MAE 423Contemporary Issue Project

Deepak Kumar

Dr Paul E. DesJadin

Table of Contents

Problem statement ................................................................................................ 2

Introduction ........................................................................................................... 3

Assumptions .......................................................................................................... 4

Method of solution ............................................................................................... 5

Discussion and results ........................................................................................... 7

Summary & conclusion ........................................................................................

16

References ........................................................................................................... 17

1

Problem Statement

A non-ideal turbojet is to be studied at varying Mach numbers. Specific thrust, thrust specific

fuel consumption, propulsion efficiency, thermal efficiency, and overall efficiency will be

analyzed at the given set of Mach numbers. We will also be studying about the effects of

compressor ratios with the above parameters. The Mach numbers used in this analysis will be

0.2, 0.4, 0.6, 0.8, 1.4, 1.8, and 2.0. The compressor ratio that will be used for the study will be

between 2 and 100, in an increment of 0.5. Finally the stoichiometric ratio range is set to be

0.5 < ф <1.5.

The turbojet engine to be analyzed is given by figure 1

Figure 1

2

Introduction

This project is an analysis of an air breathing turbojet engine. The ambient air from the free

stream flow is drawn in trough the diffuser into the compressor. The air velocity is decreased as

the air is carried to the compressor. The air is then compressed in a dynamic compressor. The

compressor increases the pressure and the temperature of the air. Work is done by the

compressor to obtain the required compression ratio, the resulting temperature change is

dependent on the efficiency of the compressor. The air is once again heated in the combustion

chamber by burning fuel in an air and fuel mixture. The high temperature and pressure gas is

allowed to expand through a turbine to generate the necessary power needed to drive the

compressor. During this process there is a loss in the temperature and pressure of the gas. As

the gas leaves the turbine the gas is still at a higher temperature compared to the ambient

temperature, as a result the turbine inlet temperature is high. The air is finally accelerated and

exhausted through the nozzle. Engine cooling system uses the relatively cool air from the

compression system that bypasses the combustor via air system flow paths to cool the turbine

nozzle guide vanes and blades to ensure acceptable metal temperatures at very high gas

temperatures.

3

Assumptions

The following are the assumption used to calculate all data for this study.

Table 1

M1 2πb 0.93ηt 0.9Pe Pa

Pa (P1) 20000 paTa (T1) 216 K

Qr 42000000 J/Kgηc 0.85ηb 0.85ηn 0.95

Tturb inlet 1750 Kϒ 1.4

Ua=M2sqrt(ϒRTa) 589.198778 m/s

ϒc 1.4ϒt 1.3R 287 J/ Kg-Kπc 2τλ 8.101851852

Cpc 1004.5Cpt 1243.666667

Cpc/Cpt 0.807692308φstc 0.069097569JP8 166 MWAir 2402.4 MW

4

Method of solutions

Air to fuel ratio

The Chemical reaction of JP8 and air:

Molecular Weights:

Carbon = 12 g/mol

Oxygen = 16 g/mol

Nitrogen = 14 g/mol

Hydrogen = 1g/mol

Therefore the fuel to air ratio is as follows

5

Specific Thrust

I = specific thrust

Thrust Specific Fuel Consumption

Propulsion Efficiency

Thermal Efficiency

Overall Efficiency

6

Discussion and Results

a)

1 10 1000.0000

200.0000

400.0000

600.0000

800.0000

1000.0000

1200.0000

Specific Thrust vs πc

0.2 mach0.4 mach0.6 mach0.8 mach1.4 mach1.8 mach2.0 mach

Compressor Ratio

Spec

ific t

hrus

t

Graph 1

The graph above represents the effects of increasing Mach number and compression ratio on

the Specific Thrust. It is clearly seen from the graph that the specific thrust reduces as the Mach

number increases. The increase in the compression ratio increases the specific till it reaches a

max specific thrust as the components of the engine reach performance limits. All the values

are constrained by the stoichiometric ratio range.

7

1 10 1000.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.3000

TSFC vs πc

0.2 mach0.4 mach0.6 mach0.8 mach1.4 mach.8 mach2.0 mach

Compressor ratio

TSFC

Graph 2

From the graph above we can see that the TSFC increases as the Mach number increases within

the same range of the stoichiometric ratio. From the graph it can also be deduced that the inlet

pressure ratio reduces to produce the same thrust with the increasing fuel flow.

8

1 10 1000.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

Propulsion efficiency vs πc

M=0.2M=0.4M=0.6M=0.8M=1.4M=1.8M=2

Compressure pressure ratio

Prop

ulsi

on E

ffici

ency

Graph 3

It is obvious from the above graph that the propulsion efficiency is approximately 0.65 at Mach

2.0 and for Mach 0.2 is between 0.2 and 0.1. The propulsion efficiency decreases with

increasing compressor ratio. The propulsion efficiency also tends to remain constant after

reaching its critical conditions.

9

1 10 1000.1000

0.1500

0.2000

0.2500

0.3000

0.3500

0.4000

0.4500

Thermal efficiency vs πc

M=0.2M=0.4M=0.6M=0.8M=1.4M=1.8M=2

Compressure pressure ratio

Ther

mal

Effi

cienc

y

Graph 4

From the graph above, the thermal efficiency increases with the increasing compressor ratio.

The max thermal efficiency at all Mach number seem to be approximately close to each other.

10

1 10 1000.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.3000

Overall efficiency vs πc

M=0.2M=0.4M=0.6M=0.8M=1.4M=1.8M=2

Compressure pressure ratio

Ove

rall

Efficie

ncy

Graph 5

As the Mach number increases, the overall efficiency increases with increasing compressor ratio.

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b) Maximum values of I and TSFC

Table 2

M πc I [Ns/Kg]TSFC [Kg/N

hr] ηp ηth ηo

0.2 35.0 1058.577 0.253 0.159 0.445 0.04910.4 32.5 1004.676 0.260 0.281 0.446 0.09370.6 28.5 954.070 0.258 0.370 0.448 0.13510.8 24.0 906.695 0.251 0.436 0.449 0.17381.4 12.0 782.889 0.227 0.635 0.445 0.27091.8 7.0 714.236 0.216 0.824 0.441 0.30242.0 5.0 683.784 0.314 0.944 0.439 0.3136

c) We can conclude from the table given in part b, that max specific thrust reduces as the Mach

number climbs. The thrust specific fuel consumption reaches maximum with the as the Mach

number increases.

d) Lean fuel stability is constrained by the operating range as the flight Mach number is

increased such that the operating range of the compressor ratio decreases. Therefore the

turbojet engine will be operating at a much smaller range of operating conditions as the Mach

number increases. Essentially the turbojet engine will stall at very high Mach numbers. Thus

proving that the ram jet engines are more effective at very high Mach number than a turbojet

engine.

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e)

1 10 1000

0.05

0.1

0.15

0.2

0.25

0.3

Propulsion Efficiencyvs πc

Mach = 1.8

Mach = 2.0

Single Shock Mach = 1.8

Single Shock Mach = 2.0

Compressor Ratio

Prop

ulsio

n Effi

cienc

y

Graph 6

Highest propulsion efficiency occurs at two-shock systems. The higher the Mach number the

higher propulsion efficiency.

13

1 10 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Thermal Efficiencyvs πc

Mach = 1.8Mach = 2.0Single Shock Mach = 1.8Single Shock Mach =2.0

Compressor Ratio

Ther

mal

Effi

cienc

y

Graph 7

This graph shows the thermal efficiency of a single shock system has optimum efficiency. Higher

than the two shock system. As the Mach number increases the thermal efficiency increases.

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1 10 1000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Overall Efficiency vs πc

Mach = 1.8Mach = 2.0Single Shock Mach = 1.8Single Shock Mach = 2.0

Compressor Ratio

Ove

rall

Efficie

ncy

Graph 8

This graph settles the results without a doubt that the two-shock systems is greater than the

overall efficiency of single shock systems.

15

Summary and Conclusion

From the analysis above it is needless to say that the higher the Mach number and

compression ratio is the lower the specific thrust and thrust specific fuel consumption. From

the efficiency graphs we can say that at higher Mach number the more efficient the turbojet

engine is.

From the shock analysis the two shock system is more efficient and preferred. This clear

shows that it is better to use oblique shocks. In conclusion the Turbojet engines perform more

efficiently at greater Mach numbers. At high supersonic speed it is preferable to have oblique

shocks than a single shock system. The range of the compressor points reduce with the given

range of the stoichiometric ratio.

16

Reference

http://mit.edu/16.unified/www/FALL/thermodynamics/notes/node85.html

http://en.wikipedia.org/wiki/Overall_pressure_ratio

Mechanics and Thermodynamics of Propulsion 2nd edition Philip Hill ,Carl Peterson

http://www.grc.nasa.gov/WWW/k-12/airplane/oblique.html

http://www.oocities.org/siliconvalley/7116/jv_aerom.html

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