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UCI-Jets 2015

Department of

Mechanical and Aerospace Engineering

University of California: Irvine

By,

Nicholas Cordero

February 20, 2015

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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

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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

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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 2

nd 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