Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each...

23
1 EXERGETIC ANALYSIS OF AN AIRCRAFT TURBOJET ENGINE WITH AN AFTERBURNER M.A. Ehyaei (1)* , A. Anjiridezfuli (2) and M.A. Rosen (3) (1) Islamic Azad University, Pardis Branch, Pardis New City, Tehran, Iran (2) Islamic Azad University, Dezful Branch, Dezful City, Khuzestan, Iran (3) Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario, L1H 7K4, Canada * Corresponding author E-mail: [email protected], Tel: +98-21-88092344 Abstract: An exergy analysis is reported of a J85-GE-21 turbojet engine and its components for two altitudes: sea level and 11,000 meters. The turbojet engine with afterburning operates on the Brayton cycle and includes six main parts: diffuser, compressor, combustion chamber, turbine, afterburner and nozzle. Aircraft data are utilized in the analysis with simulation data. The highest component exergy efficiency at sea level is observed to be for the compressor, at 96.7%, followed by the nozzle and turbine with exergy efficiencies of 93.7 and 92.3%, respectively. At both considered heights, reducing of engine intake air speed leads to a reduction in the exergy efficiencies of all engine components and overall engine. The exergy efficiency of the turbojet engine is found to decrease by 0.45% for every 1°C increase in inlet air temperature. Key words: Turbojet, Afterburner, Exergy, Entropy generation, Efficiency 1. Introduction Engines are installed on aircraft for propulsion. Exhaust gases from aircraft engines exit at the rear of the engine nozzle, causing the aircraft to move forward and air to pass over the aircraft wings. This air motion creates lift. Most modern aircraft use gas turbine engines to produce the required thrust force. Such engines are relatively light and compact and have a high power to weight ratios. Aircraft gas turbines operate in an open cycle based on the Brayton cycle. Actual jet cycles are not ideal due to thermodynamic losses. The gases in the jet cycle are expanded in the gas turbine to the pressure that allows generation of the power needed by the compressor, generator, hydraulic pump and other work-consuming devices. Other gas turbine-based aerospace engines exist beyond the turbojet, including turbofan and turboshaft engines, but only turbojets are considered here. Production of jet aircraft began in 1945, and the technology has advanced significantly since then. Efforts to increase power and reduce noise and fuel consumption have led to improvements in turbojet and turbofan engines (Balli et al., 2008). Nearly 16,800 jet aircraft were operating globally in 2007, and this number is expected to increase to 35,300 by 2024 (Karakoc et al., 2006). Due to decreasing world oil reserves, increasing oil prices and increasing environmental concerns, efforts have increased to improve system efficiency. Exergy analysis is a practical and useful tool for such activities, with many engineers and scientists

Transcript of Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each...

Page 1: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

1

EXERGETIC ANALYSIS OF AN AIRCRAFT TURBOJET ENGINE WITH AN

AFTERBURNER

M.A. Ehyaei(1)*

, A. Anjiridezfuli(2)

and M.A. Rosen(3)

(1) Islamic Azad University, Pardis Branch, Pardis New City, Tehran, Iran

(2) Islamic Azad University, Dezful Branch, Dezful City, Khuzestan, Iran

(3) Faculty of Engineering and Applied Science, University of Ontario Institute of Technology,

2000 Simcoe Street North, Oshawa, Ontario, L1H 7K4, Canada

* Corresponding author E-mail: [email protected], Tel: +98-21-88092344

Abstract: An exergy analysis is reported of a J85-GE-21 turbojet engine and its components for

two altitudes: sea level and 11,000 meters. The turbojet engine with afterburning operates on the

Brayton cycle and includes six main parts: diffuser, compressor, combustion chamber, turbine,

afterburner and nozzle. Aircraft data are utilized in the analysis with simulation data. The highest

component exergy efficiency at sea level is observed to be for the compressor, at 96.7%, followed

by the nozzle and turbine with exergy efficiencies of 93.7 and 92.3%, respectively. At both

considered heights, reducing of engine intake air speed leads to a reduction in the exergy

efficiencies of all engine components and overall engine. The exergy efficiency of the turbojet

engine is found to decrease by 0.45% for every 1°C increase in inlet air temperature.

Key words: Turbojet, Afterburner, Exergy, Entropy generation, Efficiency

1. Introduction

Engines are installed on aircraft for propulsion. Exhaust gases from aircraft engines exit at the

rear of the engine nozzle, causing the aircraft to move forward and air to pass over the aircraft

wings. This air motion creates lift. Most modern aircraft use gas turbine engines to produce the

required thrust force. Such engines are relatively light and compact and have a high power to

weight ratios. Aircraft gas turbines operate in an open cycle based on the Brayton cycle. Actual

jet cycles are not ideal due to thermodynamic losses. The gases in the jet cycle are expanded in

the gas turbine to the pressure that allows generation of the power needed by the compressor,

generator, hydraulic pump and other work-consuming devices. Other gas turbine-based aerospace

engines exist beyond the turbojet, including turbofan and turboshaft engines, but only turbojets

are considered here. Production of jet aircraft began in 1945, and the technology has advanced

significantly since then. Efforts to increase power and reduce noise and fuel consumption have

led to improvements in turbojet and turbofan engines (Balli et al., 2008). Nearly 16,800 jet

aircraft were operating globally in 2007, and this number is expected to increase to 35,300 by

2024 (Karakoc et al., 2006). Due to decreasing world oil reserves, increasing oil prices and

increasing environmental concerns, efforts have increased to improve system efficiency. Exergy

analysis is a practical and useful tool for such activities, with many engineers and scientists

Page 2: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

2

suggesting that exergy analysis is a highly effective method for evaluating and enhancing

thermodynamic performance, and superior to energy analysis (Dincer and Rosen, 2007).

Many researchers have investigated aircraft engines and propulsion systems with exergy analysis

(Riggins and McClinton 1995, Riggins 1996a, 1996b, 1996c, 1997, 2003; Curran, 1973; Brilliant,

1995; Horlock, 1999). Rosen and Etele (1999, 2004) examine the importance of defining a

reference environment that varies with altitude and apply that work to a turbojet engine. Gaggioli

and Paulus (2003) propose a method to account for the exergy rate associated with thrust and lift

forces and develop aircraft exergy flow diagrams. Bejan and Siems (2001) address the

optimization of the cruise velocity and of the heat exchange processes on board an aircraft while

Rancruel and Von Spakovsky (2003) investigate engine configuration optimization methods.

Hunt et al. (1999a, 1999b) and Riggins et al. (2006) discuss methodologies for accounting for

vehicle wake effects, and Moorhouse and Hoke (2002) apply exergy methods to the analysis of

the inlet performance. More recently, exergy analysis has been applied to an advanced hypersonic

vehicle, with two main scopes: 1) to enhance the exergy approach to the design and optimization

of aerospace propulsion systems, through the use of exergy flow diagram that provides aircraft

engineers and system designers with insights into avoidable and unavoidable systemic losses, and

2) to explore the limits and merits of fuelling options for a scramjet-powered aircraft (Amati et

al., 2008).Turgut et al. (2009a) perform an exergoeconomic analysis of an aircraft turbofan

engine utilising kerosene as fuel. They develop several parameters (thrust cost rate, cost of exergy

destruction, relative cost difference and exergoeconomic cost) and calculate the thrust cost rate to

be 304.35 ($/h kN) and 138.96 ($/h kN) for hot and cold thrust, respectively. Turgut et al. (2009b)

apply exergy analysis to a General Electric CF6-80 turbofan engine using sea-level data, and find

the units with the greatest irreversibilities in the system to be the fan and the core engine exhaust,

which exhibit exergy loss rates of 47.3 MW and 35.9 MW, respectively, and the combustion

chamber, which has an exergy destruction rate of 31.5 MW.Previous studies have not examined

turbojets with afterburning and have not focused on the variations of the results with altitude.

Such information is needed and addressing these needs is the focus of this paper. The main

objective is to perform an exergy analysis of a J85-GE-21 turbojet engine and its components, for

two altitudes: sea level and 11,000 meters. Entropy generation and exergy efficiency relations are

derived for each turbojet engine component and the overall system. The effects are studied of jet

velocity and inter air temperature, on entropy generation and exergy efficiency, with the aid of a

simulation program developed for this study.

2 System modeling and analysis

The J85-GE-21 turbojet engine is designed for F-5 fighter aircraft models F and E by General

Electric in the US and now is used on this aircraft. A J85-GE-21 turbojet engine is shown in

Figure 1, where the main parts are seen to be as follows: diffuser, compressor, combustion

chamber, turbine, afterburner and nozzle.

Page 3: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

3

Figure 1 Turbojet engine; used by permission of NASA (see website: www.Nasa.gov)

The turbojet has an axial compressor with nine stages, each having a 1.2 compression ratio. The

average compression ratio of compressor is 9. The combustion chamber is of an annular type, and

has 12 fuel injectors which spray liquid fuel (JET A-1) into the combustion chamber at high

pressure. The turbine has two stages and produces the mechanical power needed by the

compressor, hydraulic pump and generator. Twenty fuel injectors spray liquid fuel into the

afterburner, where it reacts with all the oxygen in the turbine exhaust gas in to order produce

more power and propulsive force. Approximately 15% of the air exiting the diffuser passes

around engine for cooling purposes, and is called dead air. The remaining air enters the

compressor. 40% of the air exiting the compressor goes around combustion chamber and

afterburner to keep the flame in the center of these devices. Exhaust gas from turbojet engine is

expanded to medium pressure by the nozzle (Northrop, 1978). Figure 2 shows a schematic

diagram of the turbojet engine analyzed.

Page 4: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

4

Figure 2 Schematic diagram of turbojet engine

The entry conditions of the diffuser (T1,P1,V1) are known, and the following equations are used to

obtain the outlet conditions. Note that outlet diffuser temperature is measured by a sensor which

installed at the end of diffuser to determine amount of fuel entering the combustion chamber and

burning by the engine. The relevant basic equations are as follows:

(1) 2

2

0

Vhh

(2) Pvuh

(3) 101

102

hh

hhS

D

where 0

h denotes inlet diffuser specific stagnation enthalpy (J/kg), h specific enthalpy (J/kg), V

velocity (m/s), u specific internal energy (J/kg),

P pressure (Pa), v specific volume (m3/kg), ηD

diffuser efficiency, S

h0

outlet specific stagnation enthalpy for an isentropic process (J/kg), and h1

inlet diffuser specific enthalpy (J/kg).With the above relations, following equations can be written

for the diffuser:

0201 hh

(4)

02V

(5)

22

2

2222

2

1111

VvPu

VvPu (6)

where 0201

h,h are the diffuser inlet and outlet specific stagnation enthalpies (J/kg), 21

u,u are the

diffuser inlet and outlet specific internal energies (J/kg), P1, P2 are the diffuser inlet and outlet

pressures (Pa), V1 is aircraft velocity (m/s), V2 is outlet diffuser air speed (m/s), and v1, v2 are the

Page 5: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

5

diffuser inlet and outlet specific volumes (m3/kg). With these equations, the diffuser outlet

pressure and temperature can be obtained iteratively. The outlet compressor pressure is obtained

with the following equation:

34PrP

c

(7)

where 34

P,P are the compressor outlet and inlet pressures (Pa), and rc is the compressor pressure

ratio. Also, the outlet compressor temperature is obtained with the following expressions:

(8) vdPTdsdh

(9) vdPdhs

(10) dh

dhs

C

Here, dh, ds and dP are the specific enthalpy (J/kg), specific entropy (J/kgK) and pressure (Pa)

variations in the compression process, T is the average temperature in the compression process

(K), dhs is the specific enthalpy variation for isentropic compression (J/kg), and C

is the

compressor polytropic efficiency. With the ideal gas assumption and equations 8 through 10, the

following equation can be developed for the outlet temperature:

P

dPR

T

dTC

CP

(11)

Here, CP is the specific heat at constant pressure (J/kgK), which is evaluated at a mean

temperature, and R is gas constant (J//kgK). With the specific heat at constant pressure as a

function of temperature and the compressor pressure ratio, the compressor outlet temperature can

be obtained for gas mixtures by integration of above equation. The integral form of above

equation is

4

3

4

3

4

3

T

T

P

P

P

PCCP P

dPR

P

dPR

T

dTC

(12)

Here, T3 and T4 are inlet and outlet compressor temperature (K) and P3 and P4 are inlet and

outlet compressor pressure (Pa). The compressor power input WC is calculated as follows:

1234 4.0)( hmhhmW aaC

(13)

Here, m·a is air mass flow rate (kg/s) and h3 and h4 & h12 are inlet and outlet specific enthalpies

(J/kg) of the compressor.Kerosene is a fuel currently used in aviation. This fuel can have variable

functional applications by modification of some of its properties. Two types of kerosene are Jet A

and Jet A-1 (Dagaut et al., 2006; Sochet et al., 2002). Depending on the type of ball bearings, roll

Page 6: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

6

bearings, sealing and packing of selected engines, Jet A-1 or JP4 is normally used (Northrop,

1978). According to Figure 2, there are two components in which combustion occurs.

Combustion relations based on reactant and product mass balances are as follows (Bejan, 1998):

Combustion chamber:

(14)

Afterburner:

(15)

The energy balance for a combustion process can be written as follows:

where h˚f is the specific enthalpy of formation (J/kg), h0 is the specific enthalpy at the reference

condition (J/kg), ηcc is the combustion energy efficiency, and the subscripts r and p denote

reactants and products, respectively. The combustion temperature can be calculated with

equations (14) to (16). The pressure in the combustion chamber can be determined as follows:

(17)

where P5 and P6 are the inlet and outlet pressures of the combustion chamber (Pa), T5 and T6 are

the inlet and outlet temperatures (K), and n6 and n5 are the inlet and outlet number of moles.

Similarly, the pressure in the afterburner can be expressed as

(18)

where P7 and P8 are the inlet and outlet pressures of the afterburner, T7 and T8 are the inlet and

outlet temperatures, and n7 and n8 are the inlet and outlet number of moles. The turbine outlet

pressure can be expressed as follows:

rfpccpfr hhhmhhhm ))(())(( 00

(16)

2222

22222312

38306.005928.003694.002889.0

)019.00003.02059.07748.0(4944.00024.0

NOOHCO

OHCOONHC

22222

2222312

9064.0072562.026371.01228.0)151124.0

034138.0152502.0762236.0(189521.10073.0

NOOHCOOH

COONHC

7

8

7

8

78 T

T

n

nP=P

5

6

5

6

56 T

T

n

nP=P

Page 7: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

7

6T7 PrP

(19)

where 67

P,P are the turbine outlet and inlet pressures (Pa), and rT is the turbine pressure ratio.

The turbine outlet temperature can be obtained by with the following equation:

7

6

7

6

7

6

T

T

P

P

P

PTTP P

dPR

P

dPR

T

dTC

(20)

Here, T6 and T7 are the inlet and outlet turbine temperatures, P6 and P7 are inlet and outlet

turbine pressures, and ηT is the turbine polytropic efficiency. The turbine power production

TWcan be expressed as follows:

)hh()m+m(=W 76faT

(21)

where fmis the fuel mass flow rate, and h6 and h7 are the inlet and outlet specific enthalpies of

the turbine (J/kg).The nozzle outlet temperature can be determined using the following equations:

98 oohh

(22)

08V

(23)

22

2

9999

2

8888

VvPu

VvPu (24)

Here, 0908

h,h are the inlet and outlet nozzle specific stagnation enthalpies (J/kg), 98

u,u are the

inlet and outlet nozzle specific internal energies (J/kg), P8 and P9 are the inlet and outlet nozzle

pressures (Pa), V8 is inlet nozzle velocity (m/s), 9

V is outlet diffuser air speed (m/s), and v8 and

v9 are the nozzle inlet and outlet specific volumes (m3/kg).

3. Exergy analysis

In the absence of nuclear, magnetic, electric and surface tension effects, exergy can be divided

into four distinct components: physical, chemical, kinetic and potential (Bejan et al.,1998;

Bejan,1998; Dincer and Rosen, 2007):

chphptknteeeee (25)

Page 8: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

8

where et , ekn , ept, eph and ech are the total, kinetic, potential, physical and chemical specific

exergies (J/kg). Specific kinetic and potential exergies can be expressed as follows:

2

2

Vekn

(26)

ghept

(27)

where g is gravitational acceleration (m/s2) and h is height (m). Specific physical and chemical

exergies can be written as follows:

)ss(T)hh(eph 000

(28)

iiii,chich

LnxxRTexe0

(29)

where h denotes specific enthalpy (J/kg), h0 the specific enthalpy at the reference condition (J/kg),

s specific entropy (J/kgK), s0 the specific entropy at the reference condition (J/kgK), T0 the

reference temperature (K), xi the gas mole fraction, and echi is specific chemical exergy,

respectively.Exergy rates (W) can be determined with the following equations:

knknemE

(30)

ptptemE

(31)

phphemE

(32)

chchemE

(33)

where Ékn, Épt , Éph, Éch are the kinetic, potential, physical and chemical exergy rates and m

is

mass flow rate.

Page 9: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

9

The exergy efficiencies of the turbojet components follow. Since the diffuser is used to increase

pressure and reduce velocity and involves no power interaction, the diffuser exergy efficiency can

be expressed as follows:

1

2

E

E

Diffuser

(34)

where Ψ denotes exergy efficiency, É2 , É1 are outlet and inlet diffuser exergy rates (W). The

compressor exergy efficiency is calculated as follows:

C

3412

Compressor

W

EE+E=Ψ

(35)

where É4 , É3 & É12 are the outlet and inlet compressor exergy rates (W). The combustion

chamber exergy efficiency is expressible as

10513

6

ChamberCombustion

E+E+E

E=Ψ

(36)

where É6 is the outlet combustion chamber exergy rate (W), É5 is the air inlet combustion

chamber exergy rate (W) , É10 the fuel exergy consumption rate in the combustion chamber (W)

and É13 the air exergy consumption rate in the combustion chamber (W) . The turbine exergy

efficiency can be written as follows:

76EE

Wt

Turbine

(37)

where É7 is outlet turbine exergy rate (W). The afterburner exergy efficiency can be expressed as

Page 10: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

10

71114

8

rAfterburne

E+E+E

E=Ψ

(38)

where É8 is the outlet afterburner chamber exergy rate (W), É11 the fuel use exergy rate in the

afterburner (W) and É14 the air use exergy rate in the afterburner (W). The nozzle exergy

efficiency is determined as follows:

(39)

where É9 is the outlet nozzle exergy rate (W).The overall turbojet exergy efficiency can be written

as

11101

9

EEE

E

(40)

The entropy generation rates in the diffuser, compressor, combustion chamber, turbine,

afterburner and nozzle, respectively, can be expressed as follows:

)EE(T

S

o

Diffuser,gen 121

(41)

))W(EE+E(T

1=S c3412

o

Compressor,gen

(42)

)EE+E+E(T

1=S 651013

o

ChamberCombustion,gen

(43)

8

9

E

E

Nozzle

Page 11: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

11

)WEE(T

S t

oTurbine,gen

76

1

(44)

)EE+E+E(T

1=S 811147

oburnerAfter,gen

-

(45)

)EE(T

S

oNozzle,gen 98

1

(46)

where To is the reference environment temperature, which is fixed here at 298.15 K.

4 Results and discussion

Temperatures, pressures, mass flow rates, kinetic, physical and chemical exergy rates for various

parts of engine at sea level and 200 m/s aircraft velocity are shown in Table 1.

Page 12: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

12

Table 1: Thermodynamic parameters for flows in J85GE-21 turbojet engine at sea level and

200 m/s speed

Total

exergy rate

(kW)

Kinetic

exergy rate

(kW)

Chemical

exergy rate

(kW)

Physical

exergy

rate

(kW)

Mass

flow rate

(kg/sec)

Pressure

(kPa)

Temperature

(K)

Flow Flow

No.

568.2 568.2 0 0 28.4 101.3 298.1 Diffuser inlet 1

514.6 0 0 514.6 28.4 124.2 318.1 Diffuser outlet 2

437.4 0 0 437.4 24.1 124.2 318.1 Compressor inlet 3

7679.5 0 0 7679.5 24.1 1118.2 625.7 Compressor outlet 4

4607.7 0 0 4607.7 14.5 1118.2 625.7 Combustion

chamber inlet 5

18409.2 0 0 18409.2 14.9 2138.8 1709.6 Turbine inlet 6

10297.4 0 0 10297.4 14.9 534.7 1184 Afterburner inlet 7

36170.4 0 0 36170.4 19 1263.8 2933.5 Afterburner outlet 8

33892.4 1111.1 0 32781.3 19 101.3 2866.1 Nozzle outlet 9

18282.3 0 18282.3 0 0.4 2757 353

Combustion

chamber fuel

input

11

55688 0 55688 0 218.1 1103.1 353 Afterburner fuel

input 11

3071.8 0 0 3071.8 9.6 1118.2 625.7 Compressor

cooling output 12

1843.1 0 0 1843.1 5.8 1118.2 625.7

Combustion

chamber cooling

air input

13

1228.7 0 0 1228.7 3.8 1118.2 625.7 Afterburner

cooling air input 14

Exergy efficiencies and entropy generation rates for the components of the engine at sea level and

200 m/s speed are shown in Figures 3 and 4, respectively. The highest component exergy

Page 13: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

13

efficiency is exhibited by the compressor at 96.7%. The next highest exergy efficiencies are for

the nozzle (93.7%) and turbine (92.3%). The lowest exergy efficiencies are for the afterburner

(54.8%), followed by the combustion chamber (80.4%). The low fuel efficiency of the afterburner

compared to the combustion chamber results in it burning almost three times the fuel of the

combustion chamber, in order to increase the thrust force by about one third. The entropy

production rates also help identify the components with the highest irreversibilities. The greatest

entropy production rate in the engine is observed for the afterburner, followed by the combustion

chamber. Hence, the combustion processes in the aircraft engine are highly irreversible. The

nozzle, due to the rapid changes in cross sectional area has in the third highest entropy production

rates.

Figure 3 Exergy efficiencies for turbojet engine and its components at sea level and 200 m/s

speed

Figure 4 Entropy generation rates for turbojet engine and its components at sea level and

200 m/s speed

Page 14: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

14

To determine the effect of aircraft engine velocity on entropy production rate and exergy

efficiency, the engine velocity is reduced from 200 m/s to 100 m/s and the results re-determined

(see Table 2). For this case, the exergy efficiencies and entropy generation rates are shown in

Figures 5 and 6. The exergy efficiencies the overall engine of all it components decrease as the

engine velocity decreases due to the reduction air mass flow rate.

Table 2: Thermodynamic parameters for flows in J85GE-21 turbojet engine at sea level and

100 m/s speed

Total

exergy

rate (kW)

Kinetic

exergy rate

(kW)

Chemical

exergy rate

(kW)

Physical

exergy rate

(kW)

Mass

flow rate

(kg/s)

Pressure

(kPa)

Temperature

(K)

Flow Flow

No.

71 71 0 0 14.2 101.3 298.1 Diffuser inlet 1

64 0 0 64 14.2 106.7 303 Diffuser outlet 2

54.4 0 0 54.4 12.1 106.7 303 Compressor inlet 3

3483.6 0 0 3483.6 12.1 960.5 596.3 Compressor

outlet 4

2090.1 0 0 2090.1 7.2 960.5 596.3 Combustion

chamber inlet 5

9500.8 0 0 9500.8 7.6 1899.4 1684.6 Turbine inlet 6

5082.9 0 0 5082.9 7.6 474.9 1166.7 Afterburner inlet 7

19098.6 0 0 19098.6 9.9 1144.9 2948.6 Afterburner outlet 8

18000.6 592 0 17408.6 9.9 101.3 2880.2 Nozzle outlet 9

18282.3 0 18282.3 0 0.4 2757 353

Combustion

chamber fuel

input

11

55687.9 0 55687.9 0 1.2 1103.1 353 Afterburner fuel

input 11

2090 0 0 2090 4.8 960.5 596.3

Compressor

cooling output 12

1254 0 0 1254 2.9 960.5 596.3

Combustion

chamber cooling

air input

13

836 0 0 836 1.92 960.5 596.3 Afterburner

cooling air input 14

Page 15: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

15

Figure 5 Exergy efficiencies for turbojet engine and its components at sea level and 100 m/s

speed

Figure 6 Entropy generation rates for turbojet engine and its components at sea level and

100 m/s speed

To evaluate the variation of the performance of aircraft engine and its components with altitude,

the performance parameters considered earlier are evaluated for an altitude of 11,000 (m), which

is a typical altitude at which a majority of aircraft flight time is spent. The temperature and

pressure at high altitudes are much different than at sea level. For instance, these parameters were

measured as 220 K and 4.23 kPa, respectively, by the meteorological office on 17 February 2010

at 10 am at an altitude 11,000 m. The temperatures, pressures, mass flow rates, and kinetic,

Page 16: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

16

physical and chemical exergy rates for various components of the engine at altitude of 11,000 m

and a 200 m/s aircraft velocity are shown in Table 3. Exergy efficiencies and entropy generation

rates the engine and its components at an altitude of 11,000 m and an engine speed of 200 m/s are

shown in Figures 3 and 4. The compressor has the highest exergy efficiency at 95.7%, followed

by the diffuser (94.8%) and nozzle (90.5%).

Table 3: Thermodynamic parameters for flows in J85GE-21 turbojet engine at 11,000 m

altitude and 200 m/s speed

Total

exergy

rate

(kW)

Kinetic

exergy

rate

(kW)

Chemical

exergy rate

(kW)

Physical

exergy rate

(kW)

Mass flow

rate

(kg/s)

Pressure

(kPa)

Temperature

(K)

Flow Flow

No.

177.8 177.8 0 0 8.9 23.4 220.15 Diffuser inlet 1

161.3 0 0 161.3 8.9 30.8 240 Diffuser outlet 2

137.1 0 0 137.1 7.6 30.8 240 Compressor

inlet 3

1830.1 0 0 1830.1 7.6 276.9 472.23 Compressor

outlet 4

1098 0 0 1098 4.5 276.9 472.23 Combustion

chamber inlet 5

6135.3 0 0 6135.3 4.7 651.2 1586.6 Turbine inlet 6

3356.8 0 0 3356.8 4.7 162.8 1098.8 Afterburner

inlet 7

12423.2 0 0 12423.2 5.8 399.1 2823.5 Afterburner

outlet 8

11722.6 256.7 0 11465.9 5.8 23.4 2777.7 Nozzle outlet 9

5745.2 0 5745.2 0 0.13 2757 320

Combustion

chamber fuel

input

11

17500 0 17500 0 0.38 1103.2 320 Afterburner fuel

input 11

1098 0 0 1098 3.04 276.9 472.23 Compressor

cooling output 12

658.8 0 0 658.8 1.8 276.9 472.23

Combustion

chamber cooling

air input

13

439.2 0 0 439.2 1.22 276.9 472.23 Afterburner

cooling air input 14

Page 17: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

17

Figure 7 Exergy efficiencies for turbojet engine and its components at 11,000 m altitude and

200 m/s speed

Figure 8 Entropy generation rates for turbojet engine and its components at 11,000 m

altitude and 200 m/s speed

To evaluate the variation of the performance of aircraft engine and its components with aircraft

velocity at high altitude, the entropy production rates and exergy efficiencies are evaluated when

the engine velocity is reduced from 200 m/s to 100 m/s at an altitude of 11,000 m The results are

given in Table 4. For this case, the exergy efficiencies and entropy generation rates are shown in

Figures 9 and 10.

Page 18: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

18

Table 4 Thermodynamic parameters for flows in J85GE-21 turbojet engine at 11,000 m

altitude and 100 m/s speed

Total

exergy

rate

(kW)

Kinetic

exergy

rate

(kW)

Chemical

exergy rate

(kW)

Physical

exergy rate

(kW)

Mass flow

rate

(kg/s)

Pressure

(kPa)

Temperature

(K)

Flow Flow

No.

22.2 22.2 0 0 4.4 23.4 220.1 Diffuser inlet 1

20 0 0 20 4.4 25.1 225.1 Diffuser outlet 2

17 0 0 17 3.8 25.1 225.1 Compressor

inlet 3

806.3 0 0 806.3 3.8 226 442.9 Compressor

outlet 4

483.8 0 0 483.8 2.3 226 442.9 Combustion

chamber inlet 5

3367.2 0 0 3367.2 2.4 558.1 1562.6 Turbine inlet 6

1659.9 0 0 1659.9 2.4 139.5 1082.2 Afterburner

inlet 7

6588.2 0 0 6588.2 3.1 347.9 2828.85 Afterburner

outlet 8

6243.7 136.8 0 6106.9 3.1 23.4 2782.6 Nozzle outlet 9

5745.2 0 5745.2 0 0.13 2757 320

Combustion

chamber fuel

input

11

17499.9 0 17499.9 0 0.38 1103.1 320 Afterburner fuel

input 11

493.8 0 0 483.78 2.28 226 442.9 Compressor

cooling output 12

296.3 0 0 290.3 1.4 226 442.9

Combustion

chamber cooling

air input

13

197.5 0 0 193.5 0.88 226 442.9 Afterburner

cooling air input 14

Page 19: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

19

Figure 9 Exergy efficiencies for turbojet engine and its components at 11,000 m and 100 m/s

speed

Figure 10 Entropy generation rates for turbojet engine and its components at 11,000 m and

100 m/s speed

The effect of inlet air temperature on exergy efficiency for the aircraft engine is shown in Figure

11. The overall exergy efficiency of the aircraft engine is reduced 0.45% for each Centigrade

degree increase in inlet air temperature. The cause of this phenomenon is the decrease in air

density due to the increase in temperature. This observation suggests that flying in early hours of

the day or at night is economic due to the lower ambient temperature.

Page 20: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

20

48

49

50

51

52

53

54

260 265 270 275 280 285

T1(K)

Ψ(%

)

Figure 11 Variation of aircraft exergy efficiency on aircraft engine

5 Conclusions

The exergy analysis of the selected aircraft engine with afterburner operating on kerosene fuel for

various altitudes and air speeds reveals useful insights, as does the investigation of the effects of

aircraft inlet air temperature on exergy efficiency. The relations are quantified between exergy

efficiency and entropy generation for the components of the aircraft engine. The key results and

conclusions follow:

The highest component exergy efficiency is observed at sea level for the compressor

(96.7%), followed by the nozzle (93.7%) and turbine (92.3%). Similarly, the highest

exergy efficiency at an altitude of 11,000 m is exhibited by the compressor (95.7%),

followed by the nozzle (94.8%) and the diffuser (90.5%).

The lowest component exergy efficiency at sea level is observed for the afterburner

(54.8%), followed by the combustion chamber (80.4%). Correspondingly, the entropy

production rates at sea level indicate that the most irreversible process is the afterburner,

followed by the combustion chamber and nozzle.

Reducing aircraft velocity at sea level reduces the exergy efficiency of the aircraft engine

and its components.

The aircraft engine exergy efficiency is reduced 0.45% per Centigrade degree increase in

inlet air temperature.

Nomenclature

Cp Specific heat at constant pressure (J/kgK)

dh Specific enthalpy variation in process (J/kg)

dhs Specific enthalpy variation in isentropic process (J/kg)

et Specific exergy (J/kg)

chE

Chemical exergy rate (W)

knE

Kinetic exergy rate (W)

Page 21: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

21

phE

Physical exergy rate (W)

ptE

Potential exergy rate (W)

g Gravitational acceleration (m/s2)

h Height of aircraft (m)

h Specific enthalpy (J/kg)

0h

Specific enthalpy at reference condition (J/kg)

fh

Specific enthalpy of formation (J/kg)

01h

Inlet specific stagnation enthalpy (J/kg)

02h

Outlet specific stagnation enthalpy (J/kg)

S0h

Outlet specific stagnation enthalpy in isentropic process (J/kg)

m Mass flow rate (kg/s)

am

Air mass flow rate (kg/s)

fm

Fuel mass flow rate (kg/s)

n Number of moles

P Pressure (Pa)

R Gas constant (J/kgK)

rc

Compressor pressure ratio

rT

Turbine pressure ratio

T Mean temperature in compression process (K)

To Reference environment temperature (K)

u Specific internal energy (J/kg)

v Specific volume (m3/kg)

V Velocity (m/s)

V1 Aircraft velocity (m/s)

CW

Compressor input power (W)

TW

Turbine output power (W)

Greek symbols

ηc Compressor polytropic efficiency

ηD Diffuser polytropic efficiency

ηT Turbine polytropic efficiency

Second law efficiency

Page 22: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

22

Subscripts

ch Chemical

kn Kinetic

p Product

ph Physical

pt Potential

r Reactant

1 Diffuser inlet

2 Diffuser out let

3 Compressor Inlet

4 Compressor outlet

5 Combustion chamber inlet

6 Combustion chamber outlet

7 Afterburner inlet or turbine outlet

8 Afterburner outlet or nozzle inlet

9 Nozzle outlet

10 Combustion chamber inlet

11 Afterburner inlet

12 Compressor cooling air outlet

13 Combustion chamber cooling air inlet

14 Afterburner cooling air inlet

References

1. Amati, V., Bruno, C., Simone, D. and Sciubba, E. (2008) ‘Exergy analysis of hypersonic

propulsion systems: Performance comparison of two different scramjet configurations at cruise conditions’, Energy: An International Journal, Vol. 33, pp.116–129.

2. Balli, O., Aras, H., Aras, N. and Hepbasli, A. (2004) ‘Exergetic and exergoeconomic analysis

of an aircraft jet engine (AJE)’, International Journal of Exergy, Vol. 5, No. 6, pp. 567-581.

3. Bejan A. (1998) Advanced Engineering Thermodynamics, John Wiley & Sons, New York. 4. Bejan, A., Tsatsaronis, G. and Moran, M.J. (1998) Thermal Design and Optimization, John

Wiley & Sons, New York.

5. Bejan, A. and Siems, D.L. (2001) ’The need for exergy analysis and thermodynamic optimization and aircraft development’, International Journal of Exergy, Vol. 1, No. 1, pp.14-

24.

6. Brilliant, H.M. (1995) ‘Analysis of scramjet engines using exergy methods’, AIAA paper 95-2767.

7. Curran, E.T. (1973) ’The use of stream thrust concepts for the approximate evaluation of

hypersonic ramjet engine performance’, US Air Force Aero Propulsion Laboratory, Report

AFAPL-TR-73-38, Wright-Patterson Air Force Base, OH. 8. Dagaut, B. and Cathonnet, P. (2006) ’The ignition, oxidation and combustion of kerosene: A

review of experimental and kinetic modeling’, Progress in Energy and Combustion Science,

Vol. 32, No. 1, pp. 48-92.

9. Dinçer I. and Rosen, M.A. (2007) Exergy: Energy, Environment, and Sustainable

Development, Elsevier, Oxford.

10. Gaggioli, R.A. and Paulus, J.D. (2003) ‘The exergy of lift, and aircraft exergy flow

diagrams’, International Journal of Thermodynamics, Vol. 6, No. 4, pp. 149–156.

11. Horlock, J. (1999) ‘Thermodynamic availability and propulsion’, AIAA paper 99-741.

Page 23: Exergetic analysis of an aircraft turbojet engine with ... OnLine-First/0354... · derived for each turbojet engine component and the overall system. The effects are studied of jet

23

12. Hunt, L., Cummings, M. and Giles, B. (1999a) ‘Wake integration for three dimensional flow

field computations: Theoretical development’, Journal of Aircraft, Vol. 36, No. 2, pp. 357–365.

13. Hunt, L., Cummings, M. and Giles, B. (1999b) ‘Wake integration for three dimensional flow

field computations: Application’ Journal of Aircraft, Vol. 36, No. 2, pp. 366–373.

14. Karakoc, H., Turgut, E., Hepbasli, A. (2006) ‘Exergetic analysis of an aircraft turbofan

engine’, Proceedings Summer Course on Exergy and its Applications, Anadolu University,

Eskisehir, August, Turkey, pp. 14-16.

15. Moorhouse, D.J. and Hoke, C.M. (2002) ‘Thermal analysis of hypersonic inlet flow with

exergy-based design methods’, International Journal of Applied Thermodynamics, Vol. 5,

No. 4, pp. 161–168. 16. Northrop Co. (1978) Technical Order of Aircraft 1F-5E/F, Report.

17. Rancruel, D.F. and Von Spakovsky, M.R. (2003) ‘Decomposition with thermoeconomic

isolation applied to the optimal synthesis/design of an advanced fighter aircraft system’, International Journal of Thermodynamics, Vol. 6, No. 3, pp. 121-129.

18. Riggins, D. and McClinton, C. (1995) ‘Thrust modeling for hypersonic engines’, AIAA paper

95-6081.

19. Riggins, D.W. (1996a) ‘High-Speed Engine/Component Performance Assessment Using Exergy and Thrust-Based Methods’, report NASA-CR-198271, National Aeronautics and

Space Administration, Langley Research Center, Hampton, VA.

20. Riggins, D.W. (1996b) ‘The evaluation of performance losses in multi-dimensional propulsive flows’, AIAA paper 96-0375.

21. Riggins, D.W. (1996c) ‘Brayton cycle engine/component performance assessment using

energy and thrust-based methods’, AIAA paper 96-2922.

22. Riggins, D.W. (1997) ‘Evaluation of performance loss methods for high-speed engines and engine components’, Journal of Propulsion and Power, Vol. 13, No. 2, pp. 296–304.

23. Riggins, D. (2003) ‘The thermodynamic continuum of jet engine performance: The principle

of lost work due to irreversibility in aerospace system’, International Journal of Thermodynamics, Vol. 6, No. 3, pp. 107–120.

24. Riggins, D., Taylor, T. and Moorhouse, D.J. (2006) ‘Methodology for the performance

analysis of aerospace vehicles using the laws of thermodynamics’ Journal of Aircraft, Vol. 43, No. 4, pp. 953–963.

25. Rosen, M.A. and Etele, J. (1999) ‘The impact of reference environment selection on the

exergy efficiencies of aerospace engines’, ASME Advanced Energy System, Vol. 39, pp.

583–591. 26. Rosen, M.A. and Etele, J. (2004) ‘Aerospace system and exergy analysis: Application and

methodology development needs’, International Journal of Exergy, Vol. 1, No. 4, pp. 411–

425. 27. Sochet, I. and Gillard, P. (2002) ‘Flammability of kerosene in civil and military aviation’,

Journal of Loss Prevention in the Process Industries, Vol. 5, No. 3, pp. 335-345.

28. Turgut, E.T., Karakoc, T.H. and Hepbasli, A. (2009a) ‘Exergoeconomic analysis of an aircraft turbofan engine’, International Journal of Exergy, Vol. 6, No. 3, pp. 277–294.

29. Turgut, E.T., Karakoc, T.H., Hepbasli, A. and Rosen, M.A. (2009b) ‘Exergy analysis of a

turbofan aircraft engine’. International Journal of Exergy, Vol. 6, No. 2, pp. 181–199.