from 8 consecutive schlieren images. Each data point was
obtained by averaging 5-10 experiments with the error bars representing
the deviation from the mean value. . . . . . . . . . . . . . . . . . . . . .
5.5
98
Formation frequency of the large scale structures and the “initial vortex
shedding Strouhal number”, Stθj = fθj θj /Uj , as a function of the jet
Reynolds number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6
99
Flow-field schematics used in the jet compressibility analysis. Letters A,
B and C indicate the zones of the jet shear layer. . . . . . . . . . . . . . 101
xvi
5.7
Estimated convective Mach number in zone “A”, McA , (refer to the
schematic in Fig. 5.6) and the measured visible jet shear layer thickness,
δvis , at x/d≈22 as obtained from penetration width measurements. . . . 102
5.8
Estimated velocity fields for the jet and the free-stream in zones “B” and
“C”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.9
Schlieren images at selected conditions given in Table 5.3. . . . . . . . . 107
5.10 Schlieren images at selected conditions given in Table 5.3. . . . . . . . . 108
5.11 Schlieren images at selected conditions given in Table 5.3. . . . . . . . . 109
5.12 Velocity vector field (U∞ , Uj ) for a skewed mixing layer and the “effective
velocity ratio”, λ., described in the total velocity vector direction. . . . . 110
5.13 Jet-to-free-stream density ratio vs. velocity ratio. The number near the
data points corresponds to the experimental conditions summarized in
Table 5.3. “Unstable” flow jet is defined when the large structures lose
coherence downstream of the injection port and significant distortions in
the bow shock shape can be observed. . . . . . . . . . . . . . . . . . . . 111
5.14 Jet-to-free-stream density ratio vs. the “effective velocity ratio”, λ. The
number near the data points corresponds to the experimental conditions
summarized in Table 5.3. . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.15 Schematics illustrating the stability regions based on a) Rayleigh criterion
for centrifugal forces in the curved mixing layers as given in Eq. 5.15 where
vis
and b) current experimental results. . . . . . . . . . . 112
cons. = 3 + 2 hδmax
6.1
Simultaneous OH-PLIF and schlieren images visualizing hydrogen injection into supersonic crossflow. Free-stream conditions are M = 3.57,
T = 1300 K, P = 0.32 atm, V = 2500 m/s. The jet-to-freestream momentum flux ratio is J = 1.4. a) Schlieren image, b) OH-PLIF image
demonstrating the ignition and combustion regions of jet-in-crossflow at
high enthalpy condition, c) Overlaid OH-PLIF and schlieren images. . . 118
6.2
Instantaneous top-view OH-PLIF images obtained at different height
above the injection plate. Free-stream conditions are M=3.57, T=1300K,
P=0.32atm, V=2500m/s. The jet-to-freestream momentum flux ratio is
J=1.4. a) y/d=3, b) y/d=2.5, c) y/d=2, d) y/d=1 above the injection plate.119
xvii
6.3
Instantaneous OH-PLIF acquired at center-line axis of the hydrogen jet
injected into flight Mach 10 and 13 conditions. The images are obtained
by combination of 2 different instantaneous images: near the exit of the
jet (−5 < x/d < 1) and downstream of the jet (1 < x/d < 10). . . . . . . 121
6.4
Two instantaneous OH-PLIF images acquired at center-line axis of the
hydrogen jet injected into flight Mach 8 conditions. . . . . . . . . . . . . 122
6.5
Explosion limits of a stoichiometric hydrogen-oxygen mixture (after Sung
et al., 1999). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.6
Variation of ignition delay times τign of a stoichiometric mixture of H2
and air with temperature and pressure. Calculations are perfomed using
Chemkin and the GRI mechanism. a) τign vs. T , b) pτign vs. T . . . . . 125
6.7
Variation of ignition time with fuel-air equivalence ratio, φ, for cold H2
(Tjet = 300 K) injected into hot air. The values of the ignition delay time
are calculated for different air temperatures, Tair . . . . . . . . . . . . . . 126
6.8
The free-stream temperature and pressure (T2 and P2 ) behind the bow
shock, measured from schlieren images as discussed in Section 4.2.1 (see
Fig. 4.3). Ignition delay times are calculated for several conditions of air
assuming φ = 0.2. The free-stream flow properties simulate the flight
Mach 10 conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.9
Comparison of ignition delay of a stoichiometric mixture of C2 H4 (ethylene) and air/oxygen at 1 atm with a stoichiometric mixture of H2 and
air. Two different reaction mechanisms are used to calculate the ignition
delay times of C2 H4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.10 a) Variation of ignition delay of a stoichiometric mixture of C2 H4 (ethylene) and air/oxygen at various pressures. . . . . . . . . . . . . . . . . . 130
xviii
7.1
Flow-field schematics of cavities with different length to depth ratios,
L/D, in a supersonic flow. a) Open cavity flow for L/D < 7 − 10;
shear layer reattaches to the back face while spanning over the cavity.
Small aspect ratio cavities (L/D < 2 − 3) are controlled by transverse
oscillation mechanism while in larger aspect ratio cavities longitudinal
oscillation becomes the dominant mechanism. b) Closed cavity flow for
L/D > 10 − 13; shear layer reattaches to the lower wall. The pressure
increase in the back wall vicinity and the pressure decrease in the front
wall results in large drag losses. . . . . . . . . . . . . . . . . . . . . . . . 134
7.2
Typical longitudinal cavity oscillations are caused by the impingement
of the free shear layer on the rear wall which generates travelling shocks
inside the cavity. The shear layer spanning the cavity becomes unsteady
as a result of these acoustic waves deflecting the shear layer up and down,
and/or by the shock induced vortices generated at the front wall leading
edge of the cavity. As a result unsteady waves emanate from the cavity.
7.3
135
Different concepts can be employed to suppress the cavity oscillations:
a) Cavities with an angled back wall suppress the unsteady nature of the
free shear layer by eliminating the generation of the travelling shocks
inside the cavity due to the free-shear-layer impingement. b) In addition,
small disturbances produced by spoilers or by the secondary jet injection
upstream of the cavity can enhance the free-shear-layer growth rate. The
thickening of the cavity shear layer alters its instability characteristics,
such that its preferred roll-up frequency is shifted outside of the natural
frequency of the cavity, and as a result the oscillations are attenuated. . 137
xix
7.4
Instantaneous schlieren images with 200 ns of exposure time demonstrating the effect of the back wall angle on the flowfield structure of a cavity exposed to a supersonic flow. The free-stream was generated in an
expansion tube to simulate Mach 10 total enthalpy conditions at the supersonic combustor entry: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K,
p∞ = 32 kPa. The boundary layer thickness at the trailing edge of the
cavity is approximately 1mm. a) Cavity with L/D = 5 shows the unsteady nature of the shear layer at the reattachment with the trailing
edge of the back wall. b) Cavity with slanted back wall (20o ) stabilizes
the shear layer reattachment process. . . . . . . . . . . . . . . . . . . . . 138
7.5
Effect of length-to-depth ratio, L/D on a) magnitude (root-mean-square)
of pressure fluctuations on the bottom of the cavity (at x/D = 0.33),
b) drag of the cavity at Mach 1.5 and 2.5 flows. The values were adapted
from Zhang and Edwards (1990). . . . . . . . . . . . . . . . . . . . . . . 139
7.6
Cavity-actuated supersonic mixing enhancement concepts: (a) Sato et al.
(1999), studied the influence of acoustic waves, emitted from a cavity and
impinging on the initial mixing layer. (b) Yu and Schadow (1994) used
the same concept to enhance the mixing of supersonic reacting jets. . . . 143
7.7
Axisymmetric combustor of the Scramjet engine which was flight-tested
by Russian-CIAM/NASA joint program (1998). In this engine two cavities with angled-rear wall were used for flame-holding purposes. The
dimensions are in mm (McClinton et al. 1996). . . . . . . . . . . . . . . 146
7.8
Position of pressure transducers located at the bottom of the cavity to
measure the history of the flow oscillations inside the cavity. Pressure
transducer located farther downstream at x/D = 1.5 provided a more
accurate oscillation frequency measurements. . . . . . . . . . . . . . . . 151
7.9
Examples of cavity pressure traces in arbitrary units: a) L/D = 3, b) L/D =
5, c) L/D = 5 with upstream hydrogen injection, d) L/D = 7. t = 0
represents incident shock arrival at the cavity. The free-stream (N2 ) conditions represent Mach 10 total enthalpy at the supersonic combustor
entry: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa. . . . . . 152
xx
7.10 Schlieren images demonstrating the differences in the flow-field structure
of cavities with different length-to-depth ratios and back wall angle. The
depth of the cavities is constant and equal to D = 3 mm. The freestream was generated to simulate Mach 10 total enthalpy conditions at
the supersonic combustor entry: M∞ = 3.4, U∞ = 2360 m/s, T∞ =
1290 K, p∞ = 32 kPa. The boundary layer thickness at the trailing edge
of the cavity is approximately 1mm. . . . . . . . . . . . . . . . . . . . . 155
7.11 Schlieren images demonstrating jet interaction with different cavities.
The hydrogen jet is injected into a non-reacting free-stream 3 mm upstream of the cavity from a d = 1 mm orifice. The injection is performed
at angle of 30o to the plate. The free-stream, N2 , represents the flight
Mach 10 burner entry conditions. . . . . . . . . . . . . . . . . . . . . . . 156
7.12 Instantaneous OH-PLIF images demonstrating the ignition regions of a
hydrogen jet interacting with a L/D = 3 cavity. The images are obtained
from 5 single shots at the same conditions. Hydrogen is injected 3 mm
upstream the cavity leading edge at an angle of 30o . The free-stream
(air) properties represent the flight Mach 10 burner entry conditions:
M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa. Note that
a schlieren image is also included to indicate the flow-field properties
around the cavity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.13 Instantaneous OH-PLIF images demonstrating the ignition regions of a
hydrogen jet interacting with a cavity with L/D = 3 and 30o back wall.
The images are obtained from 5 single shots at the same conditions.
Hydrogen is injected 3 mm upstream the cavity leading edge at an angle
of 30o . The free-stream (air) properties represent the flight Mach 10
burner entry conditions: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K,
p∞ = 32 kPa. Note that a schlieren image is also included to indicate the
flow-field properties around the cavity. . . . . . . . . . . . . . . . . . . . 160
8.1
Flow-field schematics demonstrating different concepts of angled jet injection combined with cavity flame-holder. a) upstream injection, b) base
injection , c) cavity injection. . . . . . . . . . . . . . . . . . . . . . . . . 171
8.2
Flow-field schematic of a shock-wave/jet interaction. . . . . . . . . . . . 172
xxi
8.3
Schematic of the 25o wedge to generate a shock wave above the injection
plate.
8.4
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
(a) An oblique shock wave impinging the hydrogen jet as visualized using schlieren imaging. The shock was produced by a 25 o angled wedge
mounted above the injection plate. Flight Mach 13 free-stream condition. (b) Combined OH-PLIF and schlieren images visualizing the effect
of shock/jet interaction on OH number density. . . . . . . . . . . . . . . 174
B.1 Maps of estimated test gas (nitrogen) conditions at the exit of an expansion tube: a) pressure and temperature, b) total enthalpy and velocity of
the test gas are plotted for different initial driven and expansion section
pressures. Calculations are performed using the inviscid 1D equations for
a given driver pressure of P4 = 300 psig (helium). . . . . . . . . . . . . . 179
B.2 Maps of estimated test gas (Argon) conditions at the exit of an expansion
tube: a) pressure and temperature, b) total enthalpy, velocity and Mach
number of the test gas are plotted for different initial driven and expansion section pressures. Calculations are performed using the inviscid 1D
equations for a given driver pressure of P4 = 300 psig (helium). . . . . . 180
B.3 Maps of estimated test gas (Argon) conditions at the exit of an expansion
tube: a) pressure and temperature, b) total enthalpy, velocity and Mach
number of the test gas are plotted for different initial driven and expansion section pressures. Calculations are performed using the inviscid 1D
equations for a given driver pressure of P4 = 600 psig (helium). . . . . . 181
B.4 Maps of estimated test gas (Helium) conditions at the exit of an expansion tube: a) pressure and temperature, b) total enthalpy, velocity and
Mach number of the test gas are plotted for different initial driven and
expansion section pressures. Calculations are performed using the inviscid 1D equations for a given driver pressure of P4 = 300 psig (helium). . 182
B.5 Maps of estimated test gas (Helium) conditions at the exit of an expansion tube: a) pressure and temperature, b) total enthalpy, velocity and
Mach number of the test gas are plotted for different initial driven and
expansion section pressures. Calculations are performed using the inviscid 1D equations for a given driver pressure of P4 = 600 psig (helium). . 183
xxii
Chapter 1
Introduction
1.1
Background and Motivation
The success of future hypersonic airbreathing propulsion systems will be largely
dependent on efficient injection, mixing and combustion processes inside the supersonic / hypersonic combustion chamber. At flight speeds beyond Mach 6, air entering
the combustor must be supersonic to avoid excessive dissociation of both nitrogen and
oxygen gases. Consequently, the time available for fuel injection, fuel-air mixing and
combustion is very short, of the order of 1 msec, which results in troublesome constraints
on the combustion problem (Ferri 1973; Kumar et al. 1989).
1.1.1
Typical Scramjet Burner Entry Conditions
The combustor entry conditions (Mach number, static temperature and pressure)
of hypersonic airbreathing propulsion systems depend on the flight conditions of the
vehicle. In order to keep the density inside the combustor high for efficient combustion
and the lift at reasonably high values, the flight Mach number, M0 , should increase as
the altitude of the vehicle increases.
Residence time is another issue that has to be considered for efficient performance
of a high-speed propulsion system. The air must be compressed in the diffuser in
order to reduce velocities and increase the flow residence time and therefore to allow
a combustor of reasonable length. On the other hand, the reduced velocities at the
combustor entry are restricted by the maximum allowable compression temperature (in
1
2
11
9
8
7
T3/T0=6
7
8
Current experiments
1. Mach 8 (3 MJ/kg)
2. Mach 10 (4 MJ/kg)
3. Mach 13 (6 MJ/kg)
6
3
5
2
4
3
1
2
M3=1
1
0
5
10
15
20
10
45
q0=50 kPa
q0=100 kPa
9
8
40
7
6
35
5
30
4
3
2
p3=1 atm
1
5
Flight Mach Number, M0
25
20
0
25
Height, km
10
Burner Entry Pressure, p3, atm
Burner Entry Mach Number, M3
CHAPTER 1. INTRODUCTION
10
15
20
25
Flight Mach Number, M0
(a)
(b)
FIGURE 1.1 Typical scramjet burner entry conditions as a function of flight Mach number, calculated assuming adiabatic compression. a) The burner entry Mach number, M3 , for different temperature
ratios, T3 /T0 . b) The burner entry pressure, p3 , and the flight trajectories of constant dynamic
pressure, q0 , of 50 and 100 kPa. In our experiments, total enthalpy flows (Mach number, M3 ,
and static temperature, T3 ) simulating three nominal flight conditions (Mach 8, 10 and 13)
were generated.
the range of 1440-1670 K (Heiser and Pratt 1994)) to avoid excessive dissociation in
the exhaust flow. These constraints determine the expected values of combustor entry
Mach number and temperature, M3 and T3 , respectively.
Considering the above issues, the expected values of flow conditions at the combustor
entrance of an airbreathing propulsion system were estimated and plotted in Fig. 1.1
as a function of flight Mach number, M0 . Calculations were performed for different
burner entry temperature to atmosphere temperature ratios (T3 /T0 ) assuming adiabatic
compression (constant total enthalpy) throughout the diffuser according to Eq. 1.1:
1+
T3
=
T0
1+
γ0 −1
2
2 M0
γ3 −1
2
2 M0
(1.1)
As shown in Fig. 1.1a, for hypersonic flights beyond Mach 6, (M0 > 6) a supersonic
combustion ramjet (scramjet) where the flow remains supersonic / hypersonic throughout the engine should be considered.
Furthermore, to keep structural loads on the hypersonic vehicle at acceptable levels,
namely, to keep the dynamic pressure, q0 = 1/2ρ0 V02 , in the range of 50-100 kPa, flight
at high speeds is confined to altitudes of 25-40 km. Consequently, the burner entry
pressure, p3 , can be directly evaluated (see Fig. 1.1b) for fixed dynamic pressure, q0 ,
3
of 50 and 100 kPa, compression efficiency, ηc , of 0.9 and temperature ratio, T3 /T0 , of 6
using Eq. 1.2 (Heiser and Pratt 1994):
P3
=
P0
Ã
T3
T0
T3
T0 (1
c
! γ γ−1
− ηc ) + ηc
c
(1.2)
where γc is the average specific heat ratio; γc = 1/2(γ0 + γ3 ). Therefore, at flights
beyond Mach 8, typical pressures at the entrance of supersonic combustors range from
approximately 0.2 to 4 atm depending on the operating parameters for the flight mission,
such as the Mach number and the altitude.
Most supersonic combustion research in the open literature has focused on flight
speeds of Mach 8 and below (Allen et al. 1993; McMillin et al. 1994; Gruber et al.
1995; Parker et al. 1995; Santiago and Dutton 1997), and there are relatively few
works which have been performed for higher flight Mach numbers (Stalker 1989; Anderson et al. 1990; Bakos et al. 992a; Bakos et al. 992b; Bakos et al. 992c; Erdos
1994; Anderson 1994; Albrechcinski et al. 1995; Wendt and Stalker 1996; Bélanger and
Hornung 1996; McIntyre et al. 1997; Erdos 1998; Ben-Yakar and Hanson 002a). Due
to the large total enthalpies (greater than 3 MJ/kg) associated with high flight Mach
numbers, only impulse facilities are capable of providing the required total temperature and Mach number to replicate a combustor environment. Expansion tubes and
reflected shock tunnels are two possible types of impulse facilities for ground testing.
Of concern for high stagnation enthalpy simulations is the chemical composition of the
test gas. While in reflected shock tunnels significant amounts of dissociated species are
formed, in expansion tubes the amounts of these species are negligible (?). Therefore,
an expansion tube can provide a more correct simulation of the true flight combustion
chemistry including ignition delay and reaction times. In general, however, expansion
tubes have shorter test times than reflected shock tunnels. The principal advantages
and disadvantages of expansion tubes as compared to other hypersonic test facilities,
especially shock tunnels, are summarized in Table 1.1.
In the present study, the Stanford expansion tube facility is used to generate total enthalpy conditions in the Mach 8-13 flight range. This facility is one of the few
impulse-type facilities which can provide a wide range of total enthalpies. The freepiston reflected shock tunnel, T5, located at GALCIT (Bélanger and Hornung 1996),
4
Calspan reflected shock tunnel (Albrechcinski et al. 1995) and the HYPULSE expansion tube located at GASL (Bakos et al. 992a; Bakos et al. 992b; Erdos 1994) are
three current examples of larger impulse facilities. In these facilities, generic combustor
models with hydrogen injection have been tested using conventional measurement techniques such as pressure measurements along the combustor and flow visualization with
differential interferometry. While most of the high enthalpy and high speed combustion
flow-field studies in the open literature utilize these methods, modern laser-based diagnostics can provide flow-field and species information critical for fundamental research
(Erdos 1994; Erdos 1998; Anderson et al. 1992; Rogers et al. 1992; Ben-Yakar and
Hanson 998b).
1.1.2
Flow-Field Features of Jets in Supersonic Crossflows
Efficient performance of very high-speed combustor systems requires fuel and air
mixing at the molecular level in the near-field of the fuel injection. One of the simplest
approaches is the transverse (normal) injection of fuel from a wall orifice. As the fuel
jet, sonic at the exit, interacts with the supersonic crossflow, an interesting but rather
complicated flow-field is generated. Figure 1.2 illustrates the general flow-features of an
under-expanded transverse jet injected into a cross-flow. As the supersonic crossflow
is displaced by the fuel jet a 3-D bow shock is produced due to the blockage produced
by the flow. The bow shock causes the upstream wall boundary layer to separate,
providing a region where the boundary layer and jet fluids mix subsonically upstream
of the jet exit. This region confined by the separation shock wave formed in front of it,
is important in transverse injection flow-fields owing to its flame-holding capability in
combusting situations, as has been shown in previous publications (Parker et al. 1995;
Ben-Yakar and Hanson 998b).
The recent experimental studies performed by Fric and Roshko (1994) provide a
new insight into the vortical structure of a jet injected into a low speed crossflow. Their
photographs, obtained using the smoke-wire visualization technique, illustrate four types
of coherent structures: (1) the near-field jet-shear layer vortices; (2) the far-field counter
rotating vortex pair (CVP); (3) the horseshoe vortex which wraps around the jet column;
and (4) the downstream wake vortices originating from the horseshoe vortex. Figure 1.2
shows the presumed vortical structures for the jet in supersonic crossflow (which are
5
TABLE 1.1 Advantages and disadvantages of expansion tubes relative to shock tunnels for hypervelocity
combustion simulations.
Shock Tunnels
Expansion Tubes
Significant level of radicals such as ”O”
and ”NO” are produced in the test gas affecting the combustion chemistry. In the reflected zone of the shock tube, air dissociates due to high temperatures and recombines only partially during the fast expansion
process.
The facility needs to contain the total pressures and temperatures of the
flow it generates. As noted by Anderson
(1994), at flight Mach numbers above 12, the
total pressure requirements approaches a million psi or 68,000 atm, which can be produced
only by expansion tubes.
Free-stream Mach number is fixed by
the nozzle geometry. Simulation of different conditions requires replacement of the
nozzle with a new geometry.
Nozzle can be damaged due to the high
heat transfer rates at the throat and flying
diagrams inside the tube.
Negligible amounts of radicals are produced. The working gas never stagnates, thus
reduces the extent of dissociation. As a result
the test gas reaches to the test section with
more accurate chemical composition.
Boundary layer develops throughout
the nozzle and can be thick compared to the
dimensions of the injection port. It is usually
required to eliminate the boundary layer by,
for example, inserting a step before the fuel
injection port (Parker et al. 1995)
Test times ≈ 1 msec
Test times are of the order of 1msec. However, a substantial part of it is wasted during the nozzle start-up time (of the order of
0.5 msec), required for the supersonic flow to
be established. Test time decreases with increasing stagnation enthalpy.
Longer test section because of the longer
test time and larger core flow. However, side
wall effects should be taken into account.
Higher stagnation pressures and temperatures can be achieved in expansion
tubes even for the same initial driver pressure and sound speed, as velocity is added
to the flow through the unsteady expansion
process without stagnating it.
Variable Mach numbers and conditions
can be easily obtained by just altering the
initial filling pressures.
High heat transfer rates are avoided in
the absence of a sonic throat. However, the
test object is prone to damage from flying
diagrams arriving at the end of the expansion
tube operation.
A thin boundary layer is developed upstream of the injection port as the injection
plate is placed in the free-jet exiting the tube.
Test times ≈ 0.2 - 0.5 msec
No nozzle start-up time is required. In addition, the establishment of flow on the studied
model begins during the expansion section
gas flow prior to the test gas arrival. As a
result, less useful test time is consumed during the flow establishment.
Test section dimensions depend on the
size of the core flow at the exit of the tube
which is diminished by the boundary layer
growth on the tube walls.
6
known to exist in subsonic jet-in-crossflow) as they were partially observed by numerous
studies (Gruber et al. 1996; Gruber et al. 997a; Ben-Yakar et al. 998a).
The origin of the jet vortical structures was studied by several researchers (Fric and
Roshko 1994; Brizzi et al. 1995; Yuan et al. 1999). Among those studies, Yuan et al.
(1999) performed a large-eddy simulation of transverse jets in subsonic crossflows. Their
results revealed that the majority of the jet vortical structures arose from the Kelvin
Helmholtz (K-H) instability of the jet-shear layer in the near-field. Interestingly, they
do not observe the formation of vortex rings around the periphery of the jet as was
assumed in previous studies. Instead they find two kinds of vortices originating from
the jet exit boundary layer: 1) regularly formed spanwise rollers on the upstream and
downstream edges (large scale jet shear layer vortices), 2) quasi-steady vortices, the socalled ”hanging vortices” that form in the skewed mixing layers (mixing layers formed
from non-parallel streams) on each lateral edge of the jet leading to the formation of
the CVP.
The near-field mixing of transverse jets is dominated by the so-called ”entrainmentstretching-mixing process” driven by large scale jet-shear layer vortices. In the region
near the injector exit, the injectant fluid moves with a higher velocity tangent to the
interface than the free-stream fluid. As a result, large vortices are periodically formed
engulfing large quantities of free-stream fluid and drawing it into the jet-shear layer
(macromixing). These large scale vortices also stretch the interface between the unmixed fluids. Stretching increases the interfacial area and simultaneously steepens the
local concentration gradients along the entire surface while enhancing the diffusive micromixing.
Preliminary examinations (Gruber et al. 997a; Ben-Yakar and Hanson 002b) of the
convection characteristics of these large-scale structures, developed in a sonic transverse
jet injection into supersonic crossflows, determined that in the far-field the eddies tend
to travel with velocities that are closer to the free-stream velocity. This indicates that
in high speed free-stream conditions, these large coherent structures, where the fuel and
air are mixed by slow molecular diffusion, will also travel at high speeds. Consequently
the combustion process will be mixing controlled.
High mixing efficiency, however, must be achieved in the near-field of the fuel injection for the success of hypersonic propulsion systems. Therefore, it is important to
understand how these structures and their growth rates evolve as flow and jet conditions
7
(a)
LARGE-SCALE
STRUCTURES
M¥>1
BOW SHOCK
BARREL
SHOCK
MACH DISK
BOUNDARY LAYER
SEPARATED
REGION
INJECTANT
RECIRCULATION
ZONE
(Hydrogen or
Ethylene)
RECIRCULATION
ZONE
(b)
M¥>1
MACH DISK &
BARREL SHOCK
AVERAGE
JET BOUNDARY
3-D
BOW SHOCK
COUNTER-ROTATING
VORTEX PAIR (CVP)
HORSESHOE-VORTEX
REGION
FIGURE 1.2 Schematic of an underexpanded transverse injection into a supersonic cross-flow,
(a) instantaneous side view at the center-line axis of the jet; (b) 3-D perspective of the averaged features of the flow-field (Gruber et al. 1995).
8
are changed. Two types of fuel are being considered for use in supersonic combustion:
1) hydrogen and 2) hydrocarbon fuels. The large differences in the molecular weights
of these fuels result in a big variation in injection velocities that might lead to a wide
variation in the jet shear layer growth rate and the mixing properties. However, none
of the previous jet penetration studies (Zukoski and Spaid 1964; Schetz and Billig 1966;
Rogers 1971; Rothstein and Wantuck 1992; Papamoschou and Hubbard 1993; Gruber et al. 1995) found any dominant differences between jets with different molecular
weights. Penetration was shown to be dependent primarily on the jet-to-free-stream
momentum flux, J, expressed by:
¡
J=
ρu2
¢
jet
2
(ρu )∞
(1.3)
Most transverse jet-in-crossflow studies were, however, carried out in cold supersonic
flows (namely low velocities) generated in blow-down wind tunnels. The free-stream
temperatures and velocities in these facilities were usually lower than that expected
in a real supersonic combustor environment. Comprehensive studies still need to be
performed to determine the mixing properties of different type of fuels in a relatively
accurate supersonic combustor environment. These observations gave rise for the following question: “is there any other mechanism or controlling parameter which will
alter the large eddy characteristics of the jet shear layer to enhance its near-field mixing
in realistic conditions?”
We were therefore challenged to study the flow features of hydrogen and ethylene
transverse jets exposed to high-speed supersonic free-streams at realistic conditions
leading to high shear levels.
1.1.3
Ignition and Flame-Holding Strategies in Supersonic Combustion
Different injection strategies have been proposed (Billig 1993; Tishkoff et al. 1997;
Abbitt et al. 1993; Hartfield et al. 1994; Riggins et al. 995a; Riggins and Vitt 995b;
Fuller et al. 1998) with particular concern for rapid near-field mixing. These injection strategies, both flush-mounted injectors and intrusive injectors, typically rely on
the generation of strong streamwise counter-rotating vortices. As a result, mixing is
enhanced both in macro-scale by entrainment of large quantities of air into the fuel
9
and in micro-scale due to stretching of the fuel-air interface. Stretching increases the
interfacial area and simultaneously steepens the local concentration gradients thereby
enhancing the diffusive micro-mixing. Micro-scale mixing is required for combustion
since chemical reactions occur at the molecular level. However, efficient mixing of fuel
and air does not directly initiate the combustion process.
Ignition and flame-holding in supersonic flows (Huber et al. 1979; Miller 1994; Im
et al. 1998; Sung et al. 1999; Ben-Yakar and Hanson 998b) are two other important
factors that have to be addressed in the design of an injection system. Once the fuelair ignition is established, the combustion depends directly on the efficiency of the
mixing. In order for self-ignition (and therefore combustion) to be accomplished in a
flowing combustible mixture, it is necessary that four quantities have suitable values:
static temperature, static pressure, fuel-air mixture, and the residence time at these
conditions. The ignition is considered accomplished when sufficient free radicals are
formed to initiate the reaction system, even though no appreciable heat has yet been
released. When the conditions of spontaneous ignition exist, the distance li at which
it occurs in a medium flowing at a velocity U is: li = U τi , where τi is the ignition
delay time. As the combustor velocity U becomes larger, the ignition requires longer
distances.
The primary objective of a flame-holder in a supersonic combustion, therefore, is
to reduce the ignition delay time and provide a continuous source of radicals for the
chemical reaction to be established in the shortest distance possible. In general, flameholding is achieved by three techniques: 1) organization of a recirculation area where
the fuel and air can be mixed partially at low velocities, 2) interaction of a shock wave
with partially or fully mixed fuel and oxidizer, and 3) formation of coherent structures
containing unmixed fuel and air, wherein a diffusion flame occurs as the gases are
convected downstream.
These three stabilization techniques can be applied in a supersonic combustor in
different ways. One of the simplest approaches is the transverse (normal) injection of
fuel from a wall orifice (see Fig. 1.3a). As the fuel jet interacts with the supersonic
crossflow a bow shock is produced. As a result, the upstream wall boundary layer
separates, providing a region where the boundary layer and jet fluids mix subsonically
upstream of the jet exit. This region is important in transverse injection flowfields owing
to its flame-holding capability in combusting situations, as has been shown in previous
10
(a)
Bow Shock
M¥>1
Autoignition
Zones
Fuel
(b)
Weaker Bow Shock
(~ Mach Wave)
Smaller
Recirculation Region
Fuel
(c)
Bigger
Recirculation Region
Combined Bow and
Step-Induced Shock
Fuel
FIGURE 1.3 Flow-field schematics of traditional injection/flame-holding schemes for supersonic combustors.
a) underexpanded fuel injection normal to the crossflow, b) fuel injection at angle, c) injection
behind a sudden expansion produced by a step.
publications (Huber et al. 1979; Ben-Yakar and Hanson 998b; Ben-Yakar and Hanson
999a). However, this injection configuration has stagnation pressure losses due to the
strong 3-D bow-shock formed by the normal jet penetration, particularly at high flight
velocities.
Another way of achieving flame stabilization is by means of a step, followed by
transverse injection (see Fig. 1.3c). The step creates a larger recirculation area with the
hot gases serving as a continuous ignition source. This approach can provide sustained
combustion but, like the previously described method, has the disadvantage of stagnation pressure losses and increase in drag due to the low flow pressure base behind the
step.
On the other hand, it is possible to reduce the pressure losses associated with the
11
injection process by performing angled injection (e.g., 60o or 30o rather than 90o ) so that
the resulting bow shock is weaker (see Fig. 1.3b). In this approach, jet axial momentum
can also contribute to the net engine thrust. Riggins et al. (995a) studied the thrust
potential of a supersonic combustor at Mach 13.5 and Mach 17 flight conditions with
30o flush wall injection of hydrogen and concluded that the major component of thrust
potential gain is due to the jet momentum. In our previous work (Ben-Yakar and
Hanson 998b; Ben-Yakar and Hanson 999a), autoignition of a hydrogen jet transversely
injected into Mach 10-13 flight enthalpy flow conditions was observed in the upstream
recirculation region of the jet and behind the bow shock. However, different experiments
(McMillin et al. 1994) performed for similar geometry but at much lower total-enthalpy
flow conditions showed that ignition occurred only far downstream of the jet. Based
on those observations, angled injection is likely to reduce or eliminate these forms of
autoignition and stabilization especially at flight speeds lower than Mach 10. Therefore,
it is likely that a new technique will be required to obtain autoignition and downstream
combustion stabilization.
In recent years, cavity flame-holders, an integrated fuel injection/flame-holding approach, have been proposed as a new concept for flame-holding and stabilization in
supersonic combustors (Tishkoff et al. 1997). Cavity flame-holders, designed by CIAM
(Central Institution of Aviation Motors) in Moscow, were used for the first time in a
joint Russian/French dual-mode scramjet flight-test (hydrogen fueled) (Roudakov et al.
1993). Further experiments (Vinagradov et al. 1995; Ortweth et al. 1996; Owens et al.
1998) showed that the use of a cavity after the ramp injector significantly improved
the hydrocarbon combustion efficiency in a supersonic flow. Similar flame stabilization
zones, investigated by Ben-Yakar et al. (998a), have been employed within a solid-fuel
supersonic combustor, demonstrating self-ignition and sustained combustion of PMMA
(Plexiglas) under supersonic flow conditions.
In November 1994, NASA contracted CIAM (Roudakov et al. 1996; McClinton
et al. 1996) to continue exploring the scramjet operating envelope from dual-mode
operation below Mach 6 to the full supersonic combustion mode at Mach 6.5. The
proposed combustor design also included two cavity flame-holders (20 mm in depth by
40 mm in axial length and 30 mm by 53 mm). The performance predictions obtained by
analytical solutions indicated that these cavities would be quite effective as autoignition
and flame-holding devices. Indeed, the recent flight test of this combustor has been
12
successfully completed, encouraging further investigation of cavity flame-holders.
It is worth noting that, although there is recent interest in cavity flame-holders for
supersonic combustors, their application in subsonic combustors goes back to the 1950’s.
Probably, the first published investigation of cavity flame-holders is due to Huellmantel
et al. (1957), who studied various shapes of cavities to sustain combustion in low speed
propane-air flames. The main purpose of this thesis is to summarize relevant known
characteristics of cavities in supersonic flows and research efforts related particularly to
cavities employed in low- and high-speed combustors.
1.2
Thesis Objectives
The ultimate objective of this dissertation is to investigate near-field mixing and
flame-holding characteristics of different gaseous fuels such as hydrogen and ethylene
injected normally from a single orifice into a realistic supersonic combustor environment. We apply advanced non-intrusive flow diagnostic techniques such as Planar
Laser-Induced Fluorescence of OH radicals (OH-PLIF) and schlieren imaging using an
ultra-fast-framing rate digital camera. These techniques and the simulation of high
speed and high temperature free-stream conditions enable unique observations that
were not available in the previous studies. The thesis includes four primary elements:
1. The experimental approach: The goal is to generate a relatively accurate
supersonic burner entry condition, namely a radical-free, high total enthalpy air
flow. An expansion tube is used to generate three nominal free-stream conditions
for flight Mach 8, 10 and 13 regimes. The experimental approach is discussed in
Chapter 2 which includes descriptions of the critical parameters that have to be
considered in the simulation of a supersonic combustor environment, the facility
itself and the measurement techniques. The characterization of the test flow is
then presented summarizing determination of the useful test time, core-flow size
and boundary layer effects, issues that have to be addressed to fully characterize
the flow generated in an expansion tube. The flow visualization techniques are
discussed in detail in Chapter 3.
2. Mixing: In Chapter 4, we study the flow features of hydrogen and ethylene transverse jets exposed to high-speed supersonic free-streams at realistic conditions
13
leading to high levels of shear. Guided by the observations of these experiments,
we continue in Chapter 5 with a more fundamental study looking into the origin
of the observed phenomena. The outstanding questions that we investigate are:
How do the jet shear layer vortices develop and which parameters control their
stability and coherence? What is the contribution of the jet shear layer vortices
to the near-field mixing? Does the penetration mechanism only depend on jet-tocrossflow momentum ratio as has been proposed for the last 40 years or is there
any other mechanism leading to higher penetration and better mixing properties?
3. Ignition and flame-holding: The ignition and the flame-holding capabilities of
a hydrogen jet in high total enthalpy flow conditions are presented in Chapter 6.
We study the self-ignition regions in the near-field of the jet in flight Mach 8, 10
and 13 flow conditions using OH-PLIF flow visualization. We also compare the
near-field ignition results of a hydrogen transverse jet with an ethylene transverse
jet at flight Mach 10 conditions.
4. Cavity flame-holders: In Chapter 7, an extensive overview of cavities, which
are considered as a promising flame-holding devices for supersonic combustion, is
presented. Open questions impacting the effectiveness of the cavities as flameholders in supersonic combustors are then discussed. Preliminary experimental
results are also summarized. The goal is to study the ignition capability of a jetcavity configuration and to observe the differences in the shock wave structures
around cavities as the length-to-depth ratio and the geometry of the cavity back
wall are changed.
Chapter 2
Experimental Aspects
Our experimental approach includes the use of an expansion tube to provide a wide
range of variability in the freestream conditions with relatively accurate chemical composition. The latter is critical for supersonic combustion studies in the high total enthalpy
flows associated with hypersonic air-breathing propulsion systems.
Efforts are focused on achieving three operating points, simulating flight Mach 8, 10
and 13 total enthalpy conditions at the entrance of a supersonic combustor. The ability
of the expansion tube to provide a steady-flow test time of adequate duration and a
core-flow of sufficient size for 2 mm jet-in-crossflow studies is verified.
In the following sections, the important parameters that must be considered in the
design of a supersonic combustion experiment are discussed and the facility and the test
flow characterization techniques are then summarized. Additional test conditions are
characterized for fundamental fluid mechanical studies and are presented in Chapter 5.
2.1
Critical Parameters in Supersonic Combustion Simulation
An experimental simulation of a supersonic reacting flow requires the replication of
5 parameters (Heiser and Pratt 1994). These simulation parameters including pressure
(p), temperature (T ), velocity (u), characteristic length of the model (L) and gas composition (νi ) must be manipulated to provide the flight values of certain non-dimensional
parameters such as:
14
CHAPTER 2. EXPERIMENTAL ASPECTS
Mach number:
Reynolds number:
15
u
M∼√
T
(2.1)
ρ
u
Re ∼ √ ∼ pL 3/2
T
T
(2.2)
Damköhler number:
Da ∼
L
uτc
(2.3)
Damköhler number represents the ratio of flow residence time, L/u, through the combustor to chemical time, τc , and must be larger than 1 to achieve flame-holding and
a complete combustion process. For flame-holding considerations ignition delay time,
τi , replaces the chemical time in Damköhler number, τc = τi . For a hydrogen-air combustion process, the ignition delay time, varies inversely with pressure because of the
two-body reactions and depends exponentially on temperature. As a result, Damköhler
number can be related to basic parameters in the following form:
Da ∼
pL
u · exp(θ/T )
(2.4)
where θ is a characteristic temperature for the ignition time.
Consequently, in order to preserve the values of these three non-dimensional parameters it is required to simulate all 5 basic parameters, including temperature, pressure,
velocity, model length and the gas chemical composition. However, it is worth noting
the following point: If the chemical composition of the flow, its velocity and temperature were to be duplicated, then a constant value of the product pL would satisfy
the requirements for simulation of the three non-dimensional parameters. Therefore,
from the standpoint of mixing and flame-holding studies a correct simulation of only 4
parameters is essential: chemical composition, temperature, velocity and the product
pL.
In our experimental approach, we replicate 3 of these 4 parameters: the required
burner entry velocity and burner entry static temperature, u3 and T3 , respectively,
according to the values of burner entry Mach number, M3 , estimated in Fig. 1.1a. The
use of an expansion tube enables acceleration of the air to total enthalpy conditions
16
(3-6 MJ/kgair ) corresponding to the Mach 8-13 flight range, without exposing it to
high stagnation temperatures (3000-6000 K). Therefore, the free-stream contains only
negligible amounts of radicals, produced only by the incident shock wave. The test gas,
first shocked to its maximum temperature (1700-2150 K), is then accelerated and cooled
to the required static temperature (1250-1400 K). Through this unsteady expansion
process, the test gas gains in total temperature and total pressure.
Although in our experiments the free-stream flow composition, Mach number and
static temperature correspond to typical scramjet combustor entrance values, its static
pressure is somewhat below that of actual systems. Table 2.1 summarizes the three
nominal test flow conditions, Mach 8, Mach 10 and Mach 13, achieved in the Stanford
expansion tube facility. Furthermore, since the characteristic length scale in our experiments is small, about 2 mm (the diameter of the injection orifice), the parameter pL
is not sufficiently high to replicate a real combustor environment. This might result
in chemical kinetic limitations on the H2 - air ignition and combustion process. On the
other hand, this limitation can be circumvented if an elevated concentration of oxygen
is used in the test gas to increase the collision rates as suggested by Bakos et al. (992b).
Finally, in the current study we have shown that in high-enthalpy flows, ignition of
hydrogen, injected transversely into a free-stream of air, can be achieved in the nearvicinity of the injector, even at low pL values. Therefore, the ignition will be guaranteed
at higher pressures as the Damköhler and Reynolds numbers increase linearly with pL
in realistic systems.
In conclusion, the most important parameters that have to be replicated for supersonic combustion studies are chemical composition, temperature and velocity of the
free-stream, and the less important parameter is the product pL. Variation in pressure
affects the ignition time linearly, while variation in temperature has an exponential effect through the activation energy (and hence characteristic temperature ignition time,
θ) in chemical kinetics.
17
TABLE 2.1 Test gas (free-stream) flow properties simulating the burner entry conditions of three flight
Mach numbers. The corresponding values are from Fig. 1.1.
Flight Simulation
Mach 8
Mach 10
Mach 13
(1)
(2)
(3)
300
(2.17 MPa)
600
(4.24 MPa)
600
(4.24 MPa)
Driven section, 95% N2 + 5% CO2 , psia
0.45
(3.10 kPa)
0.5
(3.45 kPa)
0.15
(1.04 kPa)
Expansion section, He, torr
70
(9.13 kPa)
20
(2.67 kPa)
2
(0.27 kPa)
Free-stream conditions
Total enthalpy, MJ/kg
2.9 ± 0.05
3.9 ± 0.1
6.2 ± 0.15
Mach number
2.40 ± 0.03
3.38 ± 0.04
4.66 ± 0.07
1400
1290
1250
Static pressure, atm
0.65
(65.9 kPa)
0.32
(32.4 kPa)
0.04
(4 kPa)
Velocity, m/sec (measured)
1800 ± 20
2360 ± 25
3200 ± 50
Test time, µsec (measured)
170 ± 10
270 ± 10
400 ± 10
Test “slug length”, m (velocity × test time)
0.31
0.64
1.28
Establishment length for laminar boundary
layer at L1 = 50 mm, m
0.15
0.15
0.15
Maximum measured recirculation region
length, L2 , (djet = 2 mm)
∼ 1.5 djet
∼ 2 djet
∼ 4 djet
Establishment time for the jet upstream recirculation region, m based on (30−70)×L2
0.09 - 0.21
0.12 - 0.28
0.24 - 0.56
Free-stream Reynolds number at the injection port, Rex = 50 mm
29,000
22,000
3,800
Boundary layer thickness upstream of the
injection port, mm
0.65
0.75
1.80
Shock speeds in the expansion section, m/s
(measured)
Shock Mach number in the expansion section
Maximum temperature that the test gas is
exposed to, T2 , K
2468
3175
3650
2.44
3.14
3.61
1690
1750
2140
Initial filling pressures
Driven section, He, psig
Static temperature, K
18
Double
Diaphragm
IMACON 468
Ultrafast Framing Camera
for Schlieren Imaging
(inc. 8 ICCD modules,
each 576 x 384)
n
ive
Dr
Driven/Expansion
Diaphragm
Focusing
Mirror
Mirror 2
ctio
e
rS
ICCD Camera
for OH-PLIF Imaging
578 x 384 Array
n
tio
ec
S
en
iv
Dr
n
ctio
Knife
Edge
an
p
Ex
sio
e
nS
s& s
ier nter
f
i
l
p
ou
Am al C
v
r
e
nt
Dichroic
Mirror
ta
Da
el on
n
n
i
ha isit
8 C Acqu tem
s
Sy
I
ion
isit
qu rs
c
e A pute
ag
Im Com
Mirror 1
Du
mp
Ta
n
k
Long duration
Xenon Arc
Light Source
se
AG
d:Y
La
r
N
00
YM
12
as
L
ye
er
HT 1000
Frequency
Doubler
0D
HD
50
FIGURE 2.1 Expansion tube facility (12 m in length and 89 mm inner diameter) and imaging system.
2.2
2.2.1
Experimental Facility
Expansion Tube
The expansion tube facility with its dedicated lasers and optical arrangement is
schematically illustrated in Fig. 2.1. The tube is 12 m in length (including dump tank)
with an inner diameter of 89 mm, and includes three sections: driver, driven and expansion. The driver section is filled with high pressure helium gas and is separated
by double diaphragms from the lower pressure driven section, which is filled with the
desired test gas. Mylar film (6.35 µm thick) is used as the diaphragm material at the
driven/expansion interface to separate the test gas from low pressure helium gas in the
expansion section.
0.007
0.006
time, sec
0.005
0.004
19
1 Quiescent Test Gas
2 Test Gas Behind Incident Shock
3 Expanded Driver Gas
4 Driver Gas
5 Expanded Test Gas
10 Expansion Gas
20 Expansion Gas
Behind Incident Shock
first disturbance arrival
head
ction
a
f
e
r
20
ted ra 5
reflec
0.003
0.002
3
2
s1
ck,
o
h
ts
den
1
inci
0.001
4
0.000
-1
0
1
2
3
contact surface
rarefaction tail
rarefaction head
10
4
x-distance, m
4
1
Driver
Section
(He)
Driven
Section
(CO2/N2/O2)
test time
5
6
7
8
IR detector
10
Expansion
Section
(He)
Test
Section
FIGURE 2.2 Expansion tube distance-time (x-t) diagram calculated for flight Mach 13 condition. Method
of characteristics was used to solve the flow gasdynamics properties assuming one-dimensional
inviscid theory. Test time is defined as the time that the test gas has uniform flow quantities
and determined by the time arrival of the contact surface to the tube exit, and that of the
first subsequent rarefaction wave (reflected rarefaction head in our case of high total enthalpy
simulations).
The operating sequence of an expansion tube is best represented by the distance-time
(x-t) diagram shown in Fig. 2.2. A run is initiated by bursting the double diaphragms,
which generates a shock wave propagating into the test gas and producing flow of
intermediate velocity with an increased pressure and temperature. The shocked test
gas is then accelerated by an unsteady and constant area expansion process from the
driven section into the lower pressure expansion section, while gaining total temperature
20
and total pressure. The test gas emerging from the downstream end of the expansion
thus has both a higher stagnation enthalpy and higher effective stagnation pressure than
the shock tube flow from which it originated. Further detail on the operating cycle of
an expansion tube can be found in the review papers of Erdos (1994) and Anderson
(1994).
A square viewing chamber of 27×27 cm cross section is mounted at the exit of the
expansion tube (see Fig. 2.3). A rake of pitot tubes or an instrumented model with the
injection system, is positioned in this test section, which is equipped with an opposed
pair of square (13×13 cm) quartz windows for observation and a fused silica slot on top
of the chamber for admission of the vertical laser sheet.
Six piezo-electric pressure transducers are mounted along the driven and expansion
sections for shock speed and wall pressure measurements. An additional transducer,
mounted 20.3 cm downstream of the driven/expansion diaphragms, is used to monitor
the unsteady expansion process at that location.
The expansion section is also equipped with sapphire viewing ports for optical measurements during flow characterization experiments. In those tests, an InSb IR detector
(Judson J-10 InSb equipped by a Perry model 720 amplifier) is mounted at a viewing
port (see Fig. 2.4) to detect the arrival of the test gas (at the viewing port) through
the emission of IR light by small amount of CO2 (5%) seeded into the test gas (nitrogen). Also, for flow characterization tests, the injection system is replaced with a pitot
rake consisting of four pressure transducers across the diameter of the tube as shown
in Fig. 2.3. The test gas velocity can then be calculated by considering its arrival time
at the viewing port and at the pitot rake. Data from these sensors are recorded at
1 Msample/sec on a PC-based, 8-channel (12-bit) computer-scope. The flow imaging
techniques include Planar Laser-Induced Fluorescence of OH radicals (OH-PLIF) and
schlieren imaging using an ultra-high-speed framing digital camera. Detailed description of these systems and their synchronization with the expansion tube operation are
provided in Chapter 3.
2.2.2
Injection System and its Calibration
The injection system is positioned right at the exit of the expansion tube inside
the test section (Fig. 2.5a). The system consists of a flat plate with an attached high
21
FIGURE 2.3 Schematic of the test section (27 x 27 cm cross section) where a rake of 4 pitot probes, instrumented with pressure transducers, was located 2.5 cm downstream of the tube exit. The flow
history during the expansion tube operation was detected via pitot pressure information. Note
that the inner diameter of the tube is 8.9 cm.
speed solenoid valve (less than 1 msec response time, General Valve Series 9, Iota One
controller) which allows near-constant injection flow rates during the expansion tube
test time period. For the results presented here, an under-expanded transverse jet
of hydrogen with a 2 mm port diameter has been used. The jet port is located at a
distance 30 mm downstream of the tube exit and about 50 mm downstream of the flat
plate leading edge. At this location, the boundary layer thickness, developing on the flat
plate, is approximately 0.75 mm for the conditions presented in this paper. Table 4.1
summarizes the jet flow exit properties.
Calibration of the injected system was performed to determine the stagnation pressure losses through it. This was accomplished by comparing the Mach disk height of an
underexpanded jet into still air with a well-known empirical correlation. Schlieren flow
visualization (Fig. 2.6) was used to measure the Mach disk height for different pressure ratios. The expected jet Mach disk position, based on the correlation suggested
22
Globar
Sapphire
Optical Port
Wall Pressure
Transducer
Pitot
Probe
Test Gas
5%CO2 / N2
Acceleration Gas
He
CS
Focusing Lens
InSb IR
Detector
40.6 cm
2.5 cm
Band-Pass Filter
4.263 - 4.303 mm
Dx @ 104 cm
FIGURE 2.4 Optical set-up to measure the test gas velocity, assumed to be equal to the CS - contact surface
velocity. IR emission from 5% CO2 seeded in the test gas nitrogen is collected by an InSb IR
detector at the viewing port located at 101.6 cm from the end of the tube. The test gas velocity
can then be calculated by considering its time of arrival at the viewing port and at the pitot
rake.
by Ashkenas and Sherman (1966) as a function of jet stagnation pressure (Ptot,jet ) to
effective back pressure (Peb ) ratio, is given by:
y1
= 0.67 ·
djet
µ
Ptot,jet
Peb
¶1/2
(2.5)
On the basis of this correlation, measurements indicated a stagnation pressure loss
of 48% for hydrogen injection and 41% for ethylene injection during valve operation
(note that the fuels were supplied from flow lines of different length).
In addition, the valve actuation time and the tube firing have to be synchronized
such that the jet is fully developed by the time the steady test flow conditions are
obtained. Within that constraint, the time interval between the valve actuation and
the test gas arrival should be short enough to avoid significant changes in the expansion
section initial pressure. To determine the jet development time, schlieren imaging was
used to observe the temporal development of the jet. This combined with the traces
obtained using a fast response pressure transducer located at the jet exit, allowed the
determination of the optimum valve actuation time ( 1.5 msec before start of test time).
(a)
23
(b)
FIGURE 2.5 Schematic of a) Injection system, b) cavity/injection plate system.
2.2.3
Cavity/Injection Plate
The cavity/injection system (Fig. 2.5b) is designed with different cavity and jet
inserts to systematically study the following configurations: 1) 90o and 30o flush wall
gaseous fuel (hydrogen, ethylene) injection, 2) cavities with length-to-depth ratio of
L/D=3,5,7 with 90o , 60o and 30o rear-walls, 3) cavities with 30o upstream fuel injection.
In addition, a miniature pressure transducer (PCB dynamic piezo transducer, model
1105B12) was installed inside the cavity to measure the pressure oscillations and to
monitor the flow establishment time.
2.3
Test Flow Characterization in the Flight Mach 8 - 13
Range
There are several issues that have to be addressed to fully characterize the properties
of a supersonic flow generated in an impulse facility. Of particular concern are the
determination and characterization of flow conditions, the steady-flow test time, the
(a)
(b)
(d)
24
(c)
(e)
Mach Disk
Jet
Boundary
Barrel
Shock
y1
Pj, Mj=1
FIGURE 2.6 Schlieren visualization of an underexpanded gaseous injection into still air. (a)-(c) hydrogen
(d)-(e) ethylene jets. The exposure time of the images was 3 musec. Mach disk height, y1 ,
was measured for different pressure ratios, Pj /Peb , to calibrate the injection system.
core-flow size and the boundary layer effects on the flow properties.
2.3.1
Flow Conditions
A variety of flow conditions can be easily achieved using an expansion tube by simply
changing the initial filling pressures and the speed of sound of the gases at different
sections of the expansion tube. In our facility, helium gas was used in the expansion
and driver sections with a maximum filling pressure of 4.24 MPa (600 psig) in the driver
section.
The selection of correct initial pressures to achieve the required flow conditions,
however, is not straight-forward as the expansion tube combines two shock tubes in
tandem. We have, therefore, calculated the flow conditions that can be achieved in an
25
expansion tube as a function of initial filling pressures. Figure 2.7 presents maps of these
flow conditions estimated using simple one-dimensional inviscid theory (see Appendix A
for a given driver filling pressure of 4.24 MPa (600 psig). These maps provide guidelines
in the selection of the initial pressures for different conditions of interest.
Note the blank (forbidden) regions in the maps of Fig. 2.7. These are the regions
where the shocked test gas cannot expand into the expansion section as the pressure in
the expansion section is higher than the pressure of the shocked test gas.
In a conventional shock tube, for a given driver initial pressure, one must decrease
the driven section pressure to generate flows with higher velocities, temperatures and
Mach numbers. As the driven section initial filling pressure decreases the shock-induced
static pressure decreases as well. In expansion tubes, on the other hand, the flow velocity
and static pressure do not vary significantly as the driven initial pressure is changed for
a given driver and expansion section pressures. As shown in Fig. 2.7, different velocities
can be achieved primarily by manipulating the expansion section initial pressure. For
lower expansion section pressures, the flow accelerates to higher velocities and expands
to lower pressures.
In our experiments, we have used the maps in Fig. 2.7 to simulate the required
burner entry conditions of flight Mach 8, 10 and 13 based on the estimated values
from Fig. 1.1. Simulation of our flight Mach 10 condition, for example, corresponds to
4 MJ/kg of total enthalpy and a Mach number of about 3.5. Therefore, according to
the maps in Fig. 2.7, initial filling pressures of the expansion and driven sections were
determined to be 2.67 kPa (20 torr) and 3.45 kPa (0.50 psia), respectively, to simulate
flight Mach 10 total enthalpy condition at the selected driver initial pressure of 4.24 MPa
(600 psig). Initial pressures required to simulate flight Mach 8 and 13 were chosen in a
similar manner and are marked on the maps of Fig. 2.7.
As discussed in the previous section, our experimental approach includes correct
replication of the velocity and temperature of the air entering the combustor. The
static pressure in our experiments, on the other hand, is lower than the expected values
in a supersonic combustor at those flight conditions. However, the correct replication of
pressure is not as crucial as the simulation of the required total temperature and burner
entry Mach number, in the basic study of ignition and flame-holding processes of different injection schemes. Pressure dependence of the ignition process can be extrapolated
26
(a)
5
6
5
4
0.2 atm
9
8
7
0.1 atm
1
1 atm
0.6 atm
0.3 atm
600 K
0.4 atm
2
0.8 atm
400 K
0.05 atm
Driven Gas (Nitrogen) Initial Pressure, P1 (psia)
3
1.4 atm
300 K
4
Mach 8
Mach 10
1000 K
1400 K
3
1800 K
2
2200 K
Mach 13
2400 K
0.1
2
3
1
4
5
6
7 8 9
2
3
4
5
6
7 8 9
10
Expansion Gas (Helium) Initial Pressure, P10 (torr)
2
100
(b)
5
6
5
4
2
1
1800 m/s
2400 m/s
2200 m/s
3.5
4 MJ/kg
5 MJ/kg
6.5
6 MJ/kg
Mach 13
0.1
Mach 8
3
5.5
6
2
2.5
3 MJ/kg
Mach 10
4.5
3
7
2600 m/s
3000 m/s
9
8
7
3200 m/s
1
2800 m/s
2
2000 m/s
3
3400 m/s
4
4
5
6 7 8 9
2
3
4
5
6 7 8 9
10
2
100
FIGURE 2.7 Maps of estimated test gas (nitrogen) conditions (state 5) at the exit of an expansion tube:
a) pressure and temperature, b) total enthalpy and velocity of the test gas are plotted for
different initial driven and expansion section pressures. Calculations are performed using the
inviscid 1D equations for a given driver pressure of P4 = 600 psig (helium). Note that the
effective filling pressure of the driver section is taken as P4,eff = 686 psig, as its inner diameter
(10.2 cm) is larger than that of the driven and expansion sections (8.9 cm). This area difference
is accounted for in the curves presented above.
27
to higher pressures since the Damköhler number is approximately proportional to pressure in hydrogen-air combustion systems. Furthermore, the oxygen concentration can
be increased in the test gas if the combustion process is rate-limited due to low static
pressure.
Table 2.1 summarizes the initial filling pressures of the three test conditions characterized in the Stanford expansion tube. Other factors, such as the maximum available
injector pressure, were taken into account in determining these test flow conditions.
The initial driver pressure for the Mach 8 condition, for example, was chosen to be
2.17 MPa (300 psig) instead of 4.24 MPa (600 psig) to provide reasonable penetration of
the fuel jet. Penetration of fuels injected transversely into supersonic flows is known to
be strongly correlated with the jet-to-free-stream momentum flux ratio (J) defined as
¡
J=
ρu2
¢
¡
jet
(ρu2 )∞
=
γpM 2
¢
jet
(γpM 2 )∞
(2.6)
where the subscript “jet” corresponds to the jet exit conditions and ∞ corresponds to
free-stream conditions ahead of a bow shock. In our experiments, the jet-to-free-stream
momentum flux ratio was typically J = 1.5 − 2.
2.3.2
Measurement of Flow Properties
The test flow conditions (pressure, temperature, velocity, Mach number and test
time), presented in Table 2.1, were determined using the combined data of wall pressure,
pitot pressure, and IR emission. Briefly, the test flow characterization was performed
in the following stages:
1. the shock speeds at the driven and expansion sections were measured using six
piezo-electric pressure transducers mounted in the tube,
2. gasdynamic conditions of the post-shock test gas in the driven and expansion
sections were obtained from the measured shock speeds by a 1-D frozen-chemistry
code using standard thermochemical data,
3. the test gas temperature and sound speed at the exit of the tube were then
calculated assuming isentropic expansion of the shocked test gas in the driven
section to the expected value of the post-shock static pressure of the acceleration
gas in the expansion section,
28
4. the velocity of the contact surface was deduced by measuring the time interval
between its arrival at the IR detector port and the pitot probe located at the exit
of the tube,
5. test gas flow velocity was then estimated by equating the contact surface velocity with that of the test gas immediately after it.
An example of IR emission from CO2 seeded in the test gas, together with pitot and
static pressure traces measured in flight Mach 10 flow simulation is given in Fig. 2.8.
Note that in characterization experiments, instead of air, a mixture of 95% N2 +5% CO2
was used as a test gas, which provides an effective molecular weight (28.8 gr/mole)
equivalent to that value of the air. Based on the time history of the pitot pressure
at the tube exit, it is possible to identify the arrival of the shock wave, the period
of expansion section helium flow, the helium/test gas contact surface, and the steady
flow test time. It is evident that the contact surface is not a perfectly sharp boundary
between helium and test gas. Instead test gas concentration seems to increase over a
period of time.
A similar trend can be observed in IR emission which can be detected with the
arrival of the helium/test gas contact surface (CS) to the viewing port. The intensity
of IR emission increases through the CS passage as the CO2 concentration in the CS
increases. At the end of the steady test gas the emission intensity decreases as the
test gas cools down with the arrival of the expansion waves (reflected rarefaction tail).
During the steady flow test time, we observe that the IR emission is, however, not as
constant as the traces of the pitot and static pressures. Instead, an initial peak followed
by a monotonic increase are observed in the Mach 10 flow characterization (see Fig. 2.8).
In general, the intensity of IR emission increases with the volume of emitting gas, its
temperature and concentration. Since the IR emission is the integrated emission across
the tube including the wall boundary layer, it does not reflect the properties of the
core-flow only. The monotonic increase of the intensity (subsequent to the drop from
its initial peak value) can be explained as due to an increase in the volume of the hotter
CO2 in the growing boundary layer, while the initial peak signal can be attributed to
the small hot region formed by the reflected shock during the break of the helium/test
gas diaphragm.
IR Emission
CS
Arrival
Normalized Pitot Pressure
3.0
Normalized
Static Pressure
-0.2
2.0
0.0
2.5
Test Gas
0.2
0.4
440±5 msec
Dx=104 cm
2.0
0.6
Shock Wave
Arrival
0.5
1.0
Test Time
~270 msec
Helium Flow Time
~455 msec
Rarefaction
Wave
0.0
-0.2
0.0
0.2
1.5
1.0
0.8
CS Velocity:
2360±25 m/s
CS
1.5
1.0
29
0.4
0.6
CS
Test Gas
0.8
1.0
Shock Wave
Arrival
0.5
Rarefaction
Wave
0.0
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Normalized
Mach number
2.0
Test Gas
1.5
1.0
Shock Wave
Arrival
0.5
Rarefaction
Wave
0.0
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
time, msec
FIGURE 2.8 Example of IR emission, pitot pressure, wall pressure records and the Mach number variation
based on the pitot-to-static pressure ratios, as a function of time for the Mach 10 flow condition.
t = 0 represents incident shock arrival at the pitot probe, placed 2.5 cm downstream of the tube
exit, while the wall pressure transducer and IR detector are positioned 40.6 cm and 101.6 cm
upstream of the tube exit, respectively (see Fig. 2.4). Note that the time scale of the static
pressure trace is shifted by 235 µs to match the shock arrival at the pitot probe.
30
The steady test period was taken to be the time over which the pitot pressure
changed by no more than ± 5% from the average value. Accordingly the measured test
time was approximately 270 µs. The steady test period is always limited by the arrival
of waves, either the unsteady expansion waves (rarefaction tail) or the reflected waves
(reflected rarefaction head) from the intersection of the driver gas interface with the
unsteady expansion waves. In any case, the arrival of waves is clearly identifiable as
the test gas pressure rises sharply and the IR emission from cooling test gas begins to
decrease.
An average value of 2360 m/s for the test gas flow velocity was measured over the
104 cm length between the IR emission port and pitot rake (see stages 4 and 5 described
above). The test gas velocity was also estimated from measured shock speeds in the
expansion section using inviscid 1-D theory, resulting in 2130 m/s. The measured velocity (2360 m/s) therefore exceeds the estimated inviscid value based on shock speed
by approximately 10%, as may be explained by the acceleration of the flow due to the
growing boundary layer on the tube walls.
The Mach number of the test gas was calculated using the measured contact surface
velocity and calculated sound speed as described in stage 3. The results indicated an
exit Mach number of 3.38±0.04 for the flight Mach 10 condition. Mach number variation
in the test gas can also be obtained from the pitot to static pressure ratio as shown in
Fig. 2.8. It is worth noting that while the static pressure of the test gas rose sharply
after the arrival of the reflected rarefaction wave, the Mach number of the flow varied
little over the following 400 - 500 µs.
Figure 2.9 presents an example of flight Mach 13 flow characterization traces which
have features similar to those of flight Mach 10 traces. The characterization results
show a relatively long test time of 400 µs in the case of flight Mach 13 simulation; this
is much larger than the ideal values (180 µs). The test gas velocity was measured to be
3200 m/s, about 23% faster than the shock-induced ideal flow velocity. This acceleration
of the test gas is again believed to be a result of the boundary layer developed on the
tube walls.
Shorter test times (∼170 µs) are observed for low total-enthalpy conditions as shown
in Fig. 2.10 presenting an example of flight Mach 8 flow characterization traces. Note
that the static pressure stays constant for a longer period of time although the pitot
pressure increases significantly by the arrival of the first disturbances.
IR Emission
CS
Test Gas
-0.2
0.0
0.4
0.6
0.8
1.0
3.0
CS Velocity:
3200±50 m/s
325±5 msec
Dx=104 mm
2.5
2.0
CS
1.5
Test Time
~400 msec
Helium
Shock Wave Flow Time
Arrival
0.5
~180 msec
1.0
Rarefaction
Wave
0.0
-0.2
Normalized
Static Pressure
0.2
31
0.0
0.2
0.4
0.6
0.8
1.0
2.0
1.5
1.0
Test Gas
CS
Shock Wave
Arrival
0.5
Rarefraction
Wave
0.0
-0.2
0.0
0.2
0.4
time, msec
0.6
0.8
1.0
FIGURE 2.9 Example of IR emission, pitot pressure and wall pressure traces as a function of time for the
Mach 13 flow condition.
In Fig. 2.11, we compare the measured values of the free-stream velocity with the expected values estimated using the measured shock speeds in the expansion section. The
results indicate that the measured velocities are always larger than the expected ideal
values. In addition, as the flight Mach number increases and therefore the static pressure decreases the measured velocity approaches the shock velocity. These observations
suggest that boundary layer effects are significant, causing the flow to be non-uniform.
As a result of the viscous effects, the shock slows down and the contact surface (test
gas) accelerates. At the limit of a sufficiently long expansion section, boundary layer
effects would cause the shock and the contact surface to equilibrate to a constant velocity. Accordingly, an additional calculation, taking into account the viscous effects based
on Mirels’ solution (Mirels 1963; Mirels 1966) for post-shock boundary layers, has been
IR Emission
Test Gas
CS
Arrival
-0.2
32
0.0
0.2
0.4
0.6
0.8
1.0
1.2
3.0
Velocity: 1800±20 m/s
2.5
578±5 msec, Dx=104 cm
2.0
Test Time
~170 msec
CS
1.5
1.0 Shock Wave
Arrival
0.5
Helium Flow Time
~725 msec
Rarefaction
Wave
0.0
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Normalized
Static Pressure
2.0
Test Gas
CS
1.5 Shock Wave
Arrival
1.0
Rarefaction
Wave
0.5
0.0
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
time, msec
FIGURE 2.10 Example of IR emission, pitot pressure and wall pressure traces as a function of time for the
Mach 8 flow condition.
performed, and will be discussed in the following section.
2.3.3
Boundary Layer Effects on Test Time
The uniform flow time of test gas at the expansion tube exit is defined as the test
time; this period begins with the arrival of the driven/expansion contact surface at the
tube exit, and ends with arrival of the first rarefaction wave (in our case, the rarefaction
head reflected from driver/driven contact surface as shown in the x-t diagram in Figs. 2.2
and 2.11.
Under ideal conditions, where no wall effects exist, the shock wave and the contact
4000
Measured contact-surface velocity
Estimated shock-induced velocity
Measured shock velocity
3500
Velocity, m/s
33
3000
Mach 13
P=0.04atm
2500
2000
1500
Mach 10
P=0.32atm
Mach 8
P=0.65atm
1000
2.4
2.6
2.8
3.0
3.2
3.4
3.6
Expansion Section Shock Mach Number, Ms,2
FIGURE 2.11 Comparison of the measured contact-surface velocity (test gas velocity) with the shockinduced gas velocity estimated using the measured shock speeds in the expansion section.
surface would move with constant velocities and the flow between them would be uniform. However, in a real shock tube, the flow becomes non-uniform as the boundary
layer develops at the tube walls. The presence of a wall boundary layer causes the
incident shock to decelerate and the contact surface to accelerate. Consequently, the
time duration of the flow between the shock and the contact surface (expansion section
helium flow time) is reduced. In conventional shock tubes, therefore, the test time is
reduced as a result of the boundary layer growth.
In expansion tubes, on the other hand, the effect of the boundary layer in accelerating
the contact surface can actually lead to an increase in test time as observed in our
experiments. We have measured 400 µsec of steady test time at the Mach 13 condition,
while only 180 µsec of test time is expected based on 1-D inviscid calculations (see x-t
diagram in Fig. 2.12a).
To study the boundary layer effects on the test time, we have performed an improved
calculation taking into account the viscous effects based on Mirels’ boundary layer
solution. The predicted contact surface velocity from this solution was implemented in xt diagram calculations and the results are plotted together with 1-D inviscid calculations
in Fig. 2.12a. The calculations (dashed lines in Fig. 2.12a) resulted in a test time of
34
(a) Mach 13 condition
(measured test time = ~ 400 m sec)
0.0036
0.0030
0.0027
hea
d
time, sec
0.0033
0.0018
rar
efa
ctio
n
0.0024
0.0021
ideal test time
180 msec
Inviscid Solution
Mirels' Model
inc. boundary layer
3.5
4.0
450 msec
d
CS
hea
cid
ion
s
t
i
c
v
fa
In yer
rare
a
ed
yL
t
r
c
a
e
nd
refl
u
o
B
ith
Sw
ail
t
C
)
on
ured
cti
eas
a
f
M
(
k
re
hoc
ra
nt S
e
d
i
Inc
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
x-distance, m
(b) Mach 10 condition
ideal test time
140 msec
(measured test time = ~ 270 msec)
0.0042
Inviscid
Mirels' Model
inc. boundary layer
0.0039
380 msec
time, sec
0.0036
0.0033
0.0030
0.0027
t
den
Inci
0.0024
CS
ry
cid unda
s
i
v
o
n
I
hB
wit
CS
d)
ure
eas
M
(
ck
Sho
er
Lay
0.0021
0.0018
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
x-distance, m
FIGURE 2.12 X-t diagrams for the expansion section only. 1-D inviscid calculations are plotted in straight
lines and results applying Mirels’ model to include the boundary layer effects are plotted in
dashed lines. One can see the improved test time as a result of the contact surface (CS)
acceleration due to the developing boundary layer behind the incident shock in the low pressure
expansion section helium flow. The incident shock velocity was measured and assumed to be
constant along the expansion section.
35
450 µsec, agreeing well with the measured value of 400 µsec. This effect can be explained
by the fact that the contact surface, accelerated by viscous effects, arrives at the test
section earlier than if viscous affects were negligible. Therefore, the test time duration
is increased as the time of arrival of the first flow disturbance is delayed relative to the
contact surface arrival.
An additional interesting result can be observed from the x-t diagrams: the length
of the current expansion section is seen to be optimum to achieve a maximum test time
duration for flight Mach 13 simulation as the arrival of both the rarefaction wave and
the reflected rarefaction head overlap at the end of the tube (see the dashed lines in
Fig. 2.12a.) Any variation in the length of the expansion section will cause the test
time to decrease. By contrast, the x-t diagram calculated for the Mach 10 condition
(Fig. 2.12b) demonstrates that the expansion section length is longer than its optimum
value. A 30% longer test time could have been achieved if the expansion section was
1.8 m shorter than its current length.
The calculation based on Mirels’ solution also gives an improved estimation of the
expansion section helium flow time of 170 µsec, which compares well with that inferred
from the pitot pressure trace, 180 µsec (within 5.5% accuracy). The test gas velocity
obtained from this calculation, 3300 m/s, shows improved agreement with the measured
value of 3200 (within 3%). These results, summarized in Table 2.2, confirm the importance of boundary layer effects and demonstrates that the viscous calculations based on
Mirels’ model provide good estimates of the test time and the test gas velocity at the
low pressure flight Mach 13 condition.
Mirels’ solution, performed for the flight Mach 10 condition (see Fig. 2.12b), results
in a less accurate prediction of flow properties. As summarized in Table 2.2, the calculated test time based on Mirels’ solution overpredicts (by 41%) the actual test time.
The reason for the overprediction is that the initial filling pressure in the expansion
section is relatively high (20 torr), and therefore the wall boundary layer behind the
shock wave is not fully developed as assumed in Mirels’ solution. In addition, we have
assumed that the boundary layer properties of the test gas were similar to the properties
of the expansion section helium gas, which can be significantly different as the pressure
increases.
We have shown that the flow test time is affected by the boundary layer development
in the expansion section tube walls in such a way that the steady test time duration is
36
TABLE 2.2 Summary of measured, ideal (inviscid 1-D) and predicted (based on Mirels solution) properties
of test gas for Mach 10 and 13 flow conditions.
Mach 10
Mach 13
Test Time
Test Gas
Velocity
Helium Flow
Time
Measured
µsec
270 ± 10
m/s
2360 ± 25
µsec
455 ± 2
Ideal
140
2130
660
Mirels
380
2510
520
Measured
400 ± 10
3200 ± 50
180 ± 2
Ideal
180
2440
520
Mirels
450
3300
170
increased. Longer test times are important in supersonic flow experiments as the length
of the test period determines the maximum model length for which steady flow can be
fully established.
2.3.4
Core-Flow Size
The other parameter which limits the maximum model length is the radius of the
axially uniform flow called the useful core-flow. While the test time increases as the
boundary layer on the tube walls develops, the useful core-flow size, on the other hand,
becomes smaller. The thickness of the boundary layer developed in the acceleration
section can be large in comparison to the tube radius because of the low filling pressures
of the expansion section.
In our experiments, we characterized the useful core-flow size by measuring the pitot
pressure at different radial and axial locations. The results, plotted in Fig. 2.13, show
that at 12.7 mm (0.5”) away from the tube exit, pitot pressure varied only ±5% within
a 25 mm core-flow diameter for the three conditions that we have studied. As we moved
the pitot probe downstream of the tube exit, the core-flow size at the Mach 13 condition
did not change significantly. On the other hand, the flight Mach 10 and 8 conditions
resulted in a deceased core-flow size as we moved away from the tube exit. At the
Mach 8 condition, the pitot pressure at the center line of the tube decreased by 15%
37
at 63.5 mm (2.5”) downstream of the tube exit. This is expected for the flight Mach 8
condition, since the Mach number of the free-stream is only about 2.4, corresponding
to a steeper Mach wave angle.
In conclusion, the results indicate the existence of a 25 mm core-flow diameter that
is suitable for near-field studies of transverse fuel jets injected from a 2mm diameter
orifice. The injection plate is positioned as close as possible to the tube exit and 6.4 mm
(1/4”) below the centerline to allow a maximum field of study of the jet.
2.3.5
Flow Establishment Time
Undesirably, part of the steady test time is consumed during the flow establishment
process for the model under investigation. Correlations are available in the literature
(Rogers and Weidner 1993; Jacobs et al. 1992; Davies and Bernstein 1969; Holden 1971)
for predicting the flow establishment times for different flow features of the model. In
general, the test “slug length”, defined as the distance traveled by the volume of test
gas during the period of steady test time, must be larger than the characteristic length
of the flow device or process by some multiple. The criterion for the establishment of
flow over a flat plate requires that the test “slug length”, i.e., the product of test time
and gas velocity, t · u, satisfies (Davies and Bernstein 1969).

 2·L ,
1
t·u=
 3·L ,
1
for turbulent boundary layer
for laminar boundary layer
(2.7)
where L1 is the distance from the edge of the plate. The flow establishment criterion
for separated flows, on the other hand, is required to be tens of times larger than the
characteristic recirculation region length L2 , as given by (Holden 1971) for the wake of
sphere





t·u=
for separated flows
30 · L ,
2



 70 · L2 ,
based on pressure measurements
(2.8)
based on heat transfer measurements
Note that L2 is the length of the recirculation region and therefore smaller than the
characteristic distance L1 by more than an order of magnitude, resulting in similar flow
establishment times.
38
(a)
Flight Mach 13 condition
Normalized pitot pressure
1.0
0.8
useful core flow
~ 25 mm
0.6
0.4
Distance from the tube exit
12.7mm (0.5")
38.1mm (1.5")
63.5mm (2.5")
0.2
0.0
-20
-10
0
10
20
Free-stream flow radius, mm
30
40
(b)
1.0
0.8
0.6
0.4
12.7mm (0.5")
38.1mm (1.5")
63.5mm (2.5")
0.2
0.0
-20
-10
0
10
20
30
40
(c)
1.0
0.8
0.6
0.4
12.7mm (0.5")
38.1mm (1.5")
63.5mm (2.5")
0.2
0.0
-20
-10
0
10
20
30
40
FIGURE 2.13 Useful core-flow size in flight Mach 13, 10 and 8 conditions, (a), (b) and (c), respectively,
determined by measuring the radial variation of pitot pressure at different distances from the
tube exit.
39
Based on these correlations, we have estimated two flow establishment times in our
experiments and summarized the conclusions in Table 2.2. First, the boundary layer
flow establishment time was calculated by assuming laminar flow, as the local Reynolds
numbers at the injection port were relatively small. Second, the establishment time of
the recirculation region upstream of the injection port was estimated. In general, the
bow shock around the jet interacts with the approaching boundary layer and causes its
separation. This recirculation region length confined with the separation shock wave
was measured from schlieren images and used as the characteristic length, L2 , of the
separation zone.
The estimated flow establishment values indicated that the “test slug” (1.28 m) for
the flight Mach 13 condition is fairly long as compared to the predicted flow establishment times (0.15 m for boundary layer and 0.56 m for the recirculation region heat
transfer establishment time = 0.71 m in total). Therefore, about 0.60 m of a “test slug”
or 235 µs of test time is still available for measurements. By contrast, at the flight
Mach 8 condition, flow establishment seems to consume most of the steady test time.
However, it is worth noting that the expansion section helium flow prior to the test gas
arrival contributes to the establishment of jet flow even though it is not considered as a
part of the test time. Furthermore, the useful test time in our experiments is determined
using the pitot probe after the flow is established around it. Therefore, the estimated
flow establishment times given in Table 2.2 are expected to be larger than the actual
flow establishment times, so that even at the flight Mach 8 condition, part of the slug
length is useful for measurements after the flow-field is established.
To summarize, as the flight Mach number in our facility increases, a longer test
“slug length” becomes available for measurements. This is a result of the long test
times achieved with high-total enthalpy, low-pressure conditions and the fact that higher
speed implies faster flow establishment.
2.4
Summary
We used the Stanford expansion tube to generate high total enthalpy flow conditions
in the Mach 8-13 flight range. A variety of supersonic flow conditions are also simulated
in the facility for fundamental mixing studies of transverse jets. These conditions are
summarized in Chapter 5. See also Appendix B for maps of ideal flow conditions that
40
can be achieved using an expansion tube. The maps are calculated for different freestream gas (Nitrogen, Helium and Argon) and for two different initial driver pressures
(P4 = 300 and 600 psig).
Chapter 3
Flow Visualization Techniques
Much of our basic understanding of the behavior of flows has come from flow visualization. One of the best examples of this is the work of Brown and Roshko (1974),
which shows the existence of large scale structures in a two-dimensional shear layer using
shadowgraphs. A clear visualization of axisymmetric shear layers, as the one present in
the periphery of transverse jets in crossflows, is more difficult to achieve due to three
dimensional effects, especially when the jet characteristic length is as small as d=2 mm.
The flow visualization of transverse jets in supersonic crossflow studied in this work
was obtained using an ultra-high-framing-rate schlieren system and Planar Laser Induced Fluorescence (PLIF) of the hydroxyl radical (OH). The ability to image the flow
with good temporal and spatial resolution is particularly important, because of the high
velocities of the flows and also because it provides a means of examining the instantaneous turbulent structures that control the mixing and combustion processes.
3.1
Ultra-Fast Framing Rate Schlieren
The ability to capture the time evolution of unsteady supersonic flows is critical to
their understanding. Non-intrusive visualization techniques, such as schlieren and laserbased planar flow imaging, are powerful and commonly used optical methods. However,
tracking the structural evolution of high-speed flows requires acquisition of images at
fast (typically MHz) repetition rates. In addition, very short exposure times (20-200 ns)
are required to resolve instantaneous features. As the spatial resolution is increased to
41
CHAPTER 3. FLOW VISUALIZATION TECHNIQUES
42
avoid the blurring of turbulent structures, the exposure time must be reduced and the
repetition rate increased. It is challenging to fulfill the temporal resolution requirements
of high-speed imaging while maintaining meaningful spatial resolution for supersonic
flows.
Before we introduce previous and current efforts towards the development of supersonic flow visualization at ultra-fast-framing rates, it is useful to present the motivation
behind such efforts. Of great interest is the study of shear layers formed at the interface
of two parallel or skewed fluid streams. Since Brown and Roshko (1974) demonstrated
that large-scale coherent structures are dominant in subsonic shear layers and that their
structure and evolution control the mixing process, many researchers have concentrated
their efforts on measuring large-scale convection characteristics of shear layers in supersonic flows. However these studies were limited to double-pulse visualization techniques,
such as double-pulse schlieren by Papamoschou (1991), double-pulse Mie/Rayleigh scattering by Elliott et al. (1995), double-exposure planar laser-induced fluorescence (PLIF)
of acetone by Papamoschou and Bunyajitradulya (1997) and Fourguette et al. (1991)
and double-pulse imaging using simultaneous aceton/OH-PLIF by Seitzmann et al.
(1994). Those studies focused on measuring the convective velocity (Uc ) of large-scale
structures by capturing a maximum of two images that are temporally correlated.
Of particular interest to our research is the shear layer formed when a gaseous jet
interacts with a supersonic crossflow stream, an example of skewed shear layers. This
is also a common fuel injection scheme in practical systems, such as a scramjet, and
therefore fundamental study of its mixing process is important. Although there have
been numerous studies of the shear layer properties of two parallel streams, there have
been relatively few works on jets in supersonic crossflow. Among those studies only
Gruber et al. (997a) studied the large-eddy convection characteristics of jets in supersonic crossflow, again by capturing two consecutive Rayleigh/Mie scattering images.
Their results revealed the convection characteristics of helium and air jets injected into
a Mach 2 crossflow. The highly compressible helium jet exhibited larger convection
velocities in the near-field of the injection than the air jet of low compressibility. However, the accuracy of the velocity measurement was only about ±10%, as the minimum
separation between the laser pulses was limited to 1 µsec.
It is crucial to characterize the full life cycle of the flow-field. For example, the largescale eddies, formed periodically at the early stages of shear layer development, undergo
43
structural evolution as they convect downstream while entraining, pairing, engulfing,
stretching and tearing. Therefore, measurement of the formation frequency of these
eddies and their evolution should aid understanding of the origin and formation of the
jet vortical structure and, hopefully, provide tools in controlling its mixing properties.
Such studies require application of an ultra-high-speed imaging system.
In our experiments, we therefore selected a new fast-framing imaging system capable
of recording 8 consecutive high-resolution schlieren images at rates up to 100 MHz. Our
goal is to study the time evolution and convection properties of large-scale structures
present in the shear layer of the jet/free-stream interface. It is important to understand
how these structures and growth rate vary as flow conditions and fuel types are changed.
Moreover, most of the earlier jet studies were carried out in blow-down wind tunnels
where the free-stream conditions were usually of low temperature and therefore with
relatively low speeds. Free-stream velocity in the experiments of (Gruber et al. 997a),
for example, was about 515 m/s. In our experiments we employ an impulse facility which
can generate realistic conditions of a typical supersonic combustor with high velocities
(1800-3300 m/s) and high static temperatures (1300 K) (Ben-Yakar and Hanson 2000).
However, these facilities have short test times (∼0.2 - 2 ms) during which there is only a
brief opportunity to perform a flow-diagnostic measurement. As a result, application of
MHz imaging in impulse facilities becomes almost necessary as we can obtain multiple
images that are also time-correlated. In our facility, the amount of data obtained per
experiment is, therefore, increased by at least 8 times by the new ultra-high-speed
imaging system.
In the following sections, we present the components of the ultra-fast schlieren
imaging system and discuss issues of resolution, timing, synchronization and imageprocessing techniques.
3.1.1
Previous and Current High Speed Imaging Efforts
High-speed imaging requires two components: a camera which can acquire at high
framing rates and a light source with either long duration time or high pulsing rate.
Early flow visualization at high-speed framing rates was performed using a rotating
mirror camera. Mahadevan and Loth (1994), for example, utilized a rotating mirror
camera to temporally resolve compressible mixing layer structures at approximately
44
350 kHz using schlieren and Mie scattering. A Xenon flash system with square pulse
durations up to 200 µs was used as a continuous light source. The quality of images was
poor because of the low resolution and blurring of the images due to the convection of
the flow structures.
Patrie et al. (1993, 1994), on the other hand, performed 3-D snapshots of instantaneous flow structures using Mie scattering and laser-induced fluorescence of flames and
turbulent jets. Their camera system included a high-speed image converter coupled by
fiber optics to a CCD camera. Up to 20 sequential planar images were collected at the
rate of 10 MHz. The output of the system was a single digital image with 400 × 700
pixels, containing the sequence of 20 images, namely, each image was approximately
160 × 140 pixels for a 10 image set. This imaging system required post-processing algorithms to correct the spatial distortion of the images caused by electrodynamic interaction of the photoelectric currents within the camera. Island et al. (1996) used
the same imaging system to study the three-dimensionality of supersonic mixing layers.
The planar illumination for a 3-D scan was provided from a 2 µs pulse duration of a
flashlamp-pumped dye laser with a pulse energy of 3 J at 590 nm. The laser output
was reflected from a high-rpm rotating mirror. The pixel resolution was approximately
1 mm resolving only the largest scales of mixing.
Recently, several researchers including Huntley et al. (2000), Thurow et al. (2000)
and Wu et al. (000b) reported their efforts toward MHz-rate digital planar flow visualization using a prototype CCD camera manufactured by Princeton Scientific Instruments,
Inc. (PSI) with pixel format of 180 × 90 or 180 × 180. This camera has a 32 image storage buffer built onto the image sensor chip itself, and can frame at rates up to 1 MHz.
The drawback of the PSI camera is the low pixel resolution of images (the pixel size is
50 µm × 50 µm) and the low fill factor of the light sensitive area which is about 14%.
Princeton Scientific Instruments, Inc has attempted to develop this unique high-speed
framing CCD camera under a government SBIR contract. However, further development of this prototype camera is currently not possible because of the manufacturing
difficulties of the chip.
The PSI camera is typically paired with a laser working in a pulse “burst” concept
(Wu et al. 000b). The “burst”train of 30-40 pulses was formed by applying a high-speed
Pockel Cell “slicer”to the long duration output (200 µs) from a continuous wave (CW)
Nd:YAG ring laser. The energy of each of the individual pulses comprising the train was
45
0.5 - 1 mJ, with minimum separations of 1ms (1 MHz). With this energy level of pulses
the researchers succeeded in performing CO2 -enhanced Filtered Rayleigh Scattering
measurements in supersonic flows.
As summarized above, since the early 90’s, several research groups attempted to
perform high speed imaging of supersonic flows. Their results showed the excellent
potential of high speed 2-D and 3-D measurements. However, their imaging systems
were usually of low resolution and low light sensitivity.
In the following sections, we present initial results with a new commercial imaging
system that can capture images (free of distortions) at rates up to 100 MHz. The system
includes a fast framing rate camera (IMACON 468) combined with a long duration, high
intensity light source (Xenon flashlamp) to acquire 8 consecutive schlieren images of
supersonic flows with 578 × 384 pixel resolution. In this system, resolution and blurring
of the images can be controlled by adjusting the image exposure time which can be as
small as 10 ns.
A similar fast framing camera system with a maximum repetition rate of 1 MHz
is also being used by Kaminski et al. (1999) to study turbulent reacting flames. The
system performance was demonstrated at 8 kHz repetition rate using a custom-built
unit (BMI) of four double-pulsed Nd:YAG lasers with an accompanying dye laser. This
laser system allowed variable inter-framing times of 25 to 145 µsec.
3.1.2
High-Speed Schlieren Imaging Components
The ultra-fast-framing schlieren system illustrated in Fig. 3.1 comprised three components: 1) a high-speed framing camera, (Imacon 468, manufactured by Hadland Photonics), 2) a long duration light source, (Xenon flash-lamp), and 3) mirrors and knife
edge in a standard Z-arrangement.
The Imacon 468 consists of 8 independent intensified CCD cameras for high-speed
framing that can capture 8 consecutive images with variable exposure and interframing
times down to 10 ns. The single optical input is divided uniformly and distortion-free by
a special beam splitter into 8 different intensified CCD modules, each with a 576 × 384
array of 22 × 22 µm size pixels.
The light source is a high intensity Xenon flash discharge unit (Hadland Photonics
model 20-50 flash system with an extension to 200 µs duration). The unit has three
46
Power Supply
Xenon Flash
Light Source
Mirror 1
Mirror 2
Test Section
Knife
Edge
Focusing
Lens
IM
AC
ON
4
68
Camera
Input Trigger
Fiber Optic Link
Control Computer &
Image Monitor
FIGURE 3.1 Schlieren imaging set-up.
ranges providing 20 µs, 50 µs and 200 µs durations of the light source with intensity
levels of each being 125 J, 375 J and 700 J per pulse, respectively.
In the optical set-up, two f /10, 200 cm focal length concave mirrors are used to
collimate the light through the test section, and then refocus it onto a knife edge (razor
blade). This knife edge (KE) at the focal point of the second schlieren mirror is used to
partially cut off the deflected rays for observing the schlieren effect (visualization of the
density gradients). Blocking more of the light by moving the KE transverse to the optical
axis makes the system more sensitive, showing more features of the jet (Merzkirch 1965).
The KE, oriented horizontal or vertical with respect to the focused light, will emphasize
the density gradients in the horizontal or vertical directions respectively. In Fig. 3.2,
examples of schlieren images with different KE orientations are presented. These are
the images of an underexpanded hydrogen jet issuing into quiescent air. Significant
(a)
(b)
(c)
47
(d)
Knife edge
Razor blade
Light source
at the focal point
FIGURE 3.2 Examples of schlieren images of jet issuing into quiescent air as obtained for different positions
of the knife edge (razor blade) at the focal point. We use the set-up demonstrated in (d) where
the knife edge cuts the focused light at an angle to enhance both the vertical and the horizontal
density gradient effects.
differences in the details of the flow-field can be observed just by positioning the KE
at different orientations. In our experiments, the KE is positioned at 45o to emphasize
both the vertical and horizontal gradients.
The test object is then imaged with a single constant focal length lens onto the
intensified CCD camera. Two different focal length lenses (an f /12.5, 100 cm focal
length lens and an f /6, 49 cm focal length lens) were used to capture different sizes of
the field of interest. For the images presented in this paper, de-magnification of 0.44
was required and obtained using a 100 cm focal length (f /12.5) lens.
3.1.3
Timing and Synchronization
Flow establishment, timing and synchronization are important issues that have to
be addressed very carefully in preparation of an experiment in an impulse facility. The
imaging system must be synchronized with the facility operation and the delay times
must be set to allow the data to be acquired during the short steady test time. Therefore, test flow arrival and its steady duration are first studied through characterization
experiments (see Chapter 2) to determine the required delay times. The general approach is to replace the injection plate with a pitot probe and to trace the flow history at
Driver Section
Driven Section
Pressure Transducers:
Injection Valve
48
Expansion Section
P10 P9 P8
P3
P2
P1
Valve opens
Free-stream
flow is established
P8 trig in
1.1-1.2 ms
~ 1.1 ms
Pulse Generator
Trigger pulse
to the imaging system
Test time = 270 ms
P2 trig in
Pitot Pressure
Ultra-Fast Framing Camera
Hadland Imacon 468
Xenon Flashlamp
Light Source
Shock wave
arrival
Exposure time
typ. 100-200 ns
1 2 3 4 5 6 7 8
Interframing time
typ. 0.5-3 ms
20, 50 or 200 ms
FIGURE 3.3 Timing diagram of the high-speed rate imaging system and its synchronization with the expansion tube test flow time.
the injection location by analyzing the pitot pressure. An example of the pitot pressure
trace is given in the timing and synchronization diagram described in Fig. 3.3. Based on
the time history of this pitot pressure, it is possible to identify the arrival of the shock
wave, the time period of expansion section flow, the pressure rise as the contact surface
between the test gas and expansion section gas arrives, and finally the steady flow test
time. The images can be acquired during the last ∼100 µsec of the 270 µsec window of
the steady flow test time, after the free-stream flow around the jet is established.
As described in Fig. 3.3, the imaging system and the injection plate are synchronized
by the instantaneous pressure rise of one of the piezoelectric transducers located on the
tube walls as the incident shock travels through. The injection system is triggered
early enough to allow the injector valve to actuate and the underexpanded jet to be
49
fully developed by the time the steady test flow conditions are obtained. Within that
constraint, the time interval between the valve actuation and the test gas arrival should
be short enough to avoid significant changes in the expansion section initial pressure.
The delay times for the imaging system are then set to sample during the actual test
time when both the free-stream (expansion tube flow) and the flow around the jet are
established.
The high-speed camera, IMACON 468, and the long-duration light source receive
the delayed trigger pulse simultaneously. The gating/exposure times of the 8 intensifiers
and their interframing times are then controlled by the image acquisition computer. The
first ICCD is set to acquire after the build-up time of the light source as the uniform
light intensity is achieved.
3.1.4
Resolution Considerations
Each intensified CCD detector in the ultra-fast framing camera has an 8-bit dynamic
resolution (0 - 255 gray scale) 576 × 384 array with 22 × 22 µm pixel size. For the results
presented in Chapter 4, the field of view is about 28 × 18 mm (de-magnification of 0.44),
corresponding to a minimum spatial resolution of 50 × 50 µm.
Visualization without blurring from the flow velocity requires careful consideration
of the gating/exposure time. First the characteristic length scales and velocities of the
flow-field need to be known. In the experiments presented in Chapter 4, we study the
time evolution of jets issuing from a 2 mm sonic orifice into a high speed (2360 m/s)
free-stream. Of particular interest is the convection characteristics of the jet-shear layer
large eddies with dimensions ranging between 1-2 jet diameters (2 - 4 mm). We expect
these structures to travel at speeds between that of the jet at the injector exit and
the free-stream flow, namely between 1205 - 2360 m/s (∼1.2 - 2.4 mm/ns) in the case of
hydrogen injection. Therefore, to achieve 1 pixel spatial resolution (50 × 50 µm), the
exposure time must be in the range of 42 - 21 ns.
Exposure time of schlieren images are determined by optimizing the following competing factors: 1) schlieren sensitivity, 2) spatial resolution, 3) dynamic range, and 4) signal
to noise ratio. The sensitivity to detect the smallest density gradients in the flow, is controlled by the KE position when the light source intensity and the optical components
are fixed. As the KE cuts off more deflected rays, schlieren sensitivity increases while
50
less light reaches into the camera. For short exposure times, however, a high intensity
light source is required to cover the full dynamic range (256 gray levels). Therefore,
we performed an optimization between these counteracting effects to achieve the best
performance available from the system. We chose an exposure time of 100 ns to visualize
the flow-field of 28 × 18 mm, even though shorter gating times as low as 10 ns are available in our ultra-fast-framing camera. During 100 ns, the large scale structures translate
120 - 240 mm which is about 2 - 10 % of their thickness (2 - 4 mm). This corresponds to
blurring of images by 2 - 5 pixels. In addition, the ICCD modules were set to intensify
30 - 40 % of their maximum potential. We found that larger gain results in noise levels
that confuse the details of the flow features.
Figure 3.4 represents 3 examples of schlieren images captured with different exposure
times, 100 ns, 200 ns and 3 µs. Schlieren images with a 100 ns exposure time (Fig. 3.4a)
provide the instantaneous features of the flow-field with an optimized spatial resolution
(2 - 5 pixels). Increase of the exposure time to 200 ns (Fig. 3.4b) results in a significant
blurring of the features, as the flow structures translate larger distances (4 - 10 pixels).
Instantaneous flow features are eventually diminished with further increase of the integration time to the order of microseconds (Fig. 3.4c). While, the instantaneous features
of the flow are wiped out due to the integration during the long exposure time, these
images, on the other hand, provide information on the average features of the flow-field.
Note that the noise level in the long exposure image is very low as the intensifier is set
to its minimum value. Average features with laser-based diagnostic techniques can be
achieved only by capturing a large number of images as the integration time is fixed
with the laser pulse width or the fluorescence time. As noted in the introduction it is
very difficult to achieve multiple images in an impulse facility because of the short test
times. Observations obtained from the schlieren images of Fig. 3.4 will be discussed in
Chapter 4.
Temporal resolution, or the interframing time, was chosen so that we could capture
events occurring on very short time scales, less than or equal to the convection time of
the flow through the region of interest. For the jet diameter (2 mm) and free-stream velocities up to 4000 m/s, studied in our investigation, framing rates of 2 MHz to 200 KHz
(interframing times between 0.5 - 5 µsec) are needed to resolve and to follow the development of the flow structures (convection of large eddies, fluctuation of shock waves
around the jet.)
51
(a)
(b)
(c)
FIGURE 3.4 Examples of schlieren images with different integration/exposure times: a) 100 ns exposure
time, resolving the instantaneous features of the flow-field, b) 200 ns exposure time, resulting
in blurring of the image, c) 3 µs exposure time, averaging the general features while enhancing
the weak shocks such as upstream separation shock wave and downstream recompression wave.
52
(Dt )
Ucx =
x 2 - x1
y -y
; Ucy = 2 1
Dt
Dt
æy -y ö
F = arctançç 2 1 ÷÷
è x 2 - x1 ø
F
FIGURE 3.5 Timing diagram of the high-speed rate imaging system and its synchronization with the expansion tube test flow time.
3.1.5
Image Processing and Analysis
Post image processing of the images was performed using several image processing
software packages (IPLab, Matlab, Adobe Photoshop and Premiere). Background images were acquired just prior to each test and subtracted from the schlieren image to
eliminate speckle from the imperfections in the test section windows. Normalization of
the intensity levels and the “gamma-factor” were changed to improve the contrast of
the images. “Gamma-factor” is a factor applied to intensity distribution of images to
enhance the perception of the human eye which has a non-linear sensitivity.
To compute the convection characteristics of the large-scale eddies each individual
structure was tracked with the cross-correlation method using the fast Fourier transform
(FFT). In this tracking procedure, we measured the displacement of a particular feature
in the streamwise and transverse directions. Guidelines for a fully automated classical
cross-correlation method can be found in Smith and Dutton (1999). We utilized an
FFT in our cross-correlation method to decrease the image-processing time.
53
The cross-correlation is calculated (see Fig. 3.5) from the complex conjugate multiplication of their Fourier transforms:
Rf g (∆x, ∆y, ∆t) ⇔ F (∆x, ∆y, ∆t + ∆t) · G∗ (∆x, ∆y, ∆t)
(3.1)
The size of the interrogation window (128 × 128 pixels for the results presented in this
paper) is selected to be large enough to include the eddy and its later location while
maintaining the maximum resolution. Figure 3.5 describes the cross-correlation procedure and presents a representative cross-correlation field of the two images shown in
the same figure. The highest cross-correlation magnitude corresponds to the convection
distance of the large-scale structure. Therefore, the correlation peak was detected by
simply scanning the correlation plane Rf g for the maximum correlation value R(i, j)
and storing its integer coordinates (i, j) with uncertainty of a ±1/2 pixel. A subpixel
accurate displacement estimate could be achieved for example by applying three point
interpolation (Raffel et al. 1998). However, the largest uncertainty in our measurements
originates in the determination of the interrogation region. In summary, displacement
measurement accuracy in our technique is ±1 pixel which corresponds to a velocity
uncertainty of ±50 m/s (∼2 % of the free-stream velocity) when the interframing time
is 1 µs.
Once the displacement from image to image is known, the large-scale convection
velocity and the convection angle are determined using
Uc,x =
x2 − x1
,
∆t
Uc,y =
µ
y2 − y1
∆t
(3.2)
¶
x2 − x1
Φ = arctan
(3.3)
y2 − y1
where ∆t is the interframing time between images. An interframing time of ∆t = 1 µs
was chosen based on the residence time of the eddies in the field-of-view. It takes the
coherent structures about 8 µs to travel 6 jet diameters near the injector port. For
interframing times larger than 3 µs, it becomes difficult to track the structures as they
travel large distances.
3.2
OH-PLIF
PLIF imaging of reactive flows relied on OH, a naturally occurring combustion
radical, as the fluorescent tracer. OH is an indicator of ignition and reaction zones. For
54
the purpose of this thesis, OH visualization provides information on whether ignition is
occurring at all, and if so, in which regions it does occur.
3.2.1
Excitation and Detection Strategy
The OH-PLIF measurements are obtained by excitation of the A2
P+
← X2 Π(1, 0)
band of OH, near 283 nm combined with detection of the strong (1,1) band near 315 nm
(ranged from ∼308 - 325 nm). This excitation strategy, which can be performed using a
frequency-doubled dye laser, was chosen to avoid fluorescence trapping, the absorption
of the emitted OH fluorescence by other OH molecules (Seitzmann and Hanson 1993).
In addition, the limited pulse energies (∼1-30 mJ) available from the frequency-doubled
dye laser sources provide a linear fluorescence measurement regime.
The isolated Q1 (7) transition at 283.266 nm is selected to minimize signal dependence
on temperature (i.e., ground state population). For J”=7.5, the population term is only
weakly sensitive to temperature over a wide range of temperatures (i.e., 1500-3000 K).
The relative uncertainty in number density for a nearly constant pressure region is
approximately ±10% due to Boltzmann temperature variations (Parker et al. 1995).
3.2.2
OH-PLIF Laser Source and Tuning
The UV laser radiation for excitation of the OH molecule is provided by the frequencydoubled output of a dye laser pumped by a pulsed Nd:YAG laser (Lumonics models
YM-1200, HD-500, HT-1000). The 532 nm output of the Nd:YAG laser (400-450 mJ)
pumps the grating-tuned dye laser which provides approximately 60 - 70 mJ/pulse at a
wavelength of 566 nm using Rhodamine 590 dye. The dye laser beam formed as a 0.5 cm
wide sheet is frequency doubled using a KT*P crystal in a temperature controlled housing, which is angled-tuned with a stepper-motor system to provide maximum energy
(8 - 10 mJ/pulse at 283 nm).
At the exit of the frequency doubler, a Pellin-Broca prism is used to separate the
UV beam from the fundamental. The beam is raised and turned toward the test section
using four UV-enhanced turning mirrors and it expands to almost 35 mm near the test
section. The beam is then focused into a 300 - 400 µm thick × 35 mm wide sheet using
a f = 50 cm spherical lens. The top test section window, through which the laser sheet
reaches the injection plate, is made of fused-silica to provide a low UV-beam reflection.
55
The laser tuning is performed using a fluorescence measurement in an atmospheric
methane/air flame. The actual laser calibration (the dial offset) is determined by measuring the OH-fluorescence across multiple excitations in the wavelength range 280 285 nm and comparing the results to the estimated spectra using the programs LINES
and SPECTRA (Seitzmann 1991). The fluorescence is collected using a Hamamatsu
photomultiplier tube (PMT) fitted with Schott UG11 and WG-305 filters, and the resulting PMT signal is integrated using a boxcar averager. The laser wavelength dial
offset did not drift significantly from day to day and, therefore, it was not necessary to
perform this tuning procedure before each experiment.
The laser linewidth in the current experiments is broader than the absorption
linewidth by almost an order of magnitude. The absorption linewidth for OH is around
0.04 cm−1 for the temperature and the number densities present in the current work,
and the laser linewidth is approximately 0.3 cm−1 . The assumption of broad excitation
is then valid, minimizing the potential errors due to laser tuning and lineshape effects.
A real-time laser sheet correction is performed using a beam splitter/dye-cell/CCD
camera arrangement (McMillin, Seitzmann, and Hanson 1994). The laser sheet energy
distribution is measured by imaging the visible fluorescence of a dye-cell containing
a Rhodamine 6G dye/methanol mixture which is excited by the partial reflection of
the laser sheet. A Cohu 4810 CCD camera with an f/1.8 Nikon (50 mm) lens is used to
detect the visible fluorescence from the dye cell. Post-image processing, performed using
commercially available software, includes remapping of the 1-D laser intensity profile
into 2-D sheet and normalization of the OH-PLIF image by this 2-D intensity profile.
3.2.3
OH-PLIF Imaging System and Its Spatial Resolution
The fluorescence is collected onto the 578 × 384 pixel array of an ICCD (Princeton
Instruments) camera using a UV lens system (Nikon 50 mm, f/4.5). UG-5 and WG-305
Schott glass filters (2 mm thick) are used to block elastic laser scattering and background
emission which was minimal in the current experiments.
For the jet-in-crossflow and the cavity experiments performed in this thesis, the
imaged region was 20 × 30 mm. The minimum flow feature that can be resolved with
an ideal detection system is ∼51 µm corresponding to 51 × 51 µm per pixel (based on
384 × 578 array with 23 µm pixels, magnification=0.45). In a real system, however,
56
the minimum spatial resolution is actually limited to about 3 - 4 pixels (McMillin 1993)
because of the imperfections in the imaging system (focusing errors, limited spatial
resolution of the intensifier). Thus, the gating time of the camera intensifier is set to
collect photons for a maximum duration of 100 ns to prevent further resolution reduction
by flow motion. In conclusion, the resulting resolution of the PLIF imaging system is
∼200 - 250µm (4 - 5 pixels).
3.2.4
Interpretation of OH-PLIF
The relationship between the fluorescence signal and number density or mole fraction
has been described by Hanson et al. (1990). Briefly, the fluorescence is proportional to
the laser energy, the fluorescence yield, the species number density, and the Boltzmann
population fraction for the absorbing transition. Effective combustion visualization with
OH PLIF requires that the variation in OH mole fraction in the region of interest affect
the fluorescence signal more than changes in the other parameters described above. The
most critical issue, typically, is the temperature dependence of the Boltzmann fraction
of the absorbing state. At the combustion pressures in this work, the fluorescence signal
can be modeled as (Hanson et al. 1990):
·
Sf = χOH
f
√J”
T
¸
(3.4)
where χOH is the OH mole fraction, and fJ” is the Boltzmann fraction of OH molecules
in the absorbing state. For the absorption transition considered here - the Q1 (7) transition of the A2
P+
← X2 Π(1, 0) band of OH, located at 283.31 nm - such effects play
a relatively minor role in interpreting the signal in the regions observed to contain OH,
and the fluorescence intensity can be qualitatively linked to OH mole fraction.
3.3
Simultaneous Schlieren and OH-PLIF
Two intensified CCD cameras are used simultaneously to collect both schlieren and
OH-PLIF images. The fluorescence signal is collected through the same exit window as
that of the schlieren system. To separate both light signals, we mount a 5 cm diameter dichroic mirror at 45 o to the optical axis perpendicular to the exit window. The
dichroic, designed for larger than 99% reflectivity between 300 and 320 nm, reflects the
OH fluorescence but is transparent to the schlieren beam.
57
Figure 3.6 shows the triggering and timing diagrams of the simultaneous schlieren
and OH-PLIF imaging. A homemade firing box and two delay generators are used to
synchronize the laser/Xenon-lamp/cameras with the expansion tube operation. Because
of the long rise time of the Xenon flash lamp and also because of its emission in UV,
OH-PLIF was performed approximately 2 µs before schlieren to avoid background noise
in OH fluorescence. The firing box is designed to keep the laser operating (i.e, pulsing
at 10 Hz) until the initiation of the expansion tube operation to minimize shot-to-shot
pump laser energy fluctuations. The laser pulsing is stopped when a firing pulse is sent
to double diaphragms to initiate the test, and then, the laser is pulsed once more to
acquire the OH-PLIF image during the useful test time. Operating the pump laser in
this fashion prevented laser misfires.
58
(a)
Expansion Section
P1
Injection
Valve
Controller
P2
Driven Section
Pressure
Transducers
P3
Driver Section
P8 P9 P10
Gage-Scope
Data acq sys
P8 trig in
P10 trig in
Firing box
(home-made)
BNC pulse
generator
Set image
delay time
Set
delay time
P2 trig in
Schlieren
light source
Laser System
for PLIF
To YAG laser
flashlamps
PLIF camera
Sclieren camera
ICCD-1
ICCD-2
From Q-switch
(b)
Injection Valve
Valve opens
Flow established
P8 trig in
1.1-1.2 ms
~ 1.1 ms
Trigger pulse
to the imaging system
Pulse Generator
Test time = 270 ms
P2 trig in
Pitot Pressure at the test section
Shock wave
arrival
OH-PLIF Imaging
Laser pulse
typ. 10 ns
OH-PLIF camera
exp. time typ. 150 ns
~3ms
Xenon Flashlamp
Schlieren Imaging
~2ms
Schlieren camera
exp. time typ. 100-200 ns
FIGURE 3.6 a) Triggering diagram and timing connections of the imaging, the injection and the data acquisition systems. b) Timing diagram of simultaneous OH-PLIF and schlieren and their synchronization with the expansion tube test flow time.
Chapter 4
Time Evolution and Mixing
Characteristics of Hydrogen and
Ethylene Transverse Jets
In this part of the investigation, flow-field properties of hydrogen and ethylene jets
injected into a supersonic flow are reported. The free-stream flow replicates a representative supersonic combustor environment associated with a hypersonic airbreathing
engine flying at Mach 10. The structural evolution, the penetration and the convection
characteristics of both jets are analyzed.
4.1
Introduction
Early studies suggested that the jet-to-free-stream momentum flux ratio, J, is the
dominant parameter which controls the transverse jet penetration while the mechanism
for mixing is controlled mainly by the counter-rotating vortex pair. However, large scale
coherent structures are dominant in the jet shear layer and their structural evolution
might have a big influence on the jet near-field mixing process. In the studies of mixing
layers of two parallel streams (Brown and Roshko 1974) the mixing process was found to
be controlled by large scale vortical structures. It is therefore important to understand
how these structures and their growth rates evolve with time in the case of transverse
jets as the crossflow and jet conditions are changed.
59
CHAPTER 4. EVOLUTION OF HYDROGEN AND ETHYLENE JETS
60
TABLE 4.1 Jet exit flow properties.
4.2
Jet exit conditions
Hydrogen
Ethylene
Mjet
1
1
Ujet , m/s
1205
315
Tjet , K
246
263
pjet , MPa
0.49
0.55
J
1.4±0.1
1.4±0.1
Mw,jet , g/gmole
2
28
γjet
1.42
1.27
djet , mm
2
2
νjet
0.16×10−6
1.32×10−6
Redjet =Ujet djet /νjet
150,000
477,000
Results and Discussion
We have studied the flow-field properties of both hydrogen and ethylene transverse
jets using non-intrusive diagnostic techniques. Time-correlated schlieren images provides information on the structural evolution and convection characteristics of the jet,
and OH-PLIF maps the regions of ignition where the fuel and the crossflow (air or
oxygen) are mixed and burn at the molecular level.
The jet exit flow properties for both fuels are presented in Table 4.1. Note that
the exit velocities of hydrogen and ethylene sonic jets are quite different because of
the substantial difference in their molecular weights. Also included in Table 4.1 is the
jet-to-free-stream momentum flux ratio (J) that is chosen to be identical (J = 1.4) for
both cases and expected to result in similar penetration heights for each case, as was
suggested in previous studies. In this chapter, we will present results obtained from only
one value of J. It is worth noting that experiments with different values of J provide
similar results.
In the following sections, we will first present the global flow-field properties of a
transverse injection into a supersonic crossflow. Then the characteristics of the large
scale eddies, their convection and mixing properties, the jet penetration and finally the
OH-PLIF results will be discussed.
4.2.1
61
General Flow-Field Features
Schlieren imaging provides a visual observation of both instantaneous and average
characteristics of the flow-field depending on the exposure time of the image. While a
short duration schlieren image (100 - 200 ns exposure time) reveals some of the instantaneous vortex and shock structure of the flow-field, a long duration schlieren image (3 µs
exposure time) provides information on the average and more steady properties.
Two instantaneous schlieren images related to hydrogen and ethylene injection cases
are shown in Fig. 4.1. Free-stream fluid (nitrogen) flows from left to right, and the fuel jet
(hydrogen or ethylene) enters from the bottom at x/d = 0. Several interesting features,
such as the large-scale structures at the jet periphery and the bow shock are very
apparent in those images. The large-scale eddies are periodically generated in the early
stages of the jet/free-stream interaction. While those eddies exist in both cases, they
demonstrate significant differences in their development as they convect downstream.
In the hydrogen case, these structures preserve their coherence with distance while in
the ethylene case they disappear beyond about 12 jet diameters downstream. This
result is not a schlieren contrast issue, rather it might be related to the enhanced
mixing characteristics of the flow-field. As will be discussed in the following section
the schlieren contrast for ethylene injection is expected to be 3 to 4 times larger than
the hydrogen case in the absence of mixing (hot nitrogen vs. cold ethylene). Since
the molecular weight of ethylene is nearly similar to nitrogen, the schlieren contrast
will diminish when the hot free-stream fluid begins to mix with the cold ethylene jet
while creating a region of reduced density gradient. The ethylene structures are bigger
and penetrate deeper into the crossflow. Besides the bow shock, additional weak shock
waves are formed around the ethylene eddies indicating their subsonic motion relative
to the free-stream. A detailed examination of these large scale structures is performed
using high speed schlieren movies and will be discussed in the following sections.
Figure 4.1 also demonstrates that the bow-shock is almost merged with the jet close
to the injection location with a very small stand-off distance and curves sharply downstream. Its local shape appears to depend strongly on the large scale shear layer structures, especially close to the jet exit where the free-stream behind the steep bow shock
is subsonic. As a result the bow-shock reveals local fluctuations in position, small in the
hydrogen case but significant in the ethylene case. Figure 4.2 shows an example for the
62
(a)
(b)
FIGURE 4.1 Examples of hydrogen (a) and ethylene (b) injections into a supersonic crossflow (nitrogen).
Exposure time of each image was 200 ns. The x-axis is normalized by the jet diameter d.
hydrogen flow-field, visualized with a longer exposure time (3 µs). Additional features
are emphasized and become visually observable: such as the upstream separation shock
wave and the downstream reattachment shock. The small instantaneous fluctuations of
the bow shock are observed to average into a smoother and slightly thicker one.
The barrel shock and the Mach disk are, however, not very clear even in the long
exposure schlieren images, most probably due to the unsteadiness of the shear layer
63
FIGURE 4.2 An example of schlieren image with 3 µs exposure time for hydrogen injection case. While the
unsteady features (coherent structures) are averaged to zero, some of the weak shocks such as
upstream separation shock wave and downstream recompression wave are emphasized.
vortical structures. Only the Prandtl-Meyer expansion fan of the underexpanded jet is
observable (the white region at the jet core) indicating that the jet is indeed underexpanded. We have therefore attempted to estimate the displacement of the first Mach
disk for our experiments by substituting an “effective back pressure” term in the Ashkenas and Sherman correlation given in Eq. 2.5. The effective back pressure introduced
in earlier works is a notion which permits an analogy between the very complicated
flow-field of an underexpanded jet emerging into a supersonic crossflow and that for the
simpler and well-understood case of a jet exhausting into a quiescent medium. Among
0 , where P 0 is
those previous studies, Schetz and Billig (1966) suggested Peb = 0.8P∞
∞
the free-stream pressure behind a normal shock wave. Later on, Billig et al. (1971)
developed a correlation to predict the height of the Mach disk, y1 , assuming that the
effective back pressure is equal to two thirds of the free-stream stagnation pressure
0
behind a normal shock: Peb = 2/3Ptot,∞
. More recently Everett et al. (1998) mea-
sured the pressure distribution around a sonic jet injected transversely into a Mach 1.6
free-stream using a pressure-sensitive-paint technique. Their averaged surface pressure
resulted in Peb ∼
= 0.35P 0 (for J<1.5) which differs greatly from the earlier works. This
∞
discrepancy was attributed to the larger jet-to-momentum flux ratios (J) used in the
64
0 ),
earlier works. We have adopted the back pressure values of Everett (Peb ∼
= 0.35P∞
as the value of J in our experiments is small. Using Eq. 2.5, the Mach disk height for
the current experiments was estimated to be around y1 ≈ 1.7 · djet which compares well
with the jet bending location (see discussion below).
The free-stream conditions behind the hydrogen bow shock could be estimated by
measuring the average bow shock position. Figure 4.3 presents two plots; the first shows
the measured bow shock position and its angle (β), while the second plot exhibits the
bow shock-induced free-stream velocity (U2 ) and its turning angle (θ). Calculations are
performed assuming a calorically perfect gas. In the region of 10 jet diameters studied in
this work, the bow shock starts almost at 90o and weakens downstream as it angle decays
continuously down to 20o -25o . Further downstream, the bow shock is expected to reach
its minimum strength or a Mach wave with an angle of 17.2o (M∞ =3.38). The induced
velocity of the free-stream behind the bow shock is subsonic upstream to the location of
the critical bow shock angle (βcr ∼ 67.6o ), defined as the minimum angle for an oblique
shock to be attached to the wedge. It is interesting to see that the bow shock reaches this
angle around 1.8-1.9 jet diameters above the wall at the expected height of the upper
side of the Mach disk. Since the Mach disk occurs at a rather high Mach number on the
jet centerline, the jet loses most of its momentum and the subsequent trajectory of the
jet turns nearly parallel to the free-stream direction. Consequently, beyond the critical
angle, the bow shock curves sharply downstream and the shock-induced free-stream
velocity becomes supersonic varying between approximately 1050 m/s to 2260 m/s at
9.5 jet diameters downstream (note that the free-stream velocity is U∞ = 2360 m/s).
In the following sections, this estimated free-stream velocity behind the bow shock will
be compared to the measured convection velocity of the large-scale structures. Before
that we will first discuss the temporal evolution of these structures.
4.2.2
Large Scale Coherent Structures
The most interesting observations are related to the coherent structures easily identified in instantaneous schlieren images. The large scale jet-shear layer vortices are considered important because of their role in the near-field mixing. These intermittently
formed eddies tend to enlarge and engulf free-stream fluid as they travel downstream
with the flow. We therefore studied the temporal evolution of large eddies and their
65
(a)
9
90
8
7
80
y/d
70
6
60
y/d
5
50
4
3
40
b
2
30
1
Bow Shock Angle, b (deg)
critical bow
shock angle:
bcr~67.6°
20
0
-1
0
1
2
3
4
5
6
7
8
9
10
x/d
(b)
50
2400
qmax=38.8°
U2
40
2000
1800
30
1600
1400
q
1200
1000
subsonic
20
supersonic
10
800
Bow Shock Angle, b (deg)
Free-stream Velocity, U2 (m/s)
2200
600
0
-1
0
1
2
3
4
5
6
7
8
9
10
x/d
FIGURE 4.3 (a) Bow shock position and its angle at the center-line of the jet as measured from the long
exposure schlieren image shown in Fig. 4.2. (b) The free-stream velocity behind the bow shock
and the flow turning angle based on the measured bow shock shape. For the calculations a
calorically perfect gas has been assumed.
66
properties for both hydrogen and ethylene jets utilizing the high-speed-framing rate
camera. Examples of instantaneous schlieren images are presented in Figs. 4.4 and 4.5
for hydrogen injection and in Figs. 4.6 and 4.7 for the ethylene case. While largescale eddies are visible in the early stages of the jet/free-stream interaction, there are
significant differences in their development for hydrogen and ethylene injection.
Hydrogen large scale coherent structures survive long distances. Coherence of these
shear layer eddies can be seen in Figs. 4.4 and 4.5, which constitute consecutive schlieren
images from two different experiments. Close to the jet exit, the spanwise rollers rise
periodically creating gaps in between the eddies. The evolution of these eddies occurs
primarily through engulfment of the cross-flow fluid into the jet but also through merging/pairing of smaller eddies in the beginning of the shear layer (see eddy number 3
in Fig. 4.4). Beyond 3-4 jet diameters downstream, the separation between the eddies
becomes constant and no further merging is visible. The energetic structures elongate
in the transverse direction while the crossflow fluid fills the braid regions in between the
eddies.
Interesting features in the evolution of ethylene large-scale structures are demonstrated in Figs. 4.6 and 4.7 through two examples of 8 consecutive schlieren images.
Larger structures appear in the near-field of the ethylene jet and persist until the jet
bends with the crossflow. In the bending region, the large scale structures begin to tilt
in the streamwise direction. Simultaneously, the shear between the accelerating crossflow and the jet increases, leading to the stretching of the large-scale structures. In the
case of ethylene injection the jet exit velocity (315 m/s) is four times smaller than in the
hydrogen case (1205 m/s). Therefore, for ethylene injection the eddies are exposed to
very large velocity gradients across the shear layer. As a result, these large-scale eddies
lose their coherence as they turn in the streamwise direction and break up into smaller
eddies through a “tilting-stretching-tearing” mechanism. Further downstream, beyond
6-8 jet diameters, the jet shear layer is not visually observable by schlieren imaging
anymore, as the vortical structures tear down into smaller scale turbulence.
The flow visualization of large scale structures using schlieren is based on the principle of refraction of light. The contrast in schlieren imaging, defined as the relative
change in the illumination, is expressed in terms of the optical index of refraction (n)
67
and parameters related to schlieren system (Saad 1985):
∆I
f L dn
=
I
ny1 dy
(4.1)
where f is the focal length of the focusing lens, L is the width of the test section and
y1 is the size of the image of the light source (where the knife edge is positioned to
cut the deflected beam). For a given schlieren system, the parameters f , L and y1 are
constant. The contrast is, therefore, directly proportional to the gradient of the index
of refraction in the flow:
∆I
dn
∝
I
dy
(4.2)
The index of refraction of a gas is expressed as a function of density (ρ) and a constant
characteristic of the gas (β), :
n=1+β
ρ
ρs
(4.3)
where ρs is the density at standard conditions (273 K and atmospheric pressure). The
density ratio for a specific gas is equal to:
ρ
P Ts
=
ρs
Ps T
(4.4)
Substituting from Eqs. 4.4 and 4.3 gives:
∆I
d
ρ
d P Ts
∝
(β ) ∝
(β
)
I
dy ρs
dy Ps T
(4.5)
Consequently, the flow visualization of large scale structures based on schlieren is
a result of the differences in the pressure, the temperature and the characteristic β
constant of the free-stream fluid and the jet fluid. As the jet turns in the streamwise
direction the static pressure between the hot free-stream (∼ 1300 K) and the cold jet
(∼ 300 K) approaches to equilibrium. The schlieren contrast between unmixed jet and
free-stream fluids can therefore be expressed in terms of:
Ts
Ts
∆I
∝ (β )∞ − (β )jet
I
T
T
(4.6)
By substituting the values of β and T in Eq. 4.6 we found that the schlieren contrast
between the ethylene jet and the free-stream nitrogen (or air) should be 3 to 4 times
larger than the hydrogen jet case. The loss of the visibility of the ethylene jet shear layer
structures can, therefore, be attributed to the loss of the coherence of the vortical structures and also to enhanced molecular-mixing. When the ethylene large structures burst
68
into smaller scale turbulent structures due to stretching, molecular mixing between the
crossflow and the ethylene jet might be enhanced. As a result, the observable schlieren
contrast degrades as the difference between β/T across the shear layer decreases.
Although the large scale eddies seem to be two-dimensional, recall that they are
part of the unsteady Kelvin-Helmholtz spanwise rollers wrapping around the jet. They
are only the traces of three-dimensional transverse vortex tubes whose cores coiled up
around the jet with their legs connected downstream of the jet exit. The schematic in
Fig. 4.8 shows a diagram of the three-dimensional unsteady structures as adapted from
Brizzi et al. (1995). Similar flow-field features were also observed by Fureby and BenYakar (2000), where a similar geometry and conditions are being studied by large eddy
simulation. In the simulation results for the hydrogen injection case, large Ω-shaped
vortices develop that grow as they convect downstream. We suggest that the vortex
tubes on the sides of the Ω-vortices are stretched by increased shear stresses in the
regions of steep velocity gradient.
Time evolution of the tearing mechanism of ethylene eddies can be easily followed
in the sequence of schlieren images. For example, the temporal development of eddy
number “0” in Fig. 4.6 is captured during the 10.6 µs of visualization time. This eddy,
generated by merging of two individual smaller eddies, is an energetic structure which
penetrates deep into the free-stream. The initially almost round eddy stretches in the
transverse direction due to the increasing velocity gradients across the layer while it is
tilting in the clockwise direction. In the 8th image the eddy numbered “0” has almost
entirely dispersed into smaller eddies as the side arms of the vortex tube cannot continue
to sustain the large shear stresses. Eddy number “-1” in Fig. 4.7 is another example
for the “tilting-stretching-tearing” mechanism. We have plotted the evolution of this
eddy in a y-x diagram shown in Fig. 4.9, by tracking different parts of its structure
across the shear layer. While the bottom part of the eddy travels at the slower jet
velocity, the upper part of it is exposed to higher crossflow velocities. The shear stress
steepens further downstream as the crossflow behind the weaker bow shock accelerates.
Consequently, the eddies begin to stretch in the transverse direction while continuously
tilting towards the fast crossflow stream.
1) t = 0.1 µs
2) t = 1.1 µs
3) t = 2.1 µs
4) t = 3.1 µs
5) t = 4.1 µs
6) t = 5.1 µs
7) t = 6.1 µs
8) t = 7.1 µs
FIGURE 4.4 An example of 8 consecutive schlieren images of underexpanded hydrogen injection (d=2 mm)
into a supersonic crossflow (nitrogen) obtained by high-speed-framing camera. Exposure time of
each image is 100 ns and interframing time is 1 µs. Free-stream conditions are: U∞ =2360 m/s,
M∞ =3.38, T∞ =1290 K, p∞ =32.4 kPa; and jet-to-free-stream momentum ratio is: J=1.4±0.1.
69
a) (Image 1) t = 0.1 µs
b) (Image 3) t = 2.1 µs
c) (Image 5) t = 2.1 µs
d) (Image 7) t = 3.1 µs
FIGURE 4.5 The second example of 4 of 8 consecutive schlieren images of hydrogen injection into flight
Mach 10 condition. Exposure time of each image is 100 ns and interframing time is 1 µs.
70
1) t = 0.1 µs
5) t = 4.1 µs
2) t = 1.1 µs
6) t = 5.1 µs
3) t = 2.1 µs
7) t = 6.1 µs
4) t = 3.1 µs
8) t = 7.1 µs
FIGURE 4.6 Time evolution of an ethylene jet in a supersonic crossflow (nitrogen) as observed from 8
consecutive schlieren images. Exposure time of each image is 100 ns and interframing time is
1.5 µs. Free-stream conditions are: U∞ =2360 m/s, M∞ =3.38, T∞ =1290 K, p∞ =32.4 kPa;
and jet-to-free-stream momentum ratio is: J=1.4±0.1.
71
1) t = 0.2 µs
5) t = 5.0 µs
2) t = 1.4 µs
6) t = 6.2 µs
3) t = 2.6 µs
7) t = 7.4 µs
4) t = 3.8 µs
8) t = 8.6 µs
FIGURE 4.7 The second example of an ethylene transverse jet flow-field in a supersonic crossflow as observed
from 8 time correlated schlieren images. Exposure time of each image is 200 ns and interframing
time is 1.2 µs.
72
73
FIGURE 4.8 Schematic of the three-dimensional shape (Ω shape) of the unsteady vortical structures formed
intermittently (Brizzi et al. 1995).
Space-time trajectories of large structures:
Following the sequential high-speed-framing rate schlieren images, space-time trajectories (x-t diagram) of the identifiable coherent structures have been traced. Figure 4.10
presents two x-t diagrams of hydrogen eddies as analyzed from the schlieren images of
Figs. 4.4 and 4.5. The spacing between the core of the eddies varies with distance,
eventually reaching an average value of almost 3 jet diameters. Occasionally, big gaps
of the order of 4 to 5 jet diameters in dimension (see Fig. 4.10b) are created as the
smaller eddies are amalgamated into the larger ones.
Two x-t diagrams showing the trajectories of the identifiable ethylene eddies are
plotted in Fig. 4.11. None of the coherent large scale eddies could be traced beyond
6-8 jet diameters downstream. The spacing between the initial eddies is larger than the
ones in the hydrogen case because of the large amounts of the crossflow intrusion in
between the eddies, and also because of the larger size of the eddies formed near the jet
exit. Information on the eddy formation frequency can also be obtained from the x-t
74
stretching
tilting
7
6
frame
number:
y/d
5
4
3
1
6
5
7
2
8
4
3
2
1
-1
0
1
2
3
4
5
6
7
8
9
10
x/d
FIGURE 4.9 Development of a large-scale ethylene structure (eddy number “-1” in Fig. 4.7) as it goes
through the tilting and stretching processes. Four different parts of the eddy structure were
independently tracked in the duration of the 8.6 µs flow visualization time.
diagrams. Only 2 eddies are formed during the 10.6 µs time evolution of the ethylene
jet, while in the hydrogen case 4 eddies are formed in even a shorter time period of
7.1 µs. Experiments with different sonic jets (see Chapter 5) revealed that the eddy
formation frequency scales linearly with the jet exit velocity.
4.2.3
Convection Characteristics
Once the centers of the large scale eddy structures are identified (as shown in the
x-t diagrams), their convection velocity and the angle of inclination may be computed.
For that purpose, each individual structure was tracked from image to image using
cross-correlation techniques, as explained in Chapter 3.
The resulting large-scale convection characteristics are summarized in Figs. 4.12
and 4.13, for hydrogen and ethylene cases respectively. Data for each case were collected
from 16 images (two experiments per case). Included also in the figures are the reference
lines for the jet exit velocity and for the free-stream velocity. The uncertainty in the
determination of the eddy displacement is ±1 pixel (±45 m/s) in the hydrogen case
75
(a)
Uc,x=Dx/Dt
9
8
Frame Number
7
6
Dt
6
Dx
eddy 4
5
5
4
3
7
4
3
eddy 3
2
2
eddy 2
1
1
eddy 1
0
Time, msec
8
0
-1
0
1
2
3
4
5
6
7
8
9
10
x/d
(b)
9
8
8
7
6
5
4
6
eddy 4
5
eddy 3
4
eddy 2
3
3
2
2
1
Time, msec
Frame Number
7
1
eddy 1
0
0
-1
0
1
2
3
4
5
6
7
8
9
10
x/d
FIGURE 4.10 Space-time trajectories of large-scale eddies present in the hydrogen jet shear layer. The center
of the eddies are tracked from the 8 successive schlieren images shown (a) in Fig. 4.4 and (b) in
Fig. 4.5.
76
(a)
9
12
8
Dt Uc,x=Dx/Dt
10
Dx
6
8
5
6
4
3
4
eddy 2
2
2
1
Time, msec
Frame Number
7
eddy 1
0
eddy 0
0
-1
0
1
2
3
4
5
6
7
8
9
10
x/d
(b)
9
8
middle part
bottom part
6
6
upper part
5
4
4
3
8
eddy 2
2
Time, msec
Frame Number
7
2
1
eddy 1
eddy 0
0
-1
0
1
0
eddy -1
2
3
4
5
6
7
8
9
10
x/d
FIGURE 4.11 Space-time trajectories of ethylene large scale eddies as tracked from 8 time-correlated
schlieren images: (a) x-t diagram of the example shown in Fig. 4.6, (b) x-t diagram of the
example shown in Fig. 4.7.
77
(a)
Convective Velocity, m/s
2500
U¥=2360 m/s
2000
Uc,x
Uc,y
1500
Ujet=1205 m/s
1000
500
0
-1
0
1
2
3
4
5
6
7
8
9
10
5
6
7
8
9
10
x/d
Convection Angle, F (deg)
(b)
70
60
50
40
30
20
10
0
-10
-1
0
1
2
3
4
x/d
FIGURE 4.12 Convection features of coherent large scale structures present in the hydrogen jet/free-stream
shear layer. The data were subtracted by analyzing the eddy displacement in 8 consecutive
schlieren images of 2 experiments (images shown in Figs. 4.4 and 4.5). (a) the convection
velocity of eddies in streamwise and transverse directions, Uc,x and Uc,y , respectively; (b) the
convection angle of eddies.
Uc,x
Uc,y
(a)
2500
Convection Velocity, m/s
78
U¥=2360 m/s
2000
1500
1000
500
0
Ujet=315 m/s
-1
0
1
2
3
4
5
6
7
8
9
10
5
6
7
8
9
10
x/d
Convection Angle, F (degrees)
(b)
90
80
70
60
50
40
30
20
10
0
-10
-20
-1
0
1
2
3
4
x/d
FIGURE 4.13 Convection features of eddies present in the ethylene jet/free-stream shear layer. The data
were subtracted by analyzing the eddy displacement in 8 consecutive schlieren images of 2
experiments (images shown in Figs. 4.6 and 4.7). (a) the convection velocity of eddies in
streamwise and transverse directions, Uc,x and Uc,y , respectively; (b) the convection angle of
eddies.
79
(a) hydrogen injection
Convection Velocity, Uc (m/s)
2500
U¥=2360 m/s
2000
1500
1000
measured, Uc
measured free-stream velocity
behind the average bow shock, U2
500
0
-1
0
1
2
3
4
5
6
7
8
9
10
x/d
(b) ethylene injection
U¥=2360 m/s
Convection Velocity, Uc (m/s)
2500
U2
2000
1500
1000
500
Ujet=315 m/s
0
-1
0
1
2
3
4
5
6
7
8
9
10
x/d
FIGURE 4.14 Measured convection velocity of large eddy structures in the hydrogen and ethylene jet shear
layers. The results are compared with the estimated values of the free-stream velocity immediately behind the bow shock.
80
and ±2 pixels (±62-71 m/s) in the ethylene case. It is important to note that some of
the eddy positions were tracked manually, especially near the injector exit where the
cross-correlation method was not able to identify the initial small eddies at the vicinity
of the bow shock.
According to the results of Fig. 4.12, the hydrogen eddies initially travel fast in
the transverse direction with velocities close to the jet exit velocity. As the jet bends
downstream, the eddies start to accelerate monotonically in the streamwise direction
and achieve almost 90% of the free-stream velocity 9 jet diameters downstream. At this
location, the jet moves at shallower angles to the crossflow direction (around 0o -10o )
with reduced transverse convection velocities (between 0-400 m/s). This reveals that
beyond 9 jet diameters the jet shear layer eddies are convected almost parallel to the
free-stream while the transverse penetration of the jet is just slightly increasing.
Convection properties of the ethylene eddies (Fig. 4.13) are somewhat different from
those in the hydrogen case. A large scattering of the velocity both in the transverse
and streamwise directions is visible. The convection characteristics were measured not
only by following the coherent large structures but also by tracking parts of the eddies
that had began to lose their coherence. We observe that the upper part of the eddies
tend to travel at higher velocities in both streamwise and transverse directions than the
lower part of the eddies (see also Fig. 4.9). The transverse velocity (y-component) of
some eddies is higher than the jet exit velocity. As the eddies stretch due to the large
velocity gradient across the jet shear layer, the transverse velocities, specially at the
upper part of the eddy, becomes as high as 700 m/s. The convection velocity in the
streamwise direction is, on the other hand, much lower than the free-stream velocity. A
result that can be attributed to the stronger (steeper) bow shock present for ethylene
injection as the eddies rise up higher into the crossflow. The convection angle of the
ethylene eddies, shown in Fig. 4.13b, are larger than the hydrogen ones, again a result
of the higher penetration of the energetic ethylene eddies in the transverse direction as
will be discussed in the following section.
The free-stream velocity behind the bow shock, U2 , is computed based on the average
bow shock position measurements as explained in section 4.2.1. The results for the
hydrogen injection are plotted in Fig. 4.14a together with the measured total convective
velocities. We observe that the convection velocities of the low density hydrogen eddies
are mainly influenced by the free-stream, as most of the eddies follow the shock-induced
81
bow shock
low U2
nitrogen
large-scale
eddies
high U2
DU2
free-stream
entrainment
low U2
ethylene
FIGURE 4.15 Schematic showing the low- and high-speed regions of the bow shock-induced free-stream
velocity around the large-scale ethylene eddies.
free-stream velocity. For the ethylene case, it is not possible to compute an average
shock-induced free-stream velocity because of the bow shock fluctuations. Instead, we
have measured two instantaneous bow shock positions and plotted the corresponding
shock-induced free-stream velocities in Fig. 4.14b together with the total convective
velocity across the ethylene shear layer. We observe large fluctuations in the values
of U2 varying in a wide range, between 1400 m/s to 2300 m/s around a single eddy.
Figure 4.15 illustrates the low- and high-speed regions of U2 . Large velocity variation
in the values of U2 around the ethylene eddies, as opposed to monotonic increase in
the hydrogen case, might be contributing to the tilting and stretching of eddies while
contributing to the mixing process. Also, the reduced convective velocity of ethylene
eddies provides longer flow residence time, crucial for the completion of the mixing
process in shorter distances.
4.2.4
Penetration and Shear Layer Properties
The upper boundary of the jet is defined by the maximum penetration of its shear
layer vortices while the penetration bandwidth can be related to the visible thickness
82
of the jet shear layer. By measuring the visually observable upper edge of the jet
in schlieren images, jet maximum penetration and bandwidth data became available.
Brown and Roshko (1974), in their mixing layer studies, have shown that the “visible”shear layer width, as would be measured in a schlieren image, corresponds to about
1% concentration of molecularly mixed fluid. The results are presented in Fig. 4.16 to
quantify the penetration properties and to compare it to previous studies.
We observe significant differences in the penetration data and its width between
hydrogen and ethylene injection. While the hydrogen jet penetrates 5.5 jet diameters
into the free-stream at about 10 jet diameters downstream of the injection port, the
ethylene jet penetrates as much as 8 jet diameters at the same location. This result is
not surprising after studying the jet large-scale structure development in the previous
sections. It is very surprising, however, when it is compared to previous studies (Schetz
and Billig 1966; Rogers 1971; Papamoschou and Hubbard 1993; Gruber et al. 1995).
These earlier studies showed that the jet transverse penetration into the crossflow is
mainly controlled by the jet-to-free-stream momentum flux ratio (J). Therefore, both
jets studied here should have comparable transverse penetration into the crossflow as
the two cases have essentially the same momentum flux ratio. However, it is very clear
from the results that the transverse penetration height of ethylene jet is higher than the
hydrogen jet case.
A power law fit to the penetration data has been proposed by various authors (McDaniel and Graves 1988; Rothstein and Wantuck 1992; Gruber et al. 1995) who found
that the upstream boundary layer properties, that is laminar/turbulent and the boundary layer thickness play an important role in the penetration of the jet. The most
comprehensive and recent study was performed by Gruber et al. (1995), who suggest a
power law fit of the form of:
µ
x
y
=c
dJ
dJ
¶1/3
(4.7)
where the constant c has the value of 1.23 for circular injection. Their measurement
technique relies on Mie scattering from ice particles in the free-stream, and defines the jet
penetration as the trajectory where the jet concentration is about 10%. The thickness
of the approaching boundary layer (δ/d=1) and the range of the jet-to-momentum ratio
(J = 1 − 3) of their experiments were similar to the ones in our experiments, so that
a comparison can be made. Therefore, the above correlation is plotted for J = 1.4
83
(a) hydrogen injection
6
Rothstein & Wantuck
McDaniel & Graves
Gruber et al.
present work
5
y/d
4
d @ 3d
3
2
1
0
-1
0
1
2
3
4
5
6
7
8
9
10
x/d
(b) ethylene injection
8
Rothstein & Wantuck
McDaniel & Graves
Gruber et al.
present work
7
6
y/d
5
d @ 6d
4
3
2
1
0
-1
0
1
2
3
4
5
6
7
8
9
10
x/d
FIGURE 4.16 Transverse penetration data of (a) hydrogen jet and (b) ethylene jet. The data points were
obtained by manually tracking the visually observable outer edge of the jet from 8 consecutive
schlieren images for J = 1.4± 0.1. Both of the figures include analysis of 2 experiments namely
16 images. For comparison, also shown in the figures is the penetration correlation given by
other studies.
84
in Fig. 4.16 together with our results measured for J = 1.4 ± 0.1. Two additional
empirical correlations suggested by McDaniel and Graves (1988) and Rothstein and
Wantuck (1992) are also included in Fig. 4.16 for further comparison.
The penetration band in our experiments lies on top of the expected 10% penetration trajectory based on Gruber’s correlation. The measurement of the “visible” jet’s
penetration as measured in schlieren images corresponds to 1% of the jet concentration,
while Gruber’s results correspond to 10%. Therefore, it is reasonable that the penetration measurements based on schlieren are somewhat lower than the ones based on
10% concentration measurements. A better agreement is achieved with the correlation
of Rothstein and Wantuck (1992) who used OH fluorescence to visualize the jet penetration. Their experimental conditions (hydrogen jet injected into a high temperature
air crossflow) are similar to our hydrogen injection case.
In summary, the penetration data for the hydrogen case agrees relatively well with
the previous studies. The differences in the observed penetration between hydrogen and
ethylene data are most probably due to the tearing mechanism explained above. The
thickness of the ethylene shear layer (the penetration width) grows to 6 jet diameters,
twice as much as the hydrogen case at the end of the field of view. The practical
impact of this result is significant as it indicates a mechanism for enhanced fuel (jet)
distribution. It might eventually be possible to enhance and control the fuel penetration
based on the flow properties.
It seems that there is an additional mechanism which controls the jet penetration
besides the jet-to-free-stream momentum flux ratio. This mechanism is expected to be
associated with the jet shear layer properties which control its growth rate and therefore
the near-field mixing of the transverse jet. Jet-to-free-stream density and velocity ratios
are the two main parameters which might influence the large scale vortical structure
development of the jet. In the next chapter (Chapter 5), we discuss the effects of these
two parameters on the penetration and the development of the jet.
4.2.5
OH-PLIF Results
To gain further insight into the coherence and the mixing properties of the injection
flow-field we have examined the ignition characteristics of hydrogen and ethylene jets
85
using Planar Laser Induced Fluorescence of OH radicals. The presence of OH, a naturally occurring combustion product, indicates that the fuel and the oxidizer are mixed
at the molecular level and the conditions for ignition to occur are met. As the total
enthalpy of the free-stream in our experiments is high (∼4 MJ/kg), namely the total
temperature is about 4000 K, autoignition of a transverse fuel jet is achieved.
Figure 4.17 contains three instantaneous side-view images of OH-PLIF captured at
the center-line of hydrogen and ethylene transverse jets injected into a reacting crossflow.
OH-PLIF is a two-dimensional visualization technique which maps the auto-ignition
locations illuminated by a roughly 0.4 mm thick laser sheet. The first image (Fig. 4.17a),
related to a hydrogen jet injected into air, demonstrates a continuous and a very thin
filament along the jet shear layer periphery. The side-view 2-D visualization clearly
shows the presence of the large scale shear layer vortices. Since a relatively cold hydrogen
jet is injected into hot air, there will be a significant variation of temperature with
equivalence ratio through the mixing layer around the jet. The ignition time is a strong
function of the mixture temperature, which will be higher at low equivalence ratios (fuel
lean). The self-ignition point is therefore on the lean side of the mixing layer around
the jet. Namely, ignition is likely to occur as soon as a fuel particle meets with the high
temperature oxidizer. Since OH appears only quite near the hydrogen jet we suspect
that the mixing is only occurring in the finite-thickness interfacial diffusion region that
separates the unmixed fluids.
Figures 4.17b and 4.17c are related to an ethylene jet injected into air and pure
oxygen crossflows, respectively. Due to longer ignition delay times associated with
ethylene, self-ignition could only be achieved when a higher concentration of oxygen was
used in the crossflow. In contrast to hydrogen, OH radicals in the ethylene case could
be detected in a wide region distributed across the jet. This is most likely a result of the
enhanced molecular-mixing related to “stretching-tilting-tearing” mechanism discussed
above. An additional interesting observation is related to the intense OH signals taking
place in the vicinity of the Mach disk. This is the region where ethylene is self-igniting
even when it is injected into air (see Fig. 4.17b). At this location, the ethylene jet
becomes subsonic behind the Mach disk and begins to lose its transverse momentum
letting the high temperature crossflow intrude deep inside the jet. Santiago and Dutton
(1997), have also shown that the regions of high turbulent kinetic energy (TKE) exist
in the jet shear layer near the Mach disk leading to better mixing properties.
86
(a)
x/d
(b)
x/d
(c)
x/d
FIGURE 4.17 OH-PLIF results mapping the ignition regions at the jet center-line of: a) hydrogen injection
into air, b) ethylene injection into air, c) ethylene injection into pure oxygen.
87
In conclusion, OH-PLIF results demonstrated that significant differences exist in
the near-field ignition properties for ethylene and hydrogen injection. These results
support the tearing mechanism suggested to enhance the near-field mixing properties
of the ethylene jet.
4.3
Summary
In this part of the thesis, we have summarized results that are related to hydrogen
and ethylene fuel jets because of their relevance to supersonic combustion. Significant
differences related to the development of large-scale coherent structures were found to
be present in the jet shear layer. The results demonstrate features not observed in
previous studies where the free-stream conditions were limited to low velocities and low
temperatures. In the current effort, the use of an impulse facility made it feasible to
achieve high temperature and high velocity conditions relevant to a realistic supersonic
combustor environment. The application of supersonic flow visualization at ultra-fastframing rates enabled a detailed study of the temporal evolution of the fuel jets.
Further investigations of the experimental results are presented in the next chapter,
which examines the dominant influences of different parameters on the stability and
structural characteristics of the shear-layer formed in the jet periphery.
Chapter 5
The Effect of Velocity and
Density Ratio on Transverse Jets
In the previous chapter, we studied the temporal evolution of the shear layer structures of ethylene and hydrogen jets because of their relevance to supersonic combustion. The large difference in the molecular weights of these two gases revealed two
important observations: 1) a “tilting-stretching-tearing”mechanism which caused the
ethylene large-scale structures to lose their coherence and to burst into smaller eddies
and 2) higher transverse penetration of the ethylene jet for a similar momentum flux
ratio, J, as the hydrogen jet due to highly energetic ethylene eddies which penetrate
deep into the free-stream.
In the current chapter, we report our study of the fundamental origin of these phenomena. The parameters expected to be influential in the stability, and the structural
characteristics, of the jet shear layer are the jet-to-crossflow density and velocity ratios.
These two parameters are, however, coupled through the molecular weight of the jet.
An increase in the jet’s molecular weight reduces the exit velocity and increases the
density. Therefore, to understand the role of each parameter on the instability of the
large-scale eddies, we must decouple the two parameters and study them independently.
The first part of this chapter discusses the effect of systematically changing the
jet molecular weight. The second part presents the independent influence of the jetto-crossflow density and velocity ratios on the flow features. To decouple these two
parameters, a variety of free-stream conditions are used. Also we discuss possible flow
88
CHAPTER 5. VELOCITY AND DENSITY RATIO EFFECTS
89
instabilities, such as centrifugal instabilities associated with curved shear layers which
could potentially cause the spanwise rollers to lose their coherence.
5.1
Effect of Jet Molecular Weight
Gaseous jets with five different molecular weights (Mw,jet =2, 4, 8, 16 and 28 g/mole)
are studied. Tables 5.1 and 5.2 summarize the composition and the properties of these
jets. The experiments are designed for similar jet-to-crossflow momentum flux ratio in
the range J = 1.67 − 1.85. Note the high Reynolds numbers associated with the jet
exit properties. Also included in Table 5.2 are the jet-to-free-stream velocity ratio (r),
the density ratio (s) and a convective Mach number parameter (McA , see section 5.1.5)
defined to estimate the compressibility level of the jet shear layer for the cases studied
here.
r=
s=
5.1.1
Ujet
U∞
(Mw /T )jet
ρjet
=
ρ∞
(Mw /T )∞
(5.1)
(5.2)
Examples of instantaneous schlieren images obtained using the ultra-fast framing
camera are presented in Fig. 5.1 for visual observations of the flow-field. A systematic
increase in the jet molecular weight gradually changes the structural characteristics of
the jet shear layer. Large-scale structures, which dominate the jet shear layer in all cases,
become larger with the increase of the molecular weight. The heavier jets penetrate
deeper into the free-stream. Consequently, the shape of the bow shock changes as it
wraps around the large eddies. This process starts to be visible for Mw =16 and becomes
very pronounced for Mw =28.
The coherent structures occur less frequently with increasing Mw , which results in a
larger spacing between the eddies. This is followed by large intrusions of the crossflow
between the eddies. In the case of Mw =28, the fast crossflow stream sweeps the jet as the
eddies lose their coherence. In the case of N2 injection shown in Fig. 5.1e (Mw =28) the
large-scale structures are not visible beyond x/d ∼ 8 − 10. In Chapter 4 we postulated
that the reason the large-scale structures lose their coherence is related to the “tiltingstretching-tearing” mechanism which is due to the large velocity differences between
90
TABLE 5.1 The general flow exit properties of gaseous jets with different molecular weights.
Jet Gas
Mw,jet
g/mole
γe
Te
K
Ue = ae
m/s
µe
Pa·s
(T=Te )
1)
H2 - Hydrogen
2
1.42
246
1205
7.76 × 10−5
2)
85.7% H2 + 14.3% CH4
4
1.40
248
850
8.28 × 10−6
3)
57.2% H2 + 42.8% CH4
8
1.37
252
600
9.30 × 10−6
4)
CH4 - Methane
16
1.32
257
420
1.14 × 10−5
5)
N2 - Nitrogen
28
1.40
248
320
1.54 × 10−5
TABLE 5.2 The specific flow exit properties of gaseous jets used in the study of the jet molecular weight
effect. The free-stream used in these experiments simulates the flight Mach 10 flow condition.
Jet
Mw,jet
g/mole
pe,eff
atm
J
ν = µ/ρ
m2 /s
Red
r
s
McA
(T=250 K)
1)
2
6.3
1.84 ± 0.1
1.24 × 10−5
194,000
0.51
0.37
0.52
2)
4
5.9
1.72 ± 0.1
7.14 × 10−6
238,000
0.36
0.74
0.43
3)
8
6.5
1.85 ± 0.1
3.69 × 10−6
324,000
0.25
1.46
0.35
4)
16
6.1
1.67 ± 0.1
2.46 × 10−6
342,000
0.18
2.87
0.27
5)
28
6.1
1.76 ± 0.1
1.84 × 10−6
349,000
0.14
5.20
0.22
the jet and the crossflow. We will provide more evidence supporting this hypothesis in
section 5.2.
5.1.2
Penetration and Shear Layer Thickness
Figure 5.2 includes plots of the transverse penetration height and the penetration
width of jets with different molecular weights but with almost identical jet-to-momentum
flux ratios (J =1.67-1.84). The data are obtained by identifying the visually observable
upper edge of the jet shear layer in the instantaneous schlieren images. The penetration
profiles clearly demonstrate an increasing improvement in the penetration height for
increasing values of the jet molecular weight. The same trend can also be observed
for the growth rate of the jet shear layer. In Chapter 4 we suggested a relationship
a) Mw = 2 g/mole
b) Mw = 4 g/mole
c) Mw = 8 g/mole
d) Mw = 16 g/mole
e) Mw = 28 g/mole
FIGURE 5.1 Examples of instantaneous schlieren images of jets with different molecular weights. Freestream conditions are: U∞ =2360 m/s, M∞ =3.38, T∞ =1290 K, p∞ =32.4 kPa.
91
92
between the jet shear layer thickness and the width of the maximum jet penetration.
Accordingly, the visible jet shear layer thickness, δvis , ranges between 4d-7d at ∼22
jet diameters downstream where the thicker shear layer is associated with the larger
Mw . The peak transverse penetration in the low Mw (2 g/mole) case is about y/d=6.5
while in the high Mw (16 g/mole) case is about y/d=10. The penetration height and
therefore its width are expected to increase further downstream especially for the higher
Mw cases.
These observations are not in agreement with other studies which state that identical
penetration heights should be observed independent of the jet molecular weight. During
the last 30-40 years of studies, the jet penetration height was believed to scale with the
momentum flux ratio J. For comparison with previous results two empirical correlations
proposed by Gruber et al. (1995) and Rothstein and Wantuck (1992) are also plotted
in Figs. 5.2a- 5.2d for J = 1.75. Gruber et al. measured the penetration of hydrogen
and air jets injected into a cold free-stream flow based on 10 % of the jet concentration.
Rothstein and Wantuck, on the other hand, used OH fluorescence imaging to detect
the hydrogen penetration injected into a high temperature reacting crossflow. The
penetration measurements obtained in this work are higher than those observed in
previous studies for all cases except the hydrogen case (Mw =2 g/mole) which agrees
reasonably well with Rothstein’s correlation. Also, note that penetration profiles of
Rothstein and Wantuck are almost 20 % higher than those reported by Gruber et al. The
variation between these works are likely due to differences in experimental conditions
and measurement techniques as we will discuss next.
We may explain the agreement between our hydrogen injection results and the
measurements of Rothstein and Wantuck through similarities in our experimental approaches. The free-stream velocity and temperature in both works are high (r < 1 in
both experiments) and the measurement techniques are quite similar. In our reacting
experiments (see Chapter 6), we demonstrated that OH radicals lie on the periphery of
the hydrogen jet shear layer observed through a simultaneous OH/PLIF and schlieren
imaging. Therefore, measurements based on OH emission and schlieren imaging should
provide similar penetration profiles.
Experimental procedure may also explain the discrepancy between the results of
Gruber et al. and Rothstein and Wantuck. The free-stream velocity and temperature
in the experiments of Gruber et al. are lower (r > 1, s < 1) than those in the work of
10
93
Rothstein 1992
Gruber et al. 1995
a) Mw=2
y/d
8
6
dvis @ 4d
4
2
0
-2
0
2
4
6
8
10
12
14
16
18
20
22
x/d
10
b) Mw=4
y/d
8
6
dvis @ 5d
4
2
0
-2
0
2
4
6
8
10
12
14
16
18
20
22
x/d
10
c) Mw=8
y/d
8
6
dvis @ 6d
4
2
0
-2
0
2
4
6
8
10
12
14
16
18
20
22
x/d
10
d) Mw=16
y/d
8
6
dvis @ 7d
4
2
0
-2
0
2
4
6
8
10
12
14
16
18
20
22
x/d
FIGURE 5.2 Jet transverse penetration along the axial distance, x/d. Data for four gases with different
molecular weights are presented: a) Mw = 2, J = 1.84, b) Mw = 4, J = 1.72, c) Mw = 8,
J = 1.85, d) Mw = 16, J = 1.67. For comparison, empirical correlations suggested by Gruber
et al. (1995) and Rothstein and Wantuck (1992) are also included for J = 1.75.
94
Rothstein and Wantuck.
As will be argued in the second part of this chapter, the velocity ratio, r, is an important factor in the development and growth rate of the jet shear layer structures and,
therefore, directly affects the penetration of the jet. An increase in the jet molecular
weight decreases the jet exit velocity and hence the velocity ratio, r. In our experiments, higher penetration is observed for lower values of r. The penetration results
of Lee et al. (1995) are an example which supports our findings. They measured jet
penetration using PLIF (Planar Laser-Induced Fluorescence) measurements of NO of a
non-reacting injectant (N2 ) and OH of a reacting injectant (H2 ) in a high temperature
supersonic flow. The penetration height indicated by NO fluorescence was significantly
larger than that indicated by OH fluorescence for the same J. Their reasoning for this
phenomena, however, was not complete. They related the differences between N2 and
H2 injections to the frictional losses in the H2 injector and to the consumption of H2
near the stoichiometric ratio. First, the frictional losses can only drop the penetration
height by 5 % at most. Second, combustion between the cold hydrogen and the hot
oxygen takes place in the lean region of the mixture where the mixture temperature
is high and not near the stoichiometric value, as Lee et al. suggested. We propose,
therefore, that the velocity ratio differences between the two cases (r = 1.1 for H2 vs.
r = 0.3 for N2 ) cause the different penetrations observed by Lee et al. (1995). Namely,
the smaller the r, the better the penetration.
Another noteworthy observation was recently recorded by Mathur et al. (1999) in a
high temperature (850 K), high velocity (1750 m/s) free-stream flow. Flame spreading
angles of ethylene gas (Mw =28) injected from a flush wall injector were measured and
found to be twice as large as the predicted spreading. Mathur et al. concluded that some
other mechanism, in addition to the transverse momentum of the fuel, must cause the
rapid spreading of the flame around the ethylene jet. Indeed, their jet-to-free-stream
velocity ratio was r = 0.18, similar to the case with Mw =16 g/mole studied in our
investigation.
Here we suggest that variables other than the jet-to-free-stream momentum flux ratio, J, influences the penetration trajectory. We can achieve higher penetration heights
as the molecular weight of the jet is increased systematically. Increase in the jet’s molecular weight decreases the jet exit velocities, namely the r. Our findings are also consistent with previous investigations where similar experimental conditions were studied.
95
We can provide an improved explanation for their observations and for the discrepancies
shown in the previous works by taking into account the velocity ratio, r, in addition to
the momentum flux ratio, J.
5.1.3
Convection Characteristics
Figures 5.3a - 5.3b summarize the convection velocity of large scale eddies in the
transverse and streamwise directions. Also included in the figures are the velocity of
the jets at the exit of the injector and the velocity of the free-stream. The convection
characteristic of nitrogen eddies (Mw =28 g/mole) could not be measured beyond x/d=8,
as they lose their coherence through the bursting mechanism explained in the previous
chapter.
From consideration of the y-momentum equation, the pressure rise behind the Mach
disk implies that the jet fluid loses its momentum in the y-direction. As the jet loses
its y-momentum, the shear layer eddies accelerate in the free-stream direction because
of the crossflow which applies drag forces on the jet. Further downstream, the eddies
eventually convect with velocities that are closer to the free-stream velocity independent
of the jet’s molecular weight. The only difference between the cases is the distance where
the eddies achieve their maximum velocity. Low density eddies (low Mw ) could follow
the free-stream velocity earlier than the denser ones with larger Mw . For example in the
case of Mw =2, the maximum convection velocity was achieved around x/d=7, while in
the case of Mw =16 the plateau was reached just after x/d=16. This result is consistent
with the fact that drag forces are the main cause of the convection of the eddies in the
streamwise direction. For the same drag force, acceleration of heavier eddies is slower
than the acceleration of lighter eddies.
5.1.4
Characteristic Large Eddy Frequencies (Possible Transverse Jet
Modes)
Since coherent structures include concentrated regions of vorticity which are the
main mechanisms for the entrainment of the crossflow into the jet shear layer, understanding the origin of vorticity is essential for understanding the structures. We have,
therefore, measured the characteristic formation frequency of the large scale eddies in
the jet shear layer using the ultra-fast-framing schlieren system. Before presenting
Uc,x
U¥=2360 m/s
2500
~2100 m/s
2000
1500
Ujet=1205 m/s
1000
b) Mw=4
Uc,y
a) Mw=2
500
0
Uc,x
Uc,y
U¥=2360 m/s
2500
~2000 m/s
2000
1500
Ujet=850 m/s
1000
500
0
0
5
10
15
20
0
5
x/d
Uc,y
U¥=2360 m/s
~1950 m/s
2000
15
20
1500
1000
Ujet=600 m/s
500
0
Uc,x
d) Mw=16
Uc,x
2500
10
x/d
c) Mw=8
96
Uc,y
U¥=2360 m/s
2500
~2050 m/s
2000
1500
1000
Ujet=420 m/s
500
0
0
5
10
x/d
15
20
0
5
10
15
20
x/d
FIGURE 5.3 Convection velocity of large scale structures in the streamwise (Mc,x ) and transverse (Mc,y )
directions as a function of axial distance x/d. The results for each case (for each molecular
weight of jet) are obtained from 4-5 experiments each including 8 consecutive schlieren images.
97
the results, we first summarize the possible instability modes of free-jets and jets-incrossflows.
Free-jets generally have two dominant instability frequencies associated with different sizes of vortices. The first is originated by the instability of the shear layer at the jet
orifice. The initial vortex shedding frequency, also called the most amplified frequency,
fθj , scales with the initial shear layer momentum thickness, θj , and jet exit velocity, Uj .
The corresponding “initial vortex shedding Strouhal number”,
Stθj =
fθj θj
Uj
(5.3)
is found to be scattered from 0.01 to 0.018 (Gutmark and Ho 1983). The second
dominant jet instability mode is related to larger scale structures present downstream
of the jet potential core. The characteristic frequency of this mode is referred to as
the “preferred mode frequency, fj ”of the jet. The initial vortices of the shear layer
grow by merging and entrainment as they convect downstream. At the end of the jet
potential core the dominant frequency is governed by the jet column instability (Crowe
and Champagne 1971). The preferred mode frequency, fj , scales with the jet exit
diameter and velocity, d and Uj to yield the “preferred mode Strouhal number”
Std =
fj d
Uj
(5.4)
While many researchers confirmed the existence of a preferred mode, their experimental results surveyed by Gutmark and Ho (1983) revealed that the value of Stj varies
widely between 0.24 to 0.64. These discrepancies were attributed to the various initial
conditions of different facilities.
To determine the origin of the large scale structures of sonic jets in crossflows, an
analogy between this and the case of a free-jet has been presented. Using the concept
of “the preferred mode frequency”, we obtain a dominant “preferred Strouhal number”
for the transverse injection case.
Figure 5.4 represents the measured dominant frequency of the eddy formation in the
beginning of the jet shear layer and the corresponding Strouhal number as measured for
different jet exit velocities. The measurements are obtained by analyzing 5-10 different
experiments for each case. Each experiment includes 8 time correlated schlieren images.
The appropriate interframing time between the images allows us to identify the newborn
98
Stj
1.2
1.0
0.8
200
400
600
800
1000
1200
400
600
800
1000
1200
700
fj, kHz
600
500
400
300
200
100
0
200
Ujet, m/s
FIGURE 5.4 Formation frequency of the large scale structures and the corresponding “preferred mode
Strouhal number”, Std = fj d/Uj , as a function of the jet exit velocity. The data were
collected from the time evolution observation of the jet from 8 consecutive schlieren images.
Each data point was obtained by averaging 5-10 experiments with the error bars representing
the deviation from the mean value.
eddies during the flow visualization time (ranging between 10-30 µs). The results show
that the characteristic frequency of the eddy formation is scaled linearly with the jet
exit velocity. This suggests that the shear layer eddies are associated with the preferred
instability mode of the jet. The corresponding “preferred mode Strouhal number” can
therefore be calculated based on Eq. 5.4. The results indicate that this “preferred mode”
corresponds to a Strouhal number of about Std = 1 for all the cases studied in this work.
A comparison with previously published results is not possible due to the lack of
such measurements in supersonic crossflows. The only comparison that can be made
is with the results of Fric (1990) performed in subsonic flows. From his measurements,
the preferred mode frequency of the subsonic transverse jet was found to decrease with
distance along the jet. Merging of the eddies was the main reason for the decrease in the
frequency, changing the Strouhal number from Std ≈ 1 − 2 down to 0.2 around x/d∼5.
Stq j / Stq j, min
99
1.8
1.6
1.4
1.2
1.0
5
1.5x10
700
5
2.5x10
5
2.5x10
2.0x10
5
3.0x10
5
3.5x10
5
3.0x10
5
4.0x10
5
3.5x10
5
5
4.0x10
fj, kHz
600
500
400
300
200
100
0
5
1.5x10
2.0x10
5
Rejet
FIGURE 5.5 Formation frequency of the large scale structures and the “initial vortex shedding Strouhal
number”, Stθj = fθj θj /Uj , as a function of the jet Reynolds number.
Std ≈ 0.2 is smaller than the values quoted for free jets. In our experiments, the number
of eddies are counted just before the bending of the jet as they become identifiable.
Further downstream, the vortex merging does not happen very often. Std ≈ 1 can
therefore be presented as the “preferred mode Strouhal number” for the transverse jets
in supersonic crossflows for the geometry examined in this work. This Strouhal number
is larger than those quoted for free-jets. It is also larger than the ones measured for
transverse jets in subsonic flows.
We can also calculate the Strouhal number based on the initial shear layer momentum thickness, θj . However, the appropriate data are not available to estimate
the momentum thickness of the jet shear layer exiting the injector port. We therefore
normalized the Stθj with its minimum value assuming that θj =
p
Rejet . Figure 5.5
summarizes the findings showing that the formation frequency is not associated with
the initial vortex shedding frequency. Stθj appears to increase with increasing Rejet .
100
These results suggest that the shear layer eddies are independent of the exit shear layer
instability characteristics, because the characteristic length scale of the mode has been
shown to be the jet diameter and not the thickness of the exit shear layer. The most
amplified frequency of the jet column instability is the origin of its large-scale structures.
5.1.5
Jet Compressibility Analysis
In studies of mixing layers of two parallel streams, it has been shown that compressibility levels control the growth rate of the mixing layer which decreases with increasing
compressibility. We have therefore attempted to analyze the effect of compressibility on
transverse jets.
Convective Mach number, Mc , is a key compressibility parameter which is based on
the velocity of the large scale structures relative to either free-streams. Papamoschou
and Roshko (1988) defined a convective Mach number for each stream:
Mc1 =
Uc − U2
U1 − Uc
; Mc2 =
a1
a2
(5.5)
where U1 and U2 are the high and low speed streams, respectively (refer to Fig. 5.6).
Assuming that entrained fluid stagnates isentropically in the frame of the structures,
the pressure-matching condition at the stagnation point yields:
r
γ2
Mc2
γ1
√
Uc
1+r s
√
=
U1
1+ s
Mc1 =
assuming γ1 = γ2
Mc1 = Mc2 = Mc =
U1 − U2
a1 + a2
(5.6)
(5.7)
(5.8)
At low compressibilities (Mc < 0.5) the structure of a non-reacting shear layer is
two-dimensional and the large eddies travel with the average convective Mach number,
Mc . As the compressibility increases, this theory seems to fail as the central mode
stabilizes and a transition from a two- to three-dimensionality occurs. Beyond Mc =0.5,
experimental results by Papamoschou (1991 and 1997) and by Dimotakis (1991) showed
that convective velocities follow the “stream selection rule” which is based on the existence of “fast” and “slow” modes. If one stream is supersonic and the other subsonic,
the convective velocity of structures will be closer to that of the fast stream (fast mode),
(a)
101
(b)
U2
Bow Shock Induced
Free-Stream
Jet
Boundary
Uc
C
M >1
U1
2
Stationary Frame
B
M1'>1
1'
Peb =?
U2-Uc
1
A
M1>1
y1
Pj, Mj=1
Uc-U1
x1
Convective Frame
FIGURE 5.6 Flow-field schematics used in the jet compressibility analysis. Letters A, B and C indicate the
zones of the jet shear layer.
and when both streams are supersonic the convective velocity will favor the slow speed
stream (slow mode).
One could basically adapt the convective Mach number concept to scale the compressibility of transverse jets. However, because of the three-dimensional complexity of
the flow-field and lack of the velocity field information, there is an additional difficulty
in predicting the convective Mach number of transverse jets in supersonic crossflows.
Neither crossflow nor jet-flow properties are uniform. The underexpanded jet accelerates inside the barrel shock and eventually gets compressed through the Mach disk,
while the crossflow changes its properties continuously behind the curved bow shock.
We, therefore, suggest separating the jet flow-field into three different zones to analyze the compressibility effects. The schematic of the proposed regions are illustrated in
Fig. 5.6 and indicated with letters A, B and C. Zone A is close to the jet exit where the
y-component of the free-stream velocity is negligible. The convective Mach number in
zone A (McA ) can therefore be calculated using the equation 5.8 and by assuming that
U1 = Ujet and U2 = 0. Figure 5.7 shows the estimated values of McA together with the
visible thickness of the jet shear layer, (δvis ) at x/d≈22 as obtained from penetration
102
8.0
7.5
A
0.50
Mc
7.0
0.45
6.5
0.40
6.0
0.35
5.5
dvis
0.30
5.0
0.25
4.5
0.20
4.0
200
400
600
800
1000
Shear Layer Thickness, dvis/d
Convective Mach Number, MCA
0.55
1200
Uj (m/s)
FIGURE 5.7 Estimated convective Mach number in zone “A”, McA , (refer to the schematic in Fig. 5.6) and
the measured visible jet shear layer thickness, δvis , at x/d≈22 as obtained from penetration
width measurements.
width measurements (see Section 5.1.2). A decrease in δvis is observed for increasing
values of McA , indicating that the compressibility properties in the initial region of the
jet shear layer affect its growth rate.
For zone B, the convective Mach number model, given by Gruber et al. (997b),
guided our calculations. Gruber et al. suggested quantifying the compressibility level
of transverse jets at a single point in the jet shear layer near the Mach disk (zone B
in our case). For this calculation, the jet velocity just upstream of the Mach disk (U1 )
is estimated. Figure 5.8a presents the estimated values of U1 with error bars obtained
for a range of assumed pressure ratios (P10 /P∞ ). Also included in this plot is the range
of the free-stream velocity downstream of the bow shock, which is determined using
the oblique shock relations for a range of shock angles (45o < β < 65o ) measured
in section 4.2.1). Evident in Fig. 5.8 is that the free-stream velocity behind the bow
shock is faster than the heavy jets (Mw = 28 and 16) and slower than the light jets
(Mw = 2 and 4). In the experiments of Gruber et al. the free-stream velocity was
slower than both the heavy and the light jets and therefore a comparative convective
Mach number could be identified to quantify the compressibility level of jets. In the
2500
(b) C-zone
U¥=2360 m/s
2500
2000
U¥=2360 m/s
2000
1500
1500
1000
U¥ behind the bow shock
500
0
200
Jet Velocity Behind the Mach disk
U1' (m/s)
Maximum Jet Velocity, U1 (m/s)
(a) B-zone
103
400
600
800
1000
1200
U¥ behind the bow shock
1000
500
0
200
400
600
Uj (m/s)
800
1000
1200
Uj (m/s)
FIGURE 5.8 Estimated velocity fields for the jet and the free-stream in zones “B” and “C”.
current experiments, however, it is difficult to find a clear dependence of δvis on McB .
We, therefore, suggest the use of the convective Mach number in zone A (McA ) as an
indicator for the jet compressibility level.
Figure 5.8b presents an estimate for the expected velocities in zone C. The value of jet
velocity U10 , immediately after the Mach disk, is calculated using the normal shock and
isentropic relations. The free-stream velocity behind the bow shock is again estimated
using the measured bow shock angle as described above. The plot indicates that the
supersonic free-stream is significantly faster than the jet which becomes subsonic behind
the Mach disk. It is possible that in this region the “stream selection rule” mentioned
above applies. According to this rule the convective velocity of structures will be closer
to that of the fast stream (fast mode) as one stream is supersonic and the other subsonic.
In the previous section, the jet shear layer eddies in zone C and beyond are indeed
demonstrated to convect with velocities close to the fast free-stream values.
In summary, we propose the convective Mach number in zone “A” as an indicator
of the jet compressibility level. The growth rate of the shear layer scales with McA .
The convective velocity of the eddies, on the other hand, seems to follow the “stream
selection rule” as observed in the shear layers of two parallel streams.
5.2
104
Effect of Density and Velocity Ratios
In this part of the investigation, we pursue the decomposition of the molecular weight
effect into its constituent parameters, velocity and density. For a given pressure and
temperature of the jet:
s
Uj ∝
γ
Mw,j
and ρ ∝ Mw,j
(5.9)
Therefore, by changing the jet molecular weight, its density and velocity are also
changed. By using different free-stream conditions we can control the jet-to-free-stream
velocity and density ratios independent of each other. For that purpose, 24 different
experimental conditions, summarized in Table 5.3, are studied. The stability of the jet
shear layer eddies are analyzed by the aid of the flow visualization.
5.2.1
Having examined the effect of jet molecular weight, we showed that the coherence
of the large scale eddies is significantly affected by the increase of the jet molecular
weight. The eddies “burst” into smaller structures by the “tilting-stretching-tearing”
mechanism discussed in the previous chapter. This “bursting” mechanism will henceforth be referred as the “instability” of the eddies. We observed the stability of the
eddies by visual observations based on schlieren imaging. In such work, the eddies are
identified as “unstable” when the structures lose coherence and significant distortions
in the bow shock shape can be observed.
Examples of schlieren images for selected experiments are shown in Figs. 5.9, 5.10
and 5.11. The first set of experiments numbered as 1 to 5 in Table 5.3, is performed in
the flight Mach 10 condition. These experiments are already discussed in detail in the
studies of jet molecular weight effect (see Section 5.1). Here we will discuss the rest of
the experiments, numbered from 6 to 24.
The first goal is to eliminate the density ratio effect by simulating conditions with
a similar velocity to the Mach 10 case, but with much lower static temperature so that
the density ratio varies minimally when the jet molecular weight is changed. Therefore,
the free-stream conditions (600/9/6) for the second set of experiments (experiments no.
6-8) have static temperature of only 243 K. Results of these experiments show that the
jet becomes unstable again as the velocity ratio is decreased to below 0.17 (see Figs. 5.9b
105
TABLE 5.3 Summary of the different conditions used in the study of jet instability analysis.
No
Free-stream
Condition
Mw,∞
γ∞
U∞
m/s
p∞
atm
T∞
K
M∞
Mw,j
r
Uj /U∞
s
ρj /ρ∞
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
600a /0.5b /20c
(flight
Mach 10)
28
1.32
2360
0.32
1290
3.38
600/9/6
28
1.4
2420
0.083
243
7.75
600/4/6
28
1.4
2572
0.1
392
6.48
600/0.3/60
28
1.29
2037
0.72
1840
2.46
300/0.45/70
(flight
Mach 8)
600/4/20
300/10/15
28
1.32
1760
0.61
1410
2.37
28
40
1.38
1.667
2212
1686
0.29
0.124
516
207
4.89
6.46
300/10/15
80a /5b
4
28
1.667
1.38
2560
520
0.26
1.9
220
550
3.04
1.1
100/0.5
28
1.33
1058
0.585
1077
1.62
2
4
8
16
28
2
16
28
2
16
2
16
28
2
16
28
2
16
28
28
2
28
2
28
0.51
0.36
0.25
0.18
0.14
0.50
0.17
0.13
0.47
0.16
0.59
0.21
0.1
0.69
0.24
0.18
0.55
0.25
0.19
0.13
2.32
0.62
1.14
0.30
0.37
0.74
1.46
2.87
5.20
0.07
0.54
0.98
0.11
0.87
0.53
4.09
7.42
0.41
3.14
5.69
0.15
0.32
0.58
6.21
0.16
2.22
0.31
4.34
The free-stream conditions are represented by the expansion tube initial filling pressures
with nomenclature referring to Fig. 2.2. a. P4 , psig, b. P1 , psia, c. P10 , torr.
and c) even though the density ratio stays at low values at which the Mach 10 condition
showed stable flow structures. The bow shock which stays smooth in the hydrogen
injection case (Fig. 5.9a) is distorted in the case of methane and nitrogen injections.
Additional shock waves are generated around shear layer structures as the velocity of
the free-stream becomes supersonic relative to the convection of the eddies. Tilting of
the eddies is visible in the region close to the wall. Note also the shock waves generated
from leading edge of the plate. These are actually weak Mach waves which are clearly
visible owing to the high sensitivity of the schlieren system. The same flow features
106
are obtained in the third set of experiments (experiments no. 9 an 10) presented in
Figs. 5.9d and e, as the flow conditions (600/4/6) are similar to the second set.
The second goal is to eliminate the velocity ratio effect by generating conditions of
high density ratio while keeping the free-stream velocity low. For that purpose we run
the facility in a shock tube mode, namely without the second diaphragm between the
expansion and driven sections (experiments no. 21 to 24). As shown in Figs. 5.11b and
5.11d, the jet eddies stay coherent for high values of s (experiments no. 22 and 24) at
which jet eddies in the Mach 10 condition lose their stability. The eddies stay coherent
without large intrusions of air into the jet. It is worth noting that these span the range
of velocity conditions at which most of the previous studies were performed. Therefore,
not many significant differences in the flow field could be observed in those studies.
Finally, note the shock waves emitting from the injection location (see Figs. 5.11a and
c). In these experiments the jet exit velocity is larger than the free-stream velocity,
r > 1. Note also the large stand-off distance of the bow shock because of the low Mach
numbers.
The results are presented in a density versus velocity ratio (s-r) diagram shown in
Fig. 5.13. Separate regions of stable and unstable flows can clearly be identified. The
plot indicates that the density ratio, s, has a little effect on the instability of the jet
shear layer structures while the velocity ratio, r, is the main controlling parameter. We
therefore propose to use an “effective velocity ratio”, λ, which will be presented in the
following section.
5.2.2
Definition of an “Effective Velocity Ratio, λ”
We propose to define an “effective velocity ratio”, λ, as a measure of the magnitude
of the velocity difference across the jet shear layer. We assume that near the jet exit
port, the jet issues in the y-direction at velocity Uj and the free-stream flows in the
x-direction at velocity U∞ . This configuration, shown schematically in Fig. 5.12, is a
special case of skewed mixing layers with a skewing angle of 90 o between high- and lowspeed streams. The jet fluid is expected to convect in the direction of the total velocity
vector. Therefore, the effective shear will be proportional to the velocity difference in
that direction. The components of Uj and U∞ in the direction of the total velocity
a) H2 injection in 600/9/6 (No.6)
d) H2 injection in 600/4/6 (No.9)
b) CH4 injection in 600/9/6 (No.7)
e) CH4 injection in 600/4/6 (No.10)
c) N2 injection in 600/9/6 (No.8)
FIGURE 5.9 Schlieren images at selected conditions given in Table 5.3.
107
a) H2 injection in 600/0.3/60 (No.11)
d) CH4 injection in 300/10(Ar)/15 (No.18)
b) CH4 injection in 600/0.3/60 (No.12)
e) N2 injection in 300/10(Ar)/15 (No.19)
c) N2 injection in 600/0.3/60 (No.13)
f) N2 injection in 300/10(He)/15 (No.20)
108
a) H2 injection in 80/0.5 (No.21)
c) H2 injection in 100/0.5 (No.23)
b) N2 injection in 80/0.5 (No.22)
d) N2 injection in 100/0.5 (No.24)
109
110
U¥ cos(a)
Uj
DU
a
U¥
Uj sin(a)
D U = Uj sin(a) - U¥ cos(a)
FIGURE 5.12 Velocity vector field (U∞ , Uj ) for a skewed mixing layer and the “effective velocity ratio”, λ.,
described in the total velocity vector direction.
vector are:
Ujk = Uj sin(α)
and
U∞k = U∞ cos(α)
(5.10)
The velocity difference ∆U is therefore equal to:
∆U
Uj sin(α) − U∞ cos(α)
=
U∞
U∞
(5.11)
by substituting tan(α) = Uj /U∞ , the effective velocity ratio, λ, can then be calculated
as the ratio of the velocity difference ∆U to the free-stream velocity U∞
∆U
1 − r2
=√
(5.12)
U∞
1 + r2
Therefore, when λ = 0, there is no shear, and when λ ∼
= 1, the shear is a maximum as
λ=
the free-stream velocity is much higher than the jet velocity.
Figure 5.14 presents the experimental results in a new “velocity-density” diagram
where the effective velocity ratio λ is used instead of r. Again two distinct regions
of stable and unstable flows are identifiable. Clearly, a critical value for the effective
velocity ratio exists in the vicinity of λcr ≈ 0.94 beyond which the jet flow becomes
unstable as the “tilting-stretching and tearing” mechanism becomes important.
5.2.3
Discussion on the Effect of the Curvature - Centrifugal Instability Analysis
Certain configurations possessing curvature are prone to centrifugal instabilities.
Curvature introduces centrifugal forces which tend to produce streamwise vortical structures of the Taylor-Görtler type. Rayleigh (1880) showed that the stability condition
111
9
Stable
Unstable
8
13
Stable
7
Unstable
20
16
6
5
s=
rj
5
r¥
4
24
12
4
3
15
22
2
3
8 10
1
19
2
18
9 6
7
0
0
0.1
0.2
0.3
0.4
r=
1
0.5
11
14
17
0.6
0.7
0.8
Uj
U¥
FIGURE 5.13 Jet-to-free-stream density ratio vs. velocity ratio. The number near the data points corresponds to the experimental conditions summarized in Table 5.3. “Unstable” flow jet is defined
when the large structures lose coherence downstream of the injection port and significant distortions in the bow shock shape can be observed.
Stable
Unstable
9
8
13
Stable
7
Unstable
20
16
6
5
s=
rj
5
r¥
4
24
12
15
3
4
22
2
1
0
0.4
3
2
11
14
17
0.5
1
6
0.6
l=
18
9
7
0.7
DU
U¥
=
108
19
0.8
æç 1 - r 2 ö÷
è
ø
1+ r 2
0.9
1
l cr
FIGURE 5.14 Jet-to-free-stream density ratio vs. the “effective velocity ratio”, λ. The number near the
data points corresponds to the experimental conditions summarized in Table 5.3.
(a)
(b)
Rayleigh-Synge criterion for
centrifugal stability:
Experimental results
112
s + 2 r < cons.
s
unstable
s
stable
stable
unstable
r
r
s=
rj
r=
r¥
Uj
U¥
FIGURE 5.15 Schematics illustrating the stability regions based on a) Rayleigh criterion for centrifugal forces
vis
in the curved mixing layers as given in Eq. 5.15 where cons. = 3 + 2 hδmax
and b) current
experimental results.
for an inviscid flow depends on the gradient of angular momentum.
Synge (1933)
gave a stability criterion taking into account that a density difference may also produce an unstable layer. The associated instability mechanism is therefore known as the
Rayleigh-Synge criterion and is given in the form of:
d ³ 2 2´
ρU r > 0
dr
(5.13)
for dr > 0, this criterion can be written as follows:
dU
dr
dρ
+2
+2 >0
ρ
U
r
(5.14)
by substituting dρ = ρ∞ − ρj , dU = U∞ − Uj and dr/r = δvis /hmax we obtain:
ρj
Uj
δvis
+2
<3+2
ρ∞
U∞
hmax
(5.15)
where the curvature radius is assumed to be the maximum jet penetration height, hmax .
Eq. 5.15 (s + 2r < const), therefore, provides a criterion for the stability of the curved
jet shear layer in case the centrifugal forces play an important role on the stability.
However, comparison of Equation 5.15 with the results presented in Fig. 5.13 indicates
the opposite trends. As shown in Fig. 5.15, the regions where a curved jet shear layer
113
is stable are actually the regions of the unstable jet shear layer as observed in our
experiments. Therefore, we can conclude that instabilities associated with curved shear
layers do not contribute to the instabilities in the case of a normal injection into a
crossflow.
Chapter 6
Autoignition and Flame-Holding
Capability of a Hydrogen
Transverse Jet
This chapter describes the experimental efforts in characterizing the ignition and the
flame-holding capabilities of a transverse jet injected into high total enthalpy supersonic
crossflows. The use of an expansion tube provides a correct simulation of true flight
combustion chemistry, including ignition delay and reaction times. The experiments are
designed to map the hydroxyl radical (OH) in the near-field of an underexpanded hydrogen jet injected into flight Mach number 8, 10 and 13 total enthalpy flow conditions.
6.1
Ignition and Flame-Holding Considerations
The stabilization of flames in supersonic flow is a difficult issue for two primary reasons: First since flow times are short, ignition delays can result in significant travel of the
jet plume through the combustor. Second, strain rates tend to be high in compressible
flows which can suppress combustion.
Transverse injection is a commonly used flame stabilization scheme in supersonic
combustors. It provides flame stabilization: 1) by organization of an upstream recirculation zone, 2) by formation of coherent structures containing unmixed fuel and air,
where a diffusion flame occurs as the gases are convected downstream, provided the
114
CHAPTER 6. IGNITION OF HYDROGEN JET
115
strain rates are not too high.
Transverse injection schemes have two main points where the ignition is likely to
occur: the region behind the jet bow shock where high temperatures and pressures are
obtained, and the recirculation regions ahead of and behind the base of the jet where
long residence times and high temperatures exist. The residence time of the hydrogenair mixture in the bow shock region is short, since the mixture expands around the
jet flow-field immediately after compression in the bow shock. For the higher Mach
number flows, however, ignition may still be initiated in the bow shock region due to
the relatively high static temperature, though a more likely place for ignition to occur is
in the recirculation region upstream the jet exit as will be shown in the results section.
In scramjet combustors, where relatively cold hydrogen is injected into hot air, there
is a significant variation of temperature with equivalence ratio (φ) through the mixing
layer around the jet. Since the temperature of the mixture will be higher at low equivalence ratios, and since ignition time is a strong function of the mixture temperature,
it is expected that the self-ignition point will be on the lean side of the mixing layer
∼ 0.2 (Huber et al. 1979)). The ignition delay times associated with
around the jet (φ =
hydrogen-air mixtures will be discussed in Section 6.3.2.
In order for self-ignition (and therefore combustion) to be accomplished in a flowing
combustible mixture, it is necessary that four quantities have suitable values: static
temperature, static pressure, fuel-air ratio, and the residence time at these conditions.
In a reacting system, ignition is considered accomplished when sufficient free radicals are
formed to initiate the reaction, even though no appreciable heat has yet been released.
When the conditions of spontaneous ignition exist, the distance li at which it occurs in
a medium flowing at a velocity u is:
li = u · τi
(6.1)
Since the ignition delay time τi varies inversely with pressure (because of the two body
reactions involved in the ignition chemistry of hydrogen and air) the product τi p is
effectively constant for a given temperature and fuel-air equivalence ratio. This allows
the use of the binary scaling law for the ignition of hydrogen-air mixtures in the following
form,
pli
≈ constant
u
(6.2)
116
This means that for a given combustor entry temperature (typically in the range of
1440-1670 K, Heiser and Pratt 1994), the ignition lengths are directly proportional to
flight velocity, V0 , by
li ∼
u
1
∼ 3
p
V0
(hyrogen fuel)
(6.3)
Remember that supersonic burner entry pressures and velocities are scaled with the
flight velocity according to: p3 ∼ 1/V02 and u3 ∼ 1/V0 (see Chapter1). Equation 6.3
indicates that the ignition lengths in a hydrogen-fueled scramjet become very large
at high flight speeds. The ignition lengths are even larger if hydrocarbon fuels are
employed. Because of the larger dependence of the ignition delay time on pressure, the
ignition length in a hydrocarbon-fueled scramjet has a larger dependence on 1/V0 as:
li ∼
u
1
∼ 2n+1
n
p
V0
(ethylene fuel)
(6.4)
where n > 1. This is one of the reasons why hydrocarbon fuels are not likely to be used
for high-flight Mach numbers.
In the supersonic combustion area, a general consensus is: storable JP-type hydrocarbon fuels can be used up to Mach 6-8. Liquid methane could be used to somewhat
higher Mach numbers, but speeds in excess of about Mach 10 requires liquid hydrogen.
Mainly because hydrogen fuel is characterized by fast reaction rates and high heat release per kilogram of fuel (120 MJ/kgfuel ). On the other hand, hydrocarbon fuels have
significant shortcomings in supersonic combustion when compared to hydrogen. The
hydrocarbon fuels have relatively long ignition delays and limited cooling capability.
Furthermore, at low speed flight conditions (flight Mach below 8), the total temperature of the free-stream is lower introducing difficulties on flame stabilization inside the
supersonic combustor. These considerations will require some innovative thinking (see
Chapter 7) especially when the fuel of choice is a heavy hydrocarbon (JP-7, decane,
etc.)
The main objective of this study is therefore to investigate the combustion characteristics of a hydrogen transverse jet in order to obtain a picture of its near-field
autoignition and flame-holding capability. The second objective is to compare the hydrogen jet autoignition capability with that of the ethylene jet.
6.2
Ignition and Flame-Holding Results
6.2.1
Simultaneous OH-PLIF/Schlieren Results
117
Figure 6.1 demonstrates an example of simultaneous schlieren and a side view OHPLIF image overlaid in a single image (Fig. 6.1c). These images are obtained at the
flow conditions simulating flight Mach 10. Apparent in the images are the regions
containing OH molecules, indicating the location of the reaction zone. The structural
evolution of the reaction zone is in good agreement with the jet position determined by
the schlieren imaging although there is a small shift between their position due to the
fact that schlieren image was taken ∼ 2 µs after the PLIF image. A significant and fairly
uniform level of OH along the outer edge of the jet plume attached to the recirculation
area upstream of the injector is visible. However, farther downstream a decrease of OH
fluorescence is obtained as the mixture expands around the jet flow-field. As explained
in Section 3.2.4, the fluorescence signal in this case is essentially proportional to the
OH mole fraction. Therefore the decrease in signal level observed in the sheet corrected
PLIF images is a direct indication of the decrease in OH mole fraction.
6.2.2
Top View OH-PLIF Images
In order to achieve a more complete picture of the combustion, we have also obtained
top PLIF views of the jet. A set of 4 instantaneous top view images collected at 4
different heights above the jet exit is shown in Fig. 6.2 (the white dots in the images
indicate the center of the jet exit.) The results show OH around the jet while the center
of the plume has no OH-formation. The bottom image at 1-jet diameter above the
plate shows two main features: 1) the jet spreads very quickly in the lateral direction
(up to about 8-jet diameters) assuming that the flame is around the jet-air interface, and
2) the OH concentration downstream of the jet remains nearly constant. By contrast,
the other three images obtained at 2, 2.5 and 3-jet diameters height demonstrate the
same tendency of the side views, namely that the OH signal level decreases as the jet
moves downstream.
118
(a)
(b)
0
2
4
6
8
10
12
14
0
2
4
6
8
Region Illuminated by
PLIF Sheet
(c)
Air
x/d
0
2
4
6
8
10
12
14
FIGURE 6.1 Simultaneous OH-PLIF and schlieren images visualizing hydrogen injection into supersonic
crossflow. Free-stream conditions are M = 3.57, T = 1300 K, P = 0.32 atm, V = 2500 m/s.
The jet-to-freestream momentum flux ratio is J = 1.4. a) Schlieren image, b) OH-PLIF image demonstrating the ignition and combustion regions of jet-in-crossflow at high enthalpy
condition, c) Overlaid OH-PLIF and schlieren images.
119
(a) y/d=3
(b) y/d=2.5
(c) y/d=2
(d) y/d=1
FIGURE 6.2 Instantaneous top-view OH-PLIF images obtained at different height above the injection
plate. Free-stream conditions are M=3.57, T=1300K, P=0.32atm, V=2500m/s. The jet-tofreestream momentum flux ratio is J=1.4. a) y/d=3, b) y/d=2.5, c) y/d=2, d) y/d=1 above
the injection plate.
6.2.3
120
Comparison of Ignition in Flight Mach 8-13 Total Enthalpy Range
Figure 6.3 compares examples of OH-PLIF imaging conducted at the center-line of
the hydrogen jet injected in flight Mach 10 and 13 conditions. Each image includes 2
separate subimages from different tests: the first has been acquired near the jet exit
while the second has been acquired farther downstream.
Apparent in the images is the isolated thin filament along the outer edge of the
plume. The center of the plume itself has no OH-signals indicating poor mixing of the
air with the core of the hydrogen jet. The OH radicals are primarily produced in the
hot separation region upstream of the jet exit and behind the bow shock and convected
downstream with the shear-layer vortices.
Ignition in our experiments is likely due to the hot and radical-rich separation region
upstream of the jet exit where the boundary layer and jet fluids mix subsonically. Although these recirculation kernels in general are small in volume, in high enthalpy flows
the temperature of these zones can be as high as the stagnation temperature of the bulk
flow. In Mach 10 condition, a low signal level of OH in the recirculation zone/boundary
layer upstream of the injector is visible. In Mach 13 condition, on the other hand, a
fairly uniform and intense OH signal level is observed even when air is used as the freestream gas. The high concentration of OH radicals in the upstream recirculation region
can be attributed to high recovery temperatures associated with high total enthalpy
flows. The ignition process will initiate instantaneously in the upstream recirculation
region as the delay times effectively approach zero (∼ 1−5 µs) at the Mach 13 condition.
Figure 6.4 presents two instantaneous OH-PLIF images obtained at the center-line of
the hydrogen jet injected at Mach 8 flight conditions. Limited amounts of OH are visible
on the leading edge of the jet, mainly behind the steep regions of the bow shock. The
ignition is quenched farther downstream. It is evident from these results that improved
injection schemes for better flame-holding would be required for practical applications
in scramjet engines flying at low Mach numbers (below 10).
a) Mach 10
Air
M¥= 3.4
V¥= 2360 m/s
P¥= 0.32 atm
T¥= 1290 K
121
x/d
H2 , J=1.4
b) Mach 13
Oxygen
M¥= 4.7
V¥= 3200 m/s
P¥= 0.04 atm
T¥= 1250 K
x/d
H2 , J=5
FIGURE 6.3 Instantaneous OH-PLIF acquired at center-line axis of the hydrogen jet injected into flight Mach
10 and 13 conditions. The images are obtained by combination of 2 different instantaneous
images: near the exit of the jet (−5 < x/d < 1) and downstream of the jet (1 < x/d < 10).
Mach 8
Air
M¥= 2.4
V¥= 1800 m/s
P¥= 0.65 atm
T¥= 1400 K
122
x/d
H2
Ht,¥= 2.9 MJ/kg
x/d
H2
J=2.3
FIGURE 6.4 Two instantaneous OH-PLIF images acquired at center-line axis of the hydrogen jet injected
into flight Mach 8 conditions.
6.3
123
Discussion of the Ignition Process
6.3.1
Ignition Characteristics of Hydrogen
Ignition of hydrogen and air in high-temperature turbulent flow fields associated
with supersonic combustors can be characterized purely by radical runaway as opposed
to thermal runaway (Im et al. 1994; Im et al. 1998; Sung et al. 1999). Thus, the heat
release of combustion is not essential for the propagation of the ignition/combustion
process.
The well-known explosion limits of a hydrogen-oxygen system are plotted in Fig. 6.5
(after Sung et al. 1999). Nishioka and Law (1997) have shown that the state of the
second explosion limit is an important boundary in the ignition response of a hydrogenair laminar mixing layer. The crossover temperature, Tc , for the second explosion limit
is defined as the temperature at which the rate of the main chain-terminating reaction
H + O2 + M −→ HO2 + M
(R1)
equals that of the rate-controlling branching reaction
H + O2 −→ OH + O
(R2)
Reaction (R2) is a two-body, temperature-sensitive branching reaction with an activation energy of 68.8 kJ/mole (16.44 kcal/mole), while (R1) is a three-body, temperature
insensitive terminating reaction because HO2 is relatively inactive. Thus increasing
temperature promotes (R2) and hence the overall ignitability. When the mixture temperature in the flow, Tmix , is larger than Tc , the system response is controlled by (R2).
The chain-branching ignition in coflow mixing layers leads to a continuous growth
of the radical pool. If the temperature is sufficiently above crossover, then the effect of
three body recombination reactions, responsible for most of the heat release in H2 -O2
combustion, is negligible, and the two streams mix and react initially without significant chemical heating. This gives rise to a thermally frozen branched-chain explosion
(Sanchez et al. 1997).
As a point of reference, we first calculated the ignition delay times, τign , for hydrogenair mixtures. The chemical kinetics software package Chemkin, developed by (Kee et al.
1980), was used for the delay time calculations. The reaction mechanism was taken
from GRI-Mech 2.12 (Bowman et al.). The ignition times based on the time when
[OH] = 1/2 [OH]max are plotted in Fig. 6.6. If the pressure and fuel-air mixture are
held constant, the effect of temperature on ignition time can be readily shown in this
124
FIGURE 6.5 Explosion limits of a stoichiometric hydrogen-oxygen mixture (after Sung et al., 1999).
figure. Note that the ignition time has a strong exponential dependence on temperature.
Over the range 1000 K to 1700 K, τi varies by about a factor of 100. At temperatures
between 800-1000 K (depending on pressure) the ignition time approaches infinity and
self-ignition cannot occur.
We have earlier discussed that at temperatures above the crossover temperature, Tc ,
the hydrogen-air system response is controlled by the two-body reaction (R2). Thus the
product pτi forms a single curve in Fig. 6.6b for all the pressures at high temperatures.
We however observe a deviation from the binary scaling law at a critical temperature
depending on pressure. This critical temperature is lower for low pressures consistent
with the second explosion limit discussed above.
125
4
10
Ignition Time (msec)
H2-air for f=1
3
10
2
10
1
10
m
.3at
p=0
1atm
2atm
4atm
0
10
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1000/T(K)
(a)
3
10
1atm
2atm
p tign (atm-msec)
H2-air for f=1
4atm
0.3atm
2
10
1
10
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1000/T(K)
(b)
FIGURE 6.6 Variation of ignition delay times τign of a stoichiometric mixture of H2 and air with temperature
and pressure. Calculations are perfomed using Chemkin and the GRI mechanism. a) τign vs.
T , b) pτign vs. T
1000
0K
30
1
=
ir
0K
50
1
=
ir
Ta
126
Ta
K
1800
Tair=
100
Tmix=1720K
Tmix=1650K
10K 20K
=10 =11
T
Tmix=1425K
T mix
Tmix=1265K
Tmix=1527K
400K
Tair=2
mix
10
00K
Tair=32
1
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Equivalence Ratio, f
FIGURE 6.7 Variation of ignition time with fuel-air equivalence ratio, φ, for cold H2 (Tjet = 300 K) injected
into hot air. The values of the ignition delay time are calculated for different air temperatures,
Tair .
6.3.2
Ignition in Supersonic Combustors
In scramjet combustors, auto-ignition is achieved by injecting a relatively cold fuel
into hot air. Therefore there is a significant variation of temperature and equivalence
ratio, φ, inside a supersonic combustor. In order to approximate the variation of temperature with φ, a simplified one-dimensional enthalpy balance between the cold hydrogen
and the hot air is used. The gases are assumed to be nonreacting, thermally and calorically perfect and ideally mixed without compressibility effects. Based on this model,
the enthalpy balance between the two streams can be written as
nair Cp,air (Tair − Tmix ) = nH2 Cp,H2 (Tmix − TH2 )
(6.5)
where n is the number of moles which is related to the equivalence ratio φ; Cp is the
specific heat at the mixed mean temperature. The mixture temperature, Tmix , can then
127
5
tign=1 ms
3200
4
2800
tign=2 ms
2400
3
tign=5 ms
tign=10 ms
2000
2
tign=43 ms
T2
1
P2
1600
-1
0
1
2
3
4
5
6
7
8
9
Free-stream Pressure, P2 (atm)
Free-stream Temperature, T2 (K)
3600
0
10
x/d
FIGURE 6.8 The free-stream temperature and pressure (T2 and P2 ) behind the bow shock, measured from
schlieren images as discussed in Section 4.2.1 (see Fig. 4.3). Ignition delay times are calculated
for several conditions of air assuming φ = 0.2. The free-stream flow properties simulate the
flight Mach 10 conditions.
be calculated by rearranging Eq. 6.5 as
Tmix =
where α =
Tair + αTH2
1+α
(6.6)
nH2 Cp,H2
nair Cp,air .
Representative ignition delay times are plotted in Fig. 6.7 as a function of φ for
various values of Tair . The results indicate that OH is likely to be formed in the hot,
∼ 0.2) where the temperatures are the highest. For
lean regions of the mixing layer (φ =
air temperatures below 1800 K the ignition delay times are much larger than 10 µs, which
exceeds the residence time of the hydrogen within the imaged region studied here (based
on the hydrogen large-scale convection velocities of 2 mm/µs and 10 jet diameters).
6.3.3
Ignition of a Hydrogen Transverse Jet
The transverse jet interacts strongly with the crossflow, producing a bow shock and
localized highly three-dimensional flow-field around it. Therefore, it is very difficult
128
to formulate the ignition characteristics of this field. We can however try to estimate
characteristic time scales of the ignition process in an attempt to explain the OH-PLIF
results.
The OH-PLIF images shown in Figs. 6.3 and 6.4 are taken at the center-line of the
jet. At this location, the average free-stream flow properties behind the bow shock were
estimated using schlieren images (see Section 4.2.1 for more details). Figure 6.8 shows
these estimated values of static temperatures and pressures of free-stream behind the
bow shock, T2 and p2 respectively, at the flight Mach 10 condition.
Considering the values of T2 and p2 and using the Eq. 6.6 we calculated the ignition
delay times at several locations along the x-axis of the jet. We assumed that the cold
hydrogen (TH2 = 300 K) interacts with hot air at the lean side of the jet shear layer
where φ=0.2. The results shown in Fig. 6.8 indicate that an instantaneous autoignition
can be achieved close to the jet exit as the ignition delay times are of the order of
1-2 µs. Further downstream beyond x/d ≈ 6, the ignition delay times become larger
(τign > 10 µs) exceeding the maximum flow residence time of the imaged region. As the
air temperature behind the weaker bow shock begins to decrease below 1800 K (Tmix <
1120 K for φ = 0.2) OH radicals can only be formed downstream of the imaged region,
beyond x/d = 10. This might be the reason for the reduced OH mole fractions observed
downstream the injection location at the flight Mach 10 condition (see Fig. 6.3a). OH
radicals generated near the jet exit are convected downstream with the shear-layer
vortices. However, since new radicals are not formed instantaneously downstream of
the injector the OH concentration dilutes and therefore the OH-PLIF signal is reduced.
6.3.4
Ignition of Ethylene Transverse Jet
In scramjet engines the hydrocarbon fuel may be partially cracked to C1 -C3 species
through its use as a coolant before reaching the combustor. It is anticipated that this
partially reacted fuel will burn as well as ethylene, namely with combustion properties
(such as ignition delay) approaching that of ethylene. We therefore studied the nearfield ignition characteristics of ethylene jet as it is a good simulant for hydrocarbons in
scramjets and the OH-PLIF results were summarized previously in Section 4.2.5.
Here, we calculated the ignition delay times for ethylene-air mixtures using two
different chemical reaction systems. Due to the large number of elementary reactions
4
H2-air
C2H4-air using GRI-mechanism
C2H4-air using LLNL-mechanism
C2H4-O2 using LLNL-mechanism
10
129
3
10
2
10
1
10
800
p=1atm, f=1
1000
1200
1400
1600
1800
2000
T(K)
FIGURE 6.9 Comparison of ignition delay of a stoichiometric mixture of C2 H4 (ethylene) and air/oxygen
at 1 atm with a stoichiometric mixture of H2 and air. Two different reaction mechanisms are
used to calculate the ignition delay times of C2 H4 .
involved in the ignition process of ethylene, a large number of data for reaction rates is
required. This makes the ignition delay times of ethylene fuel difficult to calculate. The
most comprehensive data is available in the GRI Mechanism 3.0 (Smith et al.). The
latest version of GRI-Mech was recently updated by Marinov et al. (1998) at LLNL
(Lawrence Livermore National Labs.). The calculated ignition delay times are plotted
in Fig. 6.9. Note that the LLNL chemical mechanism which is optimized for ignition
processes estimates longer ignition delay times than the GRI mechanism.
As shown in Fig. 6.9, longer ignition delay times are associated with the ethylene-air
mixtures compared to the values of hydrogen-air. Indeed, when we performed reacting experiments where ethylene fuel was injected into air simulating flight Mach 10
conditions, no ignition could be observed in the near-field of the transverse jet (see
Fig. 4.2.5b).
130
4
10
C2H4 - air for f=1
p=1 atm
p=2 atm
p=0.3 atm
3
10
C2H4 - air
C2H4 - O2
2
10
1
10
1000
1200
1400
1600
1800
2000
T(K)
FIGURE 6.10 a) Variation of ignition delay of a stoichiometric mixture of C2 H4 (ethylene) and air/oxygen
at various pressures.
Although, in our experiments the air composition, Mach number and static temperature corresponds to typical scramjet combustor entrance values, its static pressure
(0.32 atm) is somewhat below that of the actual systems (1.3 - 2.6 atm). This limitation
can be circumvented partially by using higher concentration of oxygen in the test gas. As
plotted in Fig. 6.10, the ignition delay times of a stoichiometric ethylene-oxygen mixture
at p = 0.3 atm are smaller than those for an ethylene-air mixture at similar conditions.
Indeed, in our experiments when ethylene was injected into pure oxygen crossflow (see
Fig. 4.2.5c), autoignition in the near-field of ethylene transverse jet could be achieved.
Eventough ethylene-oxygen delay times are smaller than the ones for ethylene-air, still
they are almost an order of magnitude larger than these for hydrogen-air. The reason
for ethylene autoignition in our experiments can be attributed to the longer residence
time of ethylene large-scale eddies which have slower convective velocities than the hydrogen ones. OH-radicals could be observed across the jet shear layer as opposed to
131
thin-filament observed around the hydrogen jet. The improved mixing properties of
high molecular weight transverse jets might be the primary reason for these results (see
more explanation in Chapters 4 and 5.
Note that ethylene has higher temperature or activation energies for ignition than
hydrogen. Hydrocarbons have effective activation energy for ignition in excess of 150200 kJ/mole compared with about 60 kJ/mole for hydrogen. While autoignition of ethylene fuel seems to require higher temperatures and pressures, hydrogen fuel combustion
is more challenging because of the lower reaction rates. From experiments presented in
this thesis, we therefore learned that autoignition of an ethylene transverse jet could be
achieved at flight Mach 10 conditions. This result indicates that hydrocarbons might
be a useful fuel in scramjets flying at Mach 10 conditions. This is an important result
as the long ignition delay time of ethylene (hydrocarbons) relative to hydrogen is a key
limitation for hydrocarbon-fueled scramjets. However, once ignition in hydrocarbon fuels is achieved, the combustion process would be completed faster than the hydrogen
fueled scramjet.
Chapter 7
Cavity Flame-Holders
This chapter describes ongoing research efforts in the scramjet community, in general, as well as our preliminary study on cavity flame-holders, a concept for flame-holding
and stabilization in supersonic combustors.
During the last few years, cavities have gained the attention of the scramjet community as a promising flame-holding device, owing to results obtained in flight tests and
to feasibility demonstrations in laboratory scale supersonic combustors. However, comprehensive studies are needed to determine the optimal configuration which will yield
the most effective flame-holding capability with minimum losses. In this chapter, we
summarize the flowfield characteristics of cavities and research efforts related to cavities
employed in low- and high-speed flows. Open questions impacting the effectiveness of
the cavities as flame-holders in supersonic combustors are discussed (Ben-Yakar and
Hanson 2001).
7.1
Review of Previous Research
7.1.1
Cavity Flow-Field Characteristics
Supersonic flow over cavities has been extensively studied (McMillin et al. 1994;
Roudakov et al. 1993; Vinagradov et al. 1995; Ortweth et al. 1996; Owens et al.
1998; Ben-Yakar et al. 998a; Angus et al. 1993; Roudakov et al. 1996; McClinton
et al. 1996; Huellmantel et al. 1957) for many years because of their relevance to
aerodynamic configurations. A cavity, exposed to a flow, experiences self-sustained
132
CHAPTER 7. CAVITY FLAME-HOLDERS
133
oscillations which can induce fluctuating pressures, densities and velocities in and around
the cavity, resulting in drag penalties. This problem motivated many experimental and
computational studies which have been directed toward improving the understanding
of the physics of cavity flows and the means to control their nature.
Cavity flow regimes: In general, cavities can be categorized into two basic flow
regimes depending primarily upon the length-to-depth ratio, L/D (see Fig. 7.1). In all
cases, a shear layer separates from the upstream lip and reattaches downstream. For
L/D < 7 − 10 the cavity is termed “open” as the upper shear layer reattaches to the
back face. The high pressure at the rear face as a result of the shear layer impingement,
increases the drag of the cavity. For L/D > 10 − 13 the cavity is termed “closed” as the
free shear layer reattaches to the lower wall resulting in significantly increased drag (see
Fig. 7.1b). The critical length-to-depth ratio, at which a transition between different
cavity flow regimes occurs, depends also on the boundary layer thickness at the leading
edge of the cavity, the flow Mach number and the cavity width.
Cavity oscillations: The cavity pressure fluctuations consist of both “broadband”
small amplitude pressure fluctuations typical of turbulent shear layers, as well as discrete
resonances whose frequency, amplitude, and harmonic properties depend upon the cavity
geometry and external flow conditions.
Experimental results reviewed by Zhang and Edwards (1990) found open cavities
to be dominated either by longitudinal or transverse pressure oscillations (Fig. 7.1a)
depending on L/D ratio and the Mach number (M∞ ). In the short cavity filled by a
single large vortex, the oscillation is controlled by a transverse mechanism, while in the
long cavity filled by vortices, the oscillation is controlled by a longitudinal mechanism.
The transition from transverse oscillation to longitudinal oscillation has been found to
occur near L/D = 2 at Mach 1.5 and between L/D =2 to 3 at Mach 2.5.
There are currently two primary models used to explain the longitudinal cavity
oscillation process (Fig. 7.2). The unsteady motion of the shear layer above the cavity
is the paramount mechanism for cavity oscillations and results in mass addition and
removal at the cavity trailing edge (rear wall). The shear layer impinging on the rear wall
causes free-stream flow to enter the cavity. As a result of the impingement, the cavity
pressure increases and creates an acoustic wave (compression wave) which propagates
upstream at the local sound speed and impacts the front wall. The first model proposes
that this acoustic wave induces small vortices at the leading edge of the front wall which
(a)
134
OPEN CAVITY FLOW (L/D < 7-10)
Transverse
Mechanism
transition at
L/D ~ 2-3
Longitudinal
Mechanism
D
Cp
L
(b)
0
CLOSED CAVITY FLOW (L/D > 10-13)
Cp
0
FIGURE 7.1 Flow-field schematics of cavities with different length to depth ratios, L/D, in a supersonic
flow. a) Open cavity flow for L/D < 7 − 10; shear layer reattaches to the back face while
spanning over the cavity. Small aspect ratio cavities (L/D < 2−3) are controlled by transverse
oscillation mechanism while in larger aspect ratio cavities longitudinal oscillation becomes the
dominant mechanism. b) Closed cavity flow for L/D > 10 − 13; shear layer reattaches to the
lower wall. The pressure increase in the back wall vicinity and the pressure decrease in the
front wall results in large drag losses.
grow as they are convected downstream. Due to instabilities, the shear layer deflects
upwards and downwards resulting in a shock/impingement event on the rear wall of the
cavity. The second model, on the other hand, assumes that the acoustic wave reflection
from the front wall, rather than the shedding vortices, is the cause of the shear layer
deflection and therefore the impingement event on the rear wall. The oscillation loop
is closed when the instability (caused either by vortex shedding or a reflected acoustic
wave) propagates downstream and the mass added in the beginning of the loop is ejected
at the trailing edge again.
Typically, the frequency of the longitudinal oscillations is expressed in terms of the
135
Shear layer impingement
at the rear wall
Shedding vortices and
reflected acoustic waves
FIGURE 7.2 Typical longitudinal cavity oscillations are caused by the impingement of the free shear layer
on the rear wall which generates travelling shocks inside the cavity. The shear layer spanning
the cavity becomes unsteady as a result of these acoustic waves deflecting the shear layer up
and down, and/or by the shock induced vortices generated at the front wall leading edge of
the cavity. As a result unsteady waves emanate from the cavity.
Strouhal number based on the cavity length (impingement length, L).
SL =
fm L
U∞
(7.1)
Multiple peaks of comparable strength in unsteady pressure spectra were observed in
compressible flow-induced cavity oscillations. These resonant frequencies can be predicted using the Rossiter’s semi-empirical formula (Rossiter 1964), developed based on
the coupling between the acoustic radiation and the vortex shedding (model 1),
fm =
m − α U∞
·
M∞ + k1 L
(7.2)
M∞ and U∞ are the free-stream Mach number and flow speed, respectively; fm is the
resonant frequency corresponding to the mth mode, and a and k are empirical constants.
While k represents the ratio of the speed of the convection of the shear layer vortices
to the free-stream flow speed (U∞ ), α is the phase shift between the acoustic waves
and the shear layer instability. This equation is modified by Heller and Bliss (1975) for
136
compressible flows by taking into account the effect of the higher sound speed within the
cavity, which is approximately equal to the free-stream stagnation sound speed. Their
model assumes that the pressure fluctuations are a result of the interaction of the shear
layer with the reflected acoustic waves (model 2),
fm =
m−α
p
M∞
2
1+ γ∞2−1 M∞
+
1
k
·
U∞
L
(7.3)
where γ∞ is the ratio of specific heats. Heller and Delfs (1996) determined from their
experiments that a = 0.25, k = 0.57 for cavities with L/D ratio of 4 or more and
estimated the difference between the formula and experiments as ±10%.
Therefore, the oscillatory frequency of a particular mode in a shallow cavity decreases
with increasing length or L/D ratio of the cavity. However, the dominant oscillatory
mode (the mode with the largest amplitude) jumps from a lower mode to a higher mode
as the L/D ratio increases.
Stabilization techniques for cavity oscillations: Several passive (Perng and
Dolling 1998; Zhang et al. 1998) and active (Sarno and Franke 1994; Vakili and Gauthier
1994; Lamp and Chokani 1997) control methods have been proposed and developed to
suppress the cavity oscillations (Fig. 7.3). Since the shear layer interaction with the
rear cavity wall is the main factor for fluctuations as discussed above, the stabilization
or control of the shear layer can ultimately suppress the cavity oscillations. Passive
control methods, which are usually inexpensive and simple, utilize mounted devices
such as vortex generators and spoilers upstream of the cavity or a slanted trailing edge
that modifies the shear layer so that the reattachment process does not reflect pressure
waves into the cavity. These methods are found to be very effective in suppressing the
cavity oscillations. However, since those are permanent devices, the performance of a
cavity at different conditions may actually be worse than the performance of a cavity
without passive control.
A visual observation of a cavity flow-field stabilized by an oblique rear wall is shown
in Fig. 7.4. This figure contains two instantaneous schlieren images from our recent
experimental efforts demonstrating the stabilizing effect of a slanted back wall upon
the shear-layer reattachment with the back wall. While the cavity with a 90o back
wall (Fig. 7.4a) emits shock waves at the trailing edge as the pressure increases due to
shear layer impingement and recompression of the flow, the angled back wall shown in
137
Reduced
Cavity Oscillations
(a)
q
Angled Back Wall
(No Reflected Acoustic Waves)
(b)
Small Upstream
Disturbances
Enhanced
Shear Layer Growth
Injection
q
FIGURE 7.3 Different concepts can be employed to suppress the cavity oscillations: a) Cavities with an
angled back wall suppress the unsteady nature of the free shear layer by eliminating the generation of the travelling shocks inside the cavity due to the free-shear-layer impingement. b) In
addition, small disturbances produced by spoilers or by the secondary jet injection upstream of
the cavity can enhance the free-shear-layer growth rate. The thickening of the cavity shear layer
alters its instability characteristics, such that its preferred roll-up frequency is shifted outside
of the natural frequency of the cavity, and as a result the oscillations are attenuated.
Fig. 7.4b leads to a steady shear-layer reattachment process.
Active control methods, on the other hand, can continuously change to adapt to
different flow conditions. Forcing of the shear layer can be accomplished by various
mechanical, acoustical or fluid injection methods. The use of steady or pulsating mass
injection upstream or at the leading edge of the cavity is one of the most commonly
studied techniques. Various researchers (Sarno and Franke 1994; Vakili and Gauthier
1994; Lamp and Chokani 1997) have examined the feasibility of this technique. Vakili
and Gauthier (1994) observed significant attenuation of cavity oscillations with upstream mass injection. This was attributed to the thickening of the cavity shear layer,
which altered its instability characteristics, such that its preferred roll-up frequency was
shifted outside of the natural frequencies of the cavity.
Cavity Drag: Two components produce pressure drag in the cavity. First, the
pressure in the backward facing step may be lower than the free stream pressure. This
(a)
138
Reflected Acoustic Waves
M>1
M=3.5
Shear Layer
Trailing Edge Vortex
D=3mm
Cp
L = 15 mm
0
Front
Wall
(b)
Floor
Back
Wall
Recirculation Zone
Ob
D=3mm
20°
9 mm
L = 17.2 mm
Cp
liq
ue
ock
Sh
ve
Wa
0
Front
Wall
Floor
Back
Wall
FIGURE 7.4 Instantaneous schlieren images with 200 ns of exposure time demonstrating the effect of the
back wall angle on the flowfield structure of a cavity exposed to a supersonic flow. The freestream was generated in an expansion tube to simulate Mach 10 total enthalpy conditions at
the supersonic combustor entry: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa.
The boundary layer thickness at the trailing edge of the cavity is approximately 1mm. a) Cavity
with L/D = 5 shows the unsteady nature of the shear layer at the reattachment with the
trailing edge of the back wall. b) Cavity with slanted back wall (20o ) stabilizes the shear layer
reattachment process.
results in a net force in the positive x-direction (drag force) acting on the base area
(base pressure higher than freestream would result in a thrust force). Second, the
reattachment of the shear layer at the back wall produces a region of high pressure that
imparts a force in the positive x-direction acting on the forward facing area.
In Fig. 7.5, the magnitude of pressure fluctuations on the floor of the cavity and
the drag coefficient for different L/D are given, as adapted from Zhang and Edwards
(1990). Their experimental results demonstrate a sharp rise of the oscillatory level and
the drag when the oscillatory mode inside the cavity changes from a transverse mode
to a longitudinal one. The magnitude of the fluctuations decreases gradually with the
(a)
139
0.10
M=1.5
M=2.5
Prms / (rU2/2)
0.08
0.06
0.04
0.02
0.00
0
1
2
3
4
5
6
7
8
9
10
6
7
8
9
10
L/D
(b)
0.20
M=1.5
M=2.5
Cavity Drag
0.16
Transverse
Mode
0.12
Longitudinal
Mode
0.08
0.04
0.00
0
1
2
3
4
5
L/D
FIGURE 7.5 Effect of length-to-depth ratio, L/D on a) magnitude (root-mean-square) of pressure fluctuations on the bottom of the cavity (at x/D = 0.33), b) drag of the cavity at Mach 1.5 and 2.5
flows. The values were adapted from Zhang and Edwards (1990).
increasing L/D of the cavity, while the average drag coefficient, however, rises significantly. As the L/D of the cavity increases, the shear layer thickens at the reattachment
point damping the oscillations and simultaneously increasing the pressure on the back
wall of the cavity. Subsequently, the time-mean pressure on the upstream wall of the
cavity drops as a result of the momentum diffusion across the shear layer. These combined effects of increasing pressure in the back wall of the cavity and decreasing pressure
in the upstream wall of the cavity, increase the drag of the cavity. The drag penalties
become larger as the cavity L/D ratio reaches a critical value at which the closed cavity
flowfield is established.
The drag coefficient of an open cavity is affected greatly by the cavity back wall
140
geometry. Gruber et al. (999a) studied the drag penalties of open cavities with θ = 16o
and 30o angled back wall, where θ is defined as the angle relative to the horizontal wall
(see Fig. 7.3). They concluded that the drag coefficient increases for shallower back wall
angles. First, the small back wall angles lead to the formation of an expansion wave
(rather than a compression wave) at the cavity leading edge that reduces the pressure
on the backward facing step adding drag. Second, the shear layer deflects farther into
the cavity which results in a larger area of recompression on the angled back wall, again
increasing the drag.
In contrast to Gruber et al. (999a) findings, numerical calculations of Zhang et al.
(1998) resulted in a reduced average drag coefficient as the back wall angle is decreased
from θ = 90o to θ = 67.5o and 45o . The observations from these two references agree,
however, that the pressure on the upstream face of the cavity decreases with decreasing
back wall angle. It is possible that in the 67.5o and 45o cases studied by Zhang et al.
(1998), the compressive nature of the separation wave at the upstream corner of the
cavity actually keeps the shear layer from deflecting into the cavity and could result in
lower levels of pressure drag than the 16o case that Gruber et al. (999a) studied. In
a different study, Samimy et al. (1986) used a cavity with a 20o of back wall angle to
create an undisturbed free shear layer. This geometry was chosen such that the wall
pressure across the cavity would stay unchanged, thereby minimizing the drag losses
associated with the shear layer deflection inside the cavity. These observations suggest
that there might be a critical back wall angle (between θ = 45o to 16o ) at which the
drag penalties of a cavity are minimal.
A qualitative description of the pressure distribution along the back wall surface of
cavities with and without an angled wall is plotted in Fig. 7.4. In a rectangular cavity,
below the shear layer reattachment point, the trailing edge vortex accelerates the flow
and causes a pressure decrease in the middle of the back wall. On the other hand, in
the cavity with the angled wall, the high pressure at the corner of the cavity disappears
and a monotonic increase of pressure takes place behind the reattachment point. The
drag coefficient depends strongly on the back wall pressure distribution as it is altered
by the cavity geometry. Further comprehensive studies are required to complete our
understanding of cavity geometry, particularly the effect of the back wall angle on the
drag penalty.
Cavity Residence Time: Residence time, τ , of the flow inside a cavity is a direct
141
function of the mass exchange rate in and out of the cavity. In the open cavities, mass
and momentum transfer mechanism are controlled by the longitudinal oscillations and
the vortex structure inside the cavity. Computational visualizations of Gruber et al.
(999a) demonstrate the existence of one large vortex stationed near the trailing edge of
the cavity and a secondary vortex near the upstream wall. The mass exchange of the
cavity is controlled by the large trailing vortex which interacts with the unstable shear
layer. The mass exchange between the vortices inside the cavity, on the other hand,
is relatively small, and therefore as the trailing edge vortex occupies larger volume
inside the cavity, the mass exchange increases and flow residence time inside the cavity
decreases. Consequently, the steady-state numerical calculations showed that the flow
residence time in a large cavity (L/D = 5) is smaller than the value in a small cavity
(L/D = 3), in contrast with expectation. Although the volume of the cavity increases
(increases τ ) with increasing length, the mass exchange rate, on the other hand, increases
even more (decreases τ ), resulting in a decreased residence time. However, it is not yet
clear how the flow residence time inside a cavity is affected by the unsteady nature of the
cavity. The steady state computations (Gruber et al. 999a) mentioned above, estimated
that 1 msec is the order of magnitude of residence time in an L/D = 5 cavity with 9
mm depth size in a Mach 3 cold flow. This value decreases for slanted wall cavities.
As summarized above, the cavity is a basic fluid dynamic configuration which generates both fundamental and practical interest. A cavity is often characterized by a
strong oscillation inside the cavity driven by the instability of the shear layer. Hence,
these oscillations may be controlled and suppressed by the stabilization of the shear
layer.
7.1.2
Cavity in Reacting Flows
In the past few years, the use of cavities has been considered as a means of performance improvement in a supersonic combustor. Basically there are two main directions
in which several research groups have focused their efforts: 1) cavity-actuated mixing
enhancement, 2) trapping a vortex within the cavity for flame-holding and stabilization
of supersonic combustion. Some recently performed studies, investigating the above
concepts are summarized in the following sections.
142
Cavity-Actuated Supersonic Mixing Enhancement
It is known that the normalized growth rate of the mixing layer between supersonic
air and gaseous fuel in a scramjet combustor decreases as the convective Mach number
increases due to compressibility effects (Papamoschou and Roshko 1988). Researchers
suggested that cavity flow oscillations can actually be used to provide enhanced mixing in supersonic shear layers. A shear layer develops instability waves in its initial
region. This long wavelength Kelvin-Helmholtz instability which leads to large “rollers”
are suppressed at high convective Mach numbers. As a method to enhance the K-H
instability, Kumar et al. (1989) suggested using oblique oscillating shock waves of high
frequency, and Yu and Schadow (1994) concluded that for the required frequency excitation, transverse acoustic waves emanating from cavities are powerful enough to affect
mixing in a significant manner.
Yu and Schadow (1994), therefore, suggested use of cavities to enhance the mixing
of supersonic non-reacting and reacting jets, where the cavity was attached at the exit
of the jet circular nozzle, Fig. 7.6b. When the cavity was tuned for certain frequencies,
large scale highly coherent structures were produced in the shear layer substantially
increasing the growth rate. The spreading rate of the initial shear layer with convective
Mach number Mc = 0.85 increased by a factor of three, and for jets with Mc = 1.4
by 50%. Finally, when the cavity-actuated forcing was applied to reacting supersonic
jets, 20 − 30% reduction in the afterburning flame length with modified intensity was
observed.
Sato et al. (1999) also studied the effect of an acoustic wave, emitted from a cavity
and impinging on the initial mixing layer, Fig. 7.6a. Their results revealed that the
mixing was enhanced by the acoustic disturbance and the rate of the enhancement was
controlled by the cavity shape while the total pressure losses were negligibly small.
This novel use of cavity-induced oscillations in turbulent compressible shear layers to
control the mixing rate, which have been demonstrated in the experiments mentioned
above, encourages the use of unstable cavities in high speed propulsion applications.
However, before implementing such techniques, one must consider and evaluate the
potential thrust loss and noise generation associated with the technique.
(a)
143
CAVITY
acoustic wave
M>1
mixing layer
fuel injection
(b)
SUPERSONIC
NOZZLE
initial mixing layer
supersonic jet
CAVITY
cavity actuated
mixing layer
FIGURE 7.6 Cavity-actuated supersonic mixing enhancement concepts: (a) Sato et al. (1999), studied the
influence of acoustic waves, emitted from a cavity and impinging on the initial mixing layer.
(b) Yu and Schadow (1994) used the same concept to enhance the mixing of supersonic reacting
jets.
Cavity as a Flame-Holder
While an unstable cavity can provide enhancement in the turbulent mixing and combustion as discussed above, a stable cavity can be used for flame-holding applications.
In an effort to reduce the combustor length required for efficient high speed combustion,
during the past few years, the scramjet community has proposed the use of wall cavities
to stabilize and enhance supersonic combustion. The main idea is to create a recirculation region inside the cavity with a hot pool of radicals which will reduce the induction
time, such that autoignition of the fuel/air mixture can be obtained. However, for a
stable combustion process, the cavity recirculation region has to be sufficiently stable
to provide a continuous ignition source (pilot flame). As discussed above, it is possible
to control the self-sustained oscillations occurring in cavities either by proper design of
144
the cavity or by a passive/active control system.
In the following sections, we will first discuss the literature for low-speed and then
the recent advances in high-speed combustors which utilize cavity flame-holders.
Cavity TV - “Trapped Vortex” concept in low-speed flows: Recently, cavities
have been employed in low-speed flows to stabilize combustion utilizing the so-called
“trapped-vortex” concept (Hsu et al. 1998). In this concept, a stationary vortex is
established or “trapped” inside the cavity by optimal design of the dimensions, namely,
by optimal cavity length to depth ratio (L/D). It is known that a vortex will be trapped
in the cavity when the stagnation point is located at the downstream end of the cavity
which also corresponds to the minimum drag configuration (Heller et al. 1970). Based
on this evidence, Hsu et al. (1998) designed an experimental cavity to investigate the
low-speed flame stability characteristics of a trapped-vortex combustor, while Katta
and Roquemore (998a, 998b) performed numerical calculations for this geometry. Their
results showed that a vortex is locked in a short cavity (L/D < 1).
However, when a vortex is trapped in the cavity, very little fluid is entrained into the
cavity, resulting in very little exchange of the main flow and cavity fluid. When flame
stabilization is a consideration, a continuous exchange of mass and heat between the
cavity and the main flow is required. To overcome this problem, it has been suggested
to directly inject both fuel and air into the cavity in a manner that reinforces the vortex
and increases mass transfer of the reactive gases with the freestream.
The main conclusions revealed from low-speed cavity flame-holder studies can be
summarized as follows:
1. In non-reacting flows, a stable cavity flow was observed at an optimal dimension
(L/D = 0.6) that produces minimum drag, namely, minimum pressure drop. This
was also the optimal cavity length which provided the most stable flame.
2. A sufficient amount of fuel and air must be injected directly into the cavity to
obtain good performance characteristics of a combustor with a trapped-vortex
cavity.
3. The fluid injection inside the cavity had a strong impact on the stability of the
vortex inside the cavity. When jets were injected in such a way that they reinforced
the vortex, the flame stabilization capability of the cavity was enhanced.
145
4. The optimum size (L/D) for steady flow should be larger in the case of cavities
with fluid injection than for cavities with no injection.
Cavity flame-holders in high-speed flows: In the scramjet community, there
is a growing interest in the use of cavity flame-holders. In a 1997 Air Force/NASA
workshop (Tishkoff et al. 1997), an integrated fuel injector/cavity flame-holder was
mentioned as one of the new concepts that may provide potential performance gain in
a scramjet engine. It was indeed very encouraging to see this new concept employed
and flight-tested in the scramjet engine by the Central Institute of Aviation Motors
in Moscow (Roudakov et al. 1993; Vinagradov et al. 1995; Ortweth et al. 1996;
Owens et al. 1998; Roudakov et al. 1996; McClinton et al. 1996). The combustor of
the axisymmetric scramjet engine, illustrated in Fig. 7.7, included three fuel injection
stages, two with cavity flame-holders (D = 20 mm by L = 40 mm and D = 30 mm by
L = 53 mm) and one with a step flame-holder (D = 17 mm). The injection of the fuel
(hydrogen) was performed within the cavity flame-holders from the front-facing wall at
30o to the engine axis and just upstream of the step at 45o . With this integrated injection/cavity flame-holder approach, numerical studies (McClinton et al. 1996) showed
that autoignition and flame-holding within the cavity could be obtained at Mach 6.5
flight, even without the spark ignition plugs. Their analysis also revealed that without
the cavity, the ignition is unlikely due to the small injector dimension (dj = 1.25−2 mm)
and low combustor operation pressure (p ≈ 0.4 atm) as estimated previously by Huber
et al. (1979). Finally, the joint Russian / U.S. effort demonstrated in the flight test
performed on February 12, 1998 that a positive thrust from the scramjet engine could
be successfully achieved.
One can find several recent studies investigating cavities for flame stabilization of a
supersonic combustor. Some of these works, performed for different kinds of fuels (solid,
liquid and gaseous fuels), are summarized as follows.
The combustion of kerosene in a scramjet requires additional ignition and flameholding elements because of the long ignition times and reduced reaction rates as compared to hydrogen. Owens et al. (1998) tried to determine the flame stability of kerosene
injected upstream of a cavity flame-holder with Mach 1.8 free-stream conditions. Due
to the low stagnation temperatures of 1000 K, ignition was provided by pilot hydrogen
fuel injected into the cavity. Flame-holding could be achieved only when large flow rates
71
175
248
Injector
Injector
30° Cavity 1
20 x 40
30
146
274
Step
Injector
Cavity 2
30°
30 x 53
68
FIGURE 7.7 Axisymmetric combustor of the Scramjet engine which was flight-tested by RussianCIAM/NASA joint program (1998). In this engine two cavities with angled-rear wall were
used for flame-holding purposes. The dimensions are in mm (McClinton et al. 1996).
of hydrogen were used. In this case the enlargement of the recirculation region led to
entrainment of additional quantities of fresh air contributing to the flame stability. An
additional investigation of scramjet combustors operating on kerosene was performed by
CIAM (Vinagradov et al. 1995). In their configuration, the combustion was sustained
by a row of hydrogen fuel injectors placed in front of a cavity.
The use of cavities as flame-holders in solid fuel supersonic combustors has been also
studied (Ben-Yakar et al. 998a; Angus et al. 1993). In the experiments of Ben-Yakar
et al. (998a), self-ignition and sustained combustion of PMMA (Plexiglas) solid fuel with
no external aid (such as reactive gas injection or a pilot flame) was demonstrated under
supersonic hot-air flow conditions. This was accomplished by a recirculation region
formed inside a cavity which was positioned at the entrance of the combustor. Typically,
in a subsonic solid fuel ramjet, a step is used for flame-holding purposes, and it is
known that larger step heights (leading to bigger recirculation zones) can provide better
flame stabilization. However, in supersonic flows where a large step is required, the
free-stream flow velocity would increase as well by the sudden expansion, deteriorating
the flame-holding capability. Under those considerations, a cavity consisting of a step
followed by an angled wall was chosen as a flame-holder in the supersonic solid fuel
experiments mentioned above. The results revealed that both the cavity length (L) and
the step height (D) have significant effect in sustaining the combustion. While short L
caused flameout even for relatively large D, the inverse, namely small D, did not permit
sustained combustion even though L was quite long. Ultimately, cavity length-to-depth
ratio between 1.7 < L/D < 2 showed a regime of sustained combustion.
Besides the use of cavities in liquid and solid fueled supersonic combustors, there are
147
other research groups (Yu et al. 1998; Yu et al. 1999; Niioka et al. 1995; Mathur et al.
1999; Davis and Bowersox 997a; Davis and Bowersox 997b) concentrating on characterization of cavity flame-holders in gaseous supersonic combustors. Initial experimental
efforts were performed by Yu et al. (1998, 1999). They analyzed flow stability and
flame-holding characteristics of several wall cavities with various sizes and aspect ratios
(L/D = 0.5, 1, 2, 3 and inclined cavity) in a Mach 2 air-stream. Pressure oscillations,
observed in cold flow experiments, were diminished in reacting flow, when the thin shear
layer above the cavity disappeared by three fuel jets injected at 45o upstream of the
cavity. Typically, small aspect ratio (1 < L/D < 3) cavities appeared to be good flameholders, which is consistent with the “trapped vortex” concept discussed above. The
narrow cavities (L/D = 0.5) provided very steady flame-holding, however they had relatively little effect on the downstream emission characteristics. With the inclined cavity,
which was also the longest cavity tested (L/D = 5), no flame-holding was observed.
Additional experiments were conducted by Niioka et al. 1995 in Mach 1.5 airflow. They
achieved flame stabilization using two struts and by injecting hydrogen gas in the interval between the two parts. They showed that flame stability could be controlled by
the cavity length which controls the competition between the mass transfer rate and
the chemical reaction rate, i.e., the Damköhler number.
Wright-Patterson Air Force Research Laboratories have also initiated a program
(Mathur et al. 1999; Davis and Bowersox 997a; Davis and Bowersox 997b) to examine
the effectiveness of cavities in supersonic flows. Experiments on a cavity with upstream
ethylene fuel injection were performed in the supersonic combustor facility operating at
conditions that simulate flight Mach numbers between 4 and 6. Initial results demonstrate flame-holding and large flame spreading in the cavity vicinity. In parallel, Mach 3
cold flow research is also in-progress to study the fundamental aspects of cavities. The
results showed that:
1. The cavity geometry had an effect on mass entrainment rate and residence times.
A decrease in cavity residence time was observed in cavities with longer length
and slanted walls.
2. In general, the length of the cavity determined the mass entrainment, while the
cavity depth determined the cavity residence time.
148
3. Larger cavities (L/D = 7) had significantly higher drag coefficients than the
smaller cavities (L/D = 3). Reduction of the back wall angle below 90o resulted
in additional drag penalties.
4. Cavities with offset ratios larger than 1 (upstream wall height is larger than the
back wall height) caused the cavity base to experience lower pressures and therefore larger drag penalties.
In addition, Davis and Bowersox (997a, 997b) used a combined CFD/perfectly
stirred reactor methodology as a design guide for sizing of the cavity. He recommends that initial cavity size can be estimated based on the minimum residence time
required to obtain ignition by assuming a perfectly stirred reactor cavity flow. Similar
to Gruber et al. (999a), he concluded that cavity depth, D, which mainly controls
the residence time, can be estimated using their numerically obtained empirical equation: D = τr · U/40, where τr is the required residence time for ignition and U is the
free-stream velocity.
7.1.3
Outstanding Questions
As discussed above, during the last few years, cavities have gained attention as
promising flame-holding devices. However, comprehensive studies still need to be performed to determine optimal configurations which yield the most effective flame-holding
capability with minimum losses.
We can pose the following questions concerning the effectiveness of the cavities as
stable flame-holders in supersonic combustors:
1. Can the TV concept be used in supersonic combustors? Several investigators have recognized the aerodynamic advantages of trapping vortices inside small
aspect ratio cavities (L/D < 1) both as a means of reducing the drag penalties of
cavities and also obtaining stable flame-holding in a low-speed combustor. Stable
small aspect ratio cavities may possibly be adapted to provide sustained combustion in supersonic flows. However, the cavity flow residence time associated with
high-speed flows will be smaller than in low-speed flows and might eliminate its
flame-holding capability. Therefore, stable cavities may possibly be adapted to
149
provide sustained combustion in supersonic flows as long as the Damköhler number is larger than unity (namely, the residence time inside the cavity is sufficient
to initiate the ignition process). For example in the flight tested scramjet engine,
designed by CIAM and NASA, fuel was injected within the cavity flame-holder
to provide autoignition and flame-holding (McClinton et al. 1996). Otherwise,
autoignition was unlikely due to the low total enthalpies of the Mach 6 flight
condition, and small injector dimensions and the low combustor pressures of the
design point.
2. What are the cavity dimensions and its geometry? Open cavities with
L/D < 7 − 10 are good candidates for flame-holding owing to their reduced drag
coefficients relative to the closed cavities. The dimensions of an open cavity have
to be derived from ignition and flame-holding considerations. The cavity depth
can be determined according to the required residence time to initiate ignition.
The cavity length, on the other hand, has to be chosen to provide sufficient volume
of radicals to sustain the combustion further downstream.
3. Can an unstable cavity be used to establish flame-holding?
While a
stable cavity is preferable to sustain continuous and stable combustion, an unstable
cavity can be used to enhance mixing and ignition by the shock waves emitted as
a result of strong cavity oscillations. However, unstable cavities are unlikely to
provide a continuous flame-holding region inside the cavity as will also be shown
in our preliminary ignition experiments (see Section 7.2).
4. How does fuel injection affect the cavity flow-field? Jet injection upstream
or inside the cavity can alter the shear layer specifications (its thickness and stability) directly, and therefore, the cavity performance. Raman et al. (1999), for
example, have found that jet interaction with a cavity can produce different oscillation frequencies.
5. How does the cavity flow-field affect a fuel jet injected upstream? Shock
waves emanating from a cavity can enhance the mixing of fuel jets injected upstream of the cavity. As shown by several researchers, the acoustic waves of an
unstable cavity can be used to enhance mixing. On the other hand, a stable cavity can also enhance mixing. As the jet reaches to the back wall it interacts with
150
the strong trailing edge shock wave of the cavity. It is known that an obliqueshock-wave-jet interaction enhances the molecular mixing between supersonic air
and gaseous fuel by the vorticity generated due to the baroclinic torque. This
might have immediate significance to the spreading rate of the jet and mixing
enhancement of the fuel-air, resulting in enhanced combustion efficiency.
6. Is local wall heating inside the cavity a problem? High total temperatures
of air stagnating inside the cavity can result in excessive heat transfer to the walls.
However, the transpiration technique of mass addition from a porous surface can
be used as a way to cool the cavity surfaces. This method can, furthermore,
decrease the skin friction losses on the cavity floor surface and reduce the drag
losses associated with the shock wave structure of the cavity (Castiglone et al.
1997). Fuel mass bleeding inside the cavity can alter the shear layer bending
towards the cavity by increasing the cavity pressure distribution. In this way,
the strong trailing edge reattachment shock wave can be eliminated or reduced
in strength. Therefore, an optimized transpiration cooled cavity may also be
designed to improve the pressure losses and the drag penalties.
7. At which flight conditions can a cavity flame-holder be effective? At
high flight Mach numbers, beyond Mach 8, the velocity and the total enthalpy of
air entering the combustor is high. In this hypersonic flight regime, hydrogen fuel
is preferred owing to its reduced combustion characteristic times. Ignition of the
hydrogen-air system can be purely characterized by radical runaway without the
need for thermal feedback (substantiated by direct numerical analysis of Im et al.
(1998)). Therefore, for a hydrogen-air system, a cavity flame-holder, in which
the high-stagnation temperatures will initiate ignition by radical runaway, can be
designed even though no appreciable heat has yet been released. As we move into
lower flight speeds, below Mach 8, application of a flame-holder becomes crucial.
In this supersonic flight regime, the selection of a cavity flame-holder is required
to achieve longer flow residence times inside the cavity because of the reduced
total enthalpies and longer ignition delay times associated with hydrocarbon fuels,
which are the candidate fuels for supersonic flight below Mach 8. Consequently,
cavities can be utilized in a wide range of flow conditions, in both supersonic and
hypersonic airbreathing propulsion systems.
151
x/D=1.5
L/D=3
x/D=0.5
P
P
L/D=5
cavity pressure
transducers
FIGURE 7.8 Position of pressure transducers located at the bottom of the cavity to measure the history
of the flow oscillations inside the cavity. Pressure transducer located farther downstream at
x/D = 1.5 provided a more accurate oscillation frequency measurements.
7.2
Preliminary Cavity Results
Here, we will summarize our preliminary results, where the primary objective is to
demonstrate the feasibility of the experimental set-up to provide information for cavity
flame-holder studies. These appear to be the first cavity experiments performed in such
high total enthalpy flows.
The pressure is measured within the cavity to monitor the time dependent acoustic
field. The fast response pressure measurements are performed at 1.5 D downstream the
forward face of the cavity as illustrated in Fig. 7.8. Established cavity oscillations are
observed and a sequence of oscillation cycles could be captured during the limited test
time (∼ 300 µs) of the flow facility.
Figure 7.9 shows examples of the cavity pressure development at x/D = 1.5 during a
typical expansion tube run. These pressure traces are obtained for 4 different geometries:
a) L/D = 3, b) L/D = 5, c) L/D = 5 with hydrogen injection upstream of the cavity
and d) L/D = 7. After the arrival of incident shock wave, different flow regimes exist
including: a time during which helium is flowing; a period during which the contact
region is passing; and a window in which there is a steady flow of test gas before the
arrival of rarefaction waves. These flow periods can clearly be visualized in cavity
pressure measurements where the pressure rises by the arrival of contact surface. After
(a)
152
1.0
Test Gas
Pcavity, AU
L/D = 3
0.5
0.0
~18ms
-0.5
0
200
400
600
800
1000
800
1000
t, msec
(b)
1.0
L/D = 5
Pcavity, AU
Test Gas
0.5
0.0
~38ms
-0.5
0
200
400
600
t, msec
(c)
1.0
Test Gas
L/D = 5 with
o
Pcavity, AU
30 injection
~38ms
0.5
0.0
-0.5
0
200
400
600
800
1000
800
1000
t, msec
(d)
1.0
Test Gas
Pcavity, AU
L/D = 7
0.5
0.0
~53ms
-0.5
0
200
400
600
t, msec
FIGURE 7.9 Examples of cavity pressure traces in arbitrary units: a) L/D = 3, b) L/D = 5, c) L/D = 5
with upstream hydrogen injection, d) L/D = 7. t = 0 represents incident shock arrival at the
cavity. The free-stream (N2 ) conditions represent Mach 10 total enthalpy at the supersonic
combustor entry: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa.
153
TABLE 7.1 Summary of cavity oscillation frequencies, fm , for different cavity length to depth ratios, L/D.
The table includes the expected values based on Rossiter’s formula and the ones measured in
our experiments.
L/D
Rossiter’s formula
fm , kHz Tm , µs
Present data
Tm , µs
Difference
%
3
52.2
19.2
18 ± 1
-6.3 ± 5
5
31.3
31.9
37 ± 1
16.0 ± 4
7
22.4
44.7
53 ± 2
18.6 ± 2
a period of flow establishment time (about 200 µs), several cycles of distinct pressure
oscillations are observed during the steady flow test time.
The measured frequencies, averaged from several experiments, together with the
expected frequencies estimated from Rossiter’s empirical formula are summarized in
Table 7.1. A good agreement within 6 % could be achieved for the frequency measurement of L/D = 3. For larger L/D ratios, the agreement is weaker and the difference
between the measured and the expected frequencies reaches up to 20 %. This difference
might be due to the difference in total temperature (∼ 4000 K) of the flow tested in
our experiments. Note that the formula of Rossiter’s contains two empirical parameters
derived from cold flow experiments. However, before any conclusion can be made, we
have to analyze the flow-field dynamics of different cavity geometries in more detail.
These results show that 2-D cavities with the geometry chosen here (D = 3 mm,
L/D =3, 5, 7) can be studied in an expansion tube facility despite the limited test time.
However, a longer test time is required to achieve accurate values of the acoustic field
frequencies inside/around the cavity.
7.2.1
Visual Observation of Cavities Using Ultra-Fast Schlieren
Flows around two-dimensional cavities are investigated to show the effects of variations in length-to-depth ratio (L/D) of the cavity. For this purpose cavities with
L/D =3, 5 and 7 are tested. In addition, a 30 degrees angled rear wall was tested for
the cavities with L/D =3 and 5. All the cavities have the same depth of 3 mm. The
different length-to-depth ratios are formed by removable back wall inserts.
Figure 7.10 summarizes examples of instantaneous schlieren images (200 ns exposure
154
time) obtained for cavities with L/D = 3, 5, and 7 that we have tested. In all cases,
the boundary layer separates from the upstream lip and reattaches downstream.
As the boundary layer separates from the leading edge of the cavity, a free shear layer
forms. Depending upon the pressure inside the cavity the shear layer deflects upwards
or downwards producing a compression or an expansion wave consequently. For the
cavity with L/D = 3 (Fig. 7.10a) a compression wave appears at the leading edge of
the cavity. As the cavity length is increased to L/D = 5 (Fig. 7.10b) this compression
wave weakens. Eventually, for the cavity with L/D = 7 (Fig. 7.10c), it diminishes and
an expansion wave at the leading edge takes place instead of the compression wave.
The strongest shock wave appears from the trailing edge of the cavities which is consistent with the numerical observations of Zhang et al. (1998). The shear layer deflects
downward near the trailing edge of the cavity and creates a high pressure stagnation
point on the downstream face (the dark regions as can be seen in schlieren images in
Figs. 7.10a and 7.10b). While this strong shock wave seems to be attached to the trailing edge of the cavities with L/D = 3 and 5, it moves upstream off the back wall for
the cavity with L/D = 7.
There are generally two basic flow regimes that a cavity can yield depending upon
the length-to-depth ratio, L/D (see Fig. 7.1). A cavity is termed “open” if the shear
layer reattaches to the back face while the drag of the cavity is small (Fig. 7.1a). Beyond
some critical L/D ratio, the cavity is termed “closed” as the free shear layer reattaches
to the lower wall resulting in significantly increased drag. Based upon this description,
in our experiments cavities with L/D = 3 and 5 demonstrate “open” cavity flow-field
features, while a cavity with L/D = 7 seems to be in the transition regime between
“open” and “closed” cavity.
These results are also consistent with the numerical calculations of Baurle and Gruber (1998). Their results showed that larger cavities (L/D = 7) have significantly higher
drag coefficients than the smaller cavities (L/D = 3).
Figures 7.10d and 7.10e demonstrate instantaneous flow-field structure of cavities
with a back wall angled at 30 degrees. These schlieren images reveal that the leading
edge compression waves observed for the cavities with L/D = 3 and 5 do not exist with
an angled aft wall cavity. However, the strong trailing edge shock wave still exits as the
shear layer reattaches at the angled back wall.
Additional experiments are performed in order to study the influence of upstream
(a) L/D = 3
(d) L/D = 3 with 30o angled back wall
(b) L/D = 5
(e) L/D = 5 with 30o angled back wall
155
(c) L/D = 7
FIGURE 7.10 Schlieren images demonstrating the differences in the flow-field structure of cavities with
different length-to-depth ratios and back wall angle. The depth of the cavities is constant
and equal to D = 3 mm. The free-stream was generated to simulate Mach 10 total enthalpy
conditions at the supersonic combustor entry: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K,
p∞ = 32 kPa. The boundary layer thickness at the trailing edge of the cavity is approximately
1mm.
156
(a) L/D = 3
(b) L/D = 3 with 30o back wall and upstream injection
(c) L/D = 5 with upstream injection
FIGURE 7.11 Schlieren images demonstrating jet interaction with different cavities. The hydrogen jet is
injected into a non-reacting free-stream 3 mm upstream of the cavity from a d = 1 mm orifice.
The injection is performed at angle of 30o to the plate. The free-stream, N2 , represents the
flight Mach 10 burner entry conditions.
157
fuel injection onto the cavity flow field. The results shown in Fig. 7.11 include 30 degrees
hydrogen injection from a 1 mm diameter orifice positioned at 3 mm upstream of the
cavity leading edge. Those schlieren observations present no significant differences in the
cavity flow field structure due to the upstream injection. On the other hand, some cavity
influence on the jet can be observed. The jet seems to be disturbed as it propagates
over the cavity for the case of L/D =3 and 5 by the compression waves at the leading
edge. As this leading edge shock wave diminishes for the cavities with an angled wall
the jet is not disturbed as it spans over the cavity until it reaches to the trailing edge.
As the jet reaches to the back wall it interacts with the strong trailing edge shock
wave emitting from the cavity. This shock wave - jet interaction at the trailing edge of
the cavity might have an important role in reacting cases. It is known that an oblique
shock wave - jet interaction enhances the molecular mixing between supersonic air and
gaseous fuel. The vorticity generated when a shock wave interacts with a shear layer
(due to the baroclinic torque) has immediate significance to the mixing enhancement in
supersonic flows resulting in enhanced combustion efficiency.
Furthermore, the trailing edge shock is expected to direct the fuel jet towards the
airflow, increasing the fuel penetration, the static pressure, the static temperature, and
therefore the reaction rates.
Since the fuel jet penetration is expected to decrease as the angle of injection decreases, an improved transverse penetration and lateral spreading of the fuel might be
achieved by interaction of the jet with the cavity leading edge shock wave.
7.2.2
Preliminary Ignition Results of Injection/Cavity Schemes
The ignition of a hydrogen jet interacting with a cavity is studied using OH-PLIF.
Several instantaneous OH-PLIF images obtained at the center-line of the jet are presented in Fig. 7.12 for cavity with L/D = 3 and in Fig. 7.13 for cavity with a 30o angled
back wall. Hydrogen is injected 3 mm upstream the cavity leading edge at an angle
of 30o and the free-stream (air) properties represent the flight Mach 10 burner entry
conditions: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa.
For a cavity with L/D = 3, five images (see Fig. 7.12) are obtained from different
experiments. The unsteady nature of the jet/cavity interaction is apparent as the intensity level of OH radicals change from experiment to experiment. Figure 7.12a shows
158
an ignition along the jet/cavity shear layer with a little OH fluorescence signal inside
the cavity. As the jet interacts with the hot cavity air an auto-ignition can be achieved
at the interface. The jet/cavity shear layer impinging on the back wall causes jet and
free-stream flows to enter the cavity. Figures 7.12b-e show significant levels of OH concentration inside the cavity. The intensity differences between the images might be a
result of the breathing motion of the cavity. However, quenching of OH is observed
downstream of the cavity for all of the five experiments, indicating that this cavity
configuration can not provide flame-holding.
The OH-signal levels from shot to shot are more uniform inside the cavity with an
angled back wall as the cavity oscillations are suppressed (see Fig. 7.13). This cavity
configuration provides a continuous ignition downstream of the cavity. Also visible in
Fig. 7.13a is the ignition on the upper side of the jet, most likely induced by the shock
wave attached to the cavity back wall.
In summary, the few OH-PLIF images indicate no ignition around the jet even in
the high total enthalpy conditions of flight Mach 10 due to the shallow injection angle.
Addition of a cavity downstream the injection port does provide ignition in the nearfield. However, the flame-holding capability of these cavities need to be examined in
more detail.
159
(a)
(b)
(c)
(d)
(e)
FIGURE 7.12 Instantaneous OH-PLIF images demonstrating the ignition regions of a hydrogen jet interacting with a L/D = 3 cavity. The images are obtained from 5 single shots at the same conditions. Hydrogen is injected 3 mm upstream the cavity leading edge at an angle of 30o . The
free-stream (air) properties represent the flight Mach 10 burner entry conditions: M∞ = 3.4,
U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa. Note that a schlieren image is also included to
indicate the flow-field properties around the cavity.
160
(a)
(b)
(c)
FIGURE 7.13 Instantaneous OH-PLIF images demonstrating the ignition regions of a hydrogen jet interacting with a cavity with L/D = 3 and 30o back wall. The images are obtained from 5 single
shots at the same conditions. Hydrogen is injected 3 mm upstream the cavity leading edge at
an angle of 30o . The free-stream (air) properties represent the flight Mach 10 burner entry
conditions: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa. Note that a schlieren
image is also included to indicate the flow-field properties around the cavity.
Chapter 8
Concluding Remarks
8.1
Summary of Major Results and Conclusions
8.1.1
Experimental Aspects
• We have demonstrated the feasibility of using an expansion tube to generate clean
(radical-free), high-total enthalpy supersonic flows of air associated with hypervelocity combustors.
• Characterization experiments with test gas mixtures of 95%N2 + 5%CO2 were
performed to study the facility’s performance such as the free-stream flow properties, the useful test time and the core-flow size available for mixing and combustion
studies of a 2 mm jet in crossflow. Our experimental approach included simulation
of the required total enthalpy (3-6 MJ/kgair) of flight Mach 8, 10 and 13 conditions by simulating the required burner entry Mach number, burner entry static
temperature, and consequently the burner entry velocity. As the burner entry
static temperatures were chosen to be in the range of 1250-1400 K, velocities of
1800, 2360 and 3200 m/s were generated for the flight Mach 8, 10 and 13 conditions, respectively. On the other hand, simulated static pressures were below the
desired values because of the limited maximum pressures available in the current
driver section and the limited maximum pressures at which the jet injector valve
could operate with sufficient speed.
• The steady test time duration and the core-flow size of the expansion tube flow
161
CHAPTER 8. CONCLUDING REMARKS
162
were characterized. These are important parameters which define the model dimensions where a fully established flow can be achieved. In addition, primary
effects of the boundary layer on expansion tube flow were observed. In particular, test times ranging between 170 - 400 µs, higher than the ideal values, were
observed. In contrast with shock tunnels, the expansion tube allows an increased
duration of useful test times, as the corresponding flight Mach number of the test
flow increases. The boundary layer developed on the tube walls increases the contact surface velocity and therefore delays the arrival of the first disturbance wave.
However, in our experiments the static pressure of the free-stream was low for
high enthalpy flows, causing the boundary layer effects to increase the test time.
Simulation with higher pressures might result in shorter test times, and therefore
shorter useful test “slug lengths” would be available.
• We have demonstrated that Mirels’ solution for boundary layer effect implemented
in x-t diagrams is a useful tool for prediction of test time and for optimizing the
expansion section length to achieve the maximum test duration.
• Pitot pressure surveys at the exit of the expansion tube have identified an inviscid
test core of approximately 25 mm diameter over which the pitot pressure is constant to within ±5%. While the core-flow size in Mach 10 and 13 conditions did
not diminish significantly at 6.35 cm downstream of the tube exit, the core-flow
size for the Mach 8 condition dropped by half. Since the Mach wave angle is
steeper for small free-stream Mach numbers, the boundary layer information at
the tube exit reaches to the centerline in a smaller distance at the flight Mach 8
condition.
• Finally, compared to large facilities that can average a limited number of experiments per day, many experiments per day in this facility can be performed with
the effort of just one student. Therefore, this facility provides a useful tool for
basic study of near-field features of different fuel injection configurations that have
potential for future application in scramjet engines.
8.1.2
163
Flow Visualization Techniques
We used two non-intrusive flow diagnostic techniques: Planar Laser-Induced Fluorescence of OH radicals (OH-PLIF) and schlieren imaging with an ultra-fast-framing-rate
digital camera. While schlieren showed the location of shock waves and jet penetration,
OH-PLIF mapped the regions of combustion.
Ultra-Fast Framing Rate Schlieren
• We have presented the first demonstration of an ultra-fast flow visualization system (at framing rates up to 100 MHz) based on schlieren imaging. High-temporal
and high-spatial resolutions allowed both qualitative and quantitative study of
supersonic flows. The system included a fast-framing camera (IMACON 468),
capable of acquiring 8 full resolution images in a 576 × 384 pixel format with interframing times and exposure times down to 10 ns and a Xenon flashlamp system
capable of providing up to 200 µs duration of a uniform light source. Supersonic
movies were obtained by assembling the consecutive images. These movies basically slow the flow motion by one million times, elucidating the instantaneous
unsteady features. For example, the pulsating nature of periodically formed eddies
causing the bow shock to fluctuate is very apparent and can be easily followed.
• Qualitative flow observations as well as quantitative measurements such as velocity, propagation angle and formation frequency of large-eddy structures, jet penetration and the width of the jet shear layer were obtained. A cross-correlation
technique using fast Fourier transforms has been employed to analyze the 8 consecutive images. Among those measurements, the spatial-temporal development
(x-t diagram) of unsteady structures and their frequency of formation were part
of the unique measurements available only by analysis of time correlated multiple images. For example, due to pairing and stretching, the spatial gap between
eddies is not necessarily a measure of the eddy formation frequency. Therefore,
only high-speed framing rate imaging could provide such information, necessary
for understanding the origin of the jet shear layer vortical structures, which are
the dominant mechanism in the near-field mixing of jets.
164
• We have shown optimum exposure and inter-framing times which require the optimization of four main factors including the schlieren sensitivity, the spatial resolution, the dynamic range and the signal-to-noise ratio. The image area was
28 × 18 mm and the exposure time was 100 ns. In other words, the spatial resolution was 100 × 100 µm in the near-field (x/d < 2) and 250 × 250 µm in the
far field (x/d > 8) depending on the large-scale structure movement during the
exposure time. The corresponding resolving power was 2-5 pixels, achieved by
the optimization of the four factors discussed above. Resolution considerations
became important with increasing velocities and decreasing region of interest. In
our experiments, we could achieve very high quality schlieren images even though
light deflections were minimum since the jet diameter was only 2 mm. The intensified CCD cameras and the high intensity light source allowed us to control the
sensitivity of the imaging system and achieve the required quality for quantitative
data analyses.
• The application of a high-speed-framing rate imaging system became even more
important as it was combined with an impulse facility operation. The unique
free-stream conditions with high-speed and high-temperatures studied in this investigation could only be generated for very short times. Therefore, the use of
the ultra-fast schlieren system was crucial because it increased significantly the
amount of data available from a single experiment.
OH-PLIF and Simultaneous Measurements
• The OH-PLIF measurements were obtained by excitation of the A2
P+
← X2 Π(1, 0)
band of OH, near 283 nm, and by the detection of the (1,1) band near 315 nm. A
broader excitation assumption was valid as the linewidth of the laser beam, provided from a frequency-doubled dye laser source, was broader than the absorption
linewidth. The isolated Q1 (7) transition at 283.266 nm was selected to minimize
signal dependence on temperature. Therefore, the fluorescence intensity could be
related directly to OH mole fraction.
• Simultaneous OH-PLIF and schlieren imaging could be implemented using two
intensified CCD cameras and a dichroic mirror to separate the OH fluorescence
from the schlieren beam.
8.1.3
165
Characteristics of Hydrogen and Ethylene Transverse Jets
We studied the flow-field properties of hydrogen and ethylene jets injected into flight
Mach 10 conditions at similar jet-to-free-stream momentum flux ratio. The results reveal
significant differences in the development of large-scale coherent structures present in
the jet shear layer. Previously, the momentum flux ratio was found to be the main
controlling parameter of the jet penetration; the results here demonstrated the existence
of an additional mechanism which altered the vortical structure, the penetration and
the mixing properties of the jet shear layer. These new observations became possible
by the simulation of high velocity and high temperature free-stream conditions which
could not have been achieved in the facilities that have been widely used in previous
studies. The details of the main results can be summarized in the following points:
• Visual observations, supported by the qualitative measurements of the convection velocity and jet penetration, reveal large differences between the hydrogen
and ethylene injection cases. Special attention was given to the large scale coherent structures present at the jet/free-stream interface. Instantaneous images
provided a well-resolved representation of the coherent structures at the jet periphery. While the hydrogen eddies persisted for long downstream distances, in
the ethylene case the eddies dissipated quickly. It is conjectured that increasing
stresses due to the steep velocity gradient across the shear layer are responsible
for this change. The large variation in the molecular weight between hydrogen
and ethylene leads to significantly different exit velocities at the sonic orifice. Because of the low jet exit velocity of ethylene (315 m/s), the shear layer vortical
structures tilt and stretch in the direction of the fast crossflow (2360 m/s). The
large structures eventually became unstable and were torn apart by the stretching
of the vortical structures.
• The above observations were supported by PLIF imaging of OH radicals which
maps the regions of auto-ignition. These ignition regions can be related to homogenously mixed regions since molecular mixing is required before the fuel and the
oxidizer react. Ethylene injection demonstrated high concentration of OH radicals
across the jet while in the hydrogen case only a thin flamelet could be observed
around the large eddy structures. Clearly, molecular mixing of the ethylene jet
166
was dramatically altered during or after the onset of the tilting-stretching-tearing
process.
• Eddy convection characteristics and jet transverse penetration were also different between the two cases. Hydrogen structures tended to travel with velocities
(∼2200 m/s) that were closer to the free-stream velocity as they align with the
free-stream flow in the far-field (x/d > 9). The convection velocity of ethylene
structures were slower than the hydrogen eddies due to the low jet exit velocities.
Tracking different parts of the ethylene large eddies, a wide convection velocity distribution was shown to exist across the shear layer ranging between 750-1750 m/s.
The differences in the bow shock steepness could result in the observed differences
in the convection velocity between the cases. The properties of the free-stream (the
bow shock shape and the shock-induced flow properties) were directly influenced
by the convection characteristics of the large-scale eddies.
• The ethylene jet penetrates deeper into the free-stream than the hydrogen jet.
This was an unexpected result as all of the previous studies showed that the jetto-free-stream momentum flux ratio (J) was the primary penetration controlling
mechanism. We therefore expected to observe identical penetration heights as the
J was identical for both cases in our studies. This interesting and surprising result
could again be attributed to the evolution of the jet shear layer under large velocity
gradients. The thickness of the penetration band, used as the representation of
the jet-shear-layer thickness was considerable in the ethylene injection case, due
to the tilting-stretching-tearing mechanism and also due to the larger growth rate
of the jet shear layer.
8.1.4
Density and Velocity Ratio Effects
• Following the observations of the previous section, we investigated the stability of
the jet shear layer at various speed ratios and density ratios via flow visualization
(schlieren). The high shear stresses induced by the large velocity difference across
the jet shear layer had a large effect on the structure of the layer. For the unstable
case, we noticed: 1) loss of Kelvin-Helmholtz structures with the tilting-stretchingtearing mechanism, 2) increased growth rates with decreasing values of jet-tofree-stream velocity ratio, 3) large intrusions of crossflow in between the eddies,
167
4) distortion of the bow shock around the large eddies. Stable layers showed welldefined Kelvin-Helmholtz rollers.
√
• An “effective velocity ratio” parameter, λ = (1 − r2 )/ 1 + r2 was suggested. The
results plotted in a density-effective velocity ratio (s-λ) diagram demonstrated two
separate regions of “stable” and “unstable” jet shear layers.
8.1.5
Ignition and Flame-Holding Capability of a Hydrogen Transverse Jet
The problem of hydrogen transverse injection and its flame-holding capability was
studied in very high-speed, high-total-enthalpy flow conditions. The experiments applied simultaneous OH-PLIF and schlieren imaging to map the regions where combustion occurs relative to the jet position. The main results are summarized as follows:
• At the flight Mach 10 condition, OH fluorescence was mainly observed along the
outer edge of the jet plume. Simultaneous OH-PLIF/schlieren revealed that the
structural evolution of the reaction zone is in good agreement with the jet shear
layer position determined by the schlieren imaging. The ignition was initiated in
the recirculation region upstream of the jet. The ignition product OH, convected
downstream along with the large eddies, was mainly detected along the jet shear
layer periphery in a continuous and very thin filament.
• At the flight Mach 13 condition, OH-PLIF demonstrated high signal levels of OH
fluorescence starting in the upstream recirculation region and along the jet shear
layer. The ignition delay times in this condition were effectively zero (∼ 1 − 5µs)
due to the high total enthalpies (namely high total temperatures) of the freestream.
• At the low total enthalpy Mach 8 condition, the ignition was limited to a small
region behind the bow shock and no OH fluorescence could be observed farther
downstream.
8.1.6
Cavity Flame-Holders
In this part of the thesis, we have first provided a review of cavities in supersonic flows
and their use for flame-holding in supersonic combustors. Second, we have performed a
168
preliminary investigation, where the primary objective was to demonstrate the feasibility
of the experimental set-up to provide information for cavity flameholder studies. These
appear to be the first cavity experiments performed in such high total enthalpy flows.
• In the first part of the review, the basic flow-field features of cavities studied by
various researchers are summarized, including: different flow regimes of cavities
based upon the length-to-depth ratio (open and closed), oscillations, techniques
to suppress these oscillations, drag penalties for different cavity geometries, and
flow residence time inside a cavity which is crucial to initiate the ignition. Both
experimental and numerical studies still need to be performed to answer some of
the contradictory results that have been observed by different investigators (drag
penalties of angled back wall cavities, amplitude of pressure fluctuations, flow
residence time inside an unsteady cavity).
• In the second part of the review, studies demonstrating the feasibility of cavities
to achieve ignition and to enhance flame-holding in subsonic and supersonic combustors, are described. Finally, we have introduced several questions followed by
comments that need to be addressed in the development of cavities for practical
combustors.
• Through a combination of simultaneously performed fast response pressure measurements, established cavity oscillations were observed and a sequence of oscillation cycles were captured during the limited test time ( 270 µs) of the flow
facility. The results demonstrated that short duration pulse facilities can be used
to study gasdynamic aspects of cavities, though with small dimensions (depth of
D = 3 mm), in hypersonic flows.
• In the first part of the preliminary study, flows around 2-D cavities (D = 3 mm,
L/D =3, 5 and 7) in a supersonic flow were investigated. Significant changes
in the shock wave structure around the cavities were observed as the length-todepth ratio were systematically changed. Leading edge shock waves diminished
in cavities with large L/D. In all cases a strong reattachment shock wave at the
trailing edge of the cavity was observed. A transition from an open cavity flow
to a closed cavity flow was obtained for L/D = 7. An angled back wall reduced
the leading edge shock strength. Schlieren movies of the cavities reveal the shock
169
wave fluctuations around the jet are caused by the pressure oscillations inside the
cavity.
• In the second part of the preliminary study, ignition properties of a 30o hydrogen
jet combined with a downstream cavity (L/D = 3) were investigated. While
both cavities (with and without an angled back wall) provided an autoignition in
and around the cavity, flame-holding seems to require an improved cavity design.
Recommended configurations are presented in the following section.
8.2
Recommendation For Future Work
Recommended future work can be summarized in the following topics:
Extension of Ignition Measurements of Transverse Jets
We have shown that a fundamental supersonic combustion study can be performed
using an expansion tube, providing realistic free-stream conditions with relatively accurate chemical composition. We therefore recommend the study of the near-field ignition
mechanism of transverse jets in more detail by taking advantage of the various freestream conditions. For example, this study can be performed using a set of free-stream
conditions with reasonably similar velocities and total enthalpies but with significantly
different static temperatures. Table 8.1 summarizes a set of recommended conditions
which were actually characterized in the expansion tube. Maps of Fig. 2.7 guided us in
determining the appropriate initial pressures.
Observation of the ignition processes for decreased static temperatures, while keeping
the other flow parameters constant, can reveal information about the source of the
ignition and the parameters controlling the ignition process.
Ignition in Cavity Flame-Holders
The effects of the jet in crossflow in conjunction with a cavity can easily be studied
in the current facility setup. Fig. 8.1 shows three possibilities to produce a reacting jet
in crossflow which is stabilized by a cavity flame-holder. A preliminary examination
of a 30o angled hydrogen injection upstream of the cavity showed autoignition inside
the cavity. However, a detailed investigation is still required to reveal the flame-holding
170
TABLE 8.1 Recommended free-stream flow conditions for further ignition studies.
Condition
U∞
m/s
P∞
atm
T∞
K
M∞
Htot
MJ/kg
600/0.5/20
2360 ± 25
0.32
1290
3.38 ± 0.04
3.84
600/1/20
2365 ± 27
0.31
977
3.86 ± 0.03
3.52
600/2/20
2286 ± 26
0.30
717
4.32 ± 0.05
3.06
600/3/20
2143 ± 45
0.29
604
4.39 ± 0.09
2.62
600/4/20
2212 ± 24
0.29
516
4.89 ± 0.05
2.68
properties of the configuration. Injection in the upstream wall of the cavity might
provide a larger volume of combustible mixture of fuel and air within the cavity flow.
Injection further downstream might provide a pool of radicals both upstream, as well as
downstream of the jet. It is however impossible to predict the interaction of jet/cavity
shear layers in those configurations. A detailed experimental study is therefore needed
for a better understanding of the coupling between the jet and the cavity flow. Finally,
it should be noted that for hydrocarbon fuels with chemical kinetic rates notably slower
than hydrogen, a cavity may be the only viable means for flame stabilization.
Shock Wave/Jet Interaction
Oblique shock wave impingement into the jet is one method known to enhance the
molecular mixing between supersonic air and gaseous fuel. Waves are also unavoidable
in SCRAMJETS and often originate in the inlet isolator leading to the combustion zone
or from ramps and the bow-shock in front of the jet in crossflow. Thus, we propose
to use wedge generated waves to interact with the jet injection flow-field. A schematic
showing the expected features of shock impingement into a transverse jet is drawn in
Fig. 8.2.
It is well known that vorticity is generated when a shock wave interacts with a shear
layer due to the baroclinic torque (in general, the pressure gradient caused by the shock
and the density gradient in the shear layer will not be colinear). Amplified turbulence
and vorticity have immediate significance to the mixing enhancement in supersonic
flows. Furthermore, the shock directs the airflow towards the fuel jet, increasing the air
entrainment rate, the static pressure, the static temperature, and therefore the reaction
171
(a)
Jet
Free Shear Layer
Injectant
(b)
Jet
Free Shear Layer
(c)
Shear Layer - Jet
Interaction
Jet
FIGURE 8.1 Flow-field schematics demonstrating different concepts of angled jet injection combined with
cavity flame-holder. a) upstream injection, b) base injection , c) cavity injection.
rates. There are few works (Hwanil and Driscoll 1996; Menon 1989; Marble 1994) which
have studied the effect of shock-wave/shear-layer interaction on mixing enhancement in
a supersonic combustor. The results indicated that the spreading rate of the shearlayer may be enhanced by the shock impingement, resulting in enhanced mixing and
combustion efficiency.
Shock wave jet interaction can easily be studied using the current facility/injection
system. A 25o angled wedge is actually designed to generate an oblique shock wave as
illustrated in Figure 8.3. The wedge, positioned 22 mm above the injection plate, has a
window made of sapphire to pass the OH-PLIF laser sheet into the imaged region.
A typical schlieren image demonstrating the oblique shock wave jet interaction is
shown in Fig. 8.4. The relatively strong shock, generated by the 25o wedge, directs the
air flow inward toward the hydrogen jet. In a different experiment in which simultaneous
172
SHOCK GENERATOR PLATE
M¥>1
BOW SHOCK
OBLIQUE
SHOCK
SHOCK-ENHANCED
COMBUSTION
BARREL SHOCK
MACH DISK
BOUNDARY LAYER
SEPARATED
REGION
INJECTANT
(Hydrogen)
RECIRCULATION
ZONE
RECIRCULATION
ZONE
FIGURE 8.2 Flow-field schematic of a shock-wave/jet interaction.
FIGURE 8.3 Schematic of the 25o wedge to generate a shock wave above the injection plate.
173
OH-PLIF and schlieren was applied (see Fig. 8.4b), no change in the OH signal level
was observed behind the shock impingement; meanwhile the thin filament of OH was
directed along the jet contour.
174
PLIF Sheet
25o
Slit for
OH-PLIF
Laser Sheet
M¥= 4.7
V¥= 3200 m/s
P¥= 4 kPa
T¥= 1250 K
Air
0
2
4
6
8
10
12
14
16
18
y/djet
Jet: Hydrogen, djet = 2 mm, Mjet=1, J=3
Region Illuminated by
PLIF Sheet
0
2
4
6
8
10
12
y/djet
FIGURE 8.4 (a) An oblique shock wave impinging the hydrogen jet as visualized using schlieren imaging.
The shock was produced by a 25 o angled wedge mounted above the injection plate. Flight
Mach 13 free-stream condition. (b) Combined OH-PLIF and schlieren images visualizing the
effect of shock/jet interaction on OH number density.
Appendix A
Expansion Tube Equations
In this appendix we summarize the equations used to calculate the test gas properties
at the exit of the expansion tube assuming one-dimensional, adiabatic and inviscid flow.
The nomenclature corresponds to Fig. 2.2 which defines the flow states at different
sections of the expansion tube.
As the expansion tube includes two-shock tubes in tandem, the common shock tube
equations (Gaydon and Hurle 1963) can be used in the intermediate calculations to fully
describe the test gas conditions at the exit of an expansion tube. Initially, the shock
wave strength and the post-shock conditions of the test gas (defined as state 2) in the
driven section and that of the acceleration gas (defined as state 20) in the expansion
section, must be calculated using the slightly modified shock tube equations. The test
gas flow conditions at the exit of the tube (state 5) can then be obtained by assuming
an isentropic expansion from the pressure in state 2 to the pressure in state 20.
Initially, as the primary (driver/driven) diaphragm is broken, the high-pressure
driver gas expands into the lower pressure driven section. A shock wave is formed
propagating into the test gas in the driven section. We can estimate the strength of this
incident shock for a given set of initial filling pressures. Assuming that the shock tube
is of uniform area, and that the driver gas expands isentropically from the driver into
the driven section, we find that
P4
=
P1
2
2γ1 Ms1
− (γ1 − 1)
γ1 + 1
½
µ
1−
γ4 − 1 a1
1
·
Ms1 −
γ1 + 1 a4
Ms1
¶¾−
³
2γ4
γ4 −1
´
(A.1)
where Ms1 is the shock Mach number in the driven section. The propagation of the
175
APPENDIX A. EXPANSION TUBE EQUATIONS
176
shock wave along the tube induces a velocity in the test gas behind the wave and causes
an increase in the pressure and temperature. These shock-induced properties of the
test gas can, therefore, be calculated using the calorically perfect and 1-D normal shock
relations, given by:
µ
U2lab
2a1
1
=
Ms1 −
γ1 + 1
Ms1
¶
(A.2)
2 − (γ − 1)
P2
2γ1 Ms1
1
=
P1
γ1 + 1
³
(A.3)
´³
´
γ1 −1
2 − (γ1 −1)
2
γ1 Ms1
T2
2
2 Ms1 + 1
=
³
´2
γ1 +1
T1
M2
(A.4)
s1
2
U2 , P2 and T2 represent the velocity in the laboratory reference frame, the pressure and
the temperature of the shocked test gas in the driven section, respectively.
When the secondary diaphragm breaks due to the shock-induced high pressure in
the driven section, a new shock is formed propagating into the expansion section. The
expression to calculate the shock strength in this section, taking into account the velocity
of the test gas in the driven section (the driver gas in Eq. A.1 was motionless), therefore,
includes an additional term, resulting in:
P2
=
P10
2
2γ10 Ms2
where M2 =
− (γ10 − 1)
γ10 + 1
½
µ
1−
γ2 − 1 a10
1
·
Ms2 −
γ10 + 1 a2
Ms2
¶
+
√
γ2 R2 T2 .
γ2 − 1
M2
2
¾−
³
2γ2
γ2 −1
´
(A.5)
U2lab /
Equations to predict the shock-induced properties of the acceleration gas are similar
to that of the driven section gas:
µ
lab
U20
1
2a10
Ms2 −
=
γ10 + 1
Ms2
¶
(A.6)
2 − (γ − 1)
P20
2γ10 Ms1
10
=
P10
γ10 + 1
³
´³
(A.7)
´
γ10 −1
2 − (γ10 −1)
2
γ10 Ms2
T20
2
2 Ms2 + 1
=
³
´
γ10 +1 2
T10
M2
2
s2
(A.8)
APPENDIX A. EXPANSION TUBE EQUATIONS
177
As the shocked test gas in the driven section is suddenly confronted with the much
lower pressure acceleration gas in front of it, simultaneously expands and accelerates to
match the pressure and velocity of the shocked acceleration gas (helium), namely:
P5 = P20
(A.9)
U5 = U20
(A.10)
The corresponding temperature of the expanded test gas can be obtained by assuming an isentropic expansion from condition 2 to condition 5.
T5
=
T2
µ
P5
P2
³
´
¶ γ2 −1
γ2
(A.11)
Appendix B
Maps of Estimated Expansion
Tube Test Conditions
178
APPENDIX B. MAPS OF ESTIMATED EXPANSION TUBE TEST CONDITIONS 179
(a)
5
300 K
3
800 K
0.1 atm
6
5
4
3
1000 K
0.6 atm
0.4 atm
0.2 atm
9
8
7
0.3 atm
600 K
1
0.8 atm
400 K
2
0.05 atm
4
1400 K
2
1800 K
2200 K
0.1
2
1
3
4
5
6
7
8 9
2
3
4
5
6
7
8 9
10
100
(b)
5
3
2 MJ/kg
4
3
1800 m/s
2000 m/s
2200 m/s
2.5
1600 m/s
5
2600 m/s
6
2800 m/s
9
8
7
3000 m/s
1
2400 m/s
2
3200 m/s
4
3 MJ/kg
3.5
4 MJ/kg
4.5
2
5 MJ/kg
5.5
6 MJ/kg
0.1
2
1
3
4
5
6
7
8 9
2
3
4
10
5
6
7
8 9
100
FIGURE B.1 Maps of estimated test gas (nitrogen) conditions at the exit of an expansion tube: a) pressure
and temperature, b) total enthalpy and velocity of the test gas are plotted for different initial driven and expansion section pressures. Calculations are performed using the inviscid 1D
equations for a given driver pressure of P4 = 300 psig (helium).
(a)
Temperature
5
3
300 K
0.1 atm
5
4
3
1400 K
0.6 atm
0.4 atm
1000 K
6
0.3 atm
9
8
7
0.2 atm
600 K
1
0.8 atm
400 K
2
0.05 atm
Pressure
200 K
4
2000 K
2600 K
3200 K
2
4000 K
4800 K
0.1
2
3
1
4
5
6
7
8 9
2
3
4
5
6
7
8 9
10
100
(b)
Velocity
5
Mach number
Total enthalpy
3
M=8
2 MJ/kg
M=7
2
6
4
2800 m/s
5
3
M=3
2000 m/s
3 MJ/kg
1600 m/s
2600 m/s
M=4
2200 m/s
9
8
7
2400 m/s
M=5
1
1800 m/s
M=6
3000 m/s
4
M=2
4 MJ/kg
M = 1.5
2
5 MJ/kg
6 MJ/kg
0.1
2
1
3
4
5
6
7
8 9
2
3
4
10
5
6
7
8 9
100
FIGURE B.2 Maps of estimated test gas (Argon) conditions at the exit of an expansion tube: a) pressure
and temperature, b) total enthalpy, velocity and Mach number of the test gas are plotted for
inviscid 1D equations for a given driver pressure of P4 = 300 psig (helium).
(a)
Temperature
8
7
6
Pressure
0.1 atm
1
8
7
6
0.8 atm
0.2 atm
600 K
2
0.4 atm
400 K
3
1.2 atm
300 K
4
1.8 atm
200 K
5
0.05 atm
Driven Gas (Argon) Initial Pressure, P1 (psia)
10
1000 K
1400 K
2000 K
5
4
2800 K
3
2
4000 K
5000 K
0.1
2
1
3
4
5
6
7 8 9
2
3
4
5
6
7 8 9
10
2
100
(b)
Temperature
8
7
6
Mach number
Total enthalpy
M = 10
5
2 MJ/kg
M=8
4
M=5
2
3 MJ/kg
3000 m/s
8
7
6
5
4
3
2
2600 m/s
1
2200 m/s
M=4
M=3
1800 m/s
M=6
3
3400 m/s
Driven Gas (Argon) Initial Pressure, P1 (psia)
10
4 MJ/kg
M=2
5 MJ/kg
6
6 MJ/kg
0.1
2
1
3
4
5
6 7 8 9
2
3
4
5
6 7 8 9
10
2
100
FIGURE B.3 Maps of estimated test gas (Argon) conditions at the exit of an expansion tube: a) pressure
(a)
Temperature
5
Pressure
200 K
9
8
7
0.2 atm
600 K
6
0.4 atm
1
0.3 atm
400 K
0.6 atm
300 K
2
0.8 atm
3
0.1 atm
5
4
3
0.05 atm
Driven Gas (Helium) Initial Pressure, P1 (psia)
4
2
1000 K
0.1
2
3
1
4
5
6
7
8 9
2
3
4
5
6
7
10
8 9
100
(b)
Velocity
5
Mach number
Total enthalpy
1600 m/s
M=2
2400 m/s
2800 m/s
3200 m/s
2
4 MJ/kg
2000 m/s
M=3
M=4
3
3600 m/s
4
5 MJ/kg
1
9
8
7
M=1
6
6 MJ/kg
5
4
3
7 MJ/kg
2
8 MJ/kg
0.1
2
1
3
4
5
6
7
8 9
2
3
4
10
5
6
7
8 9
100
FIGURE B.4 Maps of estimated test gas (Helium) conditions at the exit of an expansion tube: a) pressure
(a)
4
0.2 atm
2
0.1 atm
400 K
1
8
7
6
5
0.4 atm
300 K
3
1.2 atm
0.8 atm
200 K
5
0.05 atm
Pressure
8
7
6
1.8 atm
Temperature
10
600 K
800 K
4
3
1000 K
2
0.1
2
1
3
4
5
6
7 8 9
2
3
4
5
6
7 8 9
10
2
100
(b)
2
4 MJ/kg
Total enthalpy
1600 m/s
2400 m/s
M=4
Mach number
2000 m/s
3
3200 m/s
4
3600 m/s
M=5
5
4000 m/s
8
7
6
2800 m/s
Velocity
10
5 MJ/kg
M=3
M=1
6 MJ/kg
1
M=2
8
7
6
7 MJ/kg
5
4
3
8 MJ/kg
2
9 MJ/kg
0.1
2
1
3
4
5
6 7 8 9
2
3
4
5
6 7 8 9
10
2
100
FIGURE B.5 Maps of estimated test gas (Helium) conditions at the exit of an expansion tube: a) pressure
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Ben-Yakar, Adela (2000). - The Hanson Group

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