Technical Notes

JOURNAL OF PROPULSION AND POWER
Vol. 28, No. 4, July–August 2012
Technical Notes
Fluidic Thrust-Vector Control
of Supersonic Jet Using Coflow
Injection
thrust-vector control (FTVC) technique, which offers several
potential advantages over mechanical approaches: 1) no moving
parts interacting with the primary jet, 2) reduced weight and better
reliability, 3) improved stealth/low observability, 4) simplicity and
relatively low cost. Because of these advantages, there is currently
considerable interest in this type of system. A variety of approaches
to FTVC design, including coflows and counterflows, shock
methods, throat skewing, and dual-throat techniques have been
considered. Both the coflow and counterflow injection techniques are
based on the Coanda effect (an incident jet tends to remain attached to
a nearby surface) [4–10]. In the shock-injection TVC method
[11,12], an oblique shock is formed in the divergent nozzle to turn the
primary resulting from a secondary flow into the primary jet at the
divergent nozzle wall. This method is characterized by large nozzleexpansion-area ratios and large thrust losses. The fluidic throatskewing technique features symmetric injection for jet-area control
and asymmetric injection to skew the sonic plane for thrust-vector
control [13]. The dual-throat concept involves a convergent–
divergent–convergent nozzle [14–17]. A nonzero thrust-vector angle
is generated with fluidic injection at the upstream throat that controls
separation and maximizes pressure difference in the recessed cavity
created between the two geometric minimum areas. The geometry is
intended to enhance the thrust-vectoring capability by manipulating
flow separation in the recessed cavity. Indeed, fluidic control is a very
appealing method of producing vectored thrust. Unfortunately, it is
apparent that fluidic control is not without its difficulties, the most
serious of which is the hysteretic nature of these devices, which can
give rise to the attachment of the jet to the nozzle surfaces and thus
loss of control [18,19]. The technique of interest in the present
research is a coflow method based on the Coanda effect. This method
minimizes momentum loss in the jet because the control-flow
injection direction is the same as that of the main jet. For this study, a
numerical simulation was performed and the results were compared
with steady-state experimental data to understand the effect of major
operating parameters, including the pressure ratio of the main and
control nozzles as well as the development of a shock behind the
control nozzle exit.
Jun-Young Heo∗ and Hong-Gye Sung†
Korea Aerospace University,
Goyang 412-791, Republic of Korea
DOI: 10.2514/1.B34266
Nomenclature
d
E
Fa
Fv
h
Pa
Pc
Pm
p
PR
qj
t
u
x
y
d
ij
ij
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
diameter of main nozzle exit
specific total energy
axial thrust
vertical thrust
specific enthalpy
atmospheric pressure
control-flow total pressure
main-flow total pressure
static pressure
pressure ratio of control flow to main flow
specific heat flux
time
velocity
spatial coordinate
dimensionless wall distance
thrust deflection angle
Kronecker delta
density
viscous stress tensor
Superscripts
~
00
=
=
=
time average
Favre average
fluctuation associated with mass-weighted mean
II. Numerical Method
The Favre-averaged governing equations based on the conservation of mass, momentum, and energy for a compressible flow can be
written as
I. Introduction
T
HRUST-VECTOR control (TVC) systems tend to be
progressively implemented in modern aircraft and missiles to
improve the slow pitchover and limited maneuverability of the
aerodynamic control system [1–3]. A mechanical TVC system
moves a nozzle or deflectors to change the direction of a gas jet
exhausted from a nozzle. Although mechanical TVC systems are
widely applicable to conventional vehicles, they may be too heavy,
complex, and aerodynamically inefficient for small vehicles and
applications in which multidirectional TVC systems are required.
One compact TVC alternative to mechanical TVC is the fluidic
@ u~ j
@
0
@xj
@t
(1)
ij @ij u00j u00i @ u~ i
@ u~ i @ u~ i u~ j p
@xj
@xj
@t
@t
Presented at the 45th AIAA/ASME/SAE/ASEE Joint Propulsion
Conference and Exhibit , Denver, CO, 2–5 August 2009; received 28
February 2011; revision received 7 January 2012; accepted for publication 11
January 2012. Copyright © 2012 by the American Institute of Aeronautics
and Astronautics, Inc. All rights reserved. Copies of this paper may be made
for personal or internal use, on condition that the copier pay the $10.00 percopy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive,
Danvers, MA 01923; include the code 0748-4658/12 and $10.00 in
correspondence with the CCC.
∗
Research Assistant, School of Aerospace and Mechanical Engineering.
†
Professor, School of Aerospace and Mechanical Engineering;
[email protected]. Associate Fellow AIAA.
ij @ij u00j u00i @ u~ i u~ j p
@xj
@xj
u~ j @u~ i ij h00 u00i @q j
@ E~ @ E~ p
@xj
@xj
@xj
@t
(2)
(3)
To account for the important features in high-speed flow, the
combined model of compressible dissipation and pressure dilatation
proposed by Sarkar et al. [20,21] and the low-Reynolds-number k–"
model [22] was used in this study. The model was validated to be a
stable and accurate solver for the unsteady supersonic flow, including
shock–boundary-layer interaction and flow separation [23,24]. Over
858
J. PROPULSION, VOL. 28, NO. 4:
Fig. 1
Fig. 2
859
TECHNICAL NOTES
Experimental setup and schematic diagram of the FTVC nozzle.
Comparison of computational fluid dynamics (CFD) results with schlieren images from the experiment.
the entire FTVC system, the flowfields are governed by a wide variety
of time scales, from stagnation in the main and control chambers to
supersonic flow in the exhaust jet. Such a wide range of time scales
causes an unacceptable convergence problem. To overcome the
problem, a dual time-integration procedure designed for flows at all
Mach numbers is applied. Dual time-stepping and lower–uppersymmetric Gauss–Seidel are applied for time integration, and the
control-volume method is used to integrate inviscid fluxes represented by advection upstream-splitting method by pressure-based
weight functions and monotone upstream-centered schemes for
conservation laws and viscous fluxes by central difference. The code
is parallelized using a message-passing-interface library to accelerate
the calculation.
III. Model Description
A schematic and a close-up view of the FTVC nozzle are shown in
Fig. 1. The secondary nozzles are positioned above and below the
primary nozzle. The primary nozzle was designed for isentropically
expanded flow at Mach 2.0, corresponding to a Reynolds number of
1:2 106 at the exit plane, based on the height of the main nozzle
exit. In this study, the two divergent flaps were fixed at an angle of
10 deg.
IV.
In Fig. 3, the deflection angle of the jet increases with the ratio of
control-flow total pressure to main-jet total pressure for pressure
ratios above 0.4. For pressure ratios between 0.1 and 0.4, the
maximum deflection angle increases linearly:
d;max 28:97 PR 1:60;
0:1 < PR < 0:4
(4)
The jet-deflection angle reaches a maximum value of about 10 deg,
which appears to be close to the angle of the nozzle’s divergent
section wall. This angle represents a hard maximum value imposed
by the geometry not by aerodynamics.
Figure 4 shows the flow structure near the nozzle exit as the
control-flow pressure increases and the jet pressure is kept constant.
The deflection angle of the jet gradually increases as injection control
pressure increases to 150 kPa, and then the deflection angle remains
constant at a control pressure of 200 kPa. Before the jet-deflection
angle reaches its maximum, the control flow appears to be very
smooth. At Pc 200 kPa, shock waves are generated in the controlflow region, as shown in Fig. 4d, and the shock waves and nozzle
walls increase pressure. Especially, the presence of the shock waves
Results
A series of numerical and experimental tests were conducted. The
total pressure of the main jet was varied from 300 to 1000 kPa; the
pressure range of the overexpanded jet was from 300 to 600 kPa and
that of the underexpanded jet was from 790 to 1000 kPa. The total
pressure of the control flow was varied from 120 to 250 kPa to
investigate the influence of control-flow pressure on jet deflection.
Figure 2 shows the jet deflection from the nozzle axis at jet total
pressures of 300, 600, and 790 kPa with control-flow pressures of
150 and 200 kPa. By visual comparison in Fig. 2, the numerically
determined flow structures and deflection angles are similar to the
angles measured in the schlieren images from the experimental
results.
Fig. 3
Jet-deflection angle vs pressure ratio of control flow to jet flow.
860
J. PROPULSION, VOL. 28, NO. 4:
TECHNICAL NOTES
Fig. 4 Details of flow structure near the control-flow nozzle exit;
Pm 300 kPa.
prevents the jet from deflecting further due to reduce the pressure
difference between the walls (top and bottom). The deflection force
was generated by the pressure difference. However, the shock waves
lead to accelerate the pressure recovery at the jet-deflected side on
which the pressure difference reduces.
Figure 5 shows the pressure distribution along the top wall and a
schematic of the shock generation. The wavy shape of the pressure
distribution along the top nozzle wall is due to the presence of oblique
shock waves, which increase the pressure along the wall compared
with the Pc 120 kPa and Pc 150 kPa cases. The high pressure
with the wavy shape of pressure limits the deflection angle of jet flow,
which in turn limits the control range of the FTVC using coflow
injection.
As shown in Fig. 6, axial thrust has a near-linear relation with the
main-jet pressure. Thrust increases as the control pressure increases
because the mass additions of control flow in the axial direction.
Vertical thrust is generated as a result of jet deflection. Figure 7a
shows a schematic diagram of vertical thrust response to control jet
Fig. 5
Shock generation in the control-flow nozzle exit.
Fig. 6 Axial thrust vs control-flow pressure for various main-jet
pressures.
pressure: vertical thrust tends to remain constant, increase, and
decrease with increasing control pressure; these regimes may be
designated outside of control zone, control zone, and saturation zone,
respectively. Increasing control-flow pressure in the control region,
the vertical thrust increases to some extent, but it decreases above a
certain pressure ratio in the saturated control zone. This is due to the
fact that, in the saturated zone, the control flow not only causes flow
deflection but also increases the axial force because of mass addition
to the main-jet flow. As a result, the main flow is separated from the
wall that caused a decrease in vertical thrust.
Figure 8 represents the thrust ratio of vertical thrust to axial thrust.
In general, thrust ratio increases as the PR increases; but, at 1000 kPa
for main and 200 kPa for control, the deflection force of jet does not
increase, and the controllability reaches the limit. In addition,
increase in Pc to 250 kPa causes normal shock between the primary
nozzle exit and the control wall, resulting in a decrease in Fv =Fa ,
shown in Figure 8. At 300 kpa for main, maximum Fv =Fa is
maximum at PR 0:4. Increasing PR causes a normal shock and
Fig. 7 Vertical thrust vs control-flow pressure for different main-jet
pressures.
J. PROPULSION, VOL. 28, NO. 4:
TECHNICAL NOTES
[7]
[8]
[9]
[10]
[11]
Fig. 8 Thrust ratio vs pressure ratio for various main pressure
conditions.
[12]
loss of thrust as shown by decreasing Fv =Fa with increasing PR (see
Figs. 2a and 2b). To control the thrust vector effectively, the pressure
ratio should be set in the control zone; the proper range is from PR 0.1
to 0.3 in a main pressure range of between 450 kPa and 600 kPa.
[13]
V.
Conclusions
An investigation on operating parameters and dynamic characteristics of a FTVC system using a coflow control technique was studied
experimentally and numerically. The results of numerical
simulations were found to be fairly comparable with experimental
results. Jet-deflection angle and pressure distribution of the divergent
nozzle surface were measured as the ratio of control flow to mainflow pressures. The maximum deflection angle was found to increase
linearly with the pressure ratio in a range of between 0.1 and 0.4. This
observation implies that the control efficiency will be maximized at
typical pressure ratios. Shocks appear in the control-flow exit and
divergent wall as the control-flow pressure increases, which limits
the jet-deflection angle. Axial thrust increases linearly with the
control pressure increase at different main-jet pressures. The
response to control-flow pressure in terms of vertical thrust may be in
the control zone, outside of the control zone, or in the saturation zone.
Thus, the optimum PR should be found near the boundary
between the control zone and the saturation zone. That range is from
PR 0.1 to 0.3.
[14]
[15]
[16]
[17]
[18]
[19]
Acknowledgments
This study was partially supported by the Korea Research
Foundation in 2008 (KRF 2008-331-D00104), and the authors
would like to thank the Hanwha Corporation for partial funding
through a research consortium.
References
[1] Asbury, S. C., and Capone, F. J., “High-Alpha Vectoring Characteristics
of the F-18/HARV,” Journal of Propulsion and Power, Vol. 10, No. 1,
1994, pp. 116–121.
doi:10.2514/3.23719
[2] Berrier, B. L., and Re, R. J., “Effect of Several Geometric Parameters on
the Static Internal Performance of Three Nonaxisymmetric Nozzle
Concepts,” NASA TP 1468, 1979.
[3] Capone, F. J., and Maidem, D. L., “Performance of Twin TwoDimensional Wedge Nozzles Including Thrust Vectoring and Reversing
Effects at Speeds up to Mach 2.2,” NASA TN D-8449, 1977.
[4] Wilde, P. I. A., Crowther, W. J., Buonanno, A., and Savvaris, A.,
“Aircraft Control Using Fluidic Maneuver Effectors,” 26th AIAA
Applied Aerodynamics Conference, Honolulu, AIAA Paper 20086406, Aug. 2008.
[5] Mason, M. S., and Crowther, W. J., “Fluidic Thrust Vectoring for Low
Observable Air Vehicles,” 2nd AIAA Flow Control Conference,
Portland, OR, AIAA Paper 2004-2210, June 2004.
[6] Mason, M. S., and Crowther, W. J., “Fluidic Thrust Vectoring of Low
[20]
[21]
[22]
[23]
[24]
861
Observable Aircraft,” CEAS Aerodynamic Research Conference,
Confederation of European Aerospace Societies, Cambridge, England,
U.K., 2002.
Strykowski, P. J., Krothapalli, A., and Forliti, D., “Counterflow Thrust
Vectoring of Supersonic Jets,” 34th Aerospace Sciences Meeting and
Exhibit, Reno, NV, AIAA Paper 1996-115, Jan. 1996.
Prandtl, L., “Motion of Fluids with Very Little Viscosity,” NACA
TM 452, 1928.
Wille, R., and Fernholz, H., “Report on First European Mechanics
Colloquium on Coanda Effect,” Journal of Fluid Mechanics, Vol. 23,
No. 4, 1965, pp. 801–819.
doi:10.1017/S0022112065001702
Gill, K. G., Wilde, P. I. A., and Crowther, W. J., “Development of an
Integrated Propulsion and Pneumatic Power Supply System for Flapless
UAVs,” 7th AIAA/ATIO Conference, Belfast, Northern Ireland, U.K.,
AIAA Paper 2007-7726, Sept. 2007.
Deere, K. A., “Computational Investigation of the Aerodynamic Effects
on Fluidic Thrust Vectoring,” 36th AIAA/ASME/SAE/ASEE Joint
Propulsion Conference and Exhibit, Huntsville, AL, AIAA Paper 20003598, July 2000.
Waithe, K. A., and Deere, K. A., “Experimental and Computational
Investigation of Multiple Injection Ports in a Convergent-Divergent
Nozzle for Fluidic Thrust Vectoring,” 21st AIAA Applied
Aerodynamics Conference, Orlando, FL, AIAA Paper 2003-3802,
June 2003.
Yagle, P. J., Miller, D. N., Ginn, K. B., and Hamstra, J. W.,
“Demonstration of Fluidic Throat Skewing for Thrust Vectoring in
Structurally Fixed Nozzles,” Journal of Engineering for Gas Turbines
and Power, Vol. 123, No. 3, 2001, pp. 502–507.
doi:10.1115/1.1361109
Deere, K. A., Flamm, J. D., Berrier, B. L., and Johnson, S. K.,
“Computational Study of an Axisymmetric Dual Throat Fluidic Thrust
Vectoring Nozzle for a Supersonic Aircraft Application,” 43rd AIAA/
ASME/SAE/ASEE Joint Propulsion Conference and Exhibit,
Cincinnati, OH, AIAA Paper 2007-5085, July 2007.
Deere, K. A., Berrier, B. L., Flamm, J. D., and Johnson, S. K., “A
Computational Study of a Dual Throat Fluidic Thrust Vectoring Nozzle
Concept,” 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference
and Exhibit, Tucson, AZ, AIAA Paper 2005-3502, July 2005.
Flamm, J. D., Berrier, B. L., Johnson, S. K., and Deere, K. A., “An
Experimental Study of a Dual-Throat Fluidic Thrust-Vectoring Nozzle
Concept,” 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference
and Exhibit, Tucson, AZ, AIAA Paper 2005-3503, July 2005.
Flamm, J. D., Deere, K. A., Berrier, B. L., and Johnson, S. K., “Design
Enhancements of the Two-Dimensional, Dual Throat Fluidic Thrust
Vectoring Nozzle Concept,” 3rd AIAA Flow Control Conference, San
Francisco, AIAA Paper 2006-3701, June 2006.
Deere, K. A., “Summary of Fluidic Thrust Vectoring Research
Conducted at NASA Langley Research Center,” 21st AIAA Applied
Aerodynamics Conference, Orlando, FL, AIAA Paper 2003-3800,
June 2003.
Kowal, H. J., “Advances in Thrust Vectoring and the Application of
Flow-Control Technology,” Canadian Aeronautics and Space Journal,
Vol. 48, No. 2, 2002, pp. 145–151.
doi:10.5589/q02-020
Sarkar, S., Erlebacher, B., Hussaini, M., and Kreiss, H., “The Analysis
and Modeling of Dilatational Terms in Compressible Turbulence,”
Journal of Fluid Mechanics, Vol. 227, 1991, pp. 473–493.
doi:10.1017/S0022112091000204
Sarkar, S., “Modeling the Pressure-Dilatation Correlation,” Institute for
Computer Applications in Science and Engineering, Rept. 91-42,
Hampton, VA, May 1991.
Yang, Z., and Shih, T. H., “New Time Scale Based k–" Model for NearWall Turbulence,” AIAA Journal, Vol. 31, No. 7, 1993, pp. 1191–1197.
doi:10.2514/3.11752
Yeom, H. W., Yoon, S., and Sung, H. G., “Flow Dynamics at the
Minimum Starting Condition of a Supersonic Diffuser to Simulate a
Rocket’s High Altitude Performance on the Ground,” Journal of
Mechanical Science and Technology, Vol. 23, No. 1, 2009, pp. 254–
261.
doi:10.1007/s12206-008-1007-3
Sung, H. G., Yeom, H. W., Yoon, S. K., Kim, S. J., Kim, J. G.,
“Investigation of Rocket Exhaust Diffusers for Altitude Simulation,”
Journal of Propulsion and Power, Vol. 26, No. 2, 2011, pp. 240–247.
doi:10.2514/1.46226
C. Segal
Associate Editor