Thermo-ecological performance analyses and optimizations of irreversible gas cycle engines

Accepted Manuscript Research Paper Thermo-Ecological Performance analyses and optimizations of irreversible gas cycle engines Guven Gonca, Bahri Şahin PII: DOI: Reference:

S1359-4311(16)30338-6 http://dx.doi.org/10.1016/j.applthermaleng.2016.03.046 ATE 7914

To appear in:

Applied Thermal Engineering

Received Date: Accepted Date:

15 December 2015 8 March 2016

Please cite this article as: G. Gonca, B. Şahin, Thermo-Ecological Performance analyses and optimizations of irreversible gas cycle engines, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/ j.applthermaleng.2016.03.046

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Thermo-Ecological Performance analyses and optimizations of irreversible gas cycle engines Guven Gonca†,*, Bahri Şahin† † Department of Naval Architecture and Marine Engineering, Yildiz Technical University, Besiktas, 34349, Istanbul Turkey

Abstract This paper reports ecological performance analyses and optimization of irreversible gas cycle engines such as Joule-Brayton cycle (JB), Atkinson cycle (AC), Otto cycle (OC), Diesel cycle (DC), Miller cycle (MC), Dual-Atkinson cycle (DAC), Dual-Diesel cycle (DDC), Dual-Miller cycle (DMC) engines based on the ecological coefficient of performance (ECOP) criterion which covers internal irreversibility, heat leak and finite-rate of heat transfer. Comprehensive computational analyses have been conducted to investigate the global and optimal performances of the gas cycle engines. The results obtained based on the ECOP criterion are compared with a different ecological function which is named as the ecologic objectivefunction and with the maximum power output conditions. The results have been acquired introducing the compression ratio, cut-off ratio, pressure ratio, air recharging ratio, source temperature ratio and internal irreversibility parameter. The changes of cycle performances with respect to these parameters are examined and demonstrated with figures. Key words: Gas cycle engines; Performance analysis; Optimization; Power output; Irreversibility; ECOP. 1. Introduction So many analyses, studies and investigations have been carried to optimize the performance of the heat engine cycles by considering the environmental regulations and economical restrictions.

*

Corresponding author. Tel.: +90 2123832980; fax: +90 2123832989 E-mail addresses: [email protected] (G.GONCA)

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Mozurkewich and Berry [1] carried out an optimization study for an air-standard (OC) by considering heat leak, incomplete combustion and friction losses . Aizenbud et al. [2] defined the optimal motion of a piston fitted to a cylinder of a model internal combustion engine (ICE) for finite periods. Chen et al.[3] examined the relationship between the net work output and efficiency characteristics of the air standard OC taking the heat transfer losses through the cylinder wall into account. Ge et al. [4] analyzed the influences of the losses resulting from internal irreversibilities, heat transfer and friction on the performance of the irreversible OC by considering the temperature-dependent specific heats of the working fluid. Chen et al. [5] studied on the power output and efficiency of the irreversible OC by taking the influences of non-isentropic compression and expansion processes, finite-time processes and heat transfer losses into account. Abu-Nada et al. [6] thermodynamically analyzed an OC spark-ignition engine using a gas mixture model for the working fluid. Ust et al. [7] performed an optimization study for an irreversible OC considering the effects of cycle temperature and cycle pressure ratios. Chen et al. [8] performed a thermo dynamical performance analysis of an air-standard DDC by taking into account the heat-transfer and friction-like loss terms. Ozsoysal [9] determined the combustion efficiency of a DDC as a percentage of the fuel’s chemical energy and investigated the influence of combustion efficiency and irreversibilities arising from the expansion and compression processes on the thermal efficiency of the cycle. Ebrahimi [10] studied on the performance analysis of an air standard DDC based on the finitetime thermodynamics (FTT). Ust et al. [11-12] examined the impacts of the heat transfer and combustion effects on the work output, mean effective pressure and thermal efficiency of an air-standard irreversible OC [11] and DC [12]. Parlak [13] performed an optimization study for the irreversible DDC and DC based on the maximum power and maximum thermal efficiency criteria. Al-Hinti et al. [14] evaluated the net power output and cycle thermal efficiency of air-standard DC by using realistic parameters such as air–fuel ratio, fuel mass

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flow rate, intake temperature, etc. Sakhrieh et al. [15] investigated the influences of the gas mixture model on the performance characteristics of a diesel engine using a zero-dimensional single-zone combustion model. Durmayaz et al. [16] carried out a literature survey to investigate the optimization studies of thermal system functions based on the FTT and thermo economics. Gonca et al. [17-25] computationally and experimentally proved that the application of the MC into a diesel engine could abate the NO and increase the effective efficiency. Wang et al. [26-27] carried out experimental [26] and analytical [27] studies to examine the influences of the application of the MC into a gasoline engine. The results indicated that the gasoline engine operating with the MC lead to decreasing of NOx emissions, considerably. Mikalsen et al. [28] investigated the feasibility and potential advantages of the implementation of the MC into a small scale OC natural gas engine by using multidimensional simulation for a combined heat and power system. Wang et al. [29] experimentally reduced the NOx emissions released from a diesel engine with the application of the MC. Al-Sarkhi et al. [30-31] examined the effects of the temperature-dependent specific heats of the working fluid on the performance of an air standard reversible MC [30] and irreversible MC [31]. In another study, Al-Sarkhi et al. et al. [32] analyzed the cycle performance by using the maximum power density criteria. Zhao and Chen [33] conducted a performance analysis for an-air standard irreversible MC with respect to the change of the pressure ratios. Wang et al. [34] experimentally decreased the NOx emissions and SFC by applying the MC into a diesel engine. Ebrahimi [35] analyzed an air standard reversible MC with respect to variation of engine speed and variable specific heat ratio of working fluid and Ebrahimi [36] analyzed an air standard irreversible MC with respect to the variation of relative air–fuel ratio and stroke length. Ust [37] carried out an optimization study for the irreversible AC by considering the internal irreversibility to determine the optimum performance and design parameters. Zhao and Chen [38] parametrically studied on an

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irreversible AC by taking account of irreversibility arising from the internal adiabatic processes, finite-time processes and heat transfer losses. Gahruei et al. [39] compared the performance of the DC with that of the DAC by taking heat-transfer, friction losses and temperature-dependent specific-heats into consideration. Ge et al. [40] examined the influences of the heat transfer and friction losses on the performance of an AC engine. Also, they [41] examined the effects of variable specific-heats of the working fluid on the performance of the AC. Ebrahimi [42] optimized the performance of an AC heat engine by considering the cylinder wall temperature, mean piston velocity and equivalence ratio. Lin and Hou [43] investigated the effects of variable specific heats of the working fluid, friction and heat losses on the performance of an air-standard AC. Gonca and Sahin [44-45] used the FTTM [44] and ecological coefficient of performance criterion [45] to analysis the performance of the DAC. Gonca [46] investigated the heat transfer effects on the cycle performance of the DAC. Researchers carried out performance optimization and thermo dynamical analyses of engine cycles with different methods and objective functions. One of the objective functions mostly known is the ecological objective-function developed by Angulo-Brown [47]. This function is defined as the power output minus the loss rate of availability. In the recent years, a new thermo-ecological objective function named as the ecological coefficient of performance (ECOP), has been proposed by Ust [48-49]. The ECOP is the ratio of the power output to the loss rate of availability. The minimum entropy formation is obtained at the maximum ECOP. It was declared that the ECOP criterion is more comprehensible than ecological objective-function [49]. Researchers performed various studies on the application of the ECOP criterion to the heat engines [48-55]. The performances of irreversible DC engine [49], irreversible Carnot heat engine [51], irreversible Brayton heat engine [51-52], irreversible regenerative Brayton heat engine [53] were analyzed based on the ECOP criterion by Ust et al. Ust and Sahin [54] performed a numerical

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optimization for irreversible refrigerators using the ECOP criterion. Also, Ust [55] conducted a performance analysis and optimization for irreversible refrigeration cycles considering the irreversibility due to finite-rate heat transfer, heat leakage and internal dissipations. This study reports a thermo-ecological performance analysis based on the ECOP, the ecological objective-function ( E ) and the maximum power output conditions for irreversible gas cycle engines such as JB, AC, OC, DC, MC, DAC, DDC and DMC. The effects of the engine design parameters on the engine performance were examined. The general and optimal design parameters which provide the maximum ECOP, the maximum E and the maximum power output have been numerically defined. In this study, the E and ECOP functions are applied to all irreversible gas cycle engines and comprehensive comparisons are presented together. Hence, this study has a remarkable novelty. 2. Theoretical analysis of air standard gas cycles The DMC covers all gas cycles and the other gas cycles are a specific state of it. Therefore, the theoretical analyses are carried out based analysis of the DMC. P-v and T-s diagrams of the irreversible air-standard DMC (1-2-3-4-5-6-1) are depicted in Fig.1. The DMC is coupled to constant hot and cold temperature heat-reservoirs. As can be seen from the figures, the process 1-2s is an isentropic compression, as the process 1-2 considering internal irreversibility. The heat addition occurs in the 2-3 (at constant volume) and 3-4 (at constant pressure) processes. Process 4-5s is an isentropic expansion while the internal irreversibility is considered during the process 4-5. The heat rejection occurs during the process 5-6 (at constant volume) and process 6-1 (at constant pressure). In the DMC cycle, QH 1 and QH 2 are the heat transfer rates (time-dependent) from the hot source at temperature TH to the working fluid in the processes 2-3 and 3-4, QL1 and QL 2 are the heat transfer rates from the working

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fluid to the cold reservoir at temperature TL (ambient temperature) in the process 5–6 and 6– 1. QH 1 ; QH 2 and QL1 ; QL 2 are expressed by extending ref. [45] and [49] as given below:

QH 1  U H 1 AH 1

TH  T2   TH  T3   C  T  T  C T  T W H1  H 2 W  3 2 T T ln

QH 2  U H 2 AH 2

H

TH  T3

TH  T3   TH  T4   kC  1   T  T  kC T  T W H2  H 1  H 2 W  4 3 T T ln

QL1  U L1 AL1

QL2  U L2 AL2

H

(2)

3

TH  T4

T5  TL   T6  TL   C  T  T  C T  T W L1  5 L W  5 6 T T ln

(1)

2

5

(3)

L

T6  TL

T6  TL   T1  TL   kC  1   T  T  kC T  T W L2  L1  5 L W  6 1 T T ln

6

(4)

L

T1  TL

where U H 1 AH 1 ; U H 2 AH 2 and U L1 AL1 ; U L2 AL2 are the conductance of hot-reservoir and coldreservoir heat exchanger. CW is the capacity rate of the working fluid and k is the ratio of the specific heat at constant pressure to the specific heat at constant volume ( CP / CV ) of the working fluid.  H 1 ;  H 2 and  L1 ;  L2 are the effectiveness of the hot-reservoir heat exchanger and cold-reservoir heat exchanger which are given as follows:

 H 1  1  exp   N H 1 

(5)

 H 2  1  exp   N H 2 

(6)

 L1  1  exp   N L1 

(7)

 L2  1  exp   N L2 

(8)

where N H 1 ; N H 2 and N L1 ; N L2 are the numbers of heat transfer units for hot-side and cold-side based on the minimum thermal capacity rates. They may be stated as:

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NH 1 

U H 1 AH 1 U A U A U A ; N H 2  H 2 H 2 ; N L1  L1 L1 ; N L2  L2 L2 CW kCW CW kCW

(9)

The heat leakage rate, QLK , from the hot source at temperature TH to the cold source at temperature TL may be expressed as below:

QLK  CI TH  TL    CW TH  TL 

(10)

where C I is the internal conductance of the DMC and  is the ratio of the internal conductance based on the thermal capacity rate of the standard air. The total heat rate, QHT , transferred from hot-side to the working fluid is written as:





QHT  CW  H 1  k H 2 1   H 1  TH  T2    TH  TL 

(11)

the total heat rate, QLT , transferred from the working fluid to the cold-side is given as:





QLT  CW  L1  k L2 1   L1  T5  TL    TH  TL 

(12)

Using Eqs. (1)-(12), the following equations could be obtained as below:

T3   H 1TH  1   H 1  T2

(13)

T4   H 1   H 2 1   H 1  TH  1   H 1 1   H 2  T2

(14)

T6   L1TL  1   L1  T5

(15)

T1   L1   L2 1   L1  TL  1   L1 1   L2  T5

(16)

The power output may be stated using the first law of thermodynamics:



 

W  QH 1  QH 2  QL1  QL2







W  CW  H 1  k H 2 1   H 1   TH  T2    L1  k L2 1   L1  T5  TL 

(17)

From Eq. (17),  H 1  k H 2  1   H 1   TH  T2  W T5  TL     L1  k L2  1   L1  CW  L1  k L2  1   L1  

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(18)

   H 1  k H 2  1   H 1   TH  T2  W T6   L1TL  1   L1  TL      L1  k L2 1   L1  CW  L1  k L2 1   L1    

(19)

T1   L1   L2  1   L1   TL  

 H 1  k H 2  1   H 1   TH  T2 

1   L1 1   L2  TL   

 L1  k L2  1   L1 



 W  CW  L1  k L2  1   L1   

(20)

The isentropic efficiencies of the compression and expansion processes are [19,45]:

C 

T2S  T1 T2  T1

(21)

T4  T5 T4  T5S

(22)

and

E 

The following equation is acquired based on the second law of thermodynamics [19,45]:

T1kT31kT4k  T2ST5ST6 k 1 .

(23)

C and  E determine the irreversibilities of the adiabatic processes. By using thermodynamic

relations between the state points 1  6 and the Eqs. (21)-(23), following equations are obtained:

C  ( r k 1  1) (T2 / T1 )  C

(24)

and (T5 / T4 )   1 E [ 1  (  /  )k 1 ] 

(25)

where the compression ratio (r) is given as: r  v1 / v2

(26)

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Also, the following equation is attained based on the second law of thermodynamics [1]: S42  S51  0

(27)

The inequality in Eq. (27) could be reordered as follows: I S S42  S51  0 with I S  1

(28)

where I S is internal irreversibility parameter and it is given as

I S 

 S5  S6    S6  S1   S4  S3    S3  S 2 

(29)

Consequently, following equation may be acquired

T1kT3IS ( 1k )T4IS k  T2 IS T5T6 k 1

(30)

In the study, dimensionless engine design parameters are, the pressure ratio (  ), cut-off ratio (  ), source temperature-ratio (  ), air recharging ratio ( rAR ), stroke ratio (  ) and they can be given respectively as [19]:   P3 / P2  T3 / T2

(31)

  v4 / v3  T4 / T3

(32)

  TH / TL

(33)

rAR  v6 / v1  T6 / T1

(34)

  v6 / v2  rAR r

(35)

In the comparison of the thermodynamic gas cycles, the engine design parameters are used to determine the specific cycles. The DMC is converted to; Diesel cycle (DC), if QH 1 =  H 1 = N H 1 = 0 and QL2 =  L2 = N L2 = 0,

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Otto cycle (OC), if QH 2 =  H 2 = N H 2 = 0 and QL2 =  L2 = N L2 = 0, Atkinson cycle (AC), if QH 2 =  H 2 = N H 2 = 0 and QL1 =  L1 = N L1 = 0, Miller cycle (MC), if QH 2 =  H 2 = N H 2 = 0, Dual-Diesel cycle (DDC), if QL2 =  L2 = N L2 = 0, Dual-Atkinson cycle (DAC), if QL1 =  L1 = N L1 = 0, Joule-Brayton cycle (JB), if QH 1 =  H 1 = N H 1 = 0 and QL1 =  L1 = N L1 = 0, The cycle derivation from the DMC is shown in Fig. 2. The entropy-generation rate of the gas cycles may be expressed as:

Sg 

QLT QHT  TL TH

(36)

The objective function of the ecological optimization [49] is

E  W  T0 S g

(37)

The ECOP criterion is given as the proportion of the power output to the loss rate of availability as following [48-49]

ECOP 

W T0 S g

(38)

The thermal efficiency could be written as following:



W QHT

(39)

In order to obtain comparative results and figures, all equations given above are used.

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3. Results and Discussion In order to compare the results obtained for the thermodynamic gas cycles based on different performance parameters at the maximum ECOP, MEF and MP conditions, comprehensive numerical calculations are carried out evaluating compression ratio ( r ). The figures given in the text are illustrated based on numerical results. In the calculations, the constants are taken as k  1.4 and C  E  0.9 , the total number of heat-transfer units for the DMC are given as : NT  N H 1  N H 2  N L1  N L2 and X =  N H 1  N H 2  / NT

The variations of the ecological function ( E  W  T0 S g ) and ECOP with respect to the dimensionless power output ( W  W / CW TL ) for different gas cycle engines are depicted in the Fig. 3. It may be observed from this figure that the maximum ECOP and the maximum ecological function are obtained at the different dimensionless power output. The JB provides the maximum ECOP, E and W , as the OC gives the minimum values of the performance parameters. The order can be written as OC
efficiency up to 4% for JB. The highest values of η* /ηMEF are acquired with JB and the lowest values of η* /ηMEF are attained with OC. η* /ηMEF decreases with increasing I S and decreasing  . It is obviously seen from the Figs. 5 that the work output at ECOPMAX ( W* ) is lower than that at EMAX ( WMEF ). Therefore, it can be said that the ECOP is more disadvantageous than the E

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in terms of the work output up to 24% for JB. The OC generally gives the maximum values of W* / WMEF , while JB provides the minimum values of W* / WMEF . This ratio increases with

raising I S and reducing  . It may be understood from the Figs. 6 that the entropy generation at ECOPMAX ( Sg * ) is lower than that at EMAX ( Sg MEF ). Thus, it is clear that the ECOP is more advantageous than the E in terms of the entropy generation by 36% for JB. The OC leads to the maximum values of Sg * /SgMEF , as JB causes the minimum values of Sg * /SgMEF . As similar to previous figure, this

ratio raises with raising I S and diminishing  . It is clear from the Figs. 7 that the thermal efficiency at ECOPMAX ( η* ) is greater than that at WMAX ( ηMP ). It is obvious that the ECOP is more advantageous compared to the W in terms of

the thermal efficiency up to 24% for JB. For   7 , the maximum values of η* /ηMP are obtained with JB and the minimum values of η* /ηMP are acquired with OC. For I S  1.2 with the variable  , η* /ηMP takes different values for different cycles. η* /ηMP increases with increasing I S and minimizing  . As may be seen from the Figs. 8, the work output at ECOPMAX ( W* ) is lower than that at WMAX Thus, the ECOP is more disadvantageous compared to the W in terms of the work

output up to 31% for JB. For   7 , the maximum values of W* / WMP are obtained with OC and the minimum values of W* / WMP are acquired with JB. However, although the JB gives the minimum values of the W* / WMP , the OC provides the maximum values of the W* / WMP at the lower values of  , the MC gives the maximum values of W* / WMP at the higher values of  for I S  1.2 . W* / WMP increases with raising I S and  .

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It could be obviously seen from the Figs. 9 that the entropy generation at ECOPMAX ( Sg * ) is lower than that at WMAX ( Sg MP ). Therefore, the ECOP is more advantageous than the W in terms of the entropy generation by 61% for JB. The OC causes to the maximum values of Sg * /SgMP , while JB leads to the minimum values of Sg * /SgMP . for   7 . For I S  1.2 with

variable  , the JB gives the minimum results but the maximum values are obtained with the OC at the higher values of  and with the DDC and MC at lower values of  . Sg * /Sg

MP

raises

with raising I S , on the other hand, it increases with increasing  for the OC, MC, AC, DMC ,JB and abating  for the DDC, DC, DAC. The Figs. 10 show the variations of the performance parameters (ECOP, E W ,  and S g ) with respect to the X . It can be seen from the figure that the performance parameters decrease at the lower and higher values of the X. The maximum values are seen between 0.4 and 0.6 of the X. When the value of the X approximately equals to 0.5, the maximum values of the performance parameters are obtained. The minimum values of the ECOP, E W ,  and S g are acquired with the OC. As the maximum values of the ECOP W and S g are seen with the JB, the highest values of the E and  are observed with the JB and DAC. The Figs. 11 demonstrate the variations of the performance parameters (ECOP, E W ,  and S g ) with respect to the  . It may be observed from the figure that the ECOP, E ,  abate

and S g increases with increasing  , however, W does not change. The maximum values of the performance parameters are attained with the JB and the lowest values of those are obtained with the OC. Although the ECOP curves are parabolic, the other curves are linear. The Figs. 12 illustrate the variations of the performance parameters (ECOP, E , W ,  and S g ) with respect to the NT . It is clear that all of the performance parameters increase with 13

increasing NT The maximum and minimum values of the E , W , S g are obtained with the JB and OC, respectively. At the lower values of NT , the maximum ECOP and  values are attained with the JB and the minimum values of them are seen with the OC. At the higher values of NT , the maximum ECOP and  values are acquired with the DAC and the lowest values of them are seen with the DC. . Even though the ECOP and  curves are parabolic, the other curves are linear. The variations of the ECOP and E with respect to the engine design parameters  r,rAR ,  ,   are shown in the Figs. 13. As may be seen from the figures, the maximum ECOP and E values are acquired with the JB and DAC with respect to the variation of r,rAR ,  and  , respectively. The minimum ECOP and E values are attained with the OC, MC, DDC and OC for the variation of the r,rAR ,  and  , respectively. Even though the maximum ECOP values seem at the greater values of the r compared to those of the maximum E values, it is just opposite for the engine design parameters. The maximum ECOP values are obtained at the lower values of rAR ,  ,  , however, the maximum E values are attained at the higher values of the engine design parameters. It is known that entropy generation should be decreased to obtain more environmentally friendly conditions. If the combustion temperatures are decreased in the internal combustion engines, the entropy generation is abated. Also, NOx emissions are reduced. There are so many different ecological methods such as water-steam injection [56-62] and EGR [63-64] applications. By using ECOP criterion, optimum ecological conditions could be determined for the gas cycle engines without other applications. Also, better ecological conditions could be obtained by combining NOx reduction methods. 4. Conclusion 14

Thermo-ecological optimizations and analyses have been performed to determine the optimum engine design and operating parameters for the air standard irreversible gas cycle engines having a finite-rate of heat transfer, heat leakage and internal irreversibility based on the ECOP, ecological function and maximum power output criteria. According to this perspective, the optimum compression ratio ( r ), air recharging ratio ( rAR ) cut-off ratio (  ) and pressure ratio (  ) that maximize the ecological coefficient of performance ( ECOPMAX ), ecological function ( EMAX ) and non-dimensional power output (WMAX ) have been examined. A comparative study based on maximum values of these criteria has been carried out for the irreversible gas cycle engine models, the relations between the nondimensional power output and ECOP , the ECOP and the ecological function, the nondimensional power output and the ecological function have been evaluated with respect to the variation of  , I S ,

r , rAR ,  and  . It is indicated that

ECOPMAX conditions have

remarkable advantage over the EMAX conditions in terms of entropy generation and thermal efficiency, nevertheless, a little disadvantage is observed in terms of the power output. Generally, it was observed that the JB have substantial advantage over the other gas cycle engines in terms of the ECOP , the ecological function and non-dimensional power output. Comparisons at the maximum power output conditions ( WMAX ) shows that ECOPMAX conditions have considerable advantages in terms of ecological viewpoints with little loss of power output. The optimal

r , rAR ,  and  values at

ECOPMAX , EMAX and WMAX conditions

have been illustrated to provide a fine guidelines for the determination of the optimal design and operating conditions of real gas cycle engines. Nomenclature

A

Heat transfer area (m2)

AC

Atkinson cycle 15

CP

Specific heat at constant pressure (kW/kg.K)

CW

mCP (kW/K)

DC

Diesel cycle

DAC

Dual-Atkinson cycle

DDC

Dual-Diesel cycle

DMC

Dual-Miller cycle

E

Ecological performance function

ECOP Ecological coefficient of performance I S

Internal irreversibility parameter

JB

Joule-Brayton cycle

k

Isentropic exponent

m

Mass flow rate (kg/s)

MC

Miller cycle

NT

Total number of heat-transfer units

OC

Otto cycle

P

Pressure (kPa)

Q

Rate of heat transfer (kW)

r

Compression ratio, r  v1 / v2

rM

Miller cycle ratio, rM  v6 / v1

S

Entropy (kJ/K)

T

Temperature (K)

U

Overall heat-transfer coefficient (kW/m2 K)

V

Volume (m3)

W

Power output (kW) 16

Greek letters 

Stroke ratio,   v6 / v2



Pressure ratio,   T3 / T2



Heat-exchanger effectiveness



Allocation ratio  N H 1  N H 2  / NT



Thermal efficiency

C

Isentropic efficiency of compression

E

Isentropic efficiency of expansion



Cut-off ratio,   T4 / T3



Source temperature ratio   TH / TL

Subscripts

g

Generation

H

High-temperature heat-source

L

Low-temperature heat-source

MAX Maximum MEF at maximum ecological function condition MP

at maximum power output condition

W

Working fluid

0

Environment condition

Superscripts

*

at maximum ECOP condition

___

non-dimensional

17

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Figure Captions Fig. 1. P-v and T-s schematic diagrams for DMC. Fig. 2. Flowchart for the cycle derivation from DMC Fig. 3. Variations of the ECOP and ecological function with respect to non-dimensional power output for different gas cycles Fig. 4. The ratio of the thermal efficiency at ECOPMAX ( η* ) to that at EMAX ( ηMEF ) with respect to the variation of a) I S and b)  for different gas cycles. Fig. 5. The ratio of the work output at ECOPMAX ( W* ) to that at EMAX ( WMEF ) with respect to the variation of a) I S and b)  for different gas cycles. Fig. 6. The ratio of the entropy generation at ECOPMAX ( Sg * ) to that at EMAX ( Sg MEF ) with respect to the variation of a) I S and b)  for different gas cycles. Fig. 7. The ratio of the thermal efficiency at ECOPMAX ( η* ) to that at WMAX ( ηMP ) with respect to the variation of a) I S and b)  for different gas cycles. Fig. 8. The ratio of the work output at ECOPMAX ( W* ) to that at WMAX with respect to the variation of a) I S and b)  for different gas cycles. Fig. 9. The ratio of the entropy generation at ECOPMAX ( Sg * ) to that at WMAX ( Sg MP ) with respect to the variation of a) I S and b)  for different gas cycles. Fig. 10. Variations of a) the ECOP and ecological function, b) the non-dimensional power output and thermal efficiency and c) the entropy generation with respect to X for different gas cycles Fig. 11. Variations of a) the ECOP and ecological function, b) the non-dimensional power output and thermal efficiency, and c) the entropy generation with respect to  for different gas cycles

22

Fig. 12. Variations of a) the ECOP and ecological function, b) the non-dimensional power output and thermal efficiency, and c) the entropy generation with respect to NT for different gas cycles Fig. 13. Variations of the ECOP and ecological function with respect to a) compression ratio

r  ,

b) air recharging ratio  rAR  , c) cut-off ratio    , d) pressure ratio    for different gas

cycles.

23

Figures

Fig. 1.

24

Dual-Miller Cycle (DMC)

QH 1  0 , QH 2  0 QL1  0 , QL2  0 H1  0 , H2  0  L1  0 ,  L2  0 NH 1  0 , NH 2  0 N L1  0 , N L2  0

Dual-Atkinson Cycle (DAC)

Miller Cycle (MC)

QH 2 = 0 H2 = 0 NH 2 = 0

QL1 = 0  L1 = 0 N L1 = 0

Joule-Brayton Cycle (JBC)

z

QH 2 = QL1 =0  H 2 =  L1 =0 N H 2 = N L1 =0

Dual-Diesel cycle (DDC)

Atkison Cycle (AC)

Otto Cycle (OC)

QH 2 = QL1 =0  H 2 =  L1 =0 N H 2 = N L1 =0

QH 2 = QL2 =0  H 2 =  L2 =0 N H 2 = N L2 =0

Fig. 2.

25

QL2 = 0  L2 = 0 N L2 = 0

Diesel Cycle (DC)

QH 1 = QL2 =0  H 1 =  L2 =0 N H 1 = N L2 =0

Fig. 3.

26

Fig. 4a.

27

Fig. 4b.

28

Fig. 5a.

29

Fig. 5b.

30

Fig. 6a.

31

Fig. 6b.

32

Fig. 7a.

33

Fig. 7b.

34

Fig. 8a.

35

Fig. 8b.

36

Fig. 9a.

37

Fig. 9b.

38

Fig. 10a.

39

Fig. 10b.

40

Fig. 10c.

41

Fig. 11a.

42

Fig. 11b.

43

Fig. 11c.

44

Fig. 12a.

45

Fig. 12b.

46

Fig. 12c.

47

Fig. 13a.

48

Fig. 13b.

49

Fig. 13c.

50

Fig. 13d.

51

Highlights

1. Performance optimizations are performed for irreversible gas cycle engines. 2. Comprehensive computational analyses are conducted based on ECOP criterion. 3. The impacts of engine design parameters on the performance are investigated.

52