master`s thesis

MASTER'S THESIS
Performance Prediction of a Microjet
Engine Run on Alternative Fuels
Maja Nylén
2013
Master of Science in Engineering Technology
Space Engineering
Luleå University of Technology
Department of Computer Science, Electrical and Space Engineering
- To Hedvig 10 May 2013
iii
Abstract
Microjet engines have gone from being developed in private workshops meant
for the RC model aircraft world to become a common feature in various military
and commercial applications. Modern microjets emulates the full-sized engines in
function and sophistication but have documented major fuel efficient problems.
The engines are mostly run on aviation kerosene, which is rather expensive, but
a swap to a cheaper or more environmental friendly fuel may result in costly
redesigns of the entire fuel delivery system and a reduced power output. The
solution is to blend the alternative fuel with the regular fuel to maintain engine functionality to a lower cost and/or increased fuel availability. This project
aims to determine whether the performance of the Merlin VT80 microjet engine
run on different blends may be predicted by using a gas turbine model entirely
based on simple aero-thermodynamic equations. The fuels tested were blends
of Jet A-1 and standard diesel and biodiesel. Performance parameters for each
blend where collected during experimental runs for every 10th throttle setting
using different monitors and readers. An intake horn with an elliptical profile
and bell-mouth geometry was designed to enable air mass flow rate calculations
using a pressure sensor attached to the intake to measure the dynamic pressure
of the air flow which will give the flow velocity. Basic gas turbine thermodynamic
equations where used to describe the different processes at each stage throughout the engine based on relevant input parameters. The equations were used to
determine the unknown compressor pressure ratio at different speeds by testing
different compressor pressure ratio values in the equations to generate a thrust
output which was compared to the experimentally found result until a satisfying
vale was reached. The compressor map of another microjet of similar size was
researched to give reasonable values for the different efficiencies needed in the
equations. The results show that most of the data collected at the experimental
rig may be derived from the measured pump voltage which mathematical relationships are being used in the gas turbine model. When the compressor pressure
ratios and efficiencies found are used as input parameters, the model can predict
the microjet engine’s thrust output with very small deviations from the true value
regardless of what fuel blend is used. Impeller analysis suggested that the compressor geometry is too complicated to be described with simple equations which
means the compressor pressure ratio cannot be derived and thus must remain
an input parameter. This concludes that simple thermodynamic equations alone
cannot completely predict the performance of the Merlin VT80.
v
Contents
1 Introduction
1.1 Performance prediction . . . . . .
1.2 Use of alternative fuels . . . . . .
1.3 Biofuels . . . . . . . . . . . . . .
1.4 Gas Turbine Evolution . . . . . .
1.4.1 The First Jet Engine . . .
1.4.2 Microjet Engines . . . . .
1.5 Engine Theory . . . . . . . . . .
1.5.1 Gas Turbines . . . . . . .
1.5.2 The compressor . . . . . .
1.5.3 The combustion chamber
1.5.4 The turbine . . . . . . . .
1.6 The Project . . . . . . . . . . . .
1.6.1 Purpose of the project . .
1.6.2 Problem description . . .
1.6.3 Project process . . . . . .
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1
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. 6
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. 9
. 9
. 9
. 10
2 Theory
2.1 Basic physical concepts . . . . . .
2.2 Fuel properties . . . . . . . . . . .
2.3 Error analysis . . . . . . . . . . . .
2.4 The Vena Contracta Effect . . . .
2.5 Thermodynamic calculations in gas
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turbines
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11
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3 Method
3.1 The Engine . . . . . . . . . . . . .
3.2 Fuels . . . . . . . . . . . . . . . . .
3.3 The experimental rig set-up . . . .
3.4 Designing the air intake . . . . . .
3.5 Calibrating the thrust load cell . .
3.6 Calculating the air mass flow rate .
3.7 Fuel blends . . . . . . . . . . . . .
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20
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vii
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3.7.1 Solubility test . . . . . . . . . . . .
3.7.2 Density determinations . . . . . .
3.7.3 Blend properties . . . . . . . . . .
3.8 Performance characteristics measurements
3.8.1 Starting the engine . . . . . . . . .
3.8.2 Collecting data . . . . . . . . . . .
3.8.3 Engine shut down procedure . . .
3.9 Compressor map analysis . . . . . . . . .
3.10 Compressor pressure ratio investigation .
3.10.1 Impeller theory . . . . . . . . . . .
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28
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4 Results
37
4.1 Model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Performance characteristics . . . . . . . . . . . . . . . . . . . . . . 38
4.3 Parameter relationships . . . . . . . . . . . . . . . . . . . . . . . . 40
5 Discussion
5.1 Model parameters . . . . .
5.2 Performance characteristics
5.3 Parameter relationships . .
5.4 The computer model . . . .
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43
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46
6 Conclusions
47
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
A Extra figures
49
B MATLAB code
52
C Test run results
56
viii
Preface
This thesis is the final project for a Master of Science in Engineering degree focusing in Aerospace Engineering at the Department of Computer Science, Electrical and Space Engineering (SRT) at Luleå University of Technology (LTU) in
Luleå, Sweden. The project was conducted at the Department of Mechanical and
Aerospace Engineering at Monash University in Melbourne, Australia under the
supervision of Associate Professor Damon Honnery. The examiner at LTU was
Associate Professor Lars-Göran Westerberg.
I would like to thank A/Prof. Damon Honnery for the opportunity to carrying
out my project at Monash University and for all the help and guidance he has
given me. I give extra thanks to Edward Kuo for his invaluable help and support
at the rig and for always being there. I also want to thank all postdoctoral and
postgraduate students at the LTRAC lab for their support and kindness. Furthermore I would like to thank Ångpanneföreningens Forskningsstiftelse, Sven
Molin for all the help with accommodations and Helen Fox at Monash HR Immigration for help getting the visa approved in time.
Finally, I would like to thank my family and friends for their support and encouragement; without it I would not have made this far. Special thanks to Daniel,
who chose to accompany me on my journey and made the experience, not just
mine, but our adventure.
Maja Nylén
Melbourne, Australia
ix
List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
2.1
2.2
2.3
3.1
3.2
3.3
3.4
3.5
The team behind the first jet driven RC Air plane in 1983 (Photo:
RC Universe). . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The first microjet was 340mm long, had a diameter of 120mm and
weighed 1.7kg. It run on propane and produced ∼ 40N of thrust at
85, 000rpm [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simple gas turbine system [1]. . . . . . . . . . . . . . . . . . . . .
(a) An axial flow compressor with multiple stages (Photo: Gary
Brossett, 2003). (b) Centrifugal compressors; an impeller with radially tipped blades and an impeller with slightly retro-curved blades
[11]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diagram of a combustion chamber [11]. . . . . . . . . . . . . . .
An axial turbine blade [11]. . . . . . . . . . . . . . . . . . . . . .
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5
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6
6
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7
8
9
Streamline patterns and contraction coefficients for a (a): sharp
edge orifice and (b): a well-rounded orifice. Cc is the contraction
coefficient [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
The velocity flow profile into a plain pipe (a) and a radius pipe (b)
- the vena contracta effect is evident by the regions of higher Mach
number at the entry in (a) but the effect has reduced significantly
in (b) due to the well-rounded intake [14]. . . . . . . . . . . . . . . 16
A simple turbojet engine with station numbering[1]. . . . . . . . . . 16
The MERLIN VT80 microjet engine produces ∼ 85N of thrust at
150, 000rpm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The experimental rig set-up; 1) The microjet 2) Fuel mass indicator 3) Thrust indicator 4) Fuel tank 5) 5kg load cell 6) Battery 7)
30kg load cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Nomenclature and design guide lines for the bell-mouth used
in the project [14]. The finished bell-mouth got the characteristics:
ELL-70-70-150-12. (b) The bell-mouth’s velocity profile shows almost no vena contracta effect present at all.[14]. . . . . . . . . . . .
The elliptical profile expressed mathematically in MATLAB . . . . . .
(a) The ready intake horn and (b) The intake mounted to the engine.
xi
21
23
24
25
26
3.6
3.7
3.8
3.9
Calibrating the load cell using weights. . . . . . . . . . . . . . . .
The pressure sensor collar. . . . . . . . . . . . . . . . . . . . . .
Pycnometer with biodiesel (V olume = 51.233cm3 ). . . . . . . . .
Compressor map used to define a typical polytropic efficiency range
for the VT80 [22]. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.10 Nomenclature for a radial impeller and corresponding velocity triangles [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1
4.2
4.3
4.4
4.5
4.6
The predicted thrust compared to the experimental results for a
pure Jet A-1 fuel run. The results coincide well over the span of
throttle settings. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The blends perform consistently throughout the entire span of throttle settings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The thrust load cell is not consistent. . . . . . . . . . . . . . . . .
The EGT lowers as more air is pumped through the engine but at
higher throttle setting the air mass flow decreases and hence the
temperature rises. . . . . . . . . . . . . . . . . . . . . . . . . . . .
The TSFC is not consistent for the different blends at lower throttle
settings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Curve fitting for different sets of measured data. . . . . . . . . . .
. 27
. 28
. 29
. 32
. 35
. 37
. 39
. 39
. 40
. 41
. 42
A.1 The intake horn drawing. . . . . . . . . . . . . . . . . . . . . . . . 50
A.2 The discharge coefficient for ASME flow nozzle [12]. . . . . . . . . 51
xii
List of Tables
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.1
4.2
The microjet’s engine specifications [17]. . . . . . . . . . . . . . .
Fuel properties [18] [19] [20]. . . . . . . . . . . . . . . . . . . . . .
ASME Long-Radius nozzle standards [12]. . . . . . . . . . . . . .
Intake measurements. . . . . . . . . . . . . . . . . . . . . . . . .
Measured properties for the different fuels. . . . . . . . . . . . . .
The 80/20% and the 50/50% blend weight distribution. . . . . . .
The energy content and the density of different blends. . . . . . .
Measured and calculated values for the five points chosen in Figure
3.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pressure ratios and efficiencies for the VT80’s compressor. πc lies
within the expected 1-4 range and ηc within the 0.65 − 0.78 range.
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21
22
23
25
29
30
30
. 34
. 34
Technical parameters for the VT80 run on different fuel blends. . . 38
Slip factor and pressure value investigation . . . . . . . . . . . . . 38
xiii
Nomenclature
Abbreviations
AFR
ASME
CFD
CO
ECU
EGT
ELL
FAR
HHV
LHV
LTRAC
LTU
MAV
NOx
PP
RAD
RC
RPM
SOx
SRT
TIT
TSFC
UVA
Air-Fuel Ratio
American Society of Mechanical Engineers
Computational Fluid Dynamics
Carbon monoxide
Electronic Control Unit
Exhaust Gas Temperature
Elliptical profile bell-mouth
Fuel-Air Ratio
Higher Heating Value (Gross calorific value)
Lower Heating Value (Net calorific value)
Laboratory for Turbulence Research in Aerospace and Combustion
Luleå University of Technology
Micro Air Vehicles
Nitrogen Oxides
Plain pipe (sharp-edged)
Simple radius pipe
Radio Controlled
Revolutions Per Minute
Sulphur Oxides
Department of Computer Science, Electrical and Space Engineering
Turbine inlet temperature
Thrust Specific Fuel Consumption
Unmanned Aerial Vehicles
xiv
Commonly used symbols
β
c
ca
c5
Cc
F
M
ṁ
ṁf
p
π
R
Rg
Re
ρ
Tc
V
z
Intake diameter ratio, De /Di
Speed of sound
Ambient velocity
Nozzle exit velocity
Contraction coefficient
Thrust
Mach number
Air mass flow rate
Fuel mass flow rate
Static pressure
Pressure ratio
Specific gas constant (air)
Specific gas constant (hot gas)
Reynolds number
Density
Critical temperature
Flow velocity
Relative height
[m/s]
[m/s]
[m/s]
[N]
[kg/s]
[kg/s]
[Pa]
[J/kgK]
[J/kgK]
[kg/m3 ]
[K]
[m/s]
[m]
Indexes
a
B
c
i
j
jc
t
01
02
03
04
5
Ambient
Combustor
Compressor
Intake
Propelling nozzle
Critical propelling nozzle
Turbine
Compressor inlet
Compressor outlet
Turbine inlet
Turbine outlet
Nozzle exit
Constants
cpa
cpg
γa = γair
γg = γgas
R
1005
1145
1.4
1.333
286.9
[J/kgK]
[J/kgK]
[J/kgK]
xv
Chapter 1
Introduction
1.1
Performance prediction
Gas turbines are currently used all over the world; in land based industries, on
oceans and especially in the air. They are power efficient with low fuel consumption, deliver effective power well beyond the limitations of piston engines and
they provide considerable improvements in emissions compared to diesel engines.
Due to these performance capabilities, the gas turbine has been denoted one of
the most important inventions of the 20th century [1].
Micro gas turbines, or microjet engines, have over 30 years developed from being
an appreciated constituent in the Radio Controlled (RC) model aircraft world
to become a common feature in various military and commercial applications.
Some of these applications currently include cruise missiles, Unmanned Aerial
Vehicles (UVA’s) and Micro Air Vehicles (MAV’s). These vehicles are designed
to carry out missions such as real-time reconnaissance, laser marking of targets,
surveillance and even analysing the air for potential chemical or biological warfare
agents [2]. The microjet engine’s high thrust-to-weight ratio makes them highly
suitable for these types of missions. Modern microjets emulates the large engines
in function and sophistication with the advantages of compact size, light-weight,
small number of moving parts, low energy costs and emissions and multi-fuel capacity. This means microjets can be mounted on scaled airframes to support the
flight test program of the fill-sized aircraft to a much lower cost, without risking
a pilot and the ability to perform manoeuvres that are not easily simulated in a
wind tunnel.
Unfortunately the downsizing of gas turbines does result in major fuel efficiency
problems and reduced overall engine performance. For instance, current micro
1
turbine powered military target drones may only fly at desired altitude and locations for a few minutes at a time before returning to base for refuelling [3]. This
means large amounts of costly petroleum based fuels are being consumed at a
high rate, which is not economically beneficial nor particularly environmentally
friendly. Hence research on alternative fuels to be used as substitutes has become
a highly current topic as the demands and field of applications increases for the
microjet industry. Tan & Liou [4] demonstrated the performance characteristics
for the MW54 microjet engine when run on various blends of a B100 1 biofuel and
Jet A-1 kerosene. They showed that the microjet could operate and perform in a
consistent manner and that various blends produced the same amount of thrust
at the same engine speed. The Thrust Specific Fuel Consumption (TSFC)2 was
found to be significantly lower for the pure biofuel than kerosene at the 50%
throttle setting. Also, they concluded that the more efficient combustion of the
biofuel indicated a possible reduction in greenhouse gas emissions. Later, Tan
& Liou [5] also demonstrated the engine performance and emission for the MW54
microjet when run on kerosene, B100 biodiesel, HJ and JP-83 fuels. Results show
that the engine performed consistently well in the wide range of fuel and it was
found that the B100 fuel produced the least nitrogen oxides (N Ox ) but produced
the most carbon monoxide (CO) and carbon dioxide (CO2 ).
The ability to predict an engine’s performance when run on a certain fuel not only
minimize the number of costly tests but it also has great time reduction benefits
as well. Computational fluid dynamics (CFD) analyses or computer programs
based on simple aero-thermodynamic equations are usually used to calculate specific performance parameters. Jones [3] sought to optimize the performance of the
AMT Olympus HP microjet engine after alterations to individual components using the GasTurb performance simulation software. The engine was deconstructed
and the individual components were precision scanned to produce CAD models
which were used in a CFD simulation to predict their individual performances.
Due to time restrains, the model was however not capable of fully simulating the
performance when the report was published. Despite the current and relevant
topic is the amount of articles regarding computer model predictions for microjet
engines run on alternative fuels limited. Performance prediction research have
however been conducted on individual components such as the compressor and
combustion chamber. Eftari et al. [6] investigated the performance characteristics of an two-stage axial flow compressor using 1-D modelling. The intended
performance features were reached with corresponding compressor map features
outlined. Prior models on various compressor components had been used to pre1
The number after the B indicates the % of biofuel in the blend.
Described in Chapter 2
3
The military equivalent of Jet A-1
2
2
pare a comprehensive model which up until this research had not been found in
the open literature. Gieras & Stankowski [7] performed 3-D numerical CFD
simulations studies of aerodynamic flow inside the GTM-120 micro turbine combustion chamber. Since knowledge of combustion processes in micro turbines is
mostly derived from full-scale testing of large turbine engines, the authors intend
to describe what effects miniaturization of engine construction has on the air flow
and heat transfer in the engine. The results showed that the total pressure drop
for this miniature combustor (cold flow) is approximately 10%. The study also
concluded that the amount of air mass flow through the combustor affects the
total loss of total pressure, i.e. increased air mass flow gives distinct increase in
total pressure loss. An optimization of the whole combustion chamber was hence
concluded to be necessary to obtain smaller pressure losses.
Any advanced gas turbine model capable of determining engine performance base
their algorithms on simple aero-thermodynamic equations. None of the studies
mentioned above have discussed at any deeper level the possibility of using a
computer model entirely based on simple, 1-D aero-thermodynamic equations to
predict the engine performance. This project thus aims to investigate whether
a self-written computer model of this simple sort is capable of determining the
engine performance when run on alternative fuels.
1.2
Use of alternative fuels
Engines of any sort are most often designed to run on one specific fuel only. Gas
turbines are no exception. This is to make sure the functionality of the fuel delivery system is not jeopardized, since another fuel of other characteristics may
block or harm vital engine parts. Most engines would need a complete redesign
of the fuel delivery system if a different fuel is to be used. A swap to a more
environmentally friendly fuel, such as biofuels, might also have the effect of a
lowered power output in the engine due to the lower energy content. A costly
complete redesign and a decreased power output is not what most engine operators long for, but the regular fuel may however be blended with another fuel
of similar characteristics. At certain blend concentrations may a lower energy
content be compensated for by other distinguish characteristics in the alternative fuel, such as density and viscosity, and the power output therefore remains
unchanged. Since only a portion of the new, so called ’drop-in fuel ’, is added
to the regular fuel the blend may still fully compatible with the engine and the
fuel delivery system. A fuel blend of desired properties may therefore help avoid
unnecessary waste of expensive and non-environmental friendly fuels.
3
Microjet engines are designed to run on aviation kerosene4 , mostly Jet A-1. Unfortunately aviation kerosene is rather expensive and the microjet’s apparent
major fuel efficient problems makes the search for alternative fuels an interesting
topic from an economical point of view. If price is the only consideration the alternative fuel does not necessarily need to be a biofuel; a cheaper fuel like diesel
might be appropriate to use as a drop-in fuel. Also, if the accessibility to the
kerosene becomes limited the use of alternative fuels is a reassurance that the
engine still may be able to fully operate. The later is a real necessity in military
applications.
1.3
Biofuels
Biofuels are fuels produced from different renewable biological resources such as
plant material that absorbs CO2 and uses sunlight to grow. Studies suggest that
biofuels are anticipated to provide an estimated 80% reduction in overall CO2 life
cycle emissions compared to fossile fuels [8]. Fuels made from sustainable, nonfood biomass sources that do not impact the food supply chain or fresh water
resources, or causes deforestation are known as next-generation or sustainable
biofuels and examples of feedstocks, i.e. raw material frow which the fuels are
produced, include camelina, jatropha, halophytes and algae. Biodiesel is a first
generation biofuel which is made from e.g. vegetable oils and animal fats.
1.4
1.4.1
Gas Turbine Evolution
The First Jet Engine
The first really important application for the gas turbine was the military jet
engine developed during the end of World War II in which technology practically
exploded and reformed the entire aviation industry. The success lies in the gas
turbine’s ability to deliver practical high speed aircraft at a much lower engine
weight and size at higher altitudes - something the piston engine is incapable
of. The world’s first flight of a turbojet propelled aircraft, the Heinkel He 178,
was realized on 27 August 1939 in Germany and a British parallel, the Gloster
E28/39 was airborne on 15 May 1941 [9]. Even though the early jet engines were
fuel inefficient, unreliable and extremely noisy the development needed only less
than 20 years to mature and become the standard form of propulsion for civil
aircraft.
4
Kerosene, gasoline and diesel oils are all product extracted from crude oil (petroleum).
4
1.4.2
Microjet Engines
The microjet engine first evolved from model aircraft devotees longing for miniature replicas of the full-sized engine. This evolved into home-build prototypes
that were innovated and developed over time in private workshops. On 20 March
1983, a British team lead by Jerry Jackman, performed the world’s first turbine powered model flight when their RC model aircraft Barjay took off from
the Greenham common airfield, UK and accomplished a three minute flight. A
photo of Barjay and the whole team on the day of the premier flight is presented
in Figure 1.1. Jackman’s engine, seen in Figure 1.2, had a diameter of 120mm,
was 340mm long and weighed 1.7kg. Running on propane it produced over 40N
at 85,000rpm and had a top speed of 97,000rpm [2]. It is easy to presume that
micro turbines are merely scaled down versions of the operating large engines, but
the fact is that air does not scale! A miniaturization of components will result in
major changes in the air flow parameters and the heat transfer in the engine [10]
along with greater demands on the bearings and the material used due to the high
operating speeds (rpm). Also, the models operate in low speeds at low altitudes
for short durations with thrust being the aim and with low priority of the fuel
efficiency. Complete redesign is hence required when developing micro turbines
and much of the innovation actually continues to be among home-builders. Ever
smaller turbojets are constantly being developed as design techniques and material knowledge increases. For instance, the American company M-Dot Aerospace
has designed a mini-micro-turbojet that fits inside an egg and produces 6.2N of
thrust [2].
Figure 1.1: The team behind the first jet driven RC Air plane in 1983
(Photo: RC Universe).
5
Figure 1.2: The first microjet was 340mm long, had a diameter of
120mm and weighed 1.7kg. It run on propane and produced ∼ 40N of thrust at 85, 000rpm [2].
1.5
1.5.1
Engine Theory
Gas Turbines
A gas turbine, or internal combustion turbine, in its simplest form consists of
three main components; an upstream compressor, a combustion chamber in the
middle and a downstream turbine connected together as shown diagrammatically
in Figure 1.3. The compressor uses a pressure ratio to provide the turbine with
energy which in turn is used to run the compressor and so the gas turbine work
cycle is in progress.
Figure 1.3: Simple gas turbine system [1].
The process for a shaft gas turbine is as follows: the working fluid, e.g. air,
is compressed in the compressor and then expanded through the turbine which
generates power output. If combustion of fuel is performed in the compressed
air the temperature will rise in the gas and an even greater pressure ratio can be
obtained. This is clearly shown when looking at the Ideal Gas Law
pV = nRT
(1.1)
where, for an ideal gas, p is the pressure, V is the volume, n is the number of moles,
R is the universal gas constant (R = 8.314J/molK) and T is the temperature.
The now hot and more compressed air will enhance the expansion through the
turbine which generates an increased power output in addition to driving the
6
compressor. Turbojet engines has a similar mechanical layout and work process
to the simple gas turbine but the turbine is now designed to produce just enough
power to run the compressor. A high velocity jet is then produced when the
working fluid leaves the turbine at high pressure and temperature and expands
to atmospheric pressure in a propelling nozzle.
1.5.2
The compressor
Large engines with high power requirements use axial flow compressors in which
the gas is being compressed in a series of stages. However, the large number of
stages involves great constructional complexity and as the engines get smaller the
concept no longer remains suitable. The small sizes and low Reynolds numbers
also diminish the level of efficiency as the engines becomes smaller and that is
why micro turbine almost exclusively use the centrifugal compressor instead [11].
Images of both compressor models are presented in Figure 1.4. The centrifugal
compressor is extremely robust and straightforward in its construction and consists of a stationary casing containing a rotating impeller. The air is drawn into
the impeller eye and whirled around by the blade ducts and thus accelerates the
flow. The air then flows outwards at high speed in the radial direction under the
influence of centrifugal force and once outside the impeller the air is slowed in
the compressor diffuser system. This action will then convert the kinetic energy
of the air into pressure.
(a)
(b)
Figure 1.4: (a) An axial flow compressor with multiple stages (Photo:
Gary Brossett, 2003). (b) Centrifugal compressors; an
impeller with radially tipped blades and an impeller with
slightly retro-curved blades [11].
1.5.3
The combustion chamber
With no moving parts, the design of the combustion chamber seems fairly easy
but it is actually highly critical and a good design is essential for an operational
engine. If the combustion is uneven it will result in portions of inflow air that
is not heated to full temperature and consequently does little work when flowing
7
Figure 1.5: Diagram of a combustion chamber [11].
through the turbine. A diagram of a combustion chamber is presented in Figure
1.5. To get a stable combustion a stoichiometric fuel-air mixture ratio is needed
i.e. the mixture contains enough oxygen to enable complete combustion. The
stoichiometric mixture is burned in the primary zone of the chamber, where the
major part of the fuel combustion process occurs, and the hot gases are then
cooled with supplementary air in the secondary zone via air holes. The cooling is
necessary to give the hot gases a temperature which the turbine can withstand.
For model jet engines the combustion chamber cooling is not a problem since the
temperature rise is fairly low due to the low pressure ratio. However, the smaller
the engine the smaller the chamber gets and optimizing design problems occur.
The air spends an extremely short period of time in the combustion chamber,
1
only about 500
of a second [11], and within this period the air and fuel have to
mix, burn, and be cooled. Since combustion only can occur when a combustible
mixture is formed, a too short chamber will result in only a proportion of fuel
being burnt in the chamber, and the excess fuel will leave the engine unburned.
Not only will this result in lower engine efficiency but it will also cause flames
to continue into the turbine and then blow out of the exhaust. Poor combustion
hence has an unfavourable effect on the turbine efficiency and its life span since
the turbine is being exposed to overheating. This, in turn, might cause some
heating of the air during the compression process which will result in diminished
effect of the combustion and thus lower the turbine efficiency further. Therefore
it is extremely critical to restrict the combustion process to the confines of the
combustion chamber.
1.5.4
The turbine
The turbine’s method of working is the opposite of the compressor i.e. the pressure is reduced and then converted to kinetic energy. The hot gases from the
combustion chamber are deflected in the turbine blades and are forced out in
the direction opposite to rotation at high speed. Each flow duct hence form a
8
Figure 1.6: An axial turbine blade [11].
small jet that produces a thrust which is acting upon the turbine blades and the
sum of the thrust forces generates a peripheral force i.e. torque. Though axial
turbines are the standard for full-sized jet engines, both axial and centrifugal
turbines can, in theory, be used on model engines [11]. However the centrifugal
turbine have issues of mechanical nature rather than thermodynamic e.g. the
rotor might weigh up to 0.4kg which means a high moment of inertia and hence a
poor accelerating ability. Therefore, axial turbines are more likely to be chosen in
model engine context as well. A picture of an axial turbine for microjet engines
is presented in Figure 1.6.
1.6
1.6.1
The Project
Purpose of the project
The purpose of the project was to undertake a series of experiments measuring
the performance characteristics of a microjet engine operating on a range of
alternative fuels for the purpose of validating a 1-D aero-thermodynamics based
gas turbine model. The aim was to determine whether these relatively simple
gas turbine codes can be used to predict engine performance when operating on
alternative fuels. To be able to achieve this, a primary thorough investigation of
the microjet engine’s performance had to be conducted.
1.6.2
Problem description
The project had three major problems to address and try to find solutions to:
• All parameters needed to create a working gas turbine model can be found
from the experimental rig except for the air mass flow rate through the
engine. To calculate this data, an intake needed to be designed where
a pressure sensor attached to the intake enables calculations on the flow
velocity. The intake had to be made robust, light and long enough to
enable measurements of the flow before it got disturbed by the engine’s
electrical starter mounted in front of the compressor intake.
9
• When collecting the microjet engine’s performance characteristics, several
parameters are documented both manually and in a computer program. To
save time, and thus fuel, when performing test at the rig an investigation on
parameter relationships were to be conducted. If a mathematical expression could be linked from one easily measured parameter to several others
with low errors, calibrations and documentations of chosen sensors could
be eliminated.
• The experimentally found performance characteristics were to be implemented in thermal analysis calculations to derive further parameters and
help determine engine specifications, such as compressor pressure ratio and
isentropic efficiencies. The complete set of parameters were to be used to
create a simple gas turbine model that is able to describe the engine performance at different speeds when run on pure Jet A-1. By conducting further
tests with higher percentage of alternative fuel blends, the results could be
compared in the working model to determine similar behaviours and deviations characteristic to a certain blend. If only minor deviations occur
between the results, then the model has verified that the thermodynamic
codes can still predict the engine performance when operating on different
blend concentrations of alternative fuels.
1.6.3
Project process
The project was to be conducted in three different stages:
Stage 1
Preliminary work such as literature and fuel research, become an approved
trained operator for the microjet, and designing the intake.
Stage 2
The testing phase where all performance characteristics were collected.
Stage 3
Modifying data to determine the microjet engine performance and development of a workable gas turbine model to be used when validating the final
results.
10
Chapter 2
Theory
2.1
Basic physical concepts
The Reynolds number is a dimensionless parameter commonly used in the field
of fluid mechanics. It is a measure of the ratio of inertia to viscous forces on an
element of fluid and is thus defined as
Re =
ρvL
vL
=
µ
ν
(2.1)
where v is the mean velocity of the fluid, L a characteristic length, µ the dynamic viscosity, ρ the density and ν the kinematic viscosity of the fluid (ν = µρ ).
Reynolds number combines the effects of viscosity, density and velocity of a
moving fluid and can be used as a criterion to distinguish between laminar
(Re ≤ 2000) and turbulent (Re ≥ 4000) flow [12].
The Mach number is the ratio of the speed of the moving fluid to the speed of
sound in that fluid:
V
M=
(2.2)
c
The speed of sound can be calculated using
p
(2.3)
c = γRT
where γ = cp /cv , R is the specific gas constant and T is the temperature of the
fluid.
The Bernoulli’s equation for steady, inviscid, incompressible flows states that
1
p + ρV 2 + ρgz = constant along a stream line
2
11
(2.4)
The first term p is the static pressure which is the actual thermodynamic pressure
of the air as it flows. The second term 12 ρV 2 is the dynamic pressure which
depends on the flow density ρ and flow velocity V . The third term ρgz is the
hydrostatic pressure which depends on the specific weight γ = ρg and on the
relative height z. If the flow between two points (1 and 2) is assumed to be
horizontal (z1 = z2 ) then Equation 2.4 becomes
1
1
p1 + ρV1 2 = p2 + ρV2 2
2
2
(2.5)
When the cross-sectional area of the intake is much smaller than that of the
room containing the air, it is valid to assume that the air velocity in the room
is equal to zero [13], hence V1 = 0 in Equation 2.5. The difference between the
static pressure of the flow and the atmospheric, ambient pressure thus gives the
dynamic pressure which the flow velocity can be extracted from:
s
2(p1 − p2 )
V2 =
(2.6)
ρ
The pressure difference is easily measured using a pressure sensor attached to the
air intake.
The continuity equation states that the air mass flow rate (ṁ) throughout a
system is constant. It is defines as
ṁ = ρA1 V1 = ρA2 V2
(2.7)
where ρ is the density of the air, A the cross-sectional area of the flow and V the
flow speed.
The Thrust Specific Fuel Consumption (TSFC) is the ”mass of fuel burned
by an engine in one time unit divided by the thrust that the engine produces”.
It is thus expressed as
ṁf
T SF C =
(2.8)
F
where ṁf is the fuel mass flow rate and F is the net thrust. The lower the
TSFC is, the more fuel efficient the engine is considered to be. The word specific
means ”divided by mass or weight, or int his case: force” and the word thrust
in TSFC indicates that a gas turbine is being considered (Engines that produce
shaft power uses Brake Specific Fuel Consumption (BSFC))
12
The Air-Fuel Ratio (AFR) is a common reference term used for mixtures in
gas turbines and is defines as the ratio between the mass of air and the mass of
fuel in the fuel-air mixture at any given moment:
AF R =
mair
mf uel
(2.9)
Even more used in the gas turbine industry is the Fuel-Air Ratio (FAR) which
is the reciprocal of the AFR:
F AR =
1
AF R
(2.10)
Isentropic efficiency (η) is a parameter that compares the actual performance
of a device to the performance that would be achieved under idealized circumstances for the same inlet and exit conditions. It is hence a measure of the
energy degradation occurring in steady-flow devices and is commonly used in
aero-thermodynamic calculations.
Polytropic efficiency (η∞ ), or small-stage efficiency, is defined as the isentropic
efficiency of an elemental stage in the process such that it is constant throughout
the whole process [1]. It is related to the compressor pressure ratio (πc ) and the
compressor isentropic efficiency (ηc ) according to the equation
ηc =
(p02 /p01 )(γ−1/γ) − 1
(p02 /p01 )(γ−1)/(γη∞ ) − 1
(2.11)
Unlike the isentropic efficiencies in the compressor and turbine (ηt ), that tend
to vary with changes in the corresponding pressure ratio, is it reasonable to assume constant polytropic efficiency for the same process [1]. This assumption
does not only automatically allow for the variations of the isentropic efficiencies
to take place in the background but since the isentropic and polytropic efficiencies actually presents the same information but in different forms, only a minor
change in the thermodynamic equations is required to replace ηc and ηt with the
corresponding polytropic value.
2.2
Fuel properties
The Energy content (heating value) of a fuel describes the amount of heat
produced by combustion of a unit quantity of a fuel. This value can be divided
into two categories, a lower and a higher heating value based on the heat of water
vaporization:
13
The Lower heating value (LHV) or Net calorific value is the amount of
heat released by combusting a specified quantity (initially at 25◦ C) and returning the temperature of the combustion products to 150◦ C which assumes the
latent heat of vaporization of water in the reaction products is not recovered.
The Higher heating value (HHV) or Gross calorific value is the amount
of heat released by a specified quantity (initially at 25◦ C) once it is combusted
and the products have returned to a temperature of 25◦ C, which takes into account the latent heat of vaporization of water in the combustion products. The
HHV are derived only under laboratory conditions.
Since the microjet engine in this project is not recovering any heat through condensation of water vapour in the exhaust, the LHV will be used when determining
the energy content of the various fuels and blends.
2.3
Error analysis
Error is the difference between a measured and a true value of the measurement:
Error = E = XT − Xm
(2.12)
Uncertainty is the estimation of an error and is usually expressed within limits
of confidence; a 95% confidence limit is most used
The standard deviation (s) for a trend line over a set of data is calculated according to the equation
v
u
n
u 1 X
t
s=
2k
(2.13)
n−1
k=1
where k is the deviation of a measurement Xk from the mean X of the sample
given by
k = Xk − X
(2.14)
2.4
The Vena Contracta Effect
The shape of an air intake has an impact on the diameter of the jet at the intake
entrance which has to be accounted for when performing nozzle calculations. For
a sharp-edged intake, the flow will not be able to make a complete 90◦ turn and
a jet with a diameter smaller than the diameter of the intake orifice occurs at the
14
Figure 2.1: Streamline patterns and contraction coefficients for a (a):
sharp edge orifice and (b): a well-rounded orifice. Cc is
the contraction coefficient [15].
entrance. This is known as the vena contracta effect and is illustrated in Figure
2.1(a). If the intake is gradually rounded, this effect will diminish and be almost
completely gone for some ideal design parameters. The degree of contraction,
also known as the effectiveness of the flow, is given by a contraction coefficient
Cc based on the ratio of the jet to intake orifice areas according to
Cc =
Aj
Ah
(2.15)
In Figure 2.1(b) the intake is well rounded and since Cc = 1.0 the jet and the
intake diameter coincide and the effectiveness of the flow is at its maximum for
this case. Studies performed on different nozzle geometries demonstrate the vena
contracta effect through CFD simulations [14]. In Figure 2.2(a) a sharp-edged
plain pipe (PP) shows a high particle velocity (Mach 0.3) close to the entry
surrounding by a still region (Mach 0) and a reduction of velocity towards the
pipe exit (Mach 0.225). Interpretation of this result using the continuity equation
(Equation 2.7) shows that a higher velocity only occurs if the cross-sectional area
of the jet is reduced in size (since ṁ is constant). This combined with the reduced
Mach number towards the exit which shows that the cross-sectional area of the
jet increases along the pipe, demonstrates the existence of a vena contracta effect
close to the nozzle entry. The reduced effect by a well-rounded, simple radius
pipe (RAD) is clearly demonstrated in Figure 2.2(b). The particle velocity is
practically constant along the pipe, i.e. no changes in the cross-sectional area,
and only a small region of a slightly higher Mach number occurs at the very edge
of the entry.
15
Figure 2.2: The velocity flow profile into a plain pipe (a) and a radius pipe (b) - the vena contracta effect is evident by the
regions of higher Mach number at the entry in (a) but
the effect has reduced significantly in (b) due to the wellrounded intake [14].
Figure 2.3: A simple turbojet engine with station numbering[1].
2.5
Thermodynamic calculations in gas turbines
Aero-thermodynamic calculations for gas turbines can quite easily describe the
different processes at each stage throughout the entire the engine. Figure 2.3
shows the layout for a turbojet engine with a classic station numbering which are
used as indexes in the equations described in this section. The index 0 indicates
that stagnation 1 properties are used.
Intake (a → 01)
The intake (or ram) pressure ratio (πi ) is defined as
p01
γa − 1 2
πi =
= ηi
M +1
pa
γa
(2.16)
where ηi is the intake efficiency, γa = 1.4 and M is the Mach number in the
intake.
1
The value the static parameter would retain when brought to rest adiabatically and isentropically
16
Compressor (01 → 02)
The inlet pressure for the compressor (p01 ) is defined as
p01 = πi pa
(2.17)
The temperature rise (T02 − T01 ) in the compressor is determined from
h
i
T02 − T01 = T01 πc(γa −1)/γa η∞ − 1
(2.18)
where T01 is the intake temperature, πc = p02 /p01 is the compressor ratio
and η∞ is the polytropic efficiency. The pressure at the compressor outlet
(p02 ) is defined as
p02 = πc p01
(2.19)
The work required to drive the compressor (WC ) is expressed as
WC = cpa (T02 − T01 )
(2.20)
where cpa = 1005J/kgK.
Combustor (02 → 03)
Due to pressure losses in the combustion chamber, the pressure at the
turbine inlet (p03 ) can be determined using
p03 = πB p02
(2.21)
where πB = p03 /p02 .
Turbine (03 → 04)
The work extracted from the turbine (WT ) in a single spool engine is equal
to the compressor work value with an adjustment for spool mechanical
losses and is hence defined as
WT = cpg (T03 − T04 ) =
cpa (T02 − T01 )
ηm
(2.22)
where ηm is the mechanical efficiency and cpg = 1148J/kgK. An expression
for the temperature loss in the turbine can then be found using Equation
2.22
cpa (T02 − T01 )
T03 − T04 =
(2.23)
cpg ηm
The turbine inlet temperature (TIT) (T03 ) is found by adding the EGT to
the turbine temperature rise since T04 = EGT
T03 = (T03 − T04 ) + EGT
17
(2.24)
The turbine pressure ratio is defined as
γg
T03 − T04 (γg −1)η∞
p04
= 1−
πt =
p03
T03
(2.25)
where γg = 1.333. The pressure at the turbine outlet (p04 ) is defined as
p04 = πt p03
(2.26)
Propelling nozzle (04 → 05)
The propelling nozzle needs to be checked for critical flow conditions in
which a Mach number of 1 is reached at the minimum area along the duct.
This means that any further reduction in downstream pressure provides no
increase in mass flow and the duct is said to be choked. To determine the
critical conditions, the nozzle ratio πj = pa /p04 is compared to the critical
nozzle ratio (πjc )
Choked duct if
πjc > πj
→ p5 = pc
(2.27)
N on − choked duct if
πjc < πj
→ p5 = pa
(2.28)
(2.29)
where πjc is defined as
πjc
γg
pc
1 γg − 1 γg −1
=
= 1−
p04
η j γg + 1
(2.30)
ηj is the nozzle efficiency. For a choked flow the duct exit temperature (T5 ),
exit pressure (p5 ) and exit velocity (c5 ) is calculated as follows:
2
T5 = Tc = T04
(2.31)
γg + 1
p5 = pc = P04 πjc
p
c5 = γg Rg Tc
(2.32)
(2.33)
For a non-choked flow the temperature reduction in the nozzle (T04 − T5 )
and the duct exit velocity (c5 ) is calculated as follows:
"
#
γ −1
T04 − T5 = ηj T04 1 − πj
c5 =
g
γg
q
2cpg (T04 − T5 )
18
(2.34)
(2.35)
The net engine thrust (F ) is defines as
F = ṁ[(1 + F AR)(c5 − ca )] + Aj (p5 − pa )
(2.36)
where the first term is called the momentum thrust and the second term the
pressure thrust. Since the engine is stationary (ca = 0) and it is assumed
that ṁf << ṁ (F AR ≈ 0) the net thrust for a non-choked flow (p5 = pa )
will become
F = ṁc5
(2.37)
19
Chapter 3
Method
3.1
The Engine
The engine used in this project is the MERLIN VT80, a single shaft, microjet gas
turbine produced by Jets-Munt Turbines in Spain, presented in Figure 3.1. It
is specifically designed to power RC model aircraft and uses an electric starter
situated in the front to ensure an automatic start. Almost all vital components,
such as the Engine Control Unit (ECU) and rpm sensor, are integrated inside
the engine and the only external components are the fuel pump and filter. The
engine specifications are presented in Table 3.1. At maximum throttle it was
measured that the engine produces approximately 132 dB which is practically
the same level as for a full sized jet engine which means dual protection (plugs
+ earmuffs) must be worn at all time! [16]
3.2
Fuels
The fuels available for the project were Jet A-1, standard diesel and BioMaxT M
Biodiesel (B100). They have similar characteristics and are hence suitable for
blends. Some main fuel properties are listed in Table 3.2.
3.3
The experimental rig set-up
A photo of the experimental rig set-up is presented in Figure 3.2. The engine is
suspended between two metal plates which are mounted onto a baseplate. A 30kg
load cell is placed right in front of the baseplate to register the thrust produced
from the engine when the baseplate pushes against the load cell during runs. A
thrust indicator next to the engine registers the load cell values. A fuel tank is
placed on-top of a 5kg load cell and a fuel mass indicator registers its weight.
A software program is linked to the indicator and documents how the weight
20
Figure 3.1: The MERLIN VT80 microjet engine produces ∼ 85N of
thrust at 150, 000rpm.
Table 3.1: The microjet’s engine specifications [17].
Merlin VT80 engine specifications
Guaranteed thrust in ISA conditions 80N
Max. rpm
150,000
Idle rpm
45,000
Idle thrust
4.5N
Diameter
90.5mm
Length
217mm
Engine weight
950g
Installed weight
1075g
EGT at Max. rpm
550 − 650◦ C
Fuel
Kerosene =4% oil
Fuel consumption at 80N
220 g/min or 0.29 l/min
ECU processing
500 times/s
21
Table 3.2: Fuel properties [18] [19] [20].
Properties
Appearance
Boiling point
Freezing point
Flash point
Auto-ignition temp.
Density (at 15◦ C)
Kinematic viscosity
(at 40◦ C)
1
Jet A-1
Colourless
150 − 300◦ C
< −47◦ C
38 − 55◦ C
> 220◦ C
775 − 840
kg/m3
1 − 2mm2 /s
Diesel
Pale straw
170 − 390◦ C
Not available1
∼ 63◦ C
> 220◦ C
∼ 840
kg/m3
2 − 4.5mm2 /s
Biodiesel
Green
> 200◦ C
Not available1
> 120◦ C
> 200◦ C
860 − 890
kg/m3
3.5 − 5mm2 /s
Not well defined because they are mixtures
changes during runs, i.e. the fuel mass flow rate (ṁf ) can be calculated. The
fuel tank is connected to an electrical fuel pump which supplies the engine with
fuel. The full engine control settings are run either by a RC controller or using
the software program LabView. The microjet is connected to a power switch
and has an input port that receives commands, i.e. the throttle settings, from
the computer and an output port that provides another software called Fadec
with information of the engine’s properties. The parameters registered by Fadec
are the throttle setting, duty cycle, (fuel) pump power, exhaust gas temperature
(EGT), thrust and rpm. A pressure sensor mounted to the intake horn will give
information on the air mass flow rate (ṁ) through the engine and a volt meter
measures the voltage over the pump as the throttle settings changes during runs.
The entire rig is placed right in-front of an exhaust fan venting duct to minimize
the exhaust fumes inside the lab.
3.4
Designing the air intake
To be able to measure the air mass flow rate into the compressor, an air intake was
to be designed. To reduce the vena contracta effect discussed in Chapter 2, an
intake horn, or a cone, was concluded to be the most beneficial geometry for this
application. Studies performed on different nozzle geometries have shown that a
completely rounded edge in combination with a gradually decreasing nozzle will
almost entirely eliminate the vena contracta effect [14]. This geometry, when the
edge is completely round and wrapped towards the back, is called a bell-mouth.
The flow results can be further improved by designing the bell-mouth as ”short
and fat”, i.e. the length equal to the inner diameter according to the dimensions
presented in Figure 3.3(a). This bell-mouth has an elliptical profile (ELL) and
22
Figure 3.2: The experimental rig set-up; 1) The microjet 2) Fuel
mass indicator 3) Thrust indicator 4) Fuel tank 5) 5kg
load cell 6) Battery 7) 30kg load cell.
the corresponding velocity profile is presented in Figure 3.3(b) which shows a
smooth flow with almost no vena contracta effect present at all. Thus, an ELLgeometry based on these dimensions was chosen for the project. The American
Society of Mechanical Engineering (ASME) provides some flow nozzle standards
based on the so called β ratio where
β=
De
Di
(3.1)
is the ratio between the nozzle exit and inlet diameter. This ratio was used to
determine the shape for the elliptical profile. The ASME standards for low respectively high β ratios are presented in Table 3.3. For this project, β = 0.47
which is right in the middle of the two β-series and hence any of the two can be
chosen. The decision was made to use the low β-series dimensions to give the
Table 3.3: ASME Long-Radius nozzle standards [12].
β-ratio
Series
Major semi-axis (a)
Minor semi-axis (b)
0.2 ≤ β ≤ 0.5
Low β-Series
a = De
b = 32 De ,
0.45 ≤ β ≤ 0.8
High β-Series
a=
23
Di
2
b=
Di −De
2
(a)
(b)
Figure 3.3: (a) Nomenclature and design guide lines for the bellmouth used in the project [14]. The finished bell-mouth
got the characteristics: ELL-70-70-150-12. (b) The bellmouth’s velocity profile shows almost no vena contracta
effect present at all.[14].
intake the appearance of an horn rather than a cone. The wrap-round of the bellmouth edge can be made to a full ”ball” radius, i.e. a 360◦ wrap-round, if wanted.
However, it is considered unnecessary when compared to a ”half-radius” in terms
of performance and is much more complicated from a construction perspective.
Hence, a half-radius was primary the design approach but after consultations
with the project supervisor the wrap-round concept was found not vital for the
project so it was removed completely to save time during manufacturing.
It was possible to manufacture the desired elliptical profile for the horn if it could
be described by a mathematical function. However, since an ellipse is not a
function the problem was solved by expressing only one quadrant of the ellipse
for certain intervals. The equation for an (vertical) ellipse at origo
x 2
b2
+
y 2
=1
a2
with a = 70 and b = 47, according to Table 3.4, will yield the expression
r
x 2
y = 70 1 −
47
(3.2)
(3.3)
When run in MATLAB for −50 < x < 0 a mathematical expression for the elliptical
profile is achieved. The plot is presented in Figure 3.4.
Due to the electrical starter mounted in front of the compressor intake, the intake horn had to be elongated to permit air flow measurements upstream from
the starter. The elongation pipe was attached to a back piece which was designed
to fit like a hood on top of the engine front. All measurements for the three parts
24
Figure 3.4: The elliptical profile expressed mathematically in MATLAB
are presented in Table 3.4 and the final drawing can be seen in Appendix A. Aluminium was chosen as the material for the entire intake to keep the construction
strong and light weight to a low price. The finished intake is presented in Figure
3.5.
Table 3.4: Intake measurements.
Piece
Horn:
Exit inner diameter
Inlet inner diamter
Length
Corner radius
Wall thickness
Elliptical profile:
Major semi-axis
Minor semi-axis
Pipe:
Length
Wall thickness
Back piece:
Inner diameter
Length
Wall thickness
Symbol
[mm]
De
Di
L
RC
dh
70
150
70
12
2-5
a
b
70
47
Lp
dp
150
3
Dbp
Lbp
dbp
90.45
29
2
25
(a)
(b)
Figure 3.5: (a) The ready intake horn and (b) The intake mounted
to the engine.
3.5
Calibrating the thrust load cell
Due to the extra weight of the intake horn, the thrust load cell needed to be
recalibrated. By attaching a thin wire to the engine base plate and letting free
hanging weights pull it through a pulley system, the gravitational force is easily
calculated using Newton’s 2nd law
F = ma
(3.4)
When calibrated correctly, the load cell will display a thrust equal to F . A picture
of the set-up is presented in Figure 3.6. A linearizing method was used in which
a few points where measured; the force at the minimum and maximum load and
five arbitrary points in-between. The result for each point was programmed into
the computer and the pulley system was then removed from the rig. A test run of
the engine confirmed the quality of the calibration by looking at the thrust output
at maximum throttle setting and compare the result to the engine specifications
presented in Table 3.1.
3.6
Calculating the air mass flow rate
One important parameter when predicting engine performance is the compressor
throughput, i.e. the air mass flow rate (ṁ), through the compressor. It is derived
from the continuity equation (Equation 2.7) and is measured in kg air per second.
ṁ is virtually constant at all points in a model jet engine [11] which means
ṁintake = ṁcompressor
(3.5)
Using Equation 2.6 thus gives an expression for the ideal ṁ in the compressor:
s
2(patm − pstatic )
ṁcompressor = ρAi Vi = ρ πri2
(3.6)
ρ
26
Figure 3.6: Calibrating the load cell using weights.
To enable measurement of the pressure difference patm − pstatic , a ’collar’ was attached to the intake according to Figure 3.7. The collar is hollow and is connected
to the air flow inside the intake via four holes in the intake wall. A pressure sensor
that is externally attached to the collar via a tube is hence able to measure both
the static pressure inside the intake and the atmospheric pressure in the room.
The intake area (Ai ) is known and the density of the air can be determined using
ρ=
pa
RTa
(3.7)
where pa and Ta are the ambient conditions and R = 286.9 is the specific gas
constant for air. However, the true flow rate is almost always less than the
theoretically calculated value so a discharge coefficient (Cn ) for a flow nozzle has
to be included and yields the equation:
ṁreal = Cn ṁcompressor
(3.8)
Cn accounts for viscous, secondary flow separations and any vena contracta effects
and can be determined by calculating the Reynolds number using Equation 2.1
and reading of Figure A.2 found in Appendix A for β = 0.47.
27
Figure 3.7: The pressure sensor collar.
3.7
3.7.1
Fuel blends
Solubility test
A solubility test to check the stability of the different blends was conducted with
arbitrary blend concentrations. Samples of a 60/40% diesel blend and a 75/25%
biodiesel blend were prepared and left in sealed glass containers. The blends
showed no indication of layering in neither case after 24 hours. Even 6 days
later, the samples looked fine but advice was still given to prepare the blends
and perform the test on the same day to guarantee maximum stability during
the tests.
3.7.2
Density determinations
The densities for each fuel was measured using a pycnometer ; a glass flask with an
accurately known volume which has a capillary tube through its stopper to allow
air bubbles to escape. A photo of the pycnometer containing biodiesel is presented
in Figure 3.8. The weight of a dry and empty pycnometer was subtracted from
the weight of the filled equivalence and the result was divided by the pycnometer
volume of 51.233cm3 to get the density for each fuel. The results are presented
in Table 3.5 together with the LHV and the kinematic viscosity for each fuel.
3.7.3
Blend properties
The measured densities were then used to determine a suitable blend that fulfilled
the requirements for the fuel tank (max 5L), the engine rig (max 5kg) and the
amount of oil needed (5%). The results for an 80/20% and a 50/50% blend, measured by weight, is presented in Table 3.6. The density of each fuel blend was then
28
Figure 3.8: Pycnometer with biodiesel (V olume = 51.233cm3 ).
Table 3.5: Measured properties for the different fuels.
Component
Density
[kg/m3 ]
at 20◦ C
Jet A1
Standard Diesel
B100
Jet oil
789.0
835.6
877.0
1003.51
1
2
From Mobil Jet Oil II data sheet
From ASTM D1655
Energy
content
(LHV)
[M J/kg]
42.82
45.53
38.23
-
3
From [21]
4
From [18]
Kinematic
Viscosity
[mm2 /s]
at 40◦ C
1-24
2.33
4.23
27.61
easily calculated by adding the weights and dividing by the total corresponding
volume:
P
mf uel + moil
P
(3.9)
ρ blend =
V
A good approximation for the energy content in a fuel blend is to assume the
heating value to be linear with blend fraction by mass. Hence the LHV for each
blend can be found from the equation
LHVblend = m% × LHVf uel1 + m% × LHVf uel2
(3.10)
where m% is the mass fraction of each fuel. The results for these calculated blend
properties are presented in Table 3.7.
29
Table 3.6: The 80/20% and the 50/50% blend weight distribution.
Component
Jet A1
Diesel/B100
Jet oil
Total values
Weight
Volume
% of oil
Weight [kg]
(80/20%)
2.8
0.7
0.1855
Weight [kg]
(50/50%)
1.8
1.8
0.1908
3.685 kg
∼ 4.5L
5
3.791kg
∼ 4.5L
5
Table 3.7: The energy content and the density of different blends.
Blend
with Jet A-1
Diesel (20%)
Biodiesel (20%)
Diesel (50%)
Biodiesel (50%)
3.8
3.8.1
LHV
[M J/kg]
43.3
41.9
44.2
40.5
Density
[kg/m3 ]
806.3
813.3
819.5
838.1
Performance characteristics measurements
Starting the engine
The tests to determine different performance characteristics of the microjet engine were conducted in the same way for each fuel and fuel blend. First, all
sensors, exhaust fans and computer programs (LabView and Fadec) were turned
on and the trim on the engine controller was set to ’idle’ (∼ 20% throttle setting.)
Setting the controller to full throttle and back to idle again will begin the start-up
sequence where the electrical starter first will be powered up to have the rotor
turning at slow speed. Once the rotor is at speed, the pump and solenoid valves
will be energized and the fuel will ignite. When the ignition is detected, the fuel
is routed to the main injectors and the rotor speed will progressively increase
to idle rpm. At this stage the ECU will automatically disconnect power to the
starter and once the speed has reached idle and stabilizes the engine is running.
3.8.2
Collecting data
First a complete set of tests were conducted for the pure Jet A-1 fuel followed by
the same procedure for each blend. Data from every 10th throttle setting, starting
30
with idle at 20% to max throttle at 100%, was collected for each test. Each test
carried out three runs; the primary run, a repeatability run and a variability run.
The first two runs (performed equally) begun measurements at idle and increased
the throttle setting until max throttle was reached. The variability test started
at max throttle and was decreased until idle was reached. A complete set of
1-3 runs was repeated on a different day for each fuel blend to see if changing
ambient conditions had any effect on the results. Hence, atmospheric conditions
were thoroughly documented before each test and individual run.
3.8.3
Engine shut down procedure
To shut down the engine, the throttle setting and trim is lowered. It is recommended to leave the throttle setting at ∼ 25%, allowing temperatures to stabilizes
for about five seconds, before carrying out the shut-down procedure. The engine
shuts down when the throttle is completely set to zero.
3.9
Compressor map analysis
Some parameters for the microjet were not known in advance, such as the compressor pressure ratio at different speeds and the different component isentropic
efficiencies. To determine theses, the thermodynamic calculations for a gas turbine explained in Section 2.5 were put into a MATLAB script to serve as a first
draft of a performance prediction model. When basic conditions of the engine
and ambient temperatures and pressures are known, the combination of equations
will make it possible to calculate the thrust output. Compressor pressure ratio
is however a crucial input parameter which is unknown here. Hence, an iterative process had to be performed where, for different throttle settings, a range of
compressor ratios where tested to each generate a thrust output. This calculated
thrust was then compared to the true thrust value, i.e. the error was analysed.
The error was plotted against the range of pressure ratios used and where the
error became zero, i.e. the calculated value equalled the true value, it showed
at which pressure ratio the desired thrust would occur. This was repeated for
every throttle setting until a complete set of pressure ratios represented the entire
span from 20 − 100%. To get an idea of what pressure ratio ranges to expect, a
compressor map of a similar engine size was analysed. That compressor map is
presented in Figure 3.9 and is read like this: The axes show the compressor air
mass flow rate (x-axis) and the compressor pressure ratio (y-axis). The slightly
curved and tilted lines on the main part of the map are the speed lines. 1 They
propagate, as the pressure ratio on the y-axis increases, over an area of dashed
1
The mass flow rate and the speed is in their corrected values which is the value that
√corresponds
day (101.325kPa and 288.15K): m θ/δ =
p to ambient conditions at sea level
p
√ on a standard
m T01 /288.15/(p01 /101325) and N/ θ = N/ T01 /288.15 [1].
31
Figure 3.9: Compressor map used to define a typical polytropic efficiency range for the VT80 [22].
32
circles which are called efficiency islands. Where a speed line at a certain mass
flow rate and pressure ratio intersects (or closely intersects) one of the islands
shows how efficient the compressor is at those conditions. The compressor efficiency (ηc ) is denoted in percentage for each island in the map. The left hand
boundary (dashed line) of the map is called the surge line. Compressor surge is a
pulsating back flow of gas through the engine which is associated with a sudden
drop in delivery pressure and operation to the left of this line represents a region
of flow instability. There is also a right hand boundary called the choke points
which is where the speed lines terminates. Beyond this point no further increase
in mass flow can be obtained and choking is said to have occurred. Hence, this
point represents the maximum mass flow rate obtainable at each particular rotational speed. A line drawn along the centre of the efficiency islands is called the
peak efficiency line and represents the operating points for maximum efficiency.
Ideally, it is desirable to operate the compressor close to this line [1]. This compressor map indicates that it is reasonable to assume compressor pressure ratios
somewhere between 1 and 4.
When performing thermodynamic engine calculations, it is important to include
fair values of the isentropic efficiencies for each component. As discussed in Section 2.1, ηc and ηt can be substituted by η∞ to decrease the number of unknowns
in the equations. For full-sized jet engines, it is reasonable to find η∞ ≈ 0.85 but
it is not well documented if that is suitable for microjets. The assumption of constant η∞ might not even be true for microjets due to the greater amount of losses
experienced in them. By investigating the compressor map in Figure 3.9, η∞
could be determined for that particular engine and the results could give an idea
what range to expect and if it can be assumed constant or not. A rearrangement
of Equation 2.11 gives an expression for η∞ :
η∞ =
log{(p02 /p01 )(γ−1)/γ }
(γ−1)/γ
log{ (p02 /p01η)c
−
1
ηc
(3.11)
+ 1}
The peak efficiency line on the compressor map intersects the efficiency islands
at five points where the isentropic efficiencies could be directly read. The pressure ratio and mass flow rate for each point were then also read directly of the
map and all parameters were put into Equation 3.11. The values collected from
the map and the corresponding calculated η∞ values are presented in Table 3.8.
The result indicates that the polytropic efficiency in fact is not constant over a
range of pressure ratios for a microjet of similar size to the VT80 η∞ seem to
vary between 0.66 − 0.73. When running the model with the thermodynamic
equations for pressure ratios between 1-4 it became obvious that a constant η∞
was not able to generate a thrust output equal to the measured value for all
throttle setting in the entire span. This means a fair compressor ratio could not
33
Table 3.8: Measured and calculated values for the five points chosen
in Figure 3.9.
πc
1.20
1.32
1.56
2.18
2.77
ṁcorr
0.047
0.054
0.072
0.104
0.126
ηc
0.65
0.68
0.70
0.70
0.68
η∞
0.66
0.69
0.72
0.73
0.72
be obtained for all throttle settings. Hence the conclusion is that η∞ has to vary
for the VT80 microjet as well. A set of varying polytropic efficiencies with corresponding pressure ratios were then determined using the variations in Table 3.8
as a guideline. To check the plausibility of the results, Equation 2.11 were used
to get the corresponding ηc values which for microjets varies within the range
0.65 − 0.78 [11]. The remaining critical efficiencies needed such as ηi , ηj , ηm and
πB were investigated simultaneously in the model to find reasonable values for
all of them. The results are presented in Table 3.9.
Table 3.9: Pressure ratios and efficiencies for the VT80’s compressor. πc lies within the expected 1-4 range and ηc within
the 0.65 − 0.78 range.
Throttle
πc
setting[%]
20
1.11
30
1.18
40
1.23
50
1.35
60
1.54
70
1.87
80
2.30
90
2.88
100
3.60
ηi = 0.95
ηj = 0.95
η∞
ηc
0.73
0.74
0.77
0.79
0.80
0.80
0.81
0.80
0.80
ηm = 0.98
0.73
0.73
0.76
0.78
0.79
0.78
0.79
0.77
0.76
πB = 0.98
34
3.10
Compressor pressure ratio investigation
The pressure is increased in the centrifugal compressor according to the theory
discussed in Section 1.5.2. Hence it would be mathematically possible to determine the generated pressure ratio using knowledge of the impeller speed and
geometry. One goal in this project was to investigate whether πc could be determined accurately for the VT80 using basic equations to be used in the computer
model.
3.10.1
Impeller theory
The impeller eye is where the air is being drawn into the compressor but the vanes
stretches longer beyond the size of the eye, as can be seen in Figure 3.10. The
velocity of the rotating air at the impeller tip can be calculated using velocity
triangles. Figure 3.10 demonstrates graphically that the absolute velocity (C2 )
which the air leaves the impeller tip with has a tangential, or whirl component,
(Cw2 ) and a comparatively smaller radial component (Cr2 ). The impeller tip
speed (U ) would be equal to the whirl component under ideal conditions but due
to its inertia is the air trapped between the impeller vanes reluctant to move
Figure 3.10: Nomenclature for a radial impeller and corresponding
velocity triangles [1].
35
round with the impeller. This prevents the air from acquiring Cw2 equal to U
and the effect is called slip. The slip factor (σ) for radial-vane impellers can be
found from the equation
0.63π
σ =1−
(3.12)
n
where n is the number of vanes. The VT80 has n = 14 and thus σ = 0.86.
Due to friction between the casing and the air carried round by the vanes the
applied torque, and therefore the actual work input, is greater than the theoretical value. To account for this, a dimensionless power input factor (ψ) can be
introduced. Typical values for ψ lies in the region 1.035-1.04 for full-sized jet
engines. πc can now be calculated using the equation
where
γ /(γ −1)
ηc ψσU 2 a a
πc = 1 +
cpa T01
(3.13)
ψσU 2
= T02 − T01
cpa
(3.14)
The impeller tip speed is calculated according to
U = π × Ø × rpm/60
(3.15)
where Ø is the overall diameter of the impeller. Ø for the VT80 was estimated
to be 0.055m.
There is another equation valid for model jet engines that gives πc . It is defined as
3.5
ψU 2
πc =
+1
(3.16)
2cpa T
where ψ now is denoted as a dimensionless unit called the pressure value. ψ = 0.98
is a typical value for microjet engines with slightly retro-curved blades [11] and
ψ remains largely constant over a broad range of rotational speeds which makes
it easy to calculate πc or U if the other parameter is known.
36
Chapter 4
Results
4.1
Model parameters
The results from using the efficiencies and pressure ratios found in Table 3.9 in
the computer model to predict the thrust is presented in Figure 4.1. The MATLAB
code to the model is presented in Appendix B.
Figure 4.1: The predicted thrust compared to the experimental results
for a pure Jet A-1 fuel run. The results coincide well over
the span of throttle settings.
37
4.2
Performance characteristics
Some typical performance parameters for the different blends found from the
engine tests are presented in Table 4.1.
Table 4.1: Technical parameters for the VT80 run on different fuel
blends.
Blend
with Jet A-1
Speed range
[kRPM]
Thrust
[N]
3.9 − 85.6
Air mass
flow rate
[g/s]
41 − 191
Jet A-1 (100%)
45.2 − 150.3
Diesel (20%)
E.G.T
[◦ C]
500 − 604
45.3 − 150.3
3.6 − 85.3
42 − 191
504 − 584
Biodiesel (20%)
45.2 − 150.2
3.6 − 83.8
42 − 190
504 − 596
Diesel (50%)
45.2 − 150.3
3.9 − 78.9
42 − 188
504 − 588
Biodiesel (50%)
45.2 − 150.4
3.8 − 80.3
42 − 188
500 − 596
Rearranging Equations 3.13 and 3.14 using the known values from Table 3.9 and
the temperature difference generated by the computer model made it possible to
calculate σ (when ψ = 1.04) for different throttle settings. A rearrangement of
Equation 3.16 generates the pressure value ψ for different throttle settings. The
results are presented in Table 4.2.
Table 4.2: Slip factor and pressure value investigation
Throttle
[%]
20
30
40
50
60
70
80
90
100
T02 − T01
[K]
12.3
19.4
23.5
33.8
49.2
74.0
101.0
136.1
172.3
U
[m/s]
130.7
167.6
202.7
244.5
282.2
320.2
360.0
395.7
432.5
rpm
σ
ψ
(ψ = 1.04)
45,400
58,200
70,400
84,900
98,000
111,200
125,000
137,400
150,200
38
0.69
0.67
0.55
0.55
0.60
0.70
0.75
0.84
0.89
1.05
1.02
0.88
0.89
0.98
1.13
1.23
1.33
1.40
The throttle setting vs. thrust for all blends and the same plot for a pure Jet
A-1 test with all three runs documented are presented in Figure 4.2 and Figure
4.3 respectively.
Figure 4.2: The blends perform consistently throughout the entire
span of throttle settings.
Figure 4.3: The thrust load cell is not consistent.
39
The throttle setting vs. EGT and the AFR is presented in Figure 4.4.
Figure 4.4: The EGT lowers as more air is pumped through the engine but at higher throttle setting the air mass flow decreases and hence the temperature rises.
The throttle setting vs. the TSFC for all blends is presented in Figure 4.5.
4.3
Parameter relationships
From the speed (rpm) the pump voltage can be determined using the equation
V (rpm) = 1.387 × 10−6 rpm3 − 0.000276rpm2 + 0.03307rpm − 0.3208
(4.1)
The standard deviation is 0.01 and the experimental results are presented in Figure 4.6.
The air mass flow rate can be determined from the pump voltage using
ṁ(V ) = 0.0008643V 5 − 0.006199V 4 + 0.01088V 3 + 7.142 × 10−5 V 2 +
+ 0.06378V − 0.008007
(4.2)
The standard deviation is 2.81 × 10−4 and the experimental results are presented
in Figure 4.6.
40
Figure 4.5: The TSFC is not consistent for the different blends at
lower throttle settings.
The fuel mass flow rate can be determined from the pump voltage using
ṁf (V ) = 0.00154V − 5.632 × 10−6
(4.3)
The standard deviation is 3.6 × 10−5 and the experimental results are presented
in Figure 4.6.
The EGT can be calculated from the pump voltage using the equation
EGT (V ) = −14.94V 5 + 140.7V 4 − 510V 3 + 939.5V 2 − 921.7V + 1175
(4.4)
The standard deviation is 0.93 and the experimental results are presented in Figure 4.6.
The relationship between the speed (rpm) and the throttle setting is linear according to the equation
rpm(τ ) = (1.3205τ + 18.626) × 103
(4.5)
The standard deviation is 0.51 and the result is implemented in the computer
model to be used if the input parameter is the throttle setting instead of the
speed.
41
Figure 4.6: Curve fitting for different sets of measured data.
42
Chapter 5
Discussion
5.1
Model parameters
Figure 4.1 shows that when using the parameter values found in Table 3.9 in the
computer model, the predicted thrust will coincide well with the experimental
results for a pure Jet A-1 run. The microjet engine’s performance may hence
be predicted with only minor deviations from the true value and the compressor ratios and different efficiencies presented in Table 3.9 are thus considered to
be valid. The computer model uses a combustor efficiency (πB ) of 98% which,
after the model was constructed, was discovered to maybe be too high. The investigation done by Gieras & Stankowski [7] suggested that the total pressure
drop in a miniature combustor would be approximately 10% since microjets do
experience greater losses than a full-size engine. A correction was meant to be
done but the computer model was found to be quite sensitive to variations in
the efficiency parameters and a changed value for πB would result in a complete
change in the other parameters as well. This would be too time consuming to
fit within the project’s time restrictions. However, since the other efficiencies
and pressure ratios are within reasonable values and generates a predicted thrust
with only minor deviations from the true value was it concluded that πB was to
remain at 98% to save time.
5.2
Performance characteristics
The geometry for the impeller mounted in the VT80 is not known since the
component is enclosed inside the engine body and hence is not accessible. The
investigation on the slip factor was to give an idea of the geometry. Equation
3.12 says that, for a radial-vane impeller, the slip factor only depend on the number of vanes which generates a constant value for σ. However, table 4.2 shows a
varying value for σ over the span of throttle settings. It is hence concluded that
43
the impeller for the VT80 is not purely radial. If this is the case, Equation 3.15
that gives the impeller tip sped U, might also be incorrect since a back-swept
blade would result in a vector component to be used instead. The results from
the pressure value investigation using the rearrangement of Equation 3.16, also
presented in Table 4.2, suggest that ψ vary too much. It was expected for radial
impellers that ψ only varies within narrow limits i.e. practically constant. This
result suggest once more that the geometry of the impeller is not purely radial
and that U has to be modified using a vector component based on the blade
angle. In conclusion, the geometry for the VT80’s impeller seems to be far more
complex than the simple equations can handle and thus πc cannot be derived
exclusively from these equations.
Table 4.1 and Figure 4.2 both show that the microjet engine was able to operate
and perform in a consistent manner throughout the throttle setting span for the
various blends tested. This is in accordance to the results found by Tan & Liou
[4] and was hence an expected result. Though the two 50% diesel and biodiesel
blends generated a slightly lower maximum thrust output value compared to the
others is the deviation approximately negligible. Hence, in conclusion: the model
can predict the thrust output for each blend tested for without having to state
which blend is currently being investigated since they all generate the same results.
Figure 4.3 demonstrates a problem discovered with the thrust load cell when
conducting the performance tests on the engine. The load cell placed in front of
the engine baseplate measures the thrust generated by the engine during runs as
the baseplate pushes against the load cell. For the first and the repeatability run,
where the throttle setting is gradually increased, the load cell generates consistent results for the fuel/blend used at the current ambient conditions. A problem
however occurs during the variability test, where the throttle setting is gradually
decreased from maximum value. As seen in Figure 4.3 will the thrust output
registered by the load cell be slightly higher than the other two runs for the lower
throttle settings. This may be explained as follows: the load cell is experiencing
the highest level of thrust ”pushing” against it for maximum throttle and as the
setting is gradually decreased, i.e. lesser and lesser thrust is experienced, the load
cell will fail to retract at the same pace as the decreasing thrust. Thus, the thrust
output generated for lower throttle settings will result in a false, higher value than
expected. This is a problem since the three different runs made for each test are
to give statistically supported results but an average of the lower throttle settings
results will now produce an untrue value. This has to be considered when running
tests and a solution to this problem would be of high importance in future works.
44
Figure 4.4 demonstrates the peculiar behaviour the EGT was discovered to have
as the throttle setting increases: the temperature decreases up to about 70%
throttle but then starts to increase as the throttle goes towards its maximum
value. This decrease/increase in the EGT over the entire span of throttle settings can be explained by looking at the air-fuel ratio (AFR) for the same run.
As the AFR increases, i.e. more air is being pumped through the engine, the
working temperature lowers. However, the engine is not capable of maintaining
the high AFR value as the highest throttle settings are set due to the increased
amount of fuel mass flow and the temperature hence begins to increase as the
AFR decreases. This behaviour is consistent for all fuel blends used, as Figure
4.4 clearly shows.
Figure 4.5 demonstrates the TSFC for the different blends. Unlike the throttle
setting vs. thrust plot in Figure 4.2 is the TSFC not consistent over the entire
throttle setting span for the different blends. The difference between the blends
is greater for lower settings but almost none for the top values which suggests
that an added coefficient to the computer motel is not a solution to get a fair
prediction for each fuel.
5.3
Parameter relationships
The fuel pump voltage is easily measured during engine tests using a volt meter.
From this value a number of other important parameters can be derived with fair
accuracy, such as the rpm, ṁ, ṁf and EGT according to the equations presented
in Section 4.3. Figure 4.6 gives a graphic view over how well the parameters
can be described mathematically. This means that only the pump voltage needs
monitoring when performing tests which reduces the time spent performing the
tests and may reduce the time the microjet engine is running and thus save
expensive fuels. The pump voltage is also easily derived from the speed (rpm)
using Equation 4.1 which was used in the computer model since the rpm may be
in interesting parameter to predict engine performance from.
45
5.4
The computer model
The MATLAB code used for the computer model is based on the theory discussed in
Section 2.5 where the number of input parameters have been reduced significantly
using the pump voltage’s mathematical relationship to other parameters. Due to
the complexity of the compressor geometry is the compressor pressure ratio however not able to be determined using simple equations and thus is an unavoidable
input parameter. η∞ also has to be included manually in the model according to
the results presented in Table 3.9. Since not all performance characteristics seem
to coincide amongst the different fuel blend is the current model a pure Jet A-1
model. The performance of the microjet engine may now be determined by using
the input parameters: throttle setting, πc , η∞ and the ambient conditions sought
for. The model generates results close to the true values for all characteristics
found in the experimental tests.
46
Chapter 6
Conclusions
6.1
Conclusions
Simple aero-thermodynamic gas turbine equations have shown to be able to predict some performance characteristics for the Merlin VT80 when run on pure
Jet A-1 with good accuracy. An simple equation that describes the compressor
pressure ratio is however not obtainable due to the found complexity in the compressor geometry. The computer model thus has to include both πc and η∞ as
input parameters to function which is not a convenient model structure. The
similarities for the different blends when calculating the thrust output suggests
that a future model may be able to exclude further, non-relevant information to
simplify the input parameters needed. It was, for instance, found in this project
that the knowledge of which fuel blend used in the test was not relevant to predict
the engine thrust output. The amount of Jet A-1 fuel consumed in the progress
of this project really stresses the need for a cheaper alternative fuel to be used
in mirojet engines. The realisation that the pump voltage is almost the only parameter needed to be documented during tests has however given an opportunity
to lower the fuel consumption since the tests time can be reduced. Due to time
restrictions was the computer model only able to determine relevant parameters
for the pure Jet A-1 case with good accuracy at the end of this project. Future
work to address these shortcomings in the results are discussed in the next section.
6.2
Future work
To get a complete working model to describe the performance characteristics of
different fuel blends will some adjustments to existing data and more thorough
47
investigations of the engine’s different components be needed.
• The problems with the not retracting thrust load cell is a major issue that
needs to be addressed to be able to conduct thrust tests with realistic and
dependable results.
• The compressor geometry may be further investigated to determine the true
relationship between the impeller blade angles and the compressor pressure
ratio.
• An investigation on the true pressure loss in the combustor and a more
thorough denotation of the efficiencies used in the model may be vital to
find more subtle variations in the different blends.
• An deeper investigation on the pump voltage relationship to the same parameters used in this project but for all the different blends as well might
be useful to get an idea of the possible varying blend’s properties.
• Since ṁ can be derived with minor deviations from the true value is the
need for the intake reduced. The removal of it will increase accessibility
to the engine but the microjet would start to experience other conditions
which have to be investigated.
48
Appendix A
Extra figures
49
Figure A.1: The intake horn drawing.
50
Figure A.2: The discharge coefficient for ASME flow nozzle [12].
51
Appendix B
MATLAB code
52
% Microjet engine performance prediction model
Ts=50;
pa=1.0135;
Ta=294;
%Throttle setting
%Air pressure
%Air temperature
pi_c=1.35;
%compressor pressure ratio
% 20=1.11, 30=1.18, 40=1.23, 50=1.35, 60=1.54,
%70=1.87, 80=2.3, 90=2.88, 100=3.6
%polytropic efficiency
%20=0.73, 30=0.74, 40=0.77, 50=0.79, 60=0.8,
%70=0.8, 80=0.81, 90=0.8, 100=0.8
n_p=0.79;
%----------Constants------------------------cpa=1005;
%[J/kg]
cpg=1148;
%[J/Kg]
gamma_a=1.4;
% air
gamma_g=1.333;
% hot gas
R=286.9;
% spec. gas constant (air)
d=0.07;
A=d^2*pi/4;
%-------------------------------------------fprintf('___________________________________________\n')
rpm=1.3205*Ts+18.626;
rho_a=(pa*100000)/(R*Ta);
fprintf('The air density is
%g kg/m^3 \n',rho_a)
Ca=sqrt(gamma_a*R*Ta);
fprintf('The speed of sound in air is C= %g m/s\n',Ca)
V=1.387*10^(-6)*rpm^3-0.000276*rpm^2+0.03307*rpm-0.3208;
fprintf('The pump voltage is %g V\n',V)
m_ff=0.0015*V-5.632*10^(-6);
EGT=-14.94*V^5+140.7*V^4-510*V^3+939.5*V^2-921.7*V+1175;
mdot=0.0008643*V^5-0.006199*V^4+0.01088*V^3+7.142*10^(-5)*V^2+...
0.06378*V-0.008007;
c_pipe=mdot/(rho_a*A);
fprintf('The speed of air in the intake is C= %g m/s\n',c_pipe)
delta_p=c_pipe^2*rho_a/2;
fprintf('Delta p in the intake is %g Pa\n',delta_p)
M=c_pipe/Ca;
fprintf('The Mach number in the horn M= %g\n',M)
T01=(delta_p+(pa*100000))/(R*rho_a);
fprintf('The Temp in the intake is T01= %g K\n',T01)
p01_pa=((0.95*M^2*0.2)+1)^3.5;
53
fprintf('p01/pa= %g\n',p01_pa)
p01=(p01_pa)*pa;
fprintf('p01= %g bar\n',p01)
T02_T01=T01*((pi_c^((gamma_a-1)/(gamma_a*n_p)))-1);
fprintf('T02-T01= %g K (polytropic eff)\n',T02_T01)
T02=T02_T01+T01;
fprintf('T02= %g K\n',T02)
T_ratio=T02/T01;
fprintf('T02/T01= %g K\n',T_ratio)
p02=pi_c*p01;
fprintf('p02= %g bar\n',p02)
p03=p02*0.98;
fprintf('p03= %g bar\n',p03)
Wc=cpa*(T02_T01);
fprintf('The work to drive the compressor is Wc= %g J/kg\n',Wc)
T03_T04=Wc/(cpg*0.98);
fprintf('T03-T04= %g K\n',T03_T04)
T03=(T03_T04)+EGT;
fprintf('T03= %g K\n',T03)
pi_t=(1-((T03_T04)/T03))^(gamma_g/(n_p*(gamma_g-1)));
fprintf('p04/p03= %g\n',pi_t)
p04=p03*pi_t;
fprintf('p04= %g bar\n',p04)
pi_jc=(1-((gamma_g-1)/(gamma_g+1)*(1/0.95)))^4;
fprintf('The critical nozzle p-ratio is pi_jc= %g\n',pi_jc)
pi_j=pa/p04;
fprintf('The p-ratio over the nozzel is Pa/p04= %g\n',pi_j)
EPR=1/(pi_j);
fprintf('The engie p-ratio is EPR is p04/pa= %g\n',EPR)
fprintf('If pi_jc= %g < pi_j=%g then p5=pa (non-choked flow)\n',pi_jc,pi_j)
T04_T5=0.95*EGT*(1-(pi_j^(1/4)));
fprintf('T04-T5= %g K\n',T04_T5)
T5=EGT-(T04_T5);
fprintf('T5= %g K\n',T5)
c5=sqrt(2*cpg*(T04_T5));
54
fprintf('c5= %g m/s\n',c5)
F=mdot*c5;
TSFC=m_ff*3600/F;
fprintf('___________________________________________\n')
fprintf('rpm= %g \n',rpm)
fprintf('EGT= %g K\n',EGT)
fprintf('The air mass flow rate is %g kg/s\n',mdot)
fprintf('The thrust is = %g N\n',F)
fprintf('The fuel flow rate is %g kg/s\n',m_ff)
fprintf('TSFC= %g kg/h\n',TSFC)
fprintf('___________________________________________\n')
55
Appendix C
Test run results
56
Throttle
20
LHV[MJ/kg]
30
42,8
40
Density
50
789
60
[kg/m^3]
70
80
90
100
Diesel 20
Throttle
20
LHV[MJ/kg]
30
43,3
40
Density
50
806,3
60
[kg/m^3]
70
80
90
100
B20
Throttle
20
LHV[MJ/kg]
30
41,9
40
Density
50
813,3
60
[kg/m^3]
70
80
90
100
Jet A-1
rpm
45300
58300
71100
84600
98600
1E+05
1E+05
1E+05
2E+05
rpm
45450
58200
73100
84500
98000
1E+05
1E+05
1E+05
2E+05
rpm
45400
58200
70400
84900
98000
1E+05
1E+05
1E+05
2E+05
K
EGT
837
813
800
786
782
779
790
820
872
K
EGT
841
813
801
788
782
778
785
812
856
K
EGT
859
824
805
789
784
779
785
809
842
C
EGT
564
539
527
513
509
506
517
547
599
C
EGT
568
540
528
515
509
505
512
539
583
C
EGT
586
551
532
516
511
506
512
536
569
kg/s
m_dot
0,0426
0,0564
0,0705
0,0879
0,1065
0,1257
0,1480
0,1690
0,1905
kg/s
m_dot
0,0427
0,0565
0,0713
0,0880
0,1063
0,1257
0,1480
0,1711
0,1913
kg/s
m_dot
0,0425
0,0564
0,0709
0,0874
0,1064
0,1253
0,1478
0,1698
0,1902
Ftrue
3,60
7,95
12,52
17,94
25,92
35,50
49,40
64,90
83,85
Ftrue
3,91
7,22
12,11
18,38
26,25
36,30
49,80
67,40
85,20
Ftrue
3,34
6,58
10,72
17,29
26,05
36,56
50,79
65,93
86,48
kg/s
m_fuel
0,00110
0,00143
0,00170
0,00210
0,00247
0,00287
0,00343
0,00393
0,00480
kg/s
m_fuel
0,0011
0,0014
0,0017
0,0021
0,0024
0,0028
0,0033
0,0039
0,0046
kg/s
m_fuel
0,0011
0,0014
0,0018
0,0021
0,0025
0,0029
0,0034
0,0039
0,0047
kg/N.h
TSFC
1,161
0,734
0,550
0,426
0,336
0,280
0,241
0,211
0,201
kg/N.h
TSFC
0,8446
0,6199
0,4749
0,3930
0,3198
0,2761
0,2373
0,2093
0,1958
kg/N.h
TSFC
0,9264
0,6389
0,4961
0,4083
0,3341
0,2885
0,2463
0,2136
0,2019
AFR
38,68
39,33
40,13
41,63
43,13
43,21
43,46
43,54
40,47
AFR
38,82
40,32
41,31
41,89
44,28
44,51
44,51
43,59
41,37
AFR
38,70
39,46
41,46
41,87
42,96
43,78
43,15
42,79
39,69
FAR
0,0259
0,0254
0,0249
0,0240
0,0232
0,0231
0,0230
0,0230
0,0247
FAR
0,0258
0,0248
0,0242
0,0239
0,0226
0,0225
0,0225
0,0229
0,0242
FAR
0,026
0,025
0,024
0,024
0,023
0,023
0,023
0,023
0,025
Volt.
0,74
0,92
1,10
1,31
1,54
1,78
2,11
2,50
2,97
Volt.
0,74
0,92
1,11
1,31
1,53
1,78
2,11
2,49
2,95
Volt.
0,75
0,93
1,12
1,35
1,59
1,85
2,21
2,60
3,13
%
pump
6,1
7,0
8,6
10,0
11,9
14,0
17,3
20,9
26,7
%
Pump
6,3
7,3
9,0
10,0
12,0
14,0
17,0
21,0
25,5
%
Pump
7,0
7,3
9,0
10,0
12,0
14,0
18,0
21,0
26,7
TSFCxLHV
38,8
26,8
20,8
17,1
14,0
12,1
10,3
8,9
8,5
TSFCxLHV
36,6
26,8
20,6
17,0
13,8
12,0
10,3
9,1
8,5
TSFCxLHV
49,7
31,4
23,5
18,2
14,4
12,0
10,3
9,0
8,6
L/s
Vol. ff rate
0,00139
0,00182
0,00215
0,00266
0,00313
0,00363
0,00435
0,00499
0,00608
L/s
Vol. ff rate
0,00136
0,00174
0,00214
0,00260
0,00298
0,00350
0,00412
0,00487
0,00574
L/s
Vol. ff rate
0,00135
0,00176
0,00217
0,00258
0,00303
0,00357
0,00418
0,00480
0,00578
m_fuelxLHV
1,2803E-05
1,6682E-05
2,0562E-05
2,4442E-05
2,8709E-05
3,3753E-05
3,9572E-05
4,5392E-05
5,4703E-05
m_fuelxLHV
1,3231E-05
1,6839E-05
2,0748E-05
2,5258E-05
2,8867E-05
3,3978E-05
3,9992E-05
4,7209E-05
5,5628E-05
m_fuelxLHV
1,3078E-05
1,7041E-05
2,0211E-05
2,4967E-05
2,9326E-05
3,4081E-05
4,0819E-05
4,6763E-05
5,7067E-05
Throttle
20
LHV[MJ/kg]
30
44,2
40
Density
50
819,5
60
[kg/m^3]
70
80
90
100
B50
Throttle
20
LHV[MJ/kg]
30
40,5
40
Density
50
838,1
60
[kg/m^3]
70
80
90
100
Diesel 50
rpm
45300
58000
70600
84700
98300
1E+05
1E+05
1E+05
2E+05
rpm
45500
58450
71000
84500
97800
1E+05
1E+05
1E+05
2E+05
C
EGT
582
552
535
516
508
502
506
528
580
C
EGT
590
555
535
515
503
500
508
532
580
kg/s
m_dot
0,0423
0,0576
0,0701
0,0867
0,1048
0,1241
0,1465
0,1667
0,1880
kg/s
m_dot
0,0423
0,0556
0,0700
0,0870
0,1055
0,1247
0,1469
0,1670
0,1886
Ftrue
4,43
7,38
11,17
16,93
24,50
34,30
47,53
61,35
80,30
Ftrue
4,27
7,20
10,97
16,85
23,83
33,80
46,73
60,05
78,90
kg/s
m_fuel
0,0012
0,0014
0,0017
0,0020
0,0024
0,0028
0,0032
0,0038
0,0045
kg/s
m_fuel
0,0012
0,0015
0,0018
0,0022
0,0025
0,0030
0,0035
0,0040
0,0048
kg/N.h
TSFC
0,9787
0,7017
0,5579
0,4346
0,3626
0,2929
0,2466
0,2278
0,2053
kg/N.h
TSFC
0,9930
0,7350
0,5810
0,4614
0,3675
0,3098
0,2614
0,2347
0,2152
AFR
35,25
37,10
38,91
40,14
42,22
42,26
42,59
41,75
39,29
AFR
36,76
41,16
41,25
42,64
43,66
45,12
45,78
43,88
41,78
FAR
0,0284
0,0270
0,0257
0,0249
0,0237
0,0237
0,0235
0,0240
0,0255
FAR
0,0272
0,0243
0,0242
0,0235
0,0229
0,0222
0,0218
0,0228
0,0239
VALUES ARE BASED ON MEAN VALUES FROM DIFFERENT TEST RUNS
K
EGT
855
825
808
789
781
775
779
801
853
K
EGT
863
828
808
788
776
773
781
805
853
Volt.
0,75
0,91
1,08
1,29
1,51
1,76
2,09
2,47
3,00
Volt.
0,74
0,88
1,04
1,24
1,44
1,69
2,00
2,37
2,86
%
Pump
6,5
7,0
8,3
10,0
11,0
13,5
16,0
20,0
25,0
%
Pump
7,0
7,7
9,0
10,7
12,3
16,0
18,0
22,5
29,0
TSFCxLHV
40,2
29,8
23,5
18,7
14,9
12,5
10,6
9,5
8,7
TSFCxLHV
43,3
31,0
24,7
19,2
16,0
12,9
10,9
10,1
9,1
L/s
Vol. ff rate
0,00140
0,00171
0,00207
0,00248
0,00293
0,00336
0,00390
0,00464
0,00549
L/s
Vol. ff rate
0,00143
0,00179
0,00215
0,00259
0,00298
0,00352
0,00412
0,00477
0,00573
m_fuelxLHV
1,3500E-05
1,6875E-05
2,0250E-05
2,4375E-05
2,8125E-05
3,3188E-05
3,8813E-05
4,5000E-05
5,4000E-05
m_fuelxLHV
1,4119E-05
1,7189E-05
2,0872E-05
2,4965E-05
2,9467E-05
3,3764E-05
3,9289E-05
4,6656E-05
5,5250E-05
Bibliography
[1] H.I.H. Saravanamutto, G. Rogers, H. Cohen, and P. Straznicky. Gas Turbine
Theory. Pearson Education Limited, Essex, UK, 6 edition, 2009.
[2] Paul D. Marsh. Twenty years of micro-turbojet engines, 2003. RC Universe.
Accesses: 4-April-2013
http://www.rcuniverse.com/magazine/article display.cfm?article id=166.
[3] Benjamin Jones. Optimisation of a small gas turbine engine. Technical
report, Monash University, AUS, 2011.
[4] Edmond Ing Huang Tan and William W. Liou. Microgas turbine engine
characteristics using biofuel. The Hilltop Review, 5, 2011. Iss.1, Article 6.
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