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Guven Gonca - One of the best experts on this subject based on the ideXlab platform.

  • Research Article Performance Optimization of an Air-Standard Irreversible Dual-Atkinson Cycle Engine Based on the Ecological Coefficient of Performance Criterion
    2016
    Co-Authors: Guven Gonca, Bahri Sahin
    Abstract:

    License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper presents an ecological performance analysis and optimization for an air-standard irreversible Dual-Atkinson Cycle (DAC) based on the ecological coefficient of performance (ECOP) criterion which includes internal irreversibilities, heat leak, and finite-rate of heat transfer. A comprehensive numerical analysis has been realized so as to investigate the global and optimal performances of the Cycle. The results obtained based on the ECOP criterion are compared with a different ecological function which is named as the ecologic objective-function and with the maximum power output conditions. The results have been attained introducing the compression ratio, cut-off ratio, pressure ratio, Atkinson Cycle ratio, source temperature ratio, and internal irreversibility parameter. The change of Cycle performance with respect to these parameters is investigated and graphically presented. 1

  • performance analysis and optimization of irreversible dual Atkinson Cycle engine dace with heat transfer effects under maximum power and maximum power density conditions
    Applied Mathematical Modelling, 2016
    Co-Authors: Guven Gonca
    Abstract:

    Abstract This study presents an analysis considering the effects of heat transfer loss and internal irreversibility due to adiabatic compression and expansion processes on the performance of an irreversible Dual–Atkinson Cycle engine (DACE) under non-dimensional maximum power (MP), non-dimensional maximum power density (MPD) and maximum thermal efficiency (MEF) conditions. The effects of the inlet temperature, combustion constant and heat transfer constant on the engine performance are investigated. The results could be used by engine designers to optimize the performance of the internal combustion engines (ICEs).

  • thermodynamic analysis and performance maps for the irreversible dual Atkinson Cycle engine dace with considerations of temperature dependent specific heats heat transfer and friction losses
    Energy Conversion and Management, 2016
    Co-Authors: Guven Gonca
    Abstract:

    Abstract A comprehensive performance analysis depending on the non-dimensional power output, effective power, non-dimensional power density, effective power density, thermal efficiency, effective efficiency, maximum power output (MP), maximum power density (MPD) and maximum thermal efficiency (MEF) criteria has been conducted for the irreversible Dual–Atkinson Cycle engine (DACE) which includes internal irreversibilities by virtue of the irreversible-adiabatic compression process, expansion process, heat transfer and friction losses. In the analyses, Classical Thermodynamics Modeling (CTM) and a new realistic Finite-Time Thermodynamics Modeling (FTTM) have been used. The power output, power density and thermal efficiency are obtained with respect to the variation of the pressure ratio, cut-off ratio, stroke ratio, Atkinson Cycle ratio, Cycle pressure ratio and Cycle temperature ratio. The effects of the engine design and operating parameters on the general and maximum performances of the DACE have been investigated with respect to the variation of the Cycle pressure ratio and Cycle temperature ratio in the CTM section. The influences of the other engine design and operating parameters such as engine speed, mean piston speed, stroke length, equivalence ratio, compression ratio and bore–stroke length ratio on the engine performance have been investigated in the FTTM section. In addition, the energy losses depending on incomplete combustion, friction, heat transfer and exhaust output have been described as fuel input energy. In order to obtain realistic results, temperature-dependent specific heats for working fluid have been used. The DACE is a new concept for internal combustion engines and just a few studies have been carried out. This study presents new contributions to the analysis of the Dual–Atkinson Cycle engines in terms of the effects of engine design and operating parameters on the engine performance. Because CTM, FTTM, energy losses, power density and MPD analyses, for the DACE are newly presented just in this study.

  • Performance analysis and optimization of irreversible Dual–Atkinson Cycle engine (DACE) with heat transfer effects under maximum power and maximum power density conditions
    Applied Mathematical Modelling, 2016
    Co-Authors: Guven Gonca
    Abstract:

    Abstract This study presents an analysis considering the effects of heat transfer loss and internal irreversibility due to adiabatic compression and expansion processes on the performance of an irreversible Dual–Atkinson Cycle engine (DACE) under non-dimensional maximum power (MP), non-dimensional maximum power density (MPD) and maximum thermal efficiency (MEF) conditions. The effects of the inlet temperature, combustion constant and heat transfer constant on the engine performance are investigated. The results could be used by engine designers to optimize the performance of the internal combustion engines (ICEs).

  • Thermo-ecological performance analyses and optimizations of irreversible gas Cycle engines
    Applied Thermal Engineering, 2016
    Co-Authors: Guven Gonca, Bahri Sahin
    Abstract:

    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 objective-function 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.

Lingen Chen - One of the best experts on this subject based on the ideXlab platform.

  • Four-Objective Optimization of Irreversible Atkinson Cycle Based on NSGA-II.
    Entropy (Basel Switzerland), 2020
    Co-Authors: Shuangshuang Shi, Lingen Chen, Huijun Feng
    Abstract:

    Variation trends of dimensionless power density (PD) with a compression ratio and thermal efficiency (TE) are discussed according to the irreversible Atkinson Cycle (AC) model established in previous literature. Then, for the fixed Cycle temperature ratio, the maximum specific volume ratios, the maximum pressure ratios, and the TEs corresponding to the maximum power output (PO) and the maximum PD are compared. Finally, multi-objective optimization (MOO) of Cycle performance with dimensionless PO, TE, dimensionless PD, and dimensionless ecological function (EF) as the optimization objectives and compression ratio as the optimization variable are performed by applying the non-dominated sorting genetic algorithm-II (NSGA-II). The results show that there is an optimal compression ratio which will maximize the dimensionless PD. The relation curve of the dimensionless PD and compression ratio is a parabolic-like one, and the dimensionless PD and TE is a loop-shaped one. The AC engine has smaller size and higher TE under the maximum PD condition than those of under the maximum PO condition. With the increase of TE, the dimensionless PO will decrease, the dimensionless PD will increase, and the dimensionless EF will first increase and then decrease. There is no positive ideal point in Pareto frontier. The optimal solutions by using three decision-making methods are compared. This paper analyzes the performance of the PD of the AC with three losses, and performs MOO of dimensionless PO, TE, dimensionless PD, and dimensionless EF. The new conclusions obtained have theoretical guideline value for the optimal design of actual Atkinson heat engine.

  • Thermodynamic Optimization for an Endoreversible Dual-Miller Cycle (DMC) with Finite Speed of Piston.
    Entropy (Basel Switzerland), 2018
    Co-Authors: Lingen Chen, Huijun Feng
    Abstract:

    Power output ( P ), thermal efficiency ( η ) and ecological function ( E ) characteristics of an endoreversible Dual-Miller Cycle (DMC) with finite speed of the piston and finite rate of heat transfer are investigated by applying finite time thermodynamic (FTT) theory. The parameter expressions of the non-dimensional power output ( P ¯ ), η and non-dimensional ecological function ( E ¯ ) are derived. The relationships between P ¯ and cut-off ratio ( ρ ), between P ¯ and η , as well as between E ¯ and ρ are demonstrated. The influences of ρ and piston speeds in different processes on P ¯ , η and E ¯ are investigated. The results show that P ¯ and E ¯ first increase and then start to decrease with increasing ρ . The optimal cut-off ratio ρ o p t will increase if piston speeds increase in heat addition processes and heat rejection processes. As piston speeds in different processes increase, the maximum values of P ¯ and E ¯ increase. The results include the performance characteristics of various simplified Cycles of DMC, such as Otto Cycle, Diesel Cycle, Dual Cycle, Otto-Atkinson Cycle, Diesel-Atkinson Cycle, Dual-Atkinson Cycle, Otto-Miller Cycle and Diesel-Miller Cycle. Comparing performance characteristics of the DMC with different optimization objectives, when choosing E ¯ as optimization objective, η improves 26.4% compared to choosing P ¯ as optimization objective, while P ¯ improves 74.3% compared to choosing η as optimization objective. Thus, optimizing E is the best compromise between optimizing P and optimizing η . The results obtained can provide theoretical guidance to design practical DMC engines.

  • mathematical modeling and comparison of air standard dual and dual Atkinson Cycles with friction heat transfer and variable specific heats of the working fluid
    Applied Mathematical Modelling, 2013
    Co-Authors: Hamed Shahmirzae Jeshvaghani, Mohamad Hashemi Gahruei, Said Vahidi, Lingen Chen
    Abstract:

    Abstract Based on finite-time thermodynamics, a comparative performance analysis of air standard Dual and Dual-Atkinson Cycles with heat-transfer loss, friction like term losses and variable specific-heats of the working fluid have been performed. Also the effects of heat loss, as characterized by a percentage of the fuel’s energy, friction and variable specific-heats of the working fluid, on performance of the mentioned irreversible Cycles are analyzed. Moreover, detailed numerical examples show the relations between the power output and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between the power output and the thermal efficiency of Cycles. Results show the importance of consideration of heat loss effects on the both Cycles’ performance. Also performance comparison of two Cycles show that heat efficiency and power output of a Dual-Atkinson Cycle are higher than a Dual Cycle’s ones. The results obtained from this paper will provide guidance for the design of Dual-Atkinson engines.

  • Finite time thermodynamic modeling and analysis for an irreversible Atkinson Cycle
    Thermal Science, 2010
    Co-Authors: Lingen Chen, Fengrui Sun
    Abstract:

    Performance of an air-standard Atkinson Cycle is analyzed by using finite-time thermodynamics. The irreversible Cycle model which is more close to practice is founded. In this model, the nonlinear relation between the specific heats of working fluid and its temperature, the friction loss computed according to the mean velocity of the piston, the internal irreversibility described by using the compression and expansion efficiencies, and heat transfer loss are considered. The relations between the power output and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between power output and the efficiency of the Cycle are derived by detailed numerical examples. Moreover, the effects of internal irreversibility, heat transfer loss and friction loss on the Cycle performance are analyzed. The results obtained in this paper may provide guidelines for the design of practical internal combustion engines.

  • Performance of endoreversible Atkinson Cycle
    Journal of the Energy Institute, 2007
    Co-Authors: Lingen Chen, Fengrui Sun
    Abstract:

    AbstractThe performance of an air standard Atkinson Cycle with heat transfer loss and variable specific heats of working fluid is analysed by using finite time thermodynamics. The relationships between the work output and the compression ratio and between the thermal efficiency and the compression ratio, as well as the optimal relationship between the work output and the efficiency of the Cycle, are derived from detailed numerical examples. Moreover, the effects of heat transfer loss and variable specific heats of working fluid on the Cycle performance are analysed. The results show that these effects are obvious and they should be considered in practice Cycle analysis. The results obtained in the present paper may provide guidance for the design of practical internal combustion engines.

Jinxing Zhao - One of the best experts on this subject based on the ideXlab platform.

  • Optimization and matching for range-extenders of electric vehicles with artificial neural network and genetic algorithm
    Energy Conversion and Management, 2019
    Co-Authors: Jinxing Zhao, Zhang Zhendong, Shuwen Wang, Sen Wang
    Abstract:

    Abstract The primary issues for the popularization of electric vehicles are low energy density, short life, high cost, and long charging time of battery. In an extended-range electric vehicle, a range-extender is applied to realize the on-board electricity generation avoiding the range anxiety; and a large capacity battery and public charging facilities are not necessary. A primary issue is lack of an efficient range-extender that is light, compact and silent. The main reasons are that the efficiencies of range-extended engines now available are low; and the efficiency optimum operating points of the range-extended engines and generators are not matched. A 3-cylidner gasoline spark-ignition engine for an application in a range-extender has been investigated. Atkinson Cycle, exhaust gas recirculation and gasoline direct injection are applied to suppress the knocking. At most cases, a range-extender engine has only a most frequent operating point. All design parameters and operating variables of the range-extender engine can be optimized around the single operating point to maximize the efficiency while matching to the highest efficiency point of a range-extender generator. For this purpose, an optimization and matching method by combing artificial neural network and genetic algorithm has been investigated. The optimization and matching for a range-extender engine, with no generator constraint and with three different constraints of generator efficiency maps, have been conducted. The results show that both the operating points and the optimal parameters of the range-extender engine are different under the different generator constraints. A higher maximum thermal efficiency of the range-extender engine can be achieved as the power requirement decreases. The maximum efficiency of the range-extender engine can reach 40.2%, which is because of the application of high geometrical compression ratio, exhaust gas recirculation, Atkinson Cycle and single-point optimization of all parameters.

  • Finite-Time Thermodynamic Modeling and a Comparative Performance Analysis for Irreversible Otto, Miller and Atkinson Cycles.
    Entropy (Basel Switzerland), 2018
    Co-Authors: Jinxing Zhao
    Abstract:

    Finite-time thermodynamic models for an Otto Cycle, an Atkinson Cycle, an over-expansion Miller Cycle (M1), an LIVC Miller Cycle through late intake valve closure (M2) and an LIVC Miller Cycle with constant compression ratio (M3) have been established. The models for the two LIVC Miller Cycles are first developed; and the heat-transfer and friction losses are considered with the effects of real engine parameters. A comparative analysis for the energy losses and performances has been conducted. The optimum compression-ratio ranges for the efficiency and effective power are different. The comparative results of Cycle performances are influenced together by the ratios of the energy losses and the Cycle types. The Atkinson Cycle has the maximum peak power and efficiency, but the minimum power density; and the M1 Cycle can achieve the optimum comprehensive performances. The less net fuel amount and the high peak cylinder pressure (M3 Cycle) have a significantly adverse effect on the loss ratios of the heat-transfer and friction of the M2 and M3 Cycles; and the effective power and energy efficiency are always lower than the M1 and Atkinson Cycles. When greatly reducing the weights of the heat-transfer and friction, the M3 Cycle has significant advantage in the energy efficiency. The results obtained can provide guidance for selecting the Cycle type and optimizing the performances of a real engine.

  • The effects of the engine design and operation parameters on the performance of an Atkinson engine considering heat-transfer, friction, combustion efficiency and variable specific-heat
    Energy Conversion and Management, 2017
    Co-Authors: Jinxing Zhao
    Abstract:

    Abstract Atkinson Cycle engines have become particularly popular because of high energy efficiency. A novel model considering heat-transfer, friction, and variable specific-heat has been established for an Atkinson Cycle engine based on the finite-time thermodynamics. Different from the ones in previous investigations, the heat-transfer and friction losses are computed considering the effects of the Cycle conditions, and the design and operation parameters. In this way, the study can have practical physical meanings and is closer to real conditions. The effects of mean piston speed, friction coefficient, cylinder bore, stroke length, stroke-to-bore ratio, equivalence ratio, and compression ratio on the energy losses and Cycle performance have been investigated. The results show that there are the optimum values of compression and equivalence ratios making the Cycle performance the best; the energy losses from friction, heat-transfer and exhaust process monotonously increase or decrease with respect to increasing the compression ratio. Increasing the friction loss, cylinder bore and stroke length has negative effects on the Cycle performance. Increasing the mean piston speed has positive effect on the power output and the power density but less effect on the energy efficiency. The study results could provide significant guidance for designing a real Atkinson Cycle engine and optimizing the performance.

  • model based calibration for the control variables of an Atkinson Cycle engine
    International Journal of Powertrains, 2013
    Co-Authors: Jinxing Zhao
    Abstract:

    An Atkinson Cycle engine has been designed for use in hybrid vehicles. The Atkinson Cycle engine is generally operated at part load operating conditions. A novel load control strategy that combines the intake valve operation and electrically throttling control has been investigated for the purpose of improving the fuel economy at part loads. Other control variables such as spark angle also significantly impact the fuel economy. These control variables highly correlate with each other, if accurate calibrations of these control variables are conducted only through practical experiments, the costs will largely increase. This paper proposes a physical model and genetic algorithm-based automatic calibration methodology. The physical model was accurately calibrated at a series of speed-load points to match experimental results. Then the fuel economy was further optimised based on the physical model. After the optimisation, the experimental fuel economy is obviously improved with the maximum as 7.67%.

  • Fuel economy optimization of an Atkinson Cycle engine using genetic algorithm
    Applied Energy, 2013
    Co-Authors: Jinxing Zhao
    Abstract:

    An Atkinson Cycle engine with geometrical compression ratio (GCR) of 12.5 has been designed by maximizing fuel economy at full load operating conditions based on the Artificial Neural Network Method [1]. However, the Atkinson Cycle engine generally operates at part load conditions especially in the middle to high load range. Optimization of the fuel economy for part load is more important in reducing the total fuel consumption. The Atkinson Cycle engine applies the load control strategy that combines the intake valve closure (IVC) timing and electrically throttling control (ETC), which has an impact to the fuel economy. Moreover, the exhaust valve opening (EVO) timing, spark angle (SA) and air–fuel-ratio (AFR) also affect the fuel economy. If calibrating these operating variables over the entire operating range through experiments, the difficulty and cost will become a big issue. A physical model based optimization scheme by coupling MATLAB genetic algorithm (GA) and 1-D GT-Power simulation models of the Atkinson Cycle engine are proposed. The GT-Power models were improved to accurately simulate the part load conditions, by calibrating parameters of the combustion and heat transfer sub-models using experimental data taken at various speed–load points covering the entire operating range. The fuel economy was optimized based on the part-load calibrated GT-Power models using the Genetic Algorithm. After each speed–load point was optimized, the control maps for the IVC timings, SA, etc. were obtained. Then these numerically optimized control maps were input into the engine control unit (ECU) as the initial values of the engine calibration, which were further experimentally optimized. The experimental results show that the part-load GT-Power models have sufficient prediction accuracy, with maximal error of 8.5%. After optimized by GA, the fuel economy was greatly improved over the operating range, with the maximal improvement up to 7.67%.

Fengrui Sun - One of the best experts on this subject based on the ideXlab platform.

  • Finite time thermodynamic modeling and analysis for an irreversible Atkinson Cycle
    Thermal Science, 2010
    Co-Authors: Lingen Chen, Fengrui Sun
    Abstract:

    Performance of an air-standard Atkinson Cycle is analyzed by using finite-time thermodynamics. The irreversible Cycle model which is more close to practice is founded. In this model, the nonlinear relation between the specific heats of working fluid and its temperature, the friction loss computed according to the mean velocity of the piston, the internal irreversibility described by using the compression and expansion efficiencies, and heat transfer loss are considered. The relations between the power output and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between power output and the efficiency of the Cycle are derived by detailed numerical examples. Moreover, the effects of internal irreversibility, heat transfer loss and friction loss on the Cycle performance are analyzed. The results obtained in this paper may provide guidelines for the design of practical internal combustion engines.

  • Performance of endoreversible Atkinson Cycle
    Journal of the Energy Institute, 2007
    Co-Authors: Lingen Chen, Fengrui Sun
    Abstract:

    AbstractThe performance of an air standard Atkinson Cycle with heat transfer loss and variable specific heats of working fluid is analysed by using finite time thermodynamics. The relationships between the work output and the compression ratio and between the thermal efficiency and the compression ratio, as well as the optimal relationship between the work output and the efficiency of the Cycle, are derived from detailed numerical examples. Moreover, the effects of heat transfer loss and variable specific heats of working fluid on the Cycle performance are analysed. The results show that these effects are obvious and they should be considered in practice Cycle analysis. The results obtained in the present paper may provide guidance for the design of practical internal combustion engines.

  • performance of an Atkinson Cycle with heat transfer friction and variable specific heats of the working fluid
    Applied Energy, 2006
    Co-Authors: Lingen Chen, Fengrui Sun
    Abstract:

    The performance of an air standard Atkinson Cycle with heat-transfer loss, friction-like term loss and variable specific-heats of the working fluid is analyzed using finite-time thermodynamics. The relations between the power output and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between the power output and the efficiency of the Cycle are derived by detailed numerical examples. Moreover, the effects of variable specific-heats of the working fluid and the friction-like term loss on the irreversible Cycle performance are analyzed. The results show that the effects of variable specific-heats of working fluid and friction-like term loss on the irreversible Cycle performance should be considered in Cycle analysis. The results obtained in this paper provide guidance for the design of Atkinson engines.

Shuhn Shyurng Hou - One of the best experts on this subject based on the ideXlab platform.

  • Comparison of performances of air standard Atkinson and Otto Cycles with heat transfer considerations
    Energy Conversion and Management, 2007
    Co-Authors: Shuhn Shyurng Hou
    Abstract:

    In this paper, the effects of heat transfer on the net output work and the indicated thermal efficiency of an air standard Atkinson Cycle are analyzed. Comparisons of the performances of air standard Atkinson and Otto Cycles with heat transfer considerations are also discussed. We assume that the compression and power processes are adiabatic and reversible and that any convective, conductive or radiative heat transfer to the cylinder wall during the heat rejection process may be ignored. The heat loss through the cylinder wall is assumed to occur only during combustion and is further assumed to be proportional to the average temperature of both the working fluid and cylinder wall. It is found that the net output work versus efficiency characteristics, the maximum net work output and the corresponding efficiency bound are significantly influenced by the magnitude of the heat transfer. An increase in heat transfer to the combustion chamber walls decreases the peak temperature and pressure and, consequently, reduces the work per Cycle and efficiency. The effects of other parameters, in conjunction with heat transfer, including combustion constants, compression ratio and intake air temperature are also reported. An Atkinson Cycle has a greater work output and a higher thermal efficiency than the Otto Cycle at the same operating condition. The compression ratios that maximize the work of the Otto Cycle are always found to be higher than those for the Atkinson Cycle at the same operating conditions. The results are of importance to provide good guidance for performance evaluation and improvement of practical Atkinson engines.

  • Influence of heat loss on the performance of an air-standard Atkinson Cycle
    Applied Energy, 2007
    Co-Authors: Jiann-chang Lin, Shuhn Shyurng Hou
    Abstract:

    Abstract This study is aimed at investigating the effects of heat loss, as characterized by a percentage of fuel’s energy, friction and variable specific heats of the working fluid, on the performance of an air-standard Atkinson Cycle under the restriction of the maximum Cycle-temperature. A more realistic and precise relationship between the fuel’s chemical-energy and the heat leakage is derived through the resulting temperature. The variations in power output and thermal efficiency with compression ratio, and the relations between the power output and the thermal efficiency of the Cycle are presented. The results show that the power output as well as the efficiency, for which the maximum power-output occurs, will rise with the increase of maximum Cycle-temperature. The temperature-dependent specific heats of the working fluid have a significant influence on the performance. The power output and the working range of the Cycle increase while the efficiency decreases with the rise of specific heats of working fluid. The friction loss has a negative effect on the performance. Therefore, the power output and efficiency of the Atkinson Cycle decrease with increasing friction loss. It is noteworthy that the results obtained in the present study are of significance for providing guidance with respect to the performance evaluation and improvement of practical Atkinson-Cycle engines.

  • Performance analysis and comparison of an Atkinson Cycle coupled to variable temperature heat reservoirs under maximum power and maximum power density conditions
    Energy Conversion and Management, 2005
    Co-Authors: Pai-yi Wang, Shuhn Shyurng Hou
    Abstract:

    In this paper, performance analysis and comparison based on the maximum power and maximum power density conditions have been conducted for an Atkinson Cycle coupled to variable temperature heat reservoirs. The Atkinson Cycle is internally reversible but externally irreversible, since there is external irreversibility of heat transfer during the processes of constant volume heat addition and constant pressure heat rejection. This study is based purely on classical thermodynamic analysis methodology. It should be especially emphasized that all the results and conclusions are based on classical thermodynamics. The power density, defined as the ratio of power output to maximum specific volume in the Cycle, is taken as the optimization objective because it considers the effects of engine size as related to investment cost. The results show that an engine design based on maximum power density with constant effectiveness of the hot and cold side heat exchangers or constant inlet temperature ratio of the heat reservoirs will have smaller size but higher efficiency, compression ratio, expansion ratio and maximum temperature than one based on maximum power. From the view points of engine size and thermal efficiency, an engine design based on maximum power density is better than one based on maximum power conditions. However, due to the higher compression ratio and maximum temperature in the Cycle, an engine design based on maximum power density conditions requires tougher materials for engine construction than one based on maximum power conditions.