ABSTRACT
This report details the analysis and design for a turbojet based gas turbine
engine to drive an electrical generator of an Auxiliary Power Unit (APU)
which can be used for a long-haul transonic aircraft. The report is composed of
three parts. Part 1 details the analysis and design for the programming code, to
be used in MATLAB, in order to automate the calculation required for the
project. Part 2 details the analysis of the outputs using the program developed
in Part 1. This analysis is used for the justification of the selected valued of the
different design parameters required for the engine. Part 3 details the report
about the material, and component selection for the project.
1
EXECUTIVE SUMMARY
This report details the analysis and design for a turbojet based gas turbine
engine to drive an electrical generator of an Auxiliary Power Unit (APU)
which can be used for a long-haul transonic aircraft. The report is composed of
three parts.
Part 1 details the analysis and design for the programming code, to be used in
MATLAB, in order to automate the calculation required for the project.
Part 2 details the analysis of the outputs using the program developed in Part
1. This analysis is used for the justification of the selected valued of the
different design parameters required for the engine.
Part 3 details the report about the material, and component selection for the
project.
2
LIST OF CONTENTS
ABSTRACT 1
EXECUTIVE SUMMARY 2
LIST OF CONTENTS 3
1 INTRODUCTION
2 PART 1:
3 PART 2:
4 PART 3:
5 CONCLUSION
REFERENCES
3
1. INTRODUCTION
1.1 Background
The aim of this report is to give an optimal design for a turbojet based turbo
shaft engine which can be used to generate electricity as an APU in an aircraft.
The design requires selection of values for the different parameters, materials
and components for the engine. The different requirements for the engine
design are described in the next section.
The APU supplies electricity to the aircraft only when sufficient electricity is
not produced by the main engines. The APU does not produce any trust. This
means that the APU is only utilized intermittently. This is an important factor
in the design as it sets some limits over the cost and size for the project.
Fuel
Combustion
Chamber
T3, P3 T4, P4
Exhaust
Air
Gas
T2, P2 T5, P5
Compressor Turbine
Electrical
Power
Wg
APU Electrical
Generator
Fig 1.1 APU
A gas turbine (in this case a turbojet / turbo shaft) engine follows a Brayton
(Joule) cycle. Fig 1.1 shows the basic structure of the APU. Some of the
parameters have already been set which are shown in the next section.
1.2 Requirements
4
The design needs to follow some constraints. These have already been given
and are fixed. These parameters form the base around which whole design will
be developed. These given constraints are as follows:
Inlet dry air properties
R 287 J/kg/K
Cp 1500J/kg/K
Γ 1.4
Compressor properties
Compressor inlet pressure 1 bar
Compressor inlet temperature 15o C
Compressor isentropic efficiency 93%
Bleed flow from exit of compressor 1.5%
Combustion chamber properties
Combustion Pressure Loss 1%
Combustion Fuel to Air Ratio 0.025:1
Turbine properties
Turbine exit pressure 1.2
Turbine isentropic efficiency 95%
Generator properties
Electrical generator efficiency 95%
Aircraft Engine power demand (Wg) 400Kw
Some of the other design requirements that have been taken into consideration
for the design of the engine based on the role of the APU as stated in section
1.1 are:
The engine needs to be cheap.
The size of the engine should be as small
The weight of the engine should be small
The engine should have low maintenance and running cost
The other requirements at which the design has to aim at are like material that
is available, types of components that are available etc. Most of these depend
on the optimal values of compressor pressure ratio and the turbine inlet
temperature.
1.3 Design methodology and structure
The whole design process has been has been divided in to three parts.
As there are lots of calculations to be done in order to show the range of
possible values that can be chosen a MATLAB script file needs to be develop.
This will enable to automate this calculation. Part 1 details the design and
coding needed for this purpose. The output of Part 1 is in the form of different
plots.
Part 2 looks into the analysis of the plots produced from Part 1 in order to
make proper selection for the optimal design parameters.
5
Part 3 looks into the selection of different components and materials which for
the optimal design.
6
2. PART 1
2.1 Overview
This part deals with the analysis and design for the coding to be used in for the
automation of the thermodynamic calculation which would facilitate the next
stage of APU design. The coding is done using MATLAB. The program will
give the out put of the design in forms of different plots which are used in Part
2 of this report.
This section is divided into four parts Requirement Specification, Analysis,
Design, MATLAB code and Code testing.
2.2 Requirement specification
The requirements of this program are to use the predefined parameters and
constraints given for the engine design in different thermodynamic
calculations and produce the results in form of plots which can be analyzed at
a later stage.
The given constrains have been set into different variables. The MATLAB
code for this is saved in file psacon.m (See section 1.1 for the different given
constraints. )
2.3 Analysis
In order to give an over view of the program on the next page is the Program
Outline.
7
Program Outline
INPUT PROCESS
Given constraints Thermodynamic calculations for:
Range for Pressure ratio o Temperatures T3, T4, T5
Range for Turbine exit o Mass flow rate of air
temperature o Mass flow rate of fuel
o SFC
FILES
No files
OUTPUT
Plots of different calculated values
8
The different equations to be that are used in the program are:
P
rcomp 3
P
2
T3is rcomp
1
T2
T3is T2
T3 T2
comp
P3 comp P2
P4 P3 1 PLcombustor
P
rturb 4
P
5
T4
T5is 1
rturb
T5 T4 T4 T5is turb
Wg
Wnet
generator
Wnet
m5
C p T4 T5 T3 T2
m4 m5
m4
m3
1 FAR
m2 m3 / f bleed
m fuel m3 FAR
sfc m / W g
9
2.3 Design
The flow chart below shows the design and working of the program:
Start
Run psacon.m
to load the
constraints into
memory
Load the chosen
range of
Compressor
pressure ratio & T4
Calculate T3is &
T3
Calculate P3 & P4
Calculate Turbine
pressure ratio
Calculate T5is &
T5
Calculate mass
flow rates
Calculate SFC
Plot the
calculated
values
End
Fig 2.1 Program flow chart
All the calculation are done basis of the equations shown in section 2.3.
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2.4 Program code
The following section shows the program code for the configuration file
psacon.m
% PSACON
%
% (c) Ubaier Ahmad Bhat
%
% PSACon or Propulsion System Analysis Constraints is part of Propulsion
% System Analysis program.
clear
% --------------------------------------------------------------------
% Given Constraints
% Inlet Air properties
R = 287; % J/kg/K
Cp = 1005; % J/kg/K
gamma = 1.4;
% Station 2
p2 = 1; % Compressor inlet pressure in bars
p2 = p2 * 10^5; % in Pa
t2 = 15; % Comperssor inlet temp. in C
t2 = t2 + 273.15; % in K
n_comp = 0.93; % Compressor isentropic efficiency
% Station 3
bfr_comp = 0.015; % Bleed flow rate at comp. exit
p3 = []; % Compressor exit pressure , NOT KNOWN
t3 = []; % Compressor exit temp. , NOT KNOWN
% Combustion chamber (cc)
pl_cc = 0.01; % Pressure loss at cc
far_cc = 0.025/1; % Fuel to Air ratio
% Station 4
n_turb = 0.95; % Turbine isentropic efficiency
p4 = []; % Turbine inlet pressure , NOT KNOWN
t4 = []; % Turbine exit pressure , NOT KNOWN
% Station 5
p5 = 1.2; % Turbine exit pressure in bars
p5 = p5 * 10^5; % in Pa
t5 = []; % Turbine exit temp. , NOT KNOWN
% Electric generator
n_gen = 0.95; % Efficiency of generator
Wg = 400 ; % Power demand in kW
Wg = Wg * 10^3; % in W
% ---------------------------------------------------------------------
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Following is the code for the main program psa.m.
% PSA
%
% Propulsion System Analysis
% (c) Copyright 2006, 2007 Ubaier Ahmad Bhat
%
% This program is part of Propulsion System Analysis coursework for module
% 216SYS Aerospace Technology 1.
% Load the constraints from the configuration file
psacon
% Chosen values
pr_comp = 2:1:50; % Pressure ration at compressor
t4 = 1800:10:2000; % Turbine entry temperature
% Calculation of t3
t3is = t2 * pr_comp .^((gamma - 1)/gamma);
t3 = ((t3is - t2)/n_comp) + t2;
% Calculation of p3 and p4
p3 = p2 .* pr_comp;
p4 = p3 - (p3 * pl_cc);
% Calculation of pr_turb
pr_turb = p4 / p5;
% Calculation of t5
t5is = zeros(numel(t4),numel(pr_turb));
t5 = zeros(size(t5is));
for i = 1:numel(t4)
for j = 1:numel(pr_turb)
t5is(i,j) = t4(i) / (pr_turb(j) ^((gamma - 1)/gamma));
t5(i,j) = t4(i) - ((t4(i) - t5is(i,j))* n_turb);
end
end
% Calculation for total output needed
Wnet = Wg / n_gen;
% Calculation for mass flow rates
t3mint2 = t3 - t2;
t4mint5 = zeros(size(t5));
for i = 1:numel(t4)
for j = 1:numel(t5(1,:))
t4mint5(i,j) = t4(i) - t5(i,j) ;
end
end
m5 = zeros(size(t4mint5));
for i = 1:numel(t4)
for j = 1:numel(t3)
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m5(i,j) = Wnet /( Cp * (t4mint5(i,j) - t3mint2(j)));
end
end
m4 = m5;
m3 = m4 / (1 + far_cc);
m2 = m3 / 0.985;
m_fuel = m3 * far_cc;
% SFC calculation
sfc_eng = m_fuel / Wg;
% Graphical outputs
figure
surf(pr_comp,t4,Wg * ones(numel(t4),numel(pr_comp)))
hold on
surf(pr_comp,t4,Wnet * ones(numel(t4),numel(pr_comp)))
xlabel('Compressor pressure ratio')
ylabel('Turbine inlet entry temperature')
zlabel('Power out')
hold off
figure
surf(pr_comp,t4,m2)
hold on
xlabel('Compressor pressure ratio')
ylabel('Turbine inlet entry temperature')
zlabel('Mass flow rate')
hold off
figure
plot(pr_comp,m2)
hold on
xlabel('Compressor pressure ratio')
ylabel('Mass flow rate of air')
hold off
figure
surf(pr_comp,t4,m_fuel)
hold on
xlabel('Compressor pressure ratio')
ylabel('Turbine inlet entry temperature')
zlabel('Mass flow rate')
hold off
figure
plot(pr_comp,m_fuel)
hold on
xlabel('Compressor pressure ratio')
ylabel('Mass flow rate of fuel')
hold off
figure
surf(pr_comp,t4,sfc_eng)
hold on
xlabel('Compressor pressure ratio')
ylabel('Turbine inlet entry temperature')
13
zlabel('SFC')
hold off
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2.5 Testing
The screen shot shows the results after the code was run. The code runs with
out any errors.
Fig 2. Screen shot after the code run
15
3. PART 2
3.1 Overview
This part looks at the selection process for the different parameters namely
compressor pressure ratio, turbine temperature and thus mass flow rate of the
air and fuel.
3.2 Selection of parameters
3.2.1 Range
In order to select a particular value for Pressure ratio and turbine inlet
temperature a reasonable range has to be taken into consideration. The range
that has been used for this purpose is:
Range for pressure ratio: 2 to 50
Range for Turbine inlet temperature: 1800K to 2000K
This range has been selected on the bases of the possible values that can be
achieved using the latest technology.
3.2.2 Engine Output Required
Since the electric generator is not 100% efficient the output needed form the
engine is more than the output of the generator, which is set of 400kW. The
output thus needed is 421.5kW which has been calculated on the bases of the
given 95% efficiency of the engine.
5
x 10
4.25
4.2
4.15
Power out
4.1
4.05
4
2000
1950 50
45
40
1900 35
30
25
1850 20
15
10
5
1800 0
Turbine inlet entry temperature
Compressor pressure ratio
Fig 3.1 Pressure ratio range, Turbine inlet temperature range and Outputs
3.2.3 Analysis of the plots
16
Using the MATLAB script developed in Part 1 plots comparing the follow
parameters have been produced
Compressor pressure ratio. These values have been chosen form the
range selected in section 3.2.1. This parameter not only is important for
the calculations of other parameters but is also directly proportional to
the length and thus the weight of the engine.
Turbine inlet temperature. This parameter is also been chosen for the
range defined in section 3.2.1. The turbine inlet temperature is very
important in the performance of a gas turbine engine.
Mass follow rate of air through the engine – This is directly
proportional to the size of the engine. Higher the value bigger should
be the inlet diameter.
Mass flow rate of fuel – This gives an idea of how much fuel will be
used to produced the 400 kW of power that is required. His valued
helps to determine the running cost of the engine. Smaller the value
less will be the running cost.
SFC – This defines the fuel consumption per unit of power generated.
Its significance is same as the mass flow rate of the fuel.
The following are the different plots produced.
Fig 3.2
Surface plot
For Comp.
3 Pressure
ratio, Turb.
2.5 Inlet
Mass flow rate
2
temperature
and mass
1.5 flow rate
1
0.5
2000
1950 50
40
1900 30
1850 20
10
Turbine inlet entry temperature 1800 0
Compressor pressure ratio
17
Fig 3.3 Plot
2.6 showing
2.4
compressor
pressure
2.2 ratio and
2 mass flow
rate at
Mass flow rate of air
1.8
different
1.6 turbine inlet
temperature
1.4
s
1.2
1
0.8
0 5 10 15 20 25 30 35 40 45 50
Compressor pressure ratio
Fig 3.4
Surface plot
For Comp.
0.07 Pressure
0.06
ratio, Turb.
Inlet
Mass flow rate
0.05
temperature
0.04 and mass
0.03 flow rate of
0.02
fuel
0.01
2000
1950 50
40
1900 30
1850 20
10
Turbine inlet entry temperature 1800 0
Compressor pressure ratio
18
Fig 3.5 Plot
0.065
showing
0.06 compressor
0.055
pressure
ratio and
0.05
mass flow
rate of fuel
Mass flow rate of fuel
0.045
0.04
at different
turbine inlet
0.035
temperature
0.03 s
0.025
0.02
0.015
0 5 10 15 20 25 30 35 40 45 50
Compressor pressure ratio
Fig 3.6
Surface plot
-7
x 10 For Comp.
Pressure
2
ratio, Turb.
Inlet
1.5
temperature
and SFC
SFC
1
0.5
0
2000
1950 50
40
1900 30
1850 20
10
Turbine inlet entry temperature 1800 0
Compressor pressure ratio
From the analysis of these plots the following values where chosen for the
different parameters:
Compressor pressure ratio: The compressor pressure ratio chosen for the
design is 11:1. This is because as can be seen from the plots there is not much
significant difference in mass flow rate of the fuel flow rate after this point.
Another reason for choosing this value is that can be easily achieved using
current compressors without much increase in weight.
Turbine inlet temperature: The selection for this value is based on how
much fuel is consumed at the particular temperature. The temperature for the
minimum value of the mass flow rate of fuel is chosen to be 2000K. Since this
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value is too high the material chosen for the turbine must be chosen to which
can withstand this temperature. For this reason the temperature chosen is
1900K.
Mass flow rate of air: Based on the values of turbine inlet temperature and
compressor pressure ratio the value for mass flow of air is 0.7649 kg/s
Mass flow rate of fuel: Based on the values of turbine inlet temperature and
compressor pressure ratio the value for mass flow of fuel is 0.0188 kg/s.
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4. PART 3
4.1 Overview
This part deals with the selection of different components of the engine, like
the compressor type, and the materials for the engine. These selections are to
support the selections taken in part 2.
4.2 Selection for Compressor
The type of compressor chosen for this engine is an Axial compressor. This is
because it can compress the air to the required ratio of 11:1 using various
stages. The other option for a compressor is an Centrifugal type compressor
but since it can only give a pressure ratio of 4.5:1 maximum this cannot be
used.
Fig 4.1 Axial Compressor
The material chosen for the compressor is steel and nickel based alloys. This is
to keep the manufacturing cost low.
4.3 Selection for Combustion chamber
The type of combustion chamber chosen is an Annular combustion chamber
which because of its small size, less weight and low production cost.
Since the containing walls and internal parts of the combustion chamber must
be capable of resisting the high gas temperature in the primary zone the walls
should be coated with high heat resistant coatings and by cooling the inner
wall of flame tube.
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Fig 4.2 Annular combustion chamber
4.4 Selection for Turbine
The turbine has to face a very high temperature and therefore the materials
required for manufacturing it are very important. The turbine can be made for
nickel alloys. A ceramic coating can be used to enhance the heat resistively of
the blades.
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5. CONCLUSION
5.1 Overview
In this section aims to summarize the over all design for the APU and also
look at the errors or defects in the design or the method used.
5.2 Design Summery
Following are the details of the full design
Inlet dry air properties
R 287 J/kg/K
Cp 1500J/kg/K
Γ 1.4
Compressor properties
Compressor pressure ratio 11:1
Compressor inlet pressure 1 bar
Compressor inlet temperature 15o C
Compressor isentropic efficiency 93%
Bleed flow from exit of compressor 1.5%
Type Axial
Materials used Steel and Nickel
alloys
Combustion chamber properties
Combustion Pressure Loss 1%
Combustion Fuel to Air Ratio 0.025:1
Type Annular
combustion
chamber
Materials High heat
resistive
coatings, Steel
and Nickel
alloys
Turbine properties
Turbine inlet temperature 1900K
Turbine exit pressure 1.2
Turbine isentropic efficiency 95%
Materials Nickel alloys
and ceramic
coatings
Mass flow
Mass flow rate of air 0.7649 kg/s
Mass flow rate of fuel 0.0188 kg/s
23
Generator properties
Electrical generator efficiency 95%
Aircraft Engine power demand (Wg) 400Kw
5.3 Errors and defects
There have been errors in running the MATLAB script. Caution need to be
taken in selection the range of turbine inlet temperature. If the value is less
than the compressor exit temperature the plots will show negative values. This
how ever can be preventing by putting some extra code.
The analysis of the report does not show many comparisons between different
or more complex range.
24
REFERENCES
Books:
1. The Jet Engine, By Rolls-Royce Plc
2. Aircraft Engines and Gas Turbines, Second Edition by Jack L.
Kerrenbrock
3. Aircraft Engine Design, By Jack D. Mattingly, Willian H.
Heiser & Daniel H. Daley
4. Aircraft Gas Turbine Powerplants, By Sanderson Tranning
Products.
Internet
1. NASA Glenn Research Centre,
url: http://www.grc.nasa.gov/WWW/K-12/aerores.htm
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