The document presents a preliminary design of a turbofan engine aimed at achieving over 25,000 N of thrust with a thrust specific fuel consumption of less than 0.025 kg/s/kN. A MATLAB code was used to generate carpet plots of specific thrust and thrust specific fuel consumption for different bypass ratios, compressor pressure ratios, and bypass pressure ratios. The final optimal design parameters chosen were: a turbine inlet temperature of 1300 K, compressor pressure ratio of 30, bypass ratio of 6, bypass pressure ratio of 1.35, inlet diameter of 0.738 m, thrust of 25,050.9 N, and thrust specific fuel consumption of 0.0187 in order to meet mission requirements with high fuel efficiency.

1. 1
UCI-Jets 2015
Department of
Mechanical and Aerospace Engineering
University of California: Irvine
By,
Nicholas Cordero
February 20, 2015

2. 2
Abstract
The purpose of this preliminary design of a turbofan engine is to obtain optimal
parameters which will yield a thrust of more than 25,000 N for a single engine as well as have a
thrust specific fuel consumption less than .025 kg/s/kN, assuming JP-4fuel is used, in order for
UCI-Jets 2015 to win a contract for the latest passenger plane. Once this requirement is met, the
design should be optimized further in order to strike the best trade-off between fuel efficiency
and engine size for the given mission and design constraints. The turbofan is assumed to be
operating at an altitude of 35,000ft and at a Mach value of .85. Due to size and material
constraints, the inlet diameter of the engine shall not exceed 2 meters while the inlet stagnation
or total temperature of the turbine shall not exceed 1700K. The key preliminary design
parameters are bypass ratio, compressor ratio, bypass pressure ratio, inlet stagnation temperature
of turbine, and size or diameter of the engine. A Matlab code was generating to loop through the
various combinations of bypass ratios, compressor pressure ratios, and bypass pressure ratios
given a certain engine diameter and inlet stagnation temperature of turbine that will satisfy or
surpass the requirements. Carpet plots were generated from the code which showed specific
thrust and thrust specific fuel consumptions as a function of bypass ratios and compressor
pressure ratios as well as cutoff lines that showed the minimum specific thrust and maximum
thrust specific fuel consumption values that were acceptable. For each bypass and compressor
pressure ratio combination, the bypass pressure ratio which yielded the maximum specific thrust
was obtained. At this bypass pressure ratio, the specific thrust and corresponding thrust specific
fuel consumption were recorded and used for the carpet plot. These carpet plots were then
generated for maximum inlet stagnation turbine temperature of 1700K as well as a lower
temperature of 1300K. At the temperature 1300K, carpet plots were also generated for an engine

3. 3
inlet diameter of 2 meters and .737 meters. The final design parameters chosen to satisfy the
mission requirement yet strike the best trade-off between fuel efficiency and engine size for the
given mission are listed in Table 1 in the summary, and yield a thrust of 25,050.9 N and a thrust
specific fuel consumption of .0187 .
Introduction
Figure 1 Schematic Diagram of Turbofan Engine
A turbofan engine shown in Figure 1 has a similar configuration so that of a turbojet,
which consists of a diffuser which decelerates the incoming airstream, compressor which
compresses the air, burners where fuel is added and burned with the air, turbine which drives the
compressor through the expansion of the passing air, and finally a nozzle which accelerates the
exhaust mass. Afterburners are sometimes added after the turbine to increase the total
temperature at the exit of the turbine and hence increase thrust however, the disadvantage is an
increase in fuel consumption. The main difference between a turbojet engine and turbofan engine
is a ducted fan that is added to the inlet of the engine. This ducted fan in a turbofan engine allows

4. 4
a fraction of the incoming airstream to bypass the turbine and create thrust along with the thrust
created by the core engine. This requires either the same or an additional turbine to drive not
only the compressor, but the fan as well. The ratio of the bypass airflow rate to core engine
airflow rate is known as the bypass ratio.
Figure 2 Propulsion efficiency vs Airspeed for Turbojet and Turbofan Engine
Typically, turbofans are used in the high subsonic flight speed range that commercial
aircraft fly at. The exhaust bypass velocity in a turbofan engine is low relative to the exhaust
velocity from the core engine which leads to an average exhaust velocity less than that of a
turbojet engine. Since propulsion efficiency is inversely proportional to the exhaust velocity
relative to the surrounding air, this leads to a turbofan engine having higher propulsion efficiency
than that of a conventional turbojet engine at a this high subsonic flight speed range. Also since
engine noise is proportional to the exhaust velocity squared, the turbofan engine is less noisy
than that of a turbojet engine at the same thrust level. The propulsion efficiency for a turbojet
and turbofan engine at various airspeeds can be seen in Figure 2.

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Design Method
Figure 3 Schematic Diagram of a Turbojet Engine from the 2nd
Editions of Mechanics and
Thermodynamics of Propulsion by Hill
Figure 3 shows the schematic diagram of a turbojet engine which will be referenced when
deriving the equation for specific thrust and thrust specific fuel consumption. We will assume
that Figure 3 has a fan in front of the compressor at station 2 just like that shown in Figure 1,
which is a schematic diagram of a turbofan engine. The assumptions and key parameters are
listed below:
Parameters
1. (Ambient temperature) = 218.933 K
2. (Ambient temperature) = 23908.485 Pa
3. (Turbine inlet total temperature)
4. (Flight mach number) = .85
5. (Flight speed)
6. (Exhaust speed)
7. (Fan exhaust speed)
8. (Speed of sound)
9. (Specific gas constant) = 287 J/kg*K

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10. (Diffuser adiabatic efficiency) = .95
11. (Compressor adiabatic efficiency) = .9
12. (Fan nozzle adiabatic efficiency) = .99
13. (Fan adiabatic efficiency) = .92
14. (Turbine adiabatic efficiency) = .9
15. (Bypass ratio)
16. (Compressor pressure ratio)
17. (Bypass pressure ratio)
18. (Fuel-air ratio)
19. (Diffuser specific heat ratio) = 1.4
20. (Compressor specific heat ratio) = 1.37
21. (Fan stream specific heat ratio) = 1.4
22. (Nozzle specific heat ratio) = 1.36
23. (Specific thrust)
24. (Thrust specific fuel consumption)
25. (Heating value) = 45000 kJ/kg
26. (Specific heat at constant pressure) = 1.1 kJ/kg*C
Assumptions
1. Constant specific heats
2. One-dimensional analysis
3. Flow expands to ambient pressure at exit of nozzle ( )
Design Procedure

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1. Compressor inlet
The total temperature and total pressure of the compressor inlet are given as,
( ( ) )
( ( ))
knowing that
√
2. Compressor outlet
The compressor pressure ratio is given as,
which then yields the total pressure and total temperature at the compressor outlet
( (
( )
))
3. Burner fuel-air ratio
After an energy balance on the combustion process, the fuel to air ratio is
4. Turbine inlet pressure

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Assuming no total pressure losses in the burner, then the total compressor outlet pressure equals
the total turbine inlet pressure.
5. Fan inlet conditions
Since the fan is in front of the compressor at station 2, stagnation conditions are the same as for
the compressor.
6. Fan outlet conditions
The total pressure at the fan outlet is equal to the total pressure at the fan inlet times the bypass
pressure ratio,
and the total temperature at the fan outlet is given by,
( (
( )
))
7. Fan nozzle exhaust velocity
The fan nozzle kinetic energy is defined as
( )
which after simplification becomes
√ ( ( ) )
8. Turbine outlet conditions

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A power balance between the turbine and compressor and fan yields,
̇ ( ) ̇ ( ) ̇ ( )
By assuming,
̇ ̇
Then the total temperature at the turbine outlet and corresponding total pressure at the outlet are,
( ) ( )
( ( ))
9. Nozzle inlet conditions
With no after burner,
10. Nozzle outlet conditions
The nozzle kinetic energy is defined as,
( )
which after simplification becomes
√ ( ( ) )
With the exhaust velocity from the core engine and fan, the specific thrust and thrust specific
fuel consumption can be calculated as

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̇
( ) ( )
̇
( ) ( )
Defining the Specific Thrust in terms of total mass flow rate yields
̇ ( ) ( )
The maximum mass flow rate per unit area of the inlet can be estimated by,
̇
⁄
√ ⁄
̇
⁄
√ ⁄
which after multiplying by the area yields a maximum mass flow rate of
̇
⁄
√ ⁄
Then the minimum specific thrust needed in terms of total mass flow rate is
̇ ⁄
√ ⁄
[ ]

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and the maximum thrust specific fuel consumption is already given as
[ ]
Calculation Results and Analysis
Figure 4

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Figure 5
Figure 6

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Figure 7
Figure 8 T-s Diagram for Turbofan Engine

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In the figures shown above, thrust specific fuel consumption and specific thrust is plotted
for a turbofan engine with a bypass ratio varying from 0 to 10 in steps of .5, compressor ratio
varying from 16 to 40 in steps of 2, and bypass pressure ratio varying from 1 to 1.6 in steps of
.05. The heating value ( )of JP-4 fuel is used, which is approximately 45,000 . Figure 7
shows the T-s diagram for the turbofan engine with no afterburner. For each bypass and
compressor ratio combination, the bypass pressure ratio which yielded the maximum specific
thrust was obtained. At this bypass pressure ratio, the specific thrust and corresponding thrust
specific fuel consumption were recorded and used for the carpet plot. The solid red lines are
associated with the various bypass ratios while the solid blue lines are associated with the
various compressor pressure ratios. The dashed blue line is the cut off for the minimum specific
thrust and the dashed black line is the cut off for the maximum thrust specific fuel consumption.
The relationship that can be seen from all the figures is that as the specific thrust increases, thrust
specific fuel consumption increases and vice versa. Also as the total temperature at the inlet of
the turbine increases, the specific thrust increases however, the thrust specific fuel consumption
increases as well which can be seen in Figure 3 and 4. Decreasing the inlet diameter of the
engine also leads to a higher specific thrust required which can be seen in Figure 5 and 6 as the
minimum specific thrust line shifts to the right.
For the purpose of designing a turbofan engine for a passenger plane, having higher fuel
efficiency is better than having higher thrust because of the numerous amount of times this
engine will be operated for transportation. This also means that a lighter engine would be ideal
for this scenario, which relates directly to a smaller inlet diameter of the engine. Also since
TSFC increases with increasing turbine inlet temperature, it would be better to have a lower
turbine inlet temperature. The lower turbine inlet temperature would also be beneficial from a

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materials point of view, which would mean having to rely less on obtaining expensive turbine
blades that can withstand higher temperature.
First, the total temperature of the turbine inlet was reduced until a minimal temperature
was reached before the carpet plots started becoming distorted due to the reduction in energy
obtained from turbine. Then, the engine inlet diameter was reduced until the thrust specific fuel
consumption was still reasonably low accommodated by a specific thrust that was moderate. The
final temperature and diameter chosen were 1300K and .738 meters respectively and the
intersection point closest to the minimum specific thrust blue dashed line as well as the lowest
out of the solid blue lines was chosen to yield a specific thrust of .1723 or 25,050.9 N and a
thrust specific fuel consumption of .0187 . Knowing the specific thrust and thrust specific
fuel consumption, the corresponding compressor pressure ratio, bypass ratio, and bypass pressure
ratio were determined as 30, 6, and 1.35 respectively.
Summary
Final Optimal Preliminary Design Parameters
Turbine inlet temperature, 1300 K
Compressor pressure ratio, 30
Bypass, 6
Bypass pressure ratio, 1.35
Inlet diameter of engine, D .738m
Thrust, 25,050.9 N
Thrust Specific Fuel Consumption, TSFC .0187
Table 1
The final optimal preliminary design parameters to meet the mission requirement as well
as have a higher fuel efficiency are listed in Table 1. The main tradeoff in this preliminary design
analysis is between specific thrust and thrust specific fuel consumption, which in the case of the

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passenger plane, is better to have a low thrust specific fuel consumption rather than a higher
specific thrust.
Appendix
%%Code to evaluate Turbofan Engine Performance given certain design
%%parameters
%%Parameters
clc
clear all
close all
M = .85; %[] Mach Number
Pa = 23908.485; %[Pa] Ambient Pressure
Ta = 218.933; %[K] Ambient Temperature
Qr = 45000; %[kJ/kg] Fuel heating value
T04 = 1300; %[k] Inlet Turbine Temperature
Cp = 1.1; %[kJ/kg*C] Specific Heat at Constant Pressure
R = 287; %[J/kg*K] Gas Constant
Deff = .95; %[] Diffuser Adiabatic Efficiency
Ceff = .9; %[] Compressor Adiabatic Efficiency
Teff = .9; %[] Turbine Adiabatic Efficiency
Neff = .98; %[] Nozzle Adiabatic Efficiency
Feff = .92; %[] Fan efficiency
FNeff = .99; %[] Fan nozzle efficiency
yD = 1.4; %[] Specific heat ratio for Diffuser
yC = 1.37; %[] Specific heat ratio for Compressor
yT = 1.33; %[] Specific heat ratio for Turbine
yN = 1.36; %[] Specific heat ratio for Nozzle
Prc = [16:2:40];
B = [0:.5:10];
Prf = linspace(1.0,1.6,13)
for i = 1:13
for j = 1:21
STmax=0;
TSFCmax = 0;
for z = 1:13
%%Compressor inlet conditions
T02 = Ta*(1+((yD-1)/2)*M^2);
P02 = Pa*(1+Deff*((T02/Ta)-1))^(yD/(yD-1));
%%Compressor outlet conditions
P03 = P02*Prc(i);
T03 = T02*(1+(1/Ceff)*(Prc(i)^((yC-1)/yC)-1));

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%%Burner fuel-air ratio
f = ((T04/T03)-1)/((Qr/(Cp*T03))-(T04/T03));
%%Fan outlet conditions
P08 = P02*Prf(z);
T08 = T02*(1+(1/Feff)*(Prf(z)^((yD-1)/yD)-1));
%%Fan exit nozzle velocity
uef = sqrt(2*FNeff*(yD/(yD-1))*R*T08*(1-(Pa/P08)^((yD-1)/yD)));
%%Turbine inlet pressure
P04 = P03; %Assuming total pressure constant through
burner
%%Turbine outlet conditions
T05 = T04-((T03-T02)+B(j)*(T08-T02)/(1+f));
P05 = P04*(1 - (1/Teff) * (1 -(T05/T04) ) ).^(yT/(yT-1));
%%Nozzle inlet conditions (With no afterburner)
T06 = T05;
P06 = P05;
%%Nozzle exit velocity
ue = sqrt(2*Neff*(yN/(yN-1))*R*T06.*(1-(Pa./P06).^((yN-1)/yN)));
%%Spefic Thrust
ST11 = ((1+f)*ue+B(j)*uef-M*sqrt(yD*Ta*R)*(1+B(j)))/(1000);
TSFC11 = (f/((1+f)*ue+B(j)*uef-M*sqrt(yD*Ta*R)*(1+B(j))))*1000;
if ST11 >= STmax
STmax = ST11;
TSFCmax = TSFC11;
end
end
ST(i,j) = STmax/(1+B(j))
TSFC(i,j) = TSFCmax
end
if (~isreal(ST(i,j))|| ST(i,j)<0);
ST(i,j) = NaN;
end
if (~isreal(TSFC(i,j))|| TSFC(i,j)<0);
TSFC(i,j) = NaN;
end
end
figure
hold on
plot(ST,TSFC,'-r')

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plot(ST',TSFC','-b')
title('Thrust Specific Fuel Consumption vs. Specific Thrust for M=.85, T04 =
1300k, D = .738m')
xlabel('Specific Thrust (kN*s/kg)')
ylabel('TSFC (kg*s/kN)')
xlim([0,1])
ylim([.015, .035])
%%TSFC Limit
xvaltsfc=[0,1]';
yvaltsfc=[.025,.025]';
plot(xvaltsfc,yvaltsfc,'--k')
D = .738;
A = (pi/4)*D^2;
S = P02/Pa;
Theta = T02/Ta;
mdot = A*231.8*(S/sqrt(Theta));
STmin=25/mdot;
xvaluest=[STmin,STmin]';
yvaluest=[.015,.035]';
plot(xvaluest,yvaluest,'--')
hold off