exogenous

Applied Thermal Engineering 111 (2017) 152–169

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Research Paper

Advanced exergy analyses to evaluate the performance of a military aircraft turbojet engine (TJE) with afterburner system: Splitting exergy destruction into unavoidable/avoidable and endogenous/exogenous Ozgur Balli First Air Supply and Maintenance Center, TurAF, Eskisehir, Turkey

h i g h l i g h t s
Performing advanced exergy analysis for an aircraft turbojet engine.
Analyzing the performance of main engine components.
Determining inefficiencies within engine for planning future improvements.
Relations between the components were obtained as weak.

a r t i c l e

i n f o

Article history: Received 28 November 2015 Revised 18 August 2016 Accepted 7 September 2016 Available online 16 September 2016 Keywords: Conventional exergy analysis Unavoidable exergy destruction Avoidable exergy destruction Endogenous exergy destruction Exogenous exergy destruction

a b s t r a c t A conventional and advanced exergy analysis of a military aircraft turbojet engine is presented in this paper. In this framework, the main exergy parameters of the engine components are introduced while the exergy destruction rates within the engine components are split into endogenous/exogenous and avoidable/unavoidable parts. Also, the mutual interdependencies among the components of the engine and realistic improvement potentials depending on operating conditions are acquired through the analysis. As a result of the study, the exergy efficiency values of the engine are determined to be 39.41% at military (MIL) mode (maximum engine thrust operation without afterburner fuel combustion) and 17.90% at afterburner (AB) mode (maximum engine thrust operation with afterburner fuel combustion), respectively. The system has low improvement potential because the unavoidable exergy destruction rate is 93% at MIL mode and 98% at AB mode. The relationships between the components seem to be weak since the endogenous exergy destruction is 83% at MIL mode and 94% at AB mode. Finally, it may be concluded that the low pressure compressor, the high pressure compressor, the combustion chamber and afterburner exhaust duct of the engine should be focused on according to the results obtained. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Effects of energy consumption in aviation sector gives rise to potential environmental hazards. Therefore, energy consumption plays a crucial importance role to achieve sustainable development, balancing economic and social development with environmental protection. The importance of energy efficiency is also linked to environmental problems, such as global warming and atmospheric pollution [1,2]. The environmental impacts of emissions can be reduced by increasing the efficiency of resource utilization [3]. Using energy with better efficiency reduces pollutant emissions [4]. Inefficiencies in an energy system can be quantitatively determined through conventional exergy analysis while sources of the E-mail address: [email protected] http://dx.doi.org/10.1016/j.applthermaleng.2016.09.036 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

irreversibilities and real improvement potential can be deducted using a relatively new method named as advanced exergy analysis [5]. A conventional exergy analysis identifies the location, the magnitude and the sources of thermodynamic inefficiencies in a thermal system. This information, which cannot be provided by other means (e.g., an energy analysis), is very useful for improving the overall efficiency and the cost effectiveness of a system or for comparing the performance of various systems [6]. A conventional exergy analysis also identifies the system components with the highest exergy destruction or the process that cause the high exergy destruction. Efficiencies of a system’s components can be improved by reducing the exergy destruction rates within the components [7]. However, none of conventional analyzing methods is able to reveal the interactions among the system components or to estimate the real potential for improvement. Without consideration of the component interactions,

O. Balli / Applied Thermal Engineering 111 (2017) 152–169

153

Nomenclature A AB ABED CC cP _ Ex F HPC HPT HPTMS LHV LPC LPT LPTMS _ m MIL P _ W R T TJE _ W V

area (m2) afterburner operation mode afterburner exhaust duct combustion chamber specific heat capacity (kJ/kg K) exergy rate (kW) thrust (kN) high pressure compressor high pressure turbine high pressure turbine mechanical shaft lower heating value of fuel (kJ/kg) low pressure compressor low pressure turbine low pressure turbine mechanical shaft mass flow rate (kg/s) military operation mode pressure (kPa) heat rate (kW) universal gas constant (kJ/kg K) temperature (K) turbojet engine work rate or power rate (kW) velocity (m/s)

Greek letters / relative exergy destruction ratio (%) e specific exergy (kJ/kg) c fuel exergy grade function w exergetic efficiency (%) Subscripts a air ABED afterburner exhaust duct bld bleed air CC combustion chamber ch chemical

optimization strategies can be misguided, especially when complex systems with a large number of mutually affected components are considered. The knowledge of the interactions among the components and the capability of the improvement for each important component are very useful to improve the overall system [8]. It is important to understand the genesis of the rate of exergy being destroyed in a component’s process. The theory of splitting the exergy destruction helps us further understand the exergy destruction values from an exergy analysis and hence improves the accuracy of the analysis. It facilitates the improvement of energy-related systems. In order to perform this process, only an advanced exergy analysis method could be applied [9]. Component interactions determine the exogenous exergy destruction and operating inefficiencies within the component determine the endogenous exergy destruction. Moreover, part of the overall irreversibilities exists due to physical, technological and economic constraints and cannot be avoided (unavoidable exergy destruction). Irreversibilities that can be prevented through design improvements constitute the avoidable exergy destruction. The exogenous and endogenous parts can be split into avoidable and unavoidable parts facilitating the understanding of component interconnections and the estimation of the potential for improvement [10]. Splitting the exergy destruction into unavoidable and avoidable parts in the k’th component provides a realistic measure of the potential for improving the thermodynamic efficiency of a

D exh F g HPC HPT HPTMS in k kn L LPC LPT LPTMS out P Pr ph pt T TJE tot 0

destruction exhaust inlet streams as a fuel combustion gas high pressure compressor high pressure turbine high pressure turbine mechanical shaft input the k’th component kinetic losses low pressure compressor low pressure turbine low pressure turbine mechanical shaft output pressure product physical potential temperature turbojet engine total dead state conditions

Superscripts REAL real AV avoidable AV-EN avoidable-endogenous AV-EX avoidable-exogenous EN endogenous EX exogenous MEXO mexogenous UN unavoidable UN-EN unavoidable-endogenous UN-EX unavoidable-exogenous

component. The exergy destruction rate that cannot be reduced due to technological limitations such as availability and cost of materials and manufacturing methods is the unavoidable part of the exergy destruction. The remaining part represents the avoidable part of the exergy destruction [9]. As mentioned above, the advanced exergy analysis method is useful to assess all energy systems in detail. So, splitting exergy destruction within the military aircraft turbojet engine and its components is required to find out realistic improvement potentials of each component along with the overall engine. The aim of this research was to contribute to the literature by presenting the advanced exergy analysis of a military aircraft turbojet engine for the first time. The novel aspects and originality of the present study can be summarized as follows:
Evaluating the performance of an aircraft turbojet engine exergetically at main two operation modes.
Determining the afterburner combustion effect on the exergetic performance of the turbojet engine.
Splitting exergy destruction within the components of the turbojet engine as endogenous/exogenous and avoidable/unavoidable parts.
Discussing the mutual interdependencies among each component of the turbojet engine.
Presenting the prior components, which are in need of improvement.

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O. Balli / Applied Thermal Engineering 111 (2017) 152–169

2. System description 2.1. General description of a military aircraft turbojet engine (TJE) The examined engine is the J57 model two-shaft turbojet engine that was developed by the Pratt Whitney. A simplified schematic of the TJE is illustrated in Fig. 1. The engine consists of the following major sections:
Low Pressure Compressor (LPC): to be driven by the low pressure turbine, nine-stage axial-flow, the pressure ratio is 3.6735.
High Pressure Compressor (HPC): to be driven by the high pressure turbine, seven-stage axial flow, the pressure ratio is 3.093.
Combustion Chamber (CC): annular type flow, to provide an area for combustion of the air-fuel mixture.
High Pressure Turbine (HPT): single stage turbine, to extract energy to drive the HPC.
Low Pressure Turbine (LPT): two stages turbine, to extract energy to turn the LPC.
Afterburner Exhaust Duct (ABED): to consist of exhaust duct, liner, afterburner spraybars, igniter and variable exhaust nozzle, to provide an area necessary for the complete afterburner combustion of the exhaust gases-fuel mixture at the afterburner operation mode.
The operating limits of the engine are given as following [11]:
The rated military thrust and the afterburner thrust of engine are 51.1 kN and 71.1 kN, respectively.
The fuel flow rates at military and afterburner operation modes are 1.079 kg/s and 4.288 kg/s, respectively.
The maximum air mass flow is 78.43 kg/s.
The bleed air mass flow is 7.91 kg/s.
The outlet pressure values of the LPC, HPC and CC are 371.86 kPa, 1151.11 kPa and 1089.25 kPa, respectively.
The outlet temperature values of the LPC, HPC and CC are 438.71 K, 622.04 K and 1127.59 K, respectively. 2.2. Assumptions made In the present study, the assumptions made are listed as follows:
The engine is operated under steady-state condition.
The principle of ideal-gas mixture is applied for the air and combustion gaseous.
The combustion reaction is assumed to be complete.
The fuel injected to combustion chamber is the JP-8 jet fuel.
The chemical formula and the LHV of jet fuel are C12H23 and 42,800 kJ/kg, respectively [12,13].

LPC

15

HPTMS

HPT

HPC 12

13


The compressor, the gas turbine and the power turbine considered are reckoned as adiabatic.
The changes in the kinetic energy, the kinetic exergy, the potential energy and the potential exergy within the engine are assumed to be negligible.
The velocity of air mass flow entering the engine is taken zero due to the run test is performed in a static condition.
The cooling air mass flow is not considered for the analysis.
The temperature and the pressure of the dead state are measured to be 288.15 K and 101.33 kPa, respectively.
The air composes of nitrogen 77.48%, oxygen 20.59%, carbon dioxide 0.03% and water vapor 1.90%. Other small amounts of argon, CO, etc., in the air are neglected. 2.3. Operation mode The engine thrust of the J57 model two-shaft turbojet engine can be calculated from [12,13]:

_ out V out  m _ in V in þ Aout Pout  Ain Pin F¼m

where F, A, P and V are the engine thrust, the area, the pressure and the velocity of inlet and outlet streams. Incoming momentum is assumed as zero ðV in ffi 0Þ due to the engine is operated in a ground test cell and/or a ground aircraft operation test. In this study, two engine operation modes are analyzed. One of these modes is the military (MIL) mode. In MIL mode, the engine produces the maximum thrust without afterburner combustion in the ABED. The other operation mode is named as the afterburner (AB) mode. In AB mode, the engine has the afterburner combustion in the ABED. The engine produces 51.1 kN thrust at the MIL mode and 71.1 kN at the AB mode. When the engine thrust is known, the velocity of exhaust gas stream can be estimated to be 713.7 m/s for MIL mode and 950.43 m/s for AB mode from Eq. (1). The kinetic energy or exergy of the engine thrust is obtained by [12,13]:

V2 _ kn ¼ m _ g out E_ kn ¼ Ex 2000

ð2Þ

The kinetic energy (equals to kinetic exergy) values of the exhaust gases are calculated to be 18234.96 kW in the MIL mode and 33787.9 kW in AB mode. The TJE consumes 1.079 kg s1 fuel in MIL mode. When the power throttle is driven into AB mode, the extra fuel, named AB fuel, is injected in the ABED and the exhaust temperature increases above the normal operation limits. The variable exhaust nozzle system opens hydromechanically the nozzle exhaust area to decrease the exhaust temperature. The maximum fuel flow of the engine reaches 4.288 kg s1 (3.209 kg s1 for AB combustion) in the maximum AB mode.

14 LPTMS

LPT

ABED ExPr,exh

2 1

4

CC

5

7

10

8

9 11

6

3 Exbld,3

Main Fuel

ð1Þ

AB Fuel

Fig. 1. A schematic of the investigated TJE.

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O. Balli / Applied Thermal Engineering 111 (2017) 152–169

2.4. Specific heat capacity of emissions and air

3. Methodology

The specific heat capacity of the combustion gaseous can be written in the following form:

3.1. Basic exergy terms

cP;g ðTÞ ¼ 0:91559 þ

0:01138 102

Tþ

0:01540 105

T2 

0:06695 109

T3

ð3Þ

The ideal gas constant value of combustion gases is estimated to 1

be 0.290136 kJ ðkg KÞ . The specific heat capacity of air is a function of temperature is given by [12–14]:

cP;a ðTÞ ¼ 1:04841  


 3:83719T

5:49031T 3 10

10

4

10 !

þ

þ

9:45378T 2

7:92981T 4

Exergy balance for any control volume at steady state is given as [12–14]:

X


1

!

107 ! ð4Þ

1014

 X X To _ _ in  _ out  Ex _ þ _ D¼0 Ex Ex Qk  W Tk out in

ð5Þ

where Q_ k is the heat transfer rate through the boundary at temper_ is the work rate, Ex _ is the exergy rate of ature T k at location k, W _ D is the exergy destruction rate. For inlet and outlet stream, and Ex the military aircraft turbojet engine and its components, the exergy balance equations are illustrated in Table 1.

where the temperature is evaluated in K. Table 1 Exergetic balance and efficiency equations for the TJE and its components. Components

_ in as fuel (kW) Ex

_ out as product (kW) Ex

_ D destruction and losses Ex _ L as (kW) Exergy Ex

Eq.

_ 15 Ex

_ 2  Ex _ 1 Ex

_ D;LPC ¼ Ex _ 15  ðEx _ 2  Ex _ 1Þ Ex

(6)

_ 2 Ex

_ 3 þ Ex _ 4 Ex

_ 2 ¼ ðEx _ 3 þ Ex _ 4Þ Ex

(7)

_ 13 Ex

_ 5  Ex _ 4 Ex

_ D;HPC ¼ Ex _ 13  ðEx _ 5  Ex _ 4Þ Ex

(8)

_ 5 þ Ex _ 6 Ex

_ 7 Ex

_ D;CC ¼ ðEx _ 5 þ Ex _ 6 Þ  Ex _ 7 Ex

(9)

_ 7  Ex _ 8 Ex

_ 12 Ex

_ D;HPT ¼ ðEx _ 7  Ex _ 8 Þ  Ex _ 12 Ex

(10)

_ 8  Ex _ 7 Ex

_ 14 Ex

_ D;LPT ¼ ðEx _ 8  Ex _ 9 Þ  Ex _ 14 Ex

(11)

_ 9 þ Ex _ 11 Ex

_ 10 Ex

_ D;ABED ¼ ðEx _ 9 þ Ex _ 11 Þ  Ex _ 10 Ex _ 11 ¼ 0 At MIL operation, Ex

(12)

_ D;HPTMS ¼ ðEx _ 12  Ex _ 13 Þ Ex

(13)

_ 11 – 0 At AB operation, Ex

_ 12 Ex

_ 13 Ex

(continued on next page)

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O. Balli / Applied Thermal Engineering 111 (2017) 152–169

Table 1 (continued) Components

_ in as fuel (kW) Ex

_ out as product (kW) Ex

_ D destruction and losses Ex _ L as (kW) Exergy Ex

Eq.

_ 14 Ex

_ 15 Ex

_ D;LPTMS ¼ ðEx _ 14  Ex _ 15 Þ Ex

(14)

_ 1 þ Ex _ 6 þ Ex _ 11 Ex _ 1¼0 Ex _ 11 ¼ 0 at MIL operation, Ex

_ Pr;3 þ Ex _ Pr;kn;exh Ex

_ D;TJE ¼ ðEx _ 1 þ Ex _ 6 þ Ex _ 11 Þ  Ex _ Pr;3 þ Ex _ 10 Þ Ex

(15)

_ L;TJE ¼ ðEx _ 10  ExPr;kn;exh Þ Ex _ExC;TJE ¼ Ex _ D;TJE þ Ex _ L;TJE

(16)

_ 11 – 0 at AB operation Ex

(17)

Table 2 The exergy rate and other thermodynamic properties of the TJE at MIL mode. State no.

Fluid type/work

Pressure, P (kPa)

Temperature, T (K)

Mass flow rate, _ ðkg s1 Þ m

cP ðkJðkg KÞ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 _ Pr;exh Ex

Air Air Air Air Air Air Main fuel Combustion gases Combustion gases Combustion gases Combustion gases AB fuel Mechanical power Mechanical power Mechanical power Mechanical power Exhaust gases kinetic energy/exergy rate

101.33 101.33 371.86 371.86 371.86 1151.11 206.85 1089.25 450.50 195.50 179.27 206.85

288.15 288.15 438.71 438.71 438.71 622.04 298.15 1127.59 972.35 837.17 812.05 298.15

In the absence of nuclear, magnetism, electricity and surface tension effects in the thermal systems, the total exergy for a flow of matter through a system can be determined from the following:

 _ ¼m _ ekn þ ept þ eph þ ech Þ Ex

ð18Þ

Here ekn , ept , eph and ech denote the specific kinetic exergy, specific potential exergy, specific physical exergy and specific chemical exergy, respectively. In this study, the changes in the kinetic exergy and potential exergy within the system are assumed to be negligible. According to the ideal gas expression, the specific physical exergy for air and combustion gaseous with constant specific heat capacity may be written as [15]:



eph ¼ cPðTÞ T  T o  T o ln



 T P þ RT o ln To Po

ð19Þ

The specific chemical exergy of liquid fuels ðC a Hb Þ on a unit mass can be determined as follows [13,16]:

ech LHV

b 0:042 ¼ c ffi 1:04224 þ 0:011925  a a

ð20Þ

where c denotes the liquid fuel exergy grade function that is calculated to be 1.0616 for kerosene of type JP-8 jet fuel. The temperature, pressure, mass flow and thermodynamic properties in the station numbers of the engine are given in Table 2 for the MIL operation and in Table 3 for the AB operation. 3.2. Exergetic performance parameters In this study, the exergetic efficiency and the relative exergy destruction ratio are used to evaluate, the exergetic performance of the system. These are given as follows:

0.000 78.430 78.430 7.910 70.520 70.520 1.079 71.599 71.599 71.599 71.599 0.000

Low heating value, LHV ðkWÞ

Specific heat capacity, 1

Energy rate, E_ ðkWÞ

Exergy rate, _ ðkWÞ Ex

0.00 0.00 12363.76 1246.94 11116.82 25893.26 46181.20 71381.76 56380.33 43827.92 41719.02 0.00 15001.43 14776.44 12552.42 12363.76 18234.96

0.00 0.00 10784.61 1087.67 9696.93 22518.36 49025.96 50665.68 35390.66 22566.19 20739.93 0.00 15001.43 14776.44 12552.42 12363.76 18234.96

Þ

1.00375 1.00375 1.01860 1.01860 1.01860 1.05525 42800 1.14066 1.10730 1.07668 1.07370 42800


The exergy efficiency of the system or subsystems can be defined as the ratio of the exergy rate of outputs as products to the exergy rate of inputs as fuels. The exergy efficiency is calculated from [12–14]:

wk ¼

_ out;k Ex _ Pr;k Ex ¼ _ in;k _ F;k Ex Ex

ð21Þ


The relative exergy destruction ð/Þ is described as the ratio of the exergy destruction of the k’th component to the total exergy destruction in the system. It is estimated from [12–14]:

/k ¼

_ D;k Ex _ExD;tot

ð22Þ

3.3. Advanced exergy analysis Advanced exergy analysis is performed based on the results of exergy analysis; thus, the input data are irreversibilities and exergetic efficiencies of the process components. The main idea of this analysis is categorizing the irreversibility or exergy destruction of the process components. Irreversibility occurring in a device not only depends on its performance, but also is related to the irreversibility of remaining components which have been connected to it. Conventional exergy analysis calculates the irreversibility of the components accurately and easily; however, it cannot categorize the irreversibility in terms of origin. Also it cannot calculate a part of irreversibility of a component which is induced from the remaining components of the process. In advanced exergetic analysis, irreversibility of a device can be divided from two points of view: (1) origin of irreversibility production and (2) removing ability of it. Based on the first point of view, the exergy destruction is divided into two parts:

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O. Balli / Applied Thermal Engineering 111 (2017) 152–169 Table 3 The exergy rate and other thermodynamic properties of the TJE at AB mode. State no.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 _ Ex

Pr;exh

Fluid type/work

Air Air Air Air Air Air Main fuel Combustion gases Combustion gases Combustion gases Combustion gases AB fuel Mechanical power Mechanical power Mechanical power Mechanical power Exhaust gases kinetic energy/exergy rate

Pressure, P (kPa)

Temperature, T (K)

Mass flow rate, _ ðkg s1 Þ m

Specific heat

101.33 101.33 371.86 371.86 371.86 1151.11 206.85 1089.25 450.50 195.50 173.23 206.85

288.15 288.15 438.71 438.71 438.71 622.04 298.15 1127.59 972.35 837.17 1666.48 298.15

0.000 78.430 78.430 7.910 70.520 70.520 1.079 71.599 71.599 71.599 74.808 3.209

1.00375 1.00375 1.01860 1.01860 1.01860 1.05525


Endogenous exergy destruction.
Exogenous exergy destruction. The endogenous exergy destruction is due to performance of the under consideration component and it exits even if the other components work ideally. The exogenous exergy destruction is caused by the inefficiencies within the remaining components of the overall system. Based on the removing ability, the exergy destruction is divided into two other parts:
Avoidable exergy destruction.
Unavoidable exergy destruction. The unavoidable part of exergy destruction of the component presents a part which cannot be eliminated, even if the best available technologies are used. On the other hand avoidable part can be eliminated through technical improvements of the process equipment. These divisions improve our understanding from the process components and relation among them [17]. Fig. 2 demonstrates splitting the exergy destruction rate within the k’th component according to this approach [18].

1

capacity, cP ðkJðkg KÞ

Þ

Low heating value, LHV ðkWÞ

42800 1.14066 1.10730 1.07668 1.22307 42800

Energy rate, E_ ðkWÞ

Exergy rate, _ ðkWÞ Ex

0.00 0.00 12363.76 1246.94 11116.82 25893.26 46181.20 71381.76 56380.33 43827.92 130838.31 137345.20 15001.43 14776.44 12552.42 12363.76 33787.90

0.00 0.00 10784.61 1087.67 9696.93 22518.36 49025.96 50665.68 35390.66 22566.19 83195.64 145805.66 15001.43 14776.44 12552.42 12363.76 33787.90

3.3.1. Endogenous/exogenous exergy destruction A part of exergy destruction produced in a device is related to its thermodynamic performance and always exists even if other components work ideally. Accordingly another part is related to the induced destruction from the remaining components, so the total exergy destruction of k’th component can be presented as below:

_ D;k ¼ Ex _ EN þ Ex _ EX Ex D;k D;k

ð23Þ

The results of this division give deeper understanding about the process and interactions among the components. Also based on the results a suitable and accurate structural optimization can be performed on the process. Nonetheless calculation of endogenous   _ EN for a component is more difficult than exergy destruction Ex D;k

unavoidable exergy destruction and this is the main problem of advanced exergy analysis. Accuracy of calculations can directly affect the results of the analysis. The endogenous part of the exergy   _ EN is associated destruction rate within the k’th component Ex D;k

with the irreversible process through the k’th component while all other system components are operated under theoretical condi-

Fig. 2. Dividing the exergy destructions into avoidable, unavoidable, endogenous and exogenous parts [18].

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O. Balli / Applied Thermal Engineering 111 (2017) 152–169

tions and the k’th component operates with the actual case efficiency. In this framework, each component should be considered in the self-assessment cycle. The exogenous part of the exergy   _ EX indicates the destruction rate within the k’th component Ex D;k

impact of the irreversibilities within all system components out of the k’th [17–25]. The endogenous part of the exergy destruction rate within the k’th component is calculated from [5]:

_ _ EN ¼ Ex _ REAL ExD Ex D;k Pr;k _ Pr Ex

!EN ð24Þ k

3.3.2. Avoidable/unavoidable exergy destruction Splitting the exergy destruction into unavoidable and avoidable parts in the k’th component provides a realistic measure of the potential for improving the thermodynamic efficiency of a component. Part of the exergy destruction, the cost and the environmental impact of a system can be avoided with structural modifications, reduction in the investment costs/environmental impacts or efficiency improvements of individual components. The exergy destruction rate that cannot be reduced due to technological limitations such as availability and cost of materials and   _ UN part of the manufacturing methods is the unavoidable Ex D;k

exergy destruction. The remaining part represents the avoidable   _ AV part of the exergy destruction [9]. Ex D;k

_ UN is calculated by considering each component in isolation, Ex D;k separated from the system, assuming the most favorable operating conditions. These conditions refer to minimum exergy destruction and are associated with very low temperature differences and thermal/pressure losses within the components. The assumptions for simulating unavoidable conditions depend on the decision maker and are arbitrary to some extent [10]. As mentioned earlier, technological and economic limitations determine a minimum value of exergy destruction. This unavoid_ UN is calculated considering each able part of exergy destruction, Ex D;k

component in isolation, separated from the system. The ratio of  _ UN ExD is calculated exergy destruction per unit of product exergy Ex _ Pr

k

assuming operation with high efficiency and low losses. According to the product exergy in the real case, the unavoidable exergy destruction for k’th component is calculated as [17–25]:

_ _ REAL ExD _ UN ¼ Ex Ex D;k Pr;k _ExPr

!UN ð25Þ

  _ UNEN .
Unavoidable endogenous exergy destruction Ex D;k   _ UNEX
Unavoidable exogenous exergy destruction Ex D;k The avoidable/unavoidable endogenous and exogenous exergy parts of exergy destruction can be calculated from [21–24]:

_ _ UNEN ¼ Ex _ EN ExD Ex D;k Pr;k _ P Ex

!UN ð27Þ k

_ EN  Ex _ UNEN _ AVEN ¼ Ex Ex D;k D;k D;k

ð28Þ

_ UNEX ¼ Ex _ UN  Ex _ UNEN Ex D;k D;k D;k

ð29Þ

_ AVEX ¼ Ex _ EX  Ex _ UNEX Ex D;k D;k D;k

ð30Þ

These equations can be simplified and written as follows:

_ UN _ UNEN ¼ Ex _ REAL ExD Ex D;k D;k _ REAL ExD

_ EN _ UN Ex _ EN Ex Ex D D ¼ D _ExREAL _ExREAL D D

ð31Þ

_ UN _ UNEX ¼ Ex _ REAL ExD Ex D;k D;k _ REAL ExD

_ EX _ UN Ex _ EX Ex Ex D D ¼ D _ExREAL _ExREAL D D

ð32Þ

_ AV _ EN _ AV _ EN _ REAL ExD ExD ¼ ExD ExD _ AVEN ¼ Ex Ex D;k D;k _ REAL _ REAL _ REAL ExD ExD Ex D

ð33Þ

_ AV _ EX _ AV _ EX _ REAL ExD ExD ¼ ExD ExD _ AVEX ¼ Ex Ex D;k D;k _ REAL _ REAL _ REAL ExD ExD Ex D

ð34Þ

  _ AVEN can be The avoidable endogenous exergy destruction rate Ex D;k

reduced by improvement of the kth component. Similarly, the reduction in the avoidable exogenous exergy destruction rate   _ AVEX can only be achieved by improving other system compoEx D;k

nents. As mentioned above, the unavoidable parts of the endoge    _ UNEX and exogenous Ex _ UNEX exergy destruction rates nous Ex D;k

D;k

form in consequence of thermodynamic limitations indispensably [17,18]. 3.3.4. Mexogenous exergy destruction parts Mexogenous exergy destruction rate is termed as the difference between the exogenous exergy destruction rate and the combine defect of the exergy destruction of all other components within the system on the k’th component [18,19].

k

Thus, the avoidable exergy destruction for k’th component can be presented as below:

_ AV ¼ Ex _ D;k  Ex _ UN Ex D;k D;k

ð26Þ

3.3.3. Combining avoidable/unavoidable and endogenous/exogenous exergy destruction parts After splitting the total exergy destruction occurring in a component into its four categories, namely endogenous, exogenous, avoidable and unavoidable parts, the task left to be done will be to evaluate how the different categories of the exergy destruction can be combined and used to provide meaningful information. For obtaining applicable results, the splitting can be followed by dividing avoidable and unavoidable to endogenous and exogenous parts. Thus four different parts of irreversibility can be presented [17]:   _ AVEN .
Avoidable endogenous exergy destruction Ex D;k   _ AVEX .
Avoidable exogenous exergy destruction Ex D;k

_ MEXO;EX ¼ Ex _ EX  Ex D;k D;k

k1 X

_ EX;n Ex D;k

ð35Þ

n¼1 n – k

In addition to Eq. (35), the mexogenous exergy destruction rates for unavoidable-exogenous and avoidable-exogenous exergy destruction rates are estimated from the following:

_ MEXO;UNEX ¼ Ex _ UNEX  Ex D;k D;k

k1 X

_ UNEX;n Ex D;k

ð36Þ

n¼1 n – k

_ MEXO;AVEX ¼ Ex _ AVEX  Ex D;k D;k

k1 X

_ AVEX;n Ex D;k

ð37Þ

n¼1 n – k

4. Results and discussion In this study, a military aircraft turbojet engine (TJE) is evaluated through the methodology of the advanced exergy analysis.

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For this purpose, the conventional exergy analysis of the engine is performed at first. Thermodynamic cycle data of the engine under actual operating conditions are given in Table 2 for MIL mode and Table 3 for AB mode with the calculated energy and exergy rates of the flows. 4.1. Conventional exergy analysis The fuel exergy rate, the product exergy rate (kinetic and bleed), the exergy destruction and losses rates, and the exergy efficiency of whole engine are listed in Table 4. According to Table 4, the exergy efficiency of the TJE is calculated to be 39.41% for MIL mode while it is obtained to be 17.9% for AB mode. The breakdown of the exergy flow rates within the engine at MIL and AB modes is shown in Fig. 3. However, the major components of the TJE are evaluated exergetically as mentioned previously by using the data summarized in Table 2 for MIL mode and Table 3 for AB mode. As a result of the conventional exergy analysis, the previously defined useful evaluation parameters for each component of the engine are presented in Tables 5 and 6 in addition to main exergy parameters. The main findings of the exergy analysis are summarized as follows:
The exergetic efficiencies of the LPC, LPT, CC, HPT, LPT, HPTMS and LPTMS are calculated to be 87.23%, 86.77%, 70.82%, 98.21%, 97.88%, 98.5%, and 98.5%, respectively.
The exergetic efficiency of the ABED component decreases to 49.41% at AB mode while the exergetic efficiency of the ABED is obtained to be 91.91% at MIL operation mode. Because the

ABED component of the turbojet engine with afterburner is used as an extra combustion area to produce the extra thrust power at the AB mode, the exergy efficiency of the ABED reduces with starting the afterburner combustion.
For MIL operation, the CC has the maximum relative exergy destruction ratio with 76.76% due to the highest exergy destruction occurs in the combustion chamber (CC) with the rate of 20878.64 kW.
For AB operation, the highest exergy destruction occurs in the afterburner exhaust duct (ABED) with the rate of 85176.21 kW while the ABED has the maximum relative exergy destruction ratio with 77.05%. The above-mentioned results clearly indicate that the CC and the ABED, in which the combustion process occurred, have lower values of the exergy efficiency, and higher values of the relative exergy destruction due to the combustion irreversibilities. Combustion of the fuel is a very complex phenomenon and it is highly thermodynamically irreversible process and limits the conversion of the fuel energy into the useful energy. Most of the combustion irreversibility is contributed to the internal heat transfer from burned fuel to the unburned fuel that is from products to reactants. Such heat transfer is inevitable in premix and diffusion flames where highly energetic molecules are free to exchange energy with un-reacted fuel and air mixture. For typical combustion systems, about 1/3rd of the fuel exergy becomes unavailable due to inherent of the irreversibility in the combustor. Internal heat transfer, chemical reactions and mass transfer during combustion process generate entropy and reduce the potential of the products gases to do useful work [26].

Table 4 Exergetic data of the whole engine at MIL and AB modes. Operation mode

MIL AB

_ in ðkWÞ Fuel exergy rate Ex

49025.96 194831.63

Product exergy rate

Exergy efficiency, w (%)

Exergy consumption rate

_ Prkn;exh ðkWÞ Ex

_ Pr;3 ðkWÞ Ex

_ D ðkWÞ Ex

_ L ðkWÞ Ex

18234.96 33787.90

1087.67 1087.67

27198.35 110548.31

2504.97 49407.75

39.41 17.90

Fig. 3. The breakdown of the exergy flow rates within the engine at MIL and AB modes.

Table 5 Exergy rate, exergetic efficiency and relative exergy destruction ratio of the engine components at MIL mode. Component

_ in ðkWÞ Ex

_ out ðkWÞ Ex

_ D ðkWÞ Ex

w (%)

/ (%)

LPC HPC CC HPT LPT ABED HPTMS LPTMS

12363.76 14776.44 71544.32 15275.01 12824.48 22566.19 15001.43 12552.42

10784.61 12821.43 50665.68 15001.43 12552.42 20739.93 14776.44 12363.76

1579.15 1955.01 20878.64 273.59 272.06 1826.25 224.99 188.66

87.23 86.77 70.82 98.21 97.88 91.91 98.50 98.50

5.81 7.19 76.76 1.01 1.00 6.71 0.83 0.69

Total destruction

27198.35

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Table 6 Exergy rate, exergetic efficiency and relative exergy destruction ratio of the engine components at AB mode. Component

_ in ðkWÞ Ex

_ out ðkWÞ Ex

_ D ðkWÞ Ex

w (%)

/ (%)

LPC HPC CC HPT LPT ABED HPTMS LPTMS

12363.76 14776.44 71544.32 15275.01 12824.48 168371.85 15001.43 12552.42

10784.61 12821.43 50665.68 15001.43 12552.42 83195.64 14776.44 12363.76

1579.15 1955.01 20878.64 273.59 272.06 85176.21 224.99 188.66

87.23 86.77 70.82 98.21 97.88 49.41 98.50 98.50

1.43 1.77 18.89 0.25 0.25 77.05 0.20 0.17

Total destruction

110548.3

4.2. Advanced exergy analysis In the course of the advanced exergy analysis, the parameters of the engine for actual, theoretical and unavoidable cases are given in Table 7. According to the methodology explained before, the exergy destruction within the engine components is split into the endogenous/exogenous and avoidable/unavoidable parts. The unavoidable performance parameters indicate thermodynamic limitations of the progress in the design and manufacturing technology for the considered component. The exergy destruction partition of the engine components depending on these conditions is presented in Table 8 for MIL mode and AB mode. In accordance with Table 8,
For all components of the engine at MIL operation, the total   _ UN is estimated to be unavoidable exergy destruction Ex D 25177.54 kW while the total avoidable exergy destruction   _ AV is obtained to be 2019.87 kW. In this situation, the highEx D _ UN occurs in the CC between the components with the rate est Ex D of 20670.21 kW. This rate equals to 82.1% of the total unavoidable exergy destruction and 76% of total exergy destruction _ AV value is calculated to within the TJE system. The highest Ex D

be 788.78 kW in the LPC. When the endogenous and exogenous

exergy destruction rate values are evaluated, the total   _ EN is computed to be endogenous exergy destruction Ex D 23466.89 kW while the total exogenous exergy destruction   _ EX is obtained to be 3730.52 kW. However, the highest Ex D _ EN is also determined to be 20415.16 kW in the CC. This rate Ex D _ EN within the TJE system. Between equals to 87% of the total Ex D

_ EX value with the components, the LPC has the highest Ex D 1195.14 kW.
For all components of the engine at AB operation, the total   _ UN is estimated to be unavoidable exergy destruction Ex D 107878.37 kW while the total avoidable exergy destruction   _ AV is obtained to be 2668.69 kW. In this situation, the highEx D _ UN occurs in the ABED between the components with the est Ex D rate of 85176.21 kW. This rate equals to 78.96% of the total unavoidable exergy destruction and 77.05% of total exergy _ AV value is caldestruction within the TJE system. The highest Ex D

culated to be 876.76 kW in the ABED. When the endogenous and exogenous exergy destruction rate values are examined,   _ EN is computed the total endogenous exergy destruction Ex D

to be 105850.62 kW while the total exogenous exergy destruc  _ EX is obtained to be 4696.75 kW. However, the highest tion Ex D

Table 7 The real, unavoidable and theoretical conditions of the engine components. Component

Main aim for unavoidable and theoretical cases

Real

Unavoidable

Theoretical

LPC LPC CC HPT LPT ABED

To To To To To To

gLPC ¼ 86:18% gHPC ¼ 89:71%

gLPC ¼ 95:0% gHPC ¼ 95:0%

gLPC ¼ 100:0% gHPC ¼ 100:0%

HPTMS LPTMS

To maximize the mechanical/exergetic efficiency for minimizing the exergy destruction To maximize the mechanical/exergetic efficiency for minimizing the exergy destruction

maximize the isentropic efficiency maximize the isentropic efficiency minimize the pressure loses maximize the exergetic efficiency for minimizing the exergy destruction maximize the exergetic efficiency for minimizing the exergy destruction minimize the pressure loses

DP CC ¼ 5:37% wHPT ¼ 98:2% wLPT ¼ 97:88% DP ABED;MIL ¼ 8:3% DP ABED;AB ¼ 11:39% wHPTMS ¼ 98:5% wLPTMS ¼ 98:5%

DP CC ¼ 3:0% wHPT ¼ 99:0% wLPT ¼ 99:01% DP ABED;MIL ¼ 5:0% DP ABED;AB ¼ 5:0% wHPTMS ¼ 99:0% wLPTMS ¼ 99:0%

DP CC ¼ 0:0% wHPT ¼ 99:84% wLPT ¼ 99:87% DP ABED;MIL ¼ 0:0% DP ABED;AB ¼ 0:0% wHPTMS ¼ 99:5% wLPTMS ¼ 99:5%

Table 8 Endogenous, exogenous, avoidable and unavoidable exergy destructions of the engine components. Component

LPC HPC CC HPT LPT ABED HPTMS LPTMS Total

MIL operation

AB operation

_ REAL Ex D

_ UN Ex D

_ AV Ex D

_ EN Ex D

_ EX Ex D

_ REAL Ex D

_ UN Ex D

_ AV Ex D

_ EN Ex D

_ EX Ex D

1579.15 1955.01 20877.70 273.59 272.06 1826.25 224.99 188.66 27197.41

790.38 1568.84 20670.21 150.36 125.99 1598.32 148.67 124.78 25177.54

788.78 386.18 207.49 123.22 146.07 227.94 76.32 63.88 2019.87

384.01 1215.83 20415.16 24.61 15.83 1275.69 73.68 62.08 23466.89

1195.14 739.18 462.54 248.97 256.23 550.56 151.31 126.57 3730.52

1579.15 1955.01 20877.70 273.59 272.06 85176.21 224.99 188.66 110547.37

790.38 1568.84 20670.21 150.36 125.99 84299.45 148.67 124.78 107878.67

788.78 386.18 207.49 123.22 146.07 876.76 76.32 63.88 2668.69

384.01 1215.83 20415.16 24.61 15.83 83659.42 73.68 62.08 105850.62

1195.14 739.18 462.54 248.97 256.23 1516.79 151.31 126.57 4696.75

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_ EN is also determined to be 83659.42 kW in the ABED between Ex D the components. This rate equals to approximately 79% of the _ EN within the TJE system. Between the components, total Ex D

_ EX value with 1516.79 kW. The focus the ABED has the highest Ex D should be on reducing the internal inefficiencies of these components. The exogenous exergy destruction is caused in the k’th component by the irreversibilities that occur in the remaining components. It is possible to split the exogenous exergy destruction rate to understand mutual interdependencies among engine components. For this purpose, the parts of the exogenous exergy destruction rate for each component of the engine are summarized in Table 9 for MIL operation mode and Table 10 for AB mode. In accordance with Table 9, the impact of the HPC and the ABED on the inefficiencies within the LPC is remarkable while the LPC, the HPC, and ABED play key roles for irreversibilities of the CC, the HPT and the LPT at the MIL mode. According to Table 10, the impact of the ABED on the inefficiencies within other components of the engine is remarkable. The LPC and the ABED play key roles for irreversibilities of the other components at AB mode. The unavoidable-exogenous exergy destruction is caused in the k’th component by the irreversibilities that take place in the remaining components. It is potential to split the unavoidableexogenous exergy destruction rate to understand mutual interdependencies among the engine components. For this purpose, the parts of the unavoidable-exogenous exergy destruction rate for each component of the engine are given in Table 11 for the MIL mode and Table 12 for the AB mode. In accordance with Table 11, the impact of the HPC, the CC and the ABED on the inefficiencies within the LPC and the HPC is significant while the LPC, the HPC, and ABED play key roles for irreversibilities of the other components at MIL mode. According to Table 12, the impact of the ABED

on the inefficiencies within other components of the engine is noticeable. The LPC, the HPC and the CC lead the irreversibilities within the ABED at AB mode. The avoidable-exogenous exergy destruction is resulted in the k’th component by the irreversibilities that happen in the remaining components. It is probable to separate the avoidableexogenous exergy destruction rate to understand mutual interdependencies among the engine components. For this purpose, the parts of the avoidable-exogenous exergy destruction rate for each component of the engine are listed in Table 13 for MIL mode and Table 14 for AB mode. According to Table 13, the impact of the HPC, the HPT and the LPT on the inefficiencies within the LPC is notable while the LPC plays a key role for irreversibilities of the other components at MIL mode. In accordance with Table 14, the impact of the HPC and the HPT on the inefficiencies within the LPC is remarkable while the LPC leads to the irreversibilities of the other components at AB mode. At this step, a combination of the splitting exergy destruction into parts of the endogenous/exogenous and avoidable/unavoidable can be useful for better understanding. The results obtained on the engine are given in Table 15. In accordance with Table 15; _ UN and the Ex _ EN are the maximum
At MIL operation mode, the Ex D D in the CC with 20670.21 kW and 20415.16 kW, respectively. The _ UNEN of the CC is calculated to be 20212.27 kW. This means Ex D

that exergy destruction cannot be reduced because of technological limitations for the CC component. _ EN are the maximum in the _ UN and the Ex
At AB mode, the Ex D D ABED with 84299.45 kW and 83659.42 kW, respectively. The _ UNEN of the ABED is obtained to be 82798.27 kW. This means Ex D

that exergy destruction cannot be reduced because of technological limitations for the CC component.

Table 9 Interdependencies among components and the mexogenous exergy destruction rates related to exogenous exergy destruction within the engine components at MIL operation. k’th Comp.

_ EX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ EX;n Ex D;k

Comp.

_ EX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ EX;n Ex D;k

LPC

1195.14

382.89

256.23

17.60

739.18

146.46

ABED

550.56

81.25

CC

462.54

57.35

HPTMS

151.31

6.14

HPT

248.97

16.62

236.81 148.18 79.76 82.09 176.38 48.48 40.55 812.26 236.81 91.65 49.33 50.77 109.09 29.98 25.08 592.72 148.18 91.65 30.87 31.77 68.26 18.76 15.69 405.19 79.76 49.33 30.87 17.10 36.74 10.10 8.45 232.36

LPT

HPC

HPC CC HPT LPT ABED HPTMS LPTMS Total LPC CC HPT LPT ABED HPTMS LPTMS Total LPC HPC HPT LPT ABED HPTMS LPTMS Total LPC HPC CC LPT ABED HPTMS LPTMS Total

LPTMS

3730.52

4.29

LPC HPC CC HPT ABED HPTMS LPTMS Total LPC HPC CC HPT LPT HPTMS LPTMS Total LPC HPC CC HPT LPT ABED LPTMS Total LPC HPC CC HPT LPT ABED HPTMS Total

82.09 50.77 31.77 17.10 37.82 10.39 8.69 238.63 176.38 109.09 68.26 36.74 37.82 22.33 18.68 469.31 48.48 29.98 18.76 10.10 10.39 22.33 5.13 145.18 40.55 25.08 15.69 8.45 8.69 18.68 5.13 122.28

Bold italics represent the maximum values in the first two components.

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Table 10 Interdependencies among components and the mexogenous exergy destruction rates related to exogenous exergy destruction within the engine components at AB operation. k’th Comp.

_ EX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ EX;n Ex D;k

Comp.

_ EX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ EX;n Ex D;k

LPC

1195.14

304.12

256.23

13.98

739.18

116.33

ABED

1516.79

1144.03

CC

462.54

45.55

HPTMS

151.31

4.87

HPT

248.97

13.20

188.09 117.70 63.35 65.20 385.96 38.50 32.21 891.02 188.09 72.80 39.18 40.33 238.71 23.81 19.92 622.85 117.70 72.80 24.52 25.23 149.38 14.90 12.47 416.99 63.35 39.18 24.52 13.58 80.40 8.02 6.71 235.78

LPT

HPC

HPC CC HPT LPT ABED HPTMS LPTMS Total LPC CC HPT LPT ABED HPTMS LPTMS Total LPC HPC HPT LPT ABED HPTMS LPTMS Total LPC HPC CC LPT ABED HPTMS LPTMS Total

LPTMS

126.57

3.41

LPC HPC CC HPT ABED HPTMS LPTMS Total LPC HPC CC HPT LPT HPTMS LPTMS Total LPC HPC CC HPT LPT ABED LPTMS Total LPC HPC CC HPT LPT ABED HPTMS Total

65.20 40.33 25.23 13.58 82.75 8.25 6.91 242.25 140.10 86.65 54.22 29.19 30.04 17.74 14.84 372.76 38.50 23.81 14.90 8.02 8.25 48.87 4.08 146.44 32.21 19.92 12.47 6.71 6.91 40.88 4.08 123.16

Bold italics represent the maximum values in the first two components.

Table 11 Interdependencies among components and the mexogenous exergy destruction rates related to unavoidable-exogenous exergy destruction within the engine components at MIL operation. k’th Comp.

_ UNEX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ UNEX;n Ex D;k

Comp.

_ UNEX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ UNEX;n Ex D;k

LPC

598.18

139.21

118.66

5.48

593.17

136.89

ABED

481.85

90.33

CC

457.94

81.59

HPTMS

99.98

3.89

HPT

136.84

7.28

138.04 106.57 31.85 27.61 112.14 23.27 19.48 458.97 138.04 105.68 31.58 27.38 111.20 23.07 19.32 456.28 106.57 105.68 24.38 21.14 85.85 17.81 14.92 376.35 31.85 31.58 24.38 6.32 25.65 5.32 4.46 129.55

LPT

HPC

HPC CC HPT LPT ABED HPTMS LPTMS Total LPC CC HPT LPT ABED HPTMS LPTMS Total LPC HPC HPT LPT ABED HPTMS LPTMS Total LPC HPC CC LPT ABED HPTMS LPTMS Total

LPTMS

83.72

2.73

LPC HPC CC HPT ABED HPTMS LPTMS Total LPC HPC CC HPT LPT HPTMS LPTMS Total LPC HPC CC HPT LPT ABED LPTMS Total LPC HPC CC HPT LPT ABED HPTMS Total

27.61 27.38 21.14 6.32 22.24 4.62 3.86 113.18 112.14 111.20 85.85 25.65 22.24 18.74 15.69 391.52 23.27 23.07 17.81 5.32 4.62 18.74 3.26 96.09 19.48 19.32 14.92 4.46 3.86 15.69 3.26 80.99

Bold italics represent the maximum values in the first two components.

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Table 12 Interdependencies among components and the mexogenous exergy destruction rates related to unavoidable-exogenous exergy destruction within the engine components at AB operation. k’th Comp.

_ UNEX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ UNEX;n Ex D;k

Comp.

_ UNEX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ UNEX;n Ex D;k

LPC

598.18

99.68

118.66

3.92

593.17

98.02

ABED

1501.17

1220.83

CC

457.94

58.42

HPTMS

99.98

2.78

HPT

136.84

5.22

98.85 76.31 22.80 19.77 250.15 16.66 13.95 498.50 98.85 75.67 22.61 19.61 248.06 16.52 13.83 495.15 76.31 75.67 17.46 15.14 191.51 12.76 10.68 399.52 22.80 22.61 17.46 4.52 57.22 3.81 3.19 131.62

LPT

HPC

HPC CC HPT LPT ABED HPTMS LPTMS Total LPC CC HPT LPT ABED HPTMS LPTMS Total LPC HPC HPT LPT ABED HPTMS LPTMS Total LPC HPC CC LPT ABED HPTMS LPTMS Total

LPTMS

83.72

1.95

LPC HPC CC HPT ABED HPTMS LPTMS Total LPC HPC CC HPT LPT HPTMS LPTMS Total LPC HPC CC HPT LPT ABED LPTMS Total LPC HPC CC HPT LPT ABED HPTMS Total

19.77 19.61 15.14 4.52 49.62 3.30 2.77 114.74 80.29 79.62 61.47 18.37 15.93 13.42 11.24 280.34 16.66 16.52 12.76 3.81 3.30 41.81 2.33 97.20 13.95 13.83 10.68 3.19 2.77 35.01 2.33 81.76

Bold italics represent the maximum values in the first two components.

Table 13 Interdependencies among components and the mexogenous exergy destruction rates related to avoidable-exogenous exergy destruction within the engine components at MIL operation. k’th Comp.

_ AVEX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ AVEX;n Ex D;k

Comp.

_ AVEX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ AVEX;n Ex D;k

LPC

596.97

307.16

137.57

16.31

146.01

18.38

ABED

68.72

4.07

CC

4.60

0.02

HPTMS

51.33

2.27

HPT

112.14

13.39

75.13 2.37 57.70 70.79 35.36 26.41 22.05 289.80 75.13 0.58 14.11 17.31 8.65 6.46 5.39 127.64 2.37 0.58 0.44 0.55 0.27 0.20 0.17 4.58 56.24 13.76 0.43 12.96 6.47 4.84 4.04 98.74

LPT

HPC

HPC CC HPT LPT ABED HPTMS LPTMS Total LPC CC HPT LPT ABED HPTMS LPTMS Total LPC HPC HPT LPT ABED HPTMS LPTMS Total LPC HPC CC LPT ABED HPTMS LPTMS Total

LPTMS

42.86

1.58

LPC HPC CC HPT ABED HPTMS LPTMS Total LPC HPC CC HPT LPT HPTMS LPTMS Total LPC HPC CC HPT LPT ABED LPTMS Total LPC HPC CC HPT LPT ABED HPTMS Total

70.79 17.31 0.55 13.30 8.15 6.09 5.08 121.26 35.36 8.65 0.27 6.64 8.15 3.04 2.54 64.65 26.41 6.46 0.20 4.96 6.09 3.04 1.90 49.06 22.05 5.39 0.17 4.14 5.08 2.54 1.90 41.28

Bold italics represent the maximum values in the first two components.

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Table 14 Interdependencies among components and the mexogenous exergy destruction rates related to avoidable-exogenous exergy destruction within the engine components at AB operation. k’th Comp.

_ AVEX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ AVEX;n Ex D;k

Comp.

_ AVEX Ex D;k

_ MEXO Ex D;k

n’th Comp.

_ AVEX;n Ex D;k

LPC

596.97

321.90

137.57

17.09

146.01

19.26

ABED

15.61

0.22

CC

4.60

0.02

HPTMS

51.33

2.38

HPT

112.14

11.36

78.73 2.48 60.47 74.18 8.42 27.68 23.11 275.07 78.73 0.61 14.79 18.14 2.06 6.77 5.65 126.76 2.48 0.61 0.47 0.57 0.06 0.21 0.18 4.58 60.47 14.79 0.47 13.93 1.58 5.20 4.34 100.78

LPT

HPC

HPC CC HPT LPT ABED HPTMS LPTMS Total LPC CC HPT LPT ABED HPTMS LPTMS Total LPC HPC HPT LPT ABED HPTMS LPTMS Total LPC HPC CC LPT ABED HPTMS LPTMS Total

LPTMS

42.86

1.66

LPC HPC CC HPT ABED HPTMS LPTMS Total LPC HPC CC HPT LPT HPTMS LPTMS Total LPC HPC CC HPT LPT ABED LPTMS Total LPC HPC CC HPT LPT ABED HPTMS Total

74.18 18.14 0.57 13.93 1.94 6.38 5.33 120.48 8.42 2.06 0.06 1.58 1.94 0.72 0.60 15.39 27.68 6.77 0.21 5.20 6.38 0.72 1.99 48.95 23.11 5.65 0.18 4.34 5.33 0.60 1.99 41.20

Bold italics represent the maximum values in the first two components.

Table 15 Dividing the avoidable and unavoidable exergy destructions into endogenous and exogenous parts for the engine components. Component

MIL operation

LPC HPC CC HPT LPT ABED HPTMS LPTMS Total

AB operation

_ REAL Ex D

_ UNEN Ex D

_ UNEX Ex D

_ AVEN Ex D

_ AVEX Ex D

_ REAL Ex D

_ UNEN Ex D

_ UNEX Ex D

_ AVEN Ex D

_ AVEX Ex D

1579.15 1955.01 20877.70 273.59 272.06 1826.25 224.99 188.66 27197.41

192.20 975.66 20212.27 13.53 7.33 1116.47 48.68 41.06 22607.20

598.18 593.17 457.94 136.84 118.66 481.85 99.98 83.72 2570.34

191.81 240.16 202.89 11.09 8.50 159.22 24.99 21.02 859.68

596.97 146.01 4.60 112.14 137.57 68.72 51.33 42.86 1160.19

1579.15 1955.01 20877.70 273.59 272.06 85176.21 224.99 188.66 110547.37

192.20 975.66 20212.27 13.53 7.33 82798.27 48.68 41.06 104289.01

598.18 593.17 457.94 136.84 118.66 1501.17 99.98 83.72 3589.66

191.81 240.16 202.89 11.09 8.50 861.15 24.99 21.02 1561.61

596.97 146.01 4.60 112.14 137.57 15.61 51.33 42.86 1107.08

_ UNEX within the components indicate that the
The values of Ex D unavoidable-exogenous exergy destruction cannot be reduced because of technological limitations in the other components of the overall system for its given structure. _ AVEX val
For both MIL operation and AB operation, the higher Ex D

ues are estimated 596.97 kW within the LPC, 146.01 kW within the HPC, 137.57 kW within the LPT and 112.14 kW within the _ AVEX can be reduced by an improveHPT, respectively. The Ex D

ment in the structure of the overall system, or by improving the efficiency of the remaining system components, and of course by improving the efficiencies of the components. _ AVEN is estimated to be 240.16 kW within the HPC,
The higher Ex D 202.89 kW within the CC, 191.81 kW within the LPC and 159.22 kW within the ABED at MIL operation mode while the _ AVEN is computed to be 861.15 kW within the ABED, higher Ex D

240.16 kW within the HPC, 202.89 kW within the CC and

191.81 kW within the LPC at AB mode, respectively. The _ AVEN part can be reduced by improving the efficiency of the Ex D investigated component. In this framework, Figs. 4–14 are illustrated to clarify the distribution of the exergy destruction within the components and the whole engine. Fig. 4 shows that the approximately 50% of the exergy destruction within the LPC is avoidable exergy destruction while the approximately 76% of the exergy destruction within the LPC is exogenous exergy destruction. According to the result of the combination of the splitting exergy destruction, the approx  _ AVEX ¼ 5960:97 kW in the exergy destruction of imately 38% Ex D

the LPC can be reduced by an improvement in the structure of the overall system, or by improving the efficiency of the remaining system components, and of course by improving the efficiency in the LPC component.

O. Balli / Applied Thermal Engineering 111 (2017) 152–169

Fig. 4. Breakdown of the exergy destruction rates within the LPC.

Fig. 5. Breakdown of the exergy destruction rates within the HPC.

Fig. 6. Breakdown of the exergy destruction rates within the CC.

Fig. 7. Breakdown of the exergy destruction rates within the HPT.

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O. Balli / Applied Thermal Engineering 111 (2017) 152–169

Fig. 8. Breakdown of the exergy destruction rates within the LPT.

Fig. 9. Breakdown of the exergy destruction rates within the ABED at MIL operation.

Fig. 10. Breakdown of the exergy destruction rates within the ABED at AB operation.

Fig. 11. Breakdown of the exergy destruction rates within the LPTMS.

O. Balli / Applied Thermal Engineering 111 (2017) 152–169

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Fig. 12. Breakdown of the exergy destruction rates within the HPTMS.

Fig. 13. Breakdown of the exergy destruction rates within the TJE at MIL mode.

Fig. 14. Breakdown of the exergy destruction rates within the TJE at AB mode.

Fig. 5 indicates that the approximately 20% of the exergy destruction within the HPC is avoidable exergy destruction while the approximately 38% of the exergy destruction within the HPC is exogenous exergy destruction. According to the result of the combination of the splitting exergy destruction, the approximately   _ AVEX ¼ 1460:01 kW in the exergy destruction of the HPC 8% Ex D

may be decreased by an improvement in the structure of the overall system, or by improving the efficiency of the remaining system components, and of course by improving the efficiency in the HPC component. Fig. 6 points that the approximately 1% of the exergy destruction within the CC is avoidable exergy destruction while the approximately 2% of the exergy destruction within the CC is exoge-

nous exergy destruction. According to the result of the  combina _ AVEX of tion of the splitting exergy destruction, the 4.60 kW Ex D the exergy destruction within the CC may be decreased by an improvement in the structure of the overall system, or by improving the efficiency of the remaining system components, and of course by improving the efficiency in the CC component. Fig. 7 illustrates that the approximately 45% of the exergy destruction within the HPT is avoidable exergy destruction while the approximately 91% of the exergy destruction within the HPT is exogenous exergy destruction. According to the result of the combination of the splitting exergy destruction, the approximately   _ AVEX ¼ 112:14 kW in the exergy destruction of the HPT 41% Ex D

can be lessen by an improvement in the structure of the overall

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O. Balli / Applied Thermal Engineering 111 (2017) 152–169

Table 16 Dividing the avoidable and unavoidable exergy destructions into endogenous and exogenous parts for the engine. Operation mode

_ REAL Ex D

_ UN Ex D

_ AV Ex D

_ EN Ex D

_ EX Ex D

_ UNEN Ex D

_ UNEX Ex D

_ AVEN Ex D

_ AVEX Ex D

MIL AB

27197.41 110547.37

25177.54 107878.67

2019.87 2668.69

23466.89 105850.62

3730.52 4696.75

22607.20 104289.01

2570.34 3589.66

859.68 1561.61

1160.19 1107.08

system, or by improving the efficiency of the remaining system components, and of course by improving the efficiency in the HPT component. Fig. 8 shows that the approximately 54% of the exergy destruction within the LPT is avoidable exergy destruction while the approximately 94% of the exergy destruction within the LPT is exogenous exergy destruction. According to the result of the combination of the splitting exergy destruction, the approximately 50%   _ AVEX ¼ 137:57 kW in the exergy destruction of the LPT can be Ex D

decreased by an improvement in the structure of the overall system, or by improving the efficiency of the remaining system components, and of course by improving the efficiency in the LPT component. Fig. 9 indicates that the approximately 12% of the exergy destruction within the ABED is avoidable exergy destruction while the approximately 30% of the exergy destruction within the ABED is exogenous exergy destruction at MIL operation. According to the result of the combination of the splitting exergy destruction, the   _ AVEX ¼ 68:72 kW in the exergy destruction approximately 4% Ex D

of the ABED may be reduced. However, Fig. 10 shows that the approximately 1% of the exergy destruction within the ABED is avoidable exergy destruction while the approximately 2% of the exergy destruction within the ABED is exogenous exergy destruction at the AB mode. According to the result of the combination of the splitting exergy destruction, the only 68.72 kW (at the MIL mode) and 15.61 kW (at the AB mode) of the exergy destruction within the ABED may be decreased by an improvement in the structure of the overall system, or by improving the efficiency of the remaining system components, and of course by improving the efficiency in the ABED component. Figs. 11 and 12 indicate that the approximately 34% of the exergy destruction within the LPTMS and HPTMS is avoidable exergy destruction while the approximately 67% of the exergy destruction within the LPTMS/HPTMS is exogenous exergy destruction. According to the result of the combination of the splitting exergy destruction, the approximately 23%  _ AVEX ¼ 42:86 kW;Ex _ AVEX ¼ 51:33 kWÞ of the exergy destrucEx D;LPTMS

D;HPTMS

tion within the LPTMS/HPTMS can be reduced by an improvement in the structure of the overall system, or by improving the efficiency of the remaining system components, and of course by improving the efficiency in the LPTMS and HPTMS components. The unavoidable, avoidable, endogenous, exogenous and splitting parts of exergy destructions within the whole engine are given in Table 16. For the MIL operation, Fig. 13 indicates that the approximately 7% of the exergy destruction within the engine is avoidable exergy destruction while the approximately 14% of the exergy destruction within the engine is exogenous exergy destruction. According to the result of the combination of the splitting _ AVEX ¼ 1160:16 kWÞ exergy destruction, the approximately 4% ðEx

imately 1%

  _ AVEX ¼ 1107:08 kW in the exergy destruction of Ex D

the engine can be decreased by an improvement in the structure of the overall engine system or by improving the efficiency of the engine components. As mentioned above, the unavoidable endogenous exergy   _ UNEX is the main part of the total exergy destruction rate Ex D

destruction rate with the approximately 83% slice at the MIL mode and 94% slice at the AB mode. However, the avoidable exergy   _ AV is 7% of the total exergy destruction rate destruction rate Ex D

_ AV is 2% of the total exergy destruction at the MIL mode while the Ex D rate at the AB mode. These ratios indicate that technological development is close to the thermodynamic limitations. 5. Conclusions This study presents the conventional and advanced exergy analyses of a turbojet engine used on the military aircrafts. The exergy destruction rates in the real operation case split into endogenous, exogenous, avoidable and unavoidable parts and their combinations for the detail examination of irreversibilities and inefficiencies. The main remarkable results of the present study are summarized as follows:
The 83% of the total exergy destruction within the engine is endogenous at the MIL mode while the 94% of the total exergy destruction within the engine is endogenous at AB mode. So, the interactions between the system components are weak.
The 93% of the total exergy destruction is unavoidable at the MIL mode while the 98% of the total exergy destruction is unavoidable at the AB mode. These results indicate that the improvement potential of the system is very low and limited.
The improvement potentials are mostly concerned with the HPC, the CC and the ABED components itself because the unavoidable endogenous exergy destruction rate is bigger than the unavoidable exogenous exergy destruction rate.
The LPC, the HPC, the CC and the ABED have an important effect on other components according to the mexogenous exergy destruction results.
Interpreting these values, it is recommended that improvement efforts should be focused on the LPC, the HPC, the CC and the ABED. In addition to the results listed above, the advanced exergoeconomic and advanced exergoenvironmental evaluations should be conducted for future studies and advanced exergy-based analyses are recommended for evaluating the system to prevent misunderstandings based on the conventional exergy analysis.

D

in the exergy destruction of the engine can be decreased by an improvement in the structure of the overall engine system or by improving the efficiency of the engine components. For the AB operation, Fig. 14 indicates that the approximately 2% of the exergy destruction within the engine is avoidable exergy destruction while the approximately 4% of the exergy destruction within the engine is exogenous exergy destruction. According to the result of the combination of the splitting exergy destruction, the approx-

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