# Progress in Finite Time Thermodynamic Studies for Internal Combustion Engine Cycles

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Historical Background of FTT

## 3. Progress in FTT Studies for ICE Cycles

#### 3.1. The Progress in Optimum Performance Studies for AS ICE Cycles

#### 3.1.1. The Study Features

- (1)
- The influences of optimization objectives (OPBs) on cycle optimum performance.

- (2)
- The influences of specific heat (SH) models of WF on cycle optimum performance.

_{p}, b

_{v}and K are constants, C

_{p}and C

_{v}are SH of isobaric process and isochoric process, respectively. According to the relation of C

_{p}and C

_{v}, one has:

_{0}, u, u

_{1}, u

_{2}, u

_{3}are constants.

- (3)
- The influences of loss models on cycle optimum performance.

_{v1}and process 4 → 1 is constant volume heat rejection process with C

_{v2}(where C

_{v1}and C

_{v2}are SH at constant volume and C

_{v1}is smaller than C

_{v2}). The IIL of cycle is defined as:

- (4)
- The influences of WF characteristics on the cycle optimum performance.

- (5)
- The optimum performances of universal cycle.

#### 3.1.2. The Progress in Optimum Performance Studies for AS Otto Cycles

#### The Optimum Performance with Constant Specific Heats (CSH) of WF

#### The Optimum Performance with VSH of WF

#### The Optimum Performance with Variable Specific Heat Ratio (VSHR) of WF

#### 3.1.3. The Progress in Optimum Performance Studies for AS Diesel Cycle

#### The Optimum Performance with CSH of WF

#### The Optimum Performance with VSH of WF

#### The Optimum Performance with VSHR of WF

#### 3.1.4. The Progress in Optimum Performance Studies for AS Atkinson Cycles

#### The Optimum Performance with CSH of WF

#### The Optimum Performance with VSH of WF

#### The Optimum Performance with VSHR of WF

#### 3.1.5. The Progress in Optimum Performance Studies for AS Brayton Cycles

#### The Optimum Performance with CSH of WF

#### The Optimum Performance with VSH of WF

#### The Optimum Performance with VSHR of WF

#### 3.1.6. The Progress in Optimum Performance Studies for AS Dual Cycles

#### The Optimum Performance with CSH of WF

#### The Optimum Performance with VSH of WF

#### The Optimum Performance with VSHR of WF

#### 3.1.7. The Progress in Optimum Performance Studies for AS Miller Cycles

#### The Optimum Performance with CSH of WF

#### The Optimum Performance with VSH of WF

#### The Optimum Performance with VSHR of WF

#### 3.1.8. The Progress in Optimum Performance Studies for AS Porous Medium (PM) Cycles

#### The Optimum Performance with CSH of WF

#### The Optimum Performance with VSH of WF

#### The Optimum Performance with VSHR of WF

#### 3.1.9. The Progress in Optimum Performance Studies for AS Universal Cycles

#### The Optimum Performance with CSH of WF

#### The Optimum Performance with VSH of WF

_{in}is the heat rate of addition; Q

_{out}is the heat rate of rejection; Q

_{leak}is the heat leakage; P

_{μ}is the lost power due to friction; e

_{in1}, e

_{in2}, e

_{out1}and e

_{out2}are constants which equal to 1.3303 or 1.0433; M is the mass flow rate; L is the stoke length; n is the cycles running per second.

_{br}> E

_{at}> E

_{di}> E

_{pm}> E

_{du}> E

_{mi}> E

_{ot}, the order of the MP is P

_{br}> P

_{di}> P

_{du}> P

_{at}> P

_{pm}> P

_{mi}> P

_{ot}and the order of the ME is η

_{br}> η

_{pm}> η

_{at}> η

_{di}> η

_{mi}> η

_{du}> η

_{ot}.

#### The Optimum Performance with VSHR of WF

#### 3.2. The Progress in Studies of the Optimum Piston Motion Configuration for ICE Cycles

#### 3.2.1. The Optimum Path with Newton’s Heat Transfer Law (HTA) (q ≈ Δ(T))

#### 3.2.2. The Influence of HTA on the Optimum Cycle Path

^{4})), Burzler and Hoffman [274,275] derived the OPM in compression and power strokes of a four stroke Diesel engine with MP as the OPB when the WF was non-ideal. Fixing total cycle time and fuel consumed per cycle, Xia et al. [276] investigated the OPM trajectory of an Otto cycle engine for MW when HTA between WF and the environment obeys a linear phenomenological HTA (q ≈ Δ(T

^{−1})), and found that work output and efficiency could improve by more than 9% after optimizing the piston motion. Xia et al. [277] and Chen et al. [278] applied the finite combustion rate model in [259], derived the OPM trajectories of irreversible Diesel cycle engine for MW when HTA between WF and the environment obeys a linear phenomenological HTA [277] and generalized radiative HTA [278], respectively, and examined the influence of HTA on the OPM trajectories.

^{n})) [282], Dulong–Petit HTA (q ∝ Δ(T)

^{5/4}) [283] and convective-radiative HTA [284], obtained the first-order approximate analytical solutions for the Euler–Lagrange arcs. Using elimination means, Ma et al. [285,286] investigated the optimum configuration of the expansion process with generalized radiative HTA. Using the results obtained in [285,286], Ma et al. [285,287] optimized the configuration of ECE with radiative HTA (q ≈ Δ(T

^{4})) [285,287], generalized radiative HTA [285] and convective-radiative HTA [285], respectively. Considering the influences of piston motion on heat conductance, [285,288] advanced a model which was closer to realitywith the generalized radiative HTA and time-dependent heat conductance, and investigated the optimum configuration of expansion process for MW.

_{w}is the environment temperature; sign is the sign function; v is the speed; and λ is the Lagrange multiplier.

#### 3.3. The Progress in Performance Limit Studies for ICE Cycles

#### 3.3.1. The Performance Limit with Newton’s HTA (q ≈ Δ(T))

#### 3.3.2. The Influence of HTA on the Cycle Performance Limit

_{Δh}is the difference between the enthalpy flow rate of inlet and outlet of cylinder; J

_{Δs}is the difference between the entropy flow rate of inlet and outlet of cylinder; h specific enthalpy; and γ is the custom constant.

#### 3.4. The Progress in Simulation Studies for ICE Cycles

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

a | acceleration |

B | constant related to heat transfer |

b | cylinder bore (m) |

C | specific heat |

E | ecological function |

h | specific enthalpy |

J_{Δh} | the difference between the enthalpy flow rate of inlet and outlet of cylinder |

J_{Δs} | the difference between the entropy flow rate of inlet and outlet of cylinder |

K | heat transfer coefficient; coefficient of specific heats varied with temperature |

k | adiabatic exponent |

L | stroke length |

l | connecting rod length |

m | mass flow rate |

N | number of moles of working fluid |

n | cycles running per second |

P | power output |

Q | Heat rate of addition or rejection by the working fluid |

R | gas constant |

r | crank length |

S | specific entropy |

sign | sign function |

T | temperature |

t | time |

u | coefficient of specific heat ratio varied with temperature |

V | volume |

v | speed |

X | displacement |

Greek symbol | |

γ | compression ratio; custom constant |

η_{C} | Carnot efficiency |

η_{CA} | CA efficiency |

η_{c} | compression efficiency |

η_{e} | expansion efficiency |

θ | crankshaft rotation angle |

λ | Lagrange multiplier |

μ | friction coefficient |

σ | entropy generation rate |

τ | cycle period |

subscript | |

at | Atkinson cycle |

br | Brayton cycle |

di | Diesel cycle |

du | Dual cycle |

in | head addition |

mi | Miller cycle |

ot | Otto cycle |

out | heat rejection; outlet |

p | constant pressure process |

pm | PM cycle |

un | universal cycle |

v | constant volume process |

0 | environment |

1-6, 2S, 4S, 5S | state points |

## Abbreviations

AS: | air standard |

CR: | compression ratio |

CSH: | constant specific heats |

ECOP: | ecological coefficient of performance |

EF: | ecological function |

FL: | friction loss |

FTT: | finite time thermodynamics |

HTA: | Heat transfer law |

HTL: | heat transfer loss |

IIL: | internal irreversibility loss |

ME: | maximum efficiency |

MEF: | maximum ecological function |

MEG: | minimum entropy generation |

MEP: | maximum efficient power |

MP: | maximum power output |

MPD: | maximum power density |

MW: | maximum work output |

OCT: | optimal control theory |

OPB: | optimization objective |

OPM: | optimization piston motion |

SH: | specific heats |

SHR: | specific heat ratio |

VSH: | variable specific heats |

VSHR: | variable specific heat ratio |

WF: | working fluid |

## References

- Kanoglu, M.; Kazim, S.I.; Abusoglu, A. Performance characteristics of a Diesel engine power plant. Energy Convers. Manag.
**2005**, 46, 1692–1702. [Google Scholar] [CrossRef] - Qiao, A.P.; Li, Y.Q.; Gao, F. Improving the theoretical cycles of four-stroke ICE and their simulation calculations. Proc. IMechE Part D
**2006**, 220, 219–227. [Google Scholar] [CrossRef] - Ramesh, C.V. Valved heat engine working on modified Atkinson cycle. J. Energy Resour. Technol.
**2010**, 132, 015001. [Google Scholar] [CrossRef] - Nakonieczny, K. Entropy generation in a diesel engine turbocharging system. Energy
**2002**, 27, 1027–1056. [Google Scholar] [CrossRef] - Yoshida, S. Exergy analysis of a diesel engine cycle and its performance improvement. Int. J. Exergy
**2005**, 2, 284–298. [Google Scholar] [CrossRef] - Rakopoulos, C.D.; Giakoumis, E.G. The influence of cylinder wall temperature profile on the second-law diesel engine transient response. Appl. Therm. Eng.
**2005**, 25, 1779–1795. [Google Scholar] [CrossRef] - Ribeiro, B.; Martins, J.; Nunes, A. Generation of entropy in spark ignition engines. Int. J. Thermodyn.
**2007**, 10, 53–60. [Google Scholar] - Caton, J.A. Comparisons of instructional and complete version of thermodynamic engine cycle simulations for spark-ignition engines. Int. J. Mech. Eng. Educ.
**2001**, 29, 283–306. [Google Scholar] [CrossRef] - Caton, J.A. Illustration of the use of an instructional version of a thermodynamic cycle simulation for a commercial automotive spark-ignition engine. Int. J. Mech. Eng. Educ.
**2002**, 30, 283–297. [Google Scholar] [CrossRef] - Curzon, F.L.; Ahlborn, B. Efficiency of a Carnot engine at maximum power output. Am. J. Phys.
**1975**, 43, 22–24. [Google Scholar] [CrossRef] - Andresen, B. Finite-Time Thermodynamics; University of Copenhagen: Copenhagen, Denmark, 1983. [Google Scholar]
- Andresen, B.; Salamon, P.; Berry, R.S. Thermodynamics in finite time. Phys. Today
**1984**, 37, 62–70. [Google Scholar] [CrossRef] - Sieniutycz, S.; Salamon, P. Finite-Time Thermodynamics and Thermoeconomics; Taylor & Francis: New York, NY, USA, 1990. [Google Scholar]
- Chen, L.G.; Sun, F.R.; Chen, W.Z. The present state and trend of finite time thermodynamics. Adv. Mech.
**1992**, 22, 479–488. (In Chinese) [Google Scholar] - Sieniutycz, S.; Shiner, J.S. Thermodynamics of irreversible processes and its relation to chemical engineering: Second law analyses and finite time thermodynamics. J. Non-Equilib. Thermodyn.
**1994**, 19, 303–348. [Google Scholar] - Bejan, A. Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes. J. Appl. Phys.
**1996**, 79, 1191–1218. [Google Scholar] [CrossRef] - Hoffmann, K.H.; Burzler, J.M.; Schubert, S. Endoreversible thermodynamics. J. Non-Equilib. Thermodyn.
**1997**, 22, 311–355. [Google Scholar] - Berry, R.S.; Kazakov, V.A.; Sieniutycz, S.; Szwast, Z.; Tsirlin, A.M. Thermodynamic Optimization of Finite Time Processes; Wiley: Chichester, UK, 1999. [Google Scholar]
- Wu, C.; Chen, L.G.; Chen, J.C. Recent Advances in Finite Time Thermodynamics; Nova Science Publishers: New York, NY, USA, 1999. [Google Scholar]
- Chen, L.G.; Wu, C.; Sun, F.R. Finite time thermodynamic optimization or entropy generation minimization of energy systems. J. Non-Equilib. Thermodyn.
**1999**, 24, 327–359. [Google Scholar] [CrossRef] - Sieniutycz, S. Hamilton–Jacobi–Bellman framework for optimal control in multistage energy systems. Phys. Rep.
**2000**, 326, 165–285. [Google Scholar] [CrossRef] - Salamon, P.; Nulton, J.D.; Siragusa, G.; Andresen, T.R.; Limon, A. Principles of control thermodynamics. Energy
**2001**, 26, 307–319. [Google Scholar] [CrossRef] - Chen, L.G.; Wu, C.; Sun, F.R. The recent advances in finite time thermodynamics and its future application. Int. J. Energy Environ. Econ.
**2001**, 11, 69–81. [Google Scholar] - Hoffmann, K.H. Recent developments in finite time thermodynamics. Technol. Mech.
**2002**, 22, 14–25. [Google Scholar] - Hoffman, K.H.; Burzler, J.; Fischer, A.; Schaller, M.; Schubert, S. Optimal process paths for endoreversible systems. J. Non-Equilib. Thermodyn.
**2003**, 28, 233–268. [Google Scholar] [CrossRef] - Sieniutycz, S. Thermodynamic limits on production or consumption of mechanical energy in practical and industry systems. Prog. Energy Combust. Sci.
**2003**, 29, 193–246. [Google Scholar] [CrossRef] - Durmayaz, A.; Sogut, O.S.; Sahin, B.; Yavuz, H. Optimization of thermal systems based on finite-time thermodynamics and thermoeconomics. Prog. Energy Combust. Sci.
**2004**, 30, 175–217. [Google Scholar] [CrossRef] - Chen, L.G.; Sun, F.R. Advances in Finite Time Thermodynamics: Analysis and Optimization; Nova Science Publishers: New York, NY, USA, 2004. [Google Scholar]
- Chen, L.G. Finite-Time Thermodynamic Analysis of Irreversible Processes and Cycles; Higher Education Press: Beijing, China, 2005. (In Chinese) [Google Scholar]
- Muschik, W.; Hoffmann, K.H. Endoreversible thermodynamics: A tool for simulating and comparing processes of discrete systems. J. Non-Equilib. Thermodyn.
**2006**, 31, 293–317. [Google Scholar] [CrossRef] - Wu, F.; Chen, L.G.; Sun, F.R.; Yu, J.Y. Finite Time Thermodynamic Optimization for Stirling Machines; Chemical Industry Press: Beijing, China, 2008. (In Chinese) [Google Scholar]
- Sieniutycz, S.; Jezowski, J. Energy Optimization in Process Systems; Elsevier: Oxford, UK, 2009. [Google Scholar]
- Feidt, M. Optimum thermodynamics-New upperbounds. Entropy
**2009**, 11, 529–547. [Google Scholar] [CrossRef] - Andresen, B. Current trends in finite-time thermodynamics. Angew. Chem. Int. Edit.
**2011**, 50, 2690–2704. [Google Scholar] [CrossRef] [PubMed] - Zhang, W.L.; Chen, L.G.; Han, W.W.; Wu, Z.W. Advances in finite time thermodynamic studies for analyses and optimizations of direct/inverse Brayton cycles. Gas Turbine Technol.
**2012**, 25, 1–11. (In Chinese) [Google Scholar] - Wang, W.H.; Chen, L.G.; Ge, Y.L.; Sun, F.R. New advances in finite time thermodynamic studies for gas turbine cycles. Therm. Turbine
**2012**, 41, 171–178. [Google Scholar] - Chen, L.G. Progress in entransy theory and its applications. Chin. Sci. Bull.
**2012**, 57, 4404–4426. [Google Scholar] [CrossRef] - Tlili, I. Finite time thermodynamic evaluation of endoreversible Stirling heat engine at maximum power conditions. Renew. Sustain. Energy Rev.
**2012**, 16, 2234–2241. [Google Scholar] [CrossRef] - Tlili, I. Thermodynamic study on optimal solar Stirling engine cycle taking into account the irreversibilities effects. Energy Procedia
**2012**, 14, 584–591. [Google Scholar] [CrossRef] - Tlili, I. A Numerical investigation of an Alpha Stirling engine using the Ross Yoke linkage. Heat Technol.
**2012**, 30, 23–36. [Google Scholar] - Tlili, I.; Musmar, S.A. Thermodynamic evaluation of a second order simulation for Ross Stirling engine. Energy Convers. Manag.
**2013**, 68, 149–160. [Google Scholar] [CrossRef] - Qin, X.Y.; Chen, L.G.; Ge, Y.L.; Sun, F.R. Finite time thermodynamic studies on absorption thermodynamic cycles: A state of the arts review. Arab. J. Sci. Eng.
**2013**, 38, 405–419. [Google Scholar] [CrossRef] - Ngouateu, W.P.A.; Tchinda, R. Finite-time thermodynamics optimization of absorption refrigeration systems: A review. Renew. Sustain. Energy Rev.
**2013**, 21, 524–536. [Google Scholar] [CrossRef] - Li, J.; Chen, L.G.; Ge, Y.L.; Sun, F.R. Progress in the study on finite time thermodynamic optimization for direct and reverse two-heat-reservoir thermodynamic cycles. Acta Phys. Sin.
**2013**, 62, 130501. (In Chinese) [Google Scholar] - Kosloff, R. Quantum thermodynamics: A dynamical viewpoit. Entropy
**2013**, 15, 2100–2128. [Google Scholar] [CrossRef] - Sieniutycz, S.; Jezowski, J. Energy Optimization in Process Systems and Fuel Cells; Elsevier: Oxford, UK, 2013. [Google Scholar]
- Sarkar, J. A review on thermodynamic optimization of irreversible refrigerator and verification with transcritical CO
_{2}system. Int. J. Thermodyn.**2014**, 17, 71–79. [Google Scholar] [CrossRef] - Medina, A.; Curto-Risso, P.L.; Calvo-Hernández, A.; Guzmán-Vargas, L.; Angulo-Brown, F.; Sen, A.K. Quasi-Dimensional Simulation of Spark Ignition Engines: From Thermodynamic Optimization to Cyclic Variability; Springer: London, UK, 2014. [Google Scholar]
- Chen, L.G. Progress in optimization of mass transfer processes based on mass entransy dissipation extremum principle. Sci. China Technol. Sci.
**2014**, 57, 2305–2327. [Google Scholar] [CrossRef] - Vaudrey, A.V.; Lanzetta, F.; Feidt, M.H.B. Reitlinger and the origins of the efficiency at maximum power formula for heat engines. J. Non-Equilib. Thermodyn.
**2014**, 39, 199–204. [Google Scholar] [CrossRef] - Hoffmann, K.H.; Andresen, B.; Salamon, P. Finite-Time Thermodynamics Tools to Analyze Dissipative Processes. In Proceedings of the 240 Conference: Science’s Great Challences; Dinner, A.R., Rice, S.A., Eds.; Wiley: Hoboken, NJ, USA, 2014; Volume 157, pp. 57–67. [Google Scholar]
- Ding, Z.M.; Chen, L.G.; Wang, W.H.; Sun, F.R. Progress in study on finite time thermodynamic performance optimization for three kinds of microscopic energy conversion systems. Sci. Sin. Technol.
**2015**, 45, 889–918. [Google Scholar] - Ahmadi, M.H.; Ahmadi, M.A.; Sadatsakkak, S.A. Thermodynamic analysis and performance optimization of irreversible Carnot refrigerator by using multi-objective evolutionary algorithms (MOEAs). Renew. Sustain. Energy Rev.
**2015**, 51, 1055–1070. [Google Scholar] [CrossRef] - Chen, L.G.; Xia, S.J. Generalized Thermodynamic Dynamic-Optimization for Irreversible Processes; Science Press: Beijing, China, 2016. (In Chinese) [Google Scholar]
- Chen, L.G.; Xia, S.J.; Li, J. Generalized Thermodynamic Dynamic-Optimization for Irreversible Cycles; Science Press: Beijing, China, 2016. (In Chinese) [Google Scholar]
- Chen, L.G.; Meng, F.K.; Sun, F.R. Thermodynamic analyses and optimizations for thermoelectric devices, the state of the arts. Sci. China Technol. Sci.
**2016**, 59, 442–455. [Google Scholar] [CrossRef] - Yan, Z. The relation between optimum efficiency and power output of a Cannot engine. Chin. J. Eng. Thermophys.
**1985**, 6, 1–6. (In Chinese) [Google Scholar] - Ma, K.; Chen, L.G.; Sun, F.R. Profit performance optimization for a generalized irreversible combined Carnot refrigeration cycle. Sadhana Acad. Proc. Eng. Sci.
**2009**, 34, 851–864. [Google Scholar] - Rubin, M.H. Optimum configuration of a class of irreversible heat engines. Phys. Rev. A
**1979**, 19, 1272–1287. [Google Scholar] [CrossRef] - Badescu, V. Optimum strategies for steady state heat exchanger operation. J. Phys. D
**2004**, 37, 2298–2304. [Google Scholar] [CrossRef] - Salamon, P.; Nitzon, A. Finite time optimization of a Newton’s law Carnot cycle. J. Chem. Phys.
**1981**, 74, 3546–3560. [Google Scholar] [CrossRef] - Li, J.; Chen, L.G.; Sun, F.R. Heating load vs. COP characteristic of an endoreversible Carnot heat pump subjected to heat transfer law q ∝ (ΔT
^{n})^{m}. Appl. Energy**2008**, 85, 96–100. [Google Scholar] [CrossRef] - Rubin, M.H. Optimum configuration of an irreversible heat engine with fixed compression ratio. Phys. Rev. A
**1980**, 22, 1741–1752. [Google Scholar] [CrossRef] - Xia, S.J.; Chen, L.G.; Sun, F.R. Optimization for minimizing entropy generation during heat transfer processes with heat transfer law q ∝ (ΔT
^{n})^{m}. J. Therm. Sci. Technol.**2008**, 7, 226–230. (In Chinese) [Google Scholar] - Chen, W.Z.; Sun, F.R.; Chen, L.G. Finite time thermodynamic criteria for parameter choice of heat engine operating between heat reservoirs. Chin. Sci. Bull.
**1991**, 36, 763–768. (In Chinese) [Google Scholar] - Wu, C.; Chen, L.G.; Sun, F.R. Optimization of steady flow refrigeration cycles. Int. J. Ambient Energy
**1996**, 17, 199–206. [Google Scholar] [CrossRef] - Ondrechen, M.J.; Rubin, M.H.; Band, Y.B. The generalized Carnot cycles: A working fluid operating in finite-time between finite heat sources and sinks. J. Chem. Phys.
**1983**, 78, 4721–4727. [Google Scholar] [CrossRef] - Chen, L.G.; Zhou, S.B.; Sun, F.R.; Wu, C. Optimum configuration and performance of heat engines with heat leak and finite heat capacity. Open Sys. Inf. Dyn.
**2002**, 9, 85–96. [Google Scholar] [CrossRef] - Chen, L.G.; Sun, F.R.; Wu, C.; Ni, N. A generalized model of a real combined power plant and its performance. Int. J. Energy Environ. Econ.
**1999**, 9, 35–49. [Google Scholar] - Kan, X.X.; Wu, F.; Chen, L.G.; Sun, F.R.; Guo, F.Z. Exergy efficiency optimization of a thermoacoustic engine with a complex heat transfer exponent. Int. J. Sustain. Energy
**2010**, 29, 220–232. [Google Scholar] [CrossRef] - Meng, F.K.; Chen, L.G.; Sun, F.R. Extreme working temperature differences for thermoelectric refrigerating and heat pumping devices driven by thermoelectric generator. J. Energy Inst.
**2010**, 83, 108–113. [Google Scholar] [CrossRef] - Chen, L.G.; Ding, Z.M.; Sun, F.R. Performance analysis of a vacuum thermionic refrigerator with external heat transfer. J. Appl. Phys.
**2010**, 107, 104507. [Google Scholar] [CrossRef] - Ma, K.; Chen, L.G.; Sun, F.R. Optimum paths for a light-driven engine with linear phenomenological heat transfer law. Sci. China Chem.
**2010**, 53, 917–926. [Google Scholar] [CrossRef] - Klein, S.A. An explanation for observed compression ratios in international combustion engines. J. Eng. Gas Turbine Power
**1991**, 113, 511–513. [Google Scholar] [CrossRef] - Angulo-Brown, F.; Rocha-Martinez, J.A.; Navarrete-Gonzalez, T.D. A non-endoreversible Otto cycle model: Improving power output and efficiency. J. Phys. D
**1996**, 29, 80–83. [Google Scholar] [CrossRef] - Chen, L.G.; Ge, Y.L.; Sun, F.R. Unified thermodynamic description and optimization for a class of irreversible reciprocating heat engine cycles. Proc. IMechE Part D
**2008**, 222, 1489–1500. [Google Scholar] [CrossRef] - Chen, L.G.; Lin, J.X.; Sun, F.R.; Wu, C. Efficiency of an Atkinson engine at maximum power density. Energy Convers. Manag.
**1998**, 39, 337–341. [Google Scholar] [CrossRef] - Gumus, M.; Atmaca, M.; Yilmaz, T. Efficiency of an Otto engine under alternative power optimizations. Int. J. Energy Res.
**2009**, 39, 745–752. [Google Scholar] [CrossRef] - Angulo-Brown, F.; Fernandez-Betanzos, J.; Diaz-Pico, C.A. Compression ratio of an optimized Otto-cycle model. Eur. J. Phys.
**1994**, 15, 38–42. [Google Scholar] [CrossRef] - Ust, Y. Ecological performance analysis of irreversible Otto cycle. J. Eng. Nat. Sci.
**2005**, 3, 106–117. [Google Scholar] - Mehta, H.B.; Bharti, O.S. Performance analysis of an irreversible Otto cycle using Finite Time Termodynamics. In Proceedings of the World Congress on Engineering, London, UK, 1–3 July 2009.
- Lin, J.C. Ecological optimization for an Atkinson engine. JP J. Heat Mass Transf.
**2010**, 4, 95–112. [Google Scholar] - Ust, Y.; Sahin, B.; Sogut, O.S. Performance analysis and optimization of an irreversible dual-cycle based on an ecological coefficient of performance criterion. Appl. Energy
**2005**, 82, 23–39. [Google Scholar] [CrossRef] - Ge, Y.L. Finite Time Thermodynamic Analysis and Optimization for Irreversible ICE Cycles. Ph.D. Thesis, Naval University of Engineering, Wuhan, China, 2011. [Google Scholar]
- Gonca, G.; Sahin, B. Performance optimization of an air-standard irreversible Dual–Atkinson cycle engine based on the ecological coefficient of performance criterion. Sci. World J.
**2014**, 2014, 815787. [Google Scholar] [CrossRef] [PubMed] - Rocha-Martinez, J.A.; Navarrete-Gonzalez, T.D.; Pava-Miller, C.G.; Ramirez-Rojas, A.; Angulo-Brown, F. Otto and Diesel engine models with cyclic variability. Revista Mexicana de Física
**2002**, 48, 228–234. [Google Scholar] - Rocha-Martinez, J.A.; Navarrete-Gonzalez, T.D.; Pava-Miller, C.G.; Ramirez-Rojas, A.; Angulo-Brown, F. A simplified irreversible Otto engine model with fluctuations in the combustion heat. Int. J. Ambient Energy
**2006**, 27, 181–192. [Google Scholar] [CrossRef] - Ghatak, A.; Chakraborty, S. Effect of external irreversibilities and variable thermal properties of working fluid on thermal performance of a Dual ICE cycle. J. Mech. Energy
**2007**, 58, 1–12. [Google Scholar] - Abu-Nada, E.; Al-Hinti, I.; Al-Aarkhi, A.; Akash, B. Thermodynamic modeling of spark-ignition engine: Effect of temperature dependent specific heats. Int. Commun. Heat Mass Transf.
**2005**, 33, 1264–1272. [Google Scholar] [CrossRef] - Abu-Nada, E.; Al-Hinti, I.; Al-Aarkhi, A.; Akash, B. Thermodynamic analysis of spark-ignition engine using a gas mixture model for the working fluid. Int. J. Energy Res.
**2007**, 37, 1031–1046. [Google Scholar] [CrossRef] - Abu-Nada, E.; Al-Hinti, I.; Al-Aarkhi, A.; Akash, B. Effect of piston friction on the performance of SI engine: A new thermodynamic approach. ASME Trans. J. Eng. Gas Turbine Power
**2008**, 130, 022802. [Google Scholar] [CrossRef] - Abu-Nada, E.; Akash, B.; Al-Hinti, I.; Al-Sarkhi, A. Performance of spark-ignition engine under the effect of friction using gas mixture model. J. Energy Inst.
**2009**, 82, 197–205. [Google Scholar] [CrossRef] - Ebrahimi, R. Effects of variable specific heat ratio on performance of an endoreversible Otto cycle. Acta Phys. Pol. A
**2010**, 117, 887–891. [Google Scholar] [CrossRef] - Ebrahimi, R. Engine speed effects on the characteristic performance of Otto engines. J. Am. Sci.
**2009**, 5, 25–30. [Google Scholar] - Ebrahimi, R. Performance of an irreversible Diesel cycle under variable stroke length and compression ratio. J. Am. Sci.
**2009**, 5, 58–64. [Google Scholar] - Ge, Y.L. The Effects of the Variable Specific Heats of Working Fluid on the Performance of ICE Cycles. Master’s Thesis, Naval University of Engineering, Wuhan, China, 2005. [Google Scholar]
- Zhao, Y.; Lin, B.; Chen, J. Optimum criteria on the important parameters of an irreversible Otto heat engine with the temperature-dependent heat capacities of the working fluid. ASME Trans. J. Energy Res. Technol.
**2007**, 129, 348–354. [Google Scholar] [CrossRef] - Parlak, A. Comparative performance analysis of irreversible Dual and Diesel cycles under maximum power conditions. Energy Convers. Manag.
**2005**, 46, 351–359. [Google Scholar] [CrossRef] - Petrescu, S.; Harman, C.; Costea, M.; Petre, C.; Dobre, C. Irreversible finite speed thermodynamics (IFST) in simple closed systems. I. Fundamental concepts. Termotehnica
**2009**, 13, 8–18. [Google Scholar] - Zhao, Y.; Chen, J. Irreversible Otto heat engine with friction and heat leak losses and its parametric optimum criteria. J. Energy Inst.
**2008**, 81, 54–58. [Google Scholar] [CrossRef] - Zi, K.; Yang, X.; Jiang, P. Power and efficiency characteristics of engine with mechanical losses. J. Harbin Inst. Technol.
**2009**, 41, 209–212. (In Chinese) [Google Scholar] - Wu, F.; Chen, L.G.; Sun, F.R.; Wu, C. Quantum degeneracy effect on performance of irreversible Otto cycle with deal Bose gas. Energy Convers. Manag.
**2006**, 47, 3008–3018. [Google Scholar] [CrossRef] - Wang, H.; Liu, S.; He, J. Performance analysis and parametric optimum criteria of a quantum Otto heat engine with heat transfer effects. Appl. Therm. Eng.
**2009**, 29, 706–711. [Google Scholar] [CrossRef] - Wang, H.; Liu, S.; Du, J. Performance analysis and parametric optimum criteria of a regeneration Bose–Otto engine. Phys. Scr.
**2009**, 79, 055004. [Google Scholar] [CrossRef] - Qin, X.Y.; Chen, L.G.; Sun, F.R. The universal power and efficiency characteristics for irreversible reciprocating heat engine cycles. Eur. J. Phys.
**2003**, 24, 359–366. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Reciprocating heat-engine cycles. Appl. Energy
**2005**, 81, 180–186. [Google Scholar] - Rashidi, M.M.; Hajipour, A. Comparison of performance of air-standard Atkinson, Diesel and Otto cycles with constant specific heats. Int. J. Adv. Des. Manuf. Technol.
**2013**, 6, 57–62. [Google Scholar] - Wu, C.; Blank, D.A. The effect combustion on a work-optimized endoreversible Otto cycle. J. Energy Inst.
**1992**, 65, 86–89. [Google Scholar] - Blank, D.A.; Wu, C. Optimization of the endoreversible Otto cycle with respect to both power and mean effective pressure. Energy Convers. Manag.
**1993**, 34, 1255–1209. [Google Scholar] - Chen, L.G.; Wu, C.; Sun, F.R. Heat transfer effects on the net work output and efficiency characteristics for an air standard Otto cycle. Energy Convers. Manag.
**1998**, 39, 643–648. [Google Scholar] [CrossRef] - Ficher, A.; Hoffman, K.H. Can a quantitative simulation of an Otto engine be accurately rendered by a simple Novikov model with heat leak? J. Non-Equilib. Thermodyn.
**2004**, 29, 9–28. [Google Scholar] [CrossRef] - Novikov, I.I. The efficiency of atomic power stations (a review). Atommaya Energiya
**1957**, 3, 409–412. [Google Scholar] [CrossRef] - Ozsoysal, O.A. Heat loss as a percentage of fuel’s energy in air standard Otto and Diesel cycles. Energy Convers. Manag.
**2006**, 47, 1051–1062. [Google Scholar] [CrossRef] - Hou, S.S. Comparison of performances of air standard Atkinson and Otto cycles with heat transfer considerations. Energy Convers. Manag.
**2007**, 48, 1683–1690. [Google Scholar] [CrossRef] - Ozcan, H. The effects of heat transfer on the exergy efficiency of an air-standard otto cycle. Heat Mass Transf.
**2011**, 47, 571–577. [Google Scholar] [CrossRef] - Rashidi, M.M.; Hajipour, A.; Baziar, P. Influence of heat loss on the second-law efficiency of an Otto cycle. Int. J. Mechatron. Electr. Comput. Technol.
**2014**, 4, 922–933. [Google Scholar] - Chen, L.G.; Zheng, T.; Sun, F.R.; Wu, C. The power and efficiency characteristics for an irreversible Otto cycle. Int. J. Ambient Energy
**2003**, 24, 195–200. [Google Scholar] [CrossRef] - Lan, X.; Zi, K. Finite time thermodynamic theory and applications of ICE: State of the arts. J. Kunming Univ. Sci. Technol.
**2002**, 27, 89–94. (In Chinese) [Google Scholar] - Lan, X. The Thermodynamics Study on the Working Process of Diesel Engine. Master’s Thesis, Kunming University of Science and Technology, Kunming, China, 2002. [Google Scholar]
- Chen, J.; Zhao, Y.; He, J. Optimization criteria for the important parameters of an irreversible Otto heat-engine. Appl. Energy
**2006**, 83, 228–238. [Google Scholar] [CrossRef] - Ebrahimi, R. Theoretical study of combustion efficiency in an Otto engine. J. Am. Sci.
**2010**, 6, 113–116. [Google Scholar] - Ozsoysal, O.A. Effects of combustion efficiency on an Otto cycle. Int. J. Exergy
**2010**, 7, 232–242. [Google Scholar] [CrossRef] - Ebrahimi, R. Effects of gasoline-air equivalence ratio on performance of an Otto engine. J. Am. Sci.
**2010**, 6, 131–135. [Google Scholar] - Ebrahimi, R.; Ghanbarian, D.; Tadayon, M.R. Performance of an Otto engine with volumetric efficiency. J. Am. Sci.
**2010**, 6, 27–31. [Google Scholar] - Huleihil, M. Effects of pressure drops on the performance characteristics of air standard Otto cycle. Phys. Res. Int.
**2011**, 2011, 496057. [Google Scholar] [CrossRef] - Hu, H.; Xu, H.; Liu, J.; Xie, W.; Wei, J.; Zhou, J.; Zhang, Y. Optimum analysis of the performance of an irreversible Otto cycle. J. Southwest Univ. Nat. Sci. Edit.
**2011**, 33, 57–60. (In Chinese) [Google Scholar] - Ust, Y.; Sahin, B.; Safa, A. The effects of cycle temperature and cycle pressure ratios on the performance of an irreversible Otto cycle. Acta Phys. Pol. A
**2011**, 120, 413–416. [Google Scholar] [CrossRef] - Ebrahimi, R. Performance analysis of an Otto engine with ethanol and gasoline fuels. Appl. Mech. Mater.
**2012**, 110–116, 267–272. [Google Scholar] [CrossRef] - Huleihil, M.; Mazor, G. Irreversible performance characteristics of air standard Otto cycles with polytropic processes. J. Appl. Mech. Eng.
**2012**, 1, 1000111. [Google Scholar] [CrossRef] - Ladino-Luna, D.; Paez-Hernandez, R.T. Otto and Diesel Cycles Modeled by Considering Non-Instaneous Adiabats. In Proceedings of the 6th International Workshop on Nonequilibrium Thermodynamics (IWNET 2012), Røros, Norway, 19–24 August 2012.
- Joseph, A.; Thampi, G.K. Finite time thermodynamic analysis of an irreversible Otto cycle. J. Chem. Pharm. Sci.
**2015**, 6, 14–18. [Google Scholar] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Ecological optimization of an irreversible Otto cycle. Arab. J. Sci. Eng.
**2013**, 38, 373–381. [Google Scholar] [CrossRef] - Moscato, A.L.S.; del Rio Oliveira, S. Net power optimization of an irreversible Otto cycle using ECOP and ecological function. Int. Rev. Mech. Eng.
**2015**, 9, 10–20. [Google Scholar] [CrossRef] - Mao, Z.; He, J.; Zhou, F. Performance analysis of an irreversible quantum Otto power cycle. J. Nanchang Univ. Eng. Technol.
**2007**, 29, 126–130. (In Chinese) [Google Scholar] - Mao, Z. Optimum Analysis of Irreversible Quantum Thermodynamics. Master’s Thesis, Nanchang University, Nanchang, China, 2007. [Google Scholar]
- Nie, W.; Liao, Q.; Zhang, C.; He, J. Micro-/nanoscaled irreversible Otto engine cycle with friction loss and boundary effects and its performance characteristic. Energy
**2010**, 35, 4658–4662. [Google Scholar] [CrossRef] - Wu, F.; Chen, L.G.; Sun, F.R.; Wu, C. Ecological optimization performance of an irreversible quantum Otto cycle working with an ideal Fermi gas. Open Sys. Inf. Dyn.
**2006**, 13, 55–66. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Thermodynamic simulation of performance of an Otto cycle with heat transfer and variable specific heats of working fluid. Int. J. Therm. Sci.
**2005**, 44, 506–511. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. The effects of variable specific heats of working fluid on the performance of an irreversible Otto cycle. Int. J. Exergy
**2005**, 2, 274–283. [Google Scholar] [CrossRef] - Lin, J.C.; Hou, S.S. Effects of heat loss as percentage of fuel’s energy, friction and variable specific heats of working fluid on performance of air standard Otto cycle. Energy Convers. Manag.
**2008**, 49, 1218–1227. [Google Scholar] [CrossRef] - Nejad, R.M.; Marghmaleki, I.S.; Hoseini, R.; Alaei, P. Effects of irreversible different parameters on performance of air standard Otto cycle. J. Am. Sci.
**2011**, 7, 248–254. [Google Scholar] - Ebrahimi, R.; Tadayon, M.R.; Gandomkari, F.T.; Mahbobian, K. Effect of ethanol-air equivalence ratio on performance of an end reversible Otto engine. Appl. Mech. Mater.
**2012**, 110–116, 273–277. [Google Scholar] - Ge, Y.L.; Chen, L.G.; Sun, F.R. Ecological Optimization of an Irreversible Otto Cycle With Variable Specific Heats of Working Fluid. In Proceedings of the Chinese Society of Engineering Thermophysics on Engineering Thermophysics and Energy Utility, Wuhan, China, 5–7 November 2011. (In Chinese)
- Ge, Y.L.; Chen, L.G.; Sun, F.R. Finite time thermodynamic modeling and analysis for an irreversible Otto cycle. Appl. Energy
**2008**, 85, 618–624. [Google Scholar] [CrossRef] - Ebrahimi, R. Thermodynamic simulation of performance of an irreversible Otto cycle with engine speed and variable specific heat ratio of working fluid. Arab. J. Sci. Eng.
**2014**, 39, 2091–2096. [Google Scholar] [CrossRef] - Atmaca, M.; Gumus, M. Power and efficiency analysis of Diesel cycle under alternative criteria. Arab. J. Sci. Eng.
**2014**, 39, 2263–2270. [Google Scholar] [CrossRef] - Blank, D.A.; Wu, C. The effects of combustion on a power-optimized endoreversible Diesel cycle. Energy Convers. Manag.
**1993**, 34, 493–498. [Google Scholar] [CrossRef] - Chen, L.G.; Zen, F.M.; Sun, F.R.; Wu, C. Heat transfer effects on the net work output and power as function of efficiency for air standard Diesel cycle. Energy
**1996**, 21, 1201–1205. [Google Scholar] [CrossRef] - Parlak, A. The effect of heat transfer on performance of the Diesel cycle and exergy of the exhaust gas stream in a LHR Diesel engine at the optimum injection timing. Energy Convers. Manag.
**2005**, 46, 167–179. [Google Scholar] [CrossRef] - Parlak, A.; Yasar, H.; Eldogan, O. The effect of thermal barrier coating on a turbo-charged Diesel engine performance and exergy potential of the exhaust gas. Energy Convers. Manag.
**2005**, 46, 489–499. [Google Scholar] [CrossRef] - Al-Hinti, I.; Akash, B.; Abu-Nada, E.; Al-Sarkhi, A. Performance analysis of air-standard Diesel cycle using an alternative irreversible heat transfer approach. Energy Convers. Manag.
**2008**, 49, 3301–3304. [Google Scholar] [CrossRef] - Chen, L.G.; Lin, J.X.; Sun, F.R. Friction effects on power vs. efficiency characteristics for air-standard Diesel cycles. J. Eng. Thermophys.
**1997**, 18, 533–535. (In Chinese) [Google Scholar] - Chen, W.Z.; Sun, F.R. New solutions of power and efficiency for Diesel cycles with friction. J. Naval Univ. Eng.
**2001**, 13, 24–26. (In Chinese) [Google Scholar] - Zhao, Y.; Lin, B.; Zhang, Y.; Chen, J. Performance analysis and parametric optimum design of an irreversible Diesel heat engine. Energy Convers. Manag.
**2006**, 47, 3383–3392. [Google Scholar] [CrossRef] - Zheng, S.; Xia, Z.; Zhou, Y.; Lin, G. Optimization on the work output, wfficiency and other performance parameters of an irreversible Diesel heat engine. J. Xiamen Univ. Nat. Sci.
**2006**, 45, 182–185. (In Chinese) [Google Scholar] - Zheng, S. The effect of ratio of high temperature to low temperature on the performance of Diesel engine cycle. Energy Environ.
**2009**, 1, 18–19. (In Chinese) [Google Scholar] - Zheng, S.; Lin, G. Optimization of power and efficiency for an irreversible Diesel heat engine. Front. Energy Power Eng. China
**2010**, 4, 560–565. (In Chinese) [Google Scholar] [CrossRef] - Ebrahimi, R. Performance optimization of a Diesel cycle with specific heat ratio. J. Am. Sci.
**2009**, 5, 59–63. [Google Scholar] - Ozsoysal, O.A. Effects of varying air-fuel ratio on the performance of a theoretical Diesel cycle. Int. J. Exergy
**2010**, 7, 654–666. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Performance of an endoreversible Diesel cycle with variable specific heats of working fluid. Int. J. Ambient Energy
**2008**, 29, 127–136. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Performance of Diesel cycle with heat transfer, friction and variable specific heats of working fluid. J. Energy Inst.
**2007**, 80, 239–242. [Google Scholar] [CrossRef] - Al-Sarkhi, A.; Jaber, J.O.; Abu-Qudais, M.; Probert, S.D. Effects of friction and temperature-dependent specific-heat of the working fluid on the performance of a Diesel-engine. Appl. Energy
**2006**, 83, 153–165. [Google Scholar] [CrossRef] - Fallahipanah, M.; Ghazavi, M.A.; Hashemi, M.; Shahmirzaei, H. Comparison of the performance of Biodiesel, Diesel, and their compound in Diesel air standard irreversible cycles. In Proceedings of the 2011 International Conference on Environment Agriculture Engineering (IPCBEE), Chengdu, China, 29–31 July 2011; Volume 15, pp. 7–13.
- Jeshvaghani, H.S.; Fallahipanah, M.; Gahruei, M.H.; Chen, L. Performance analysis of a Diesel engines fueled by biodiesel blends via thermodynamic simulation of an air-standard Diesel cycle. Int. J. Environ. Sci. Technol.
**2014**, 11, 139–148. [Google Scholar] [CrossRef] - Zhao, Y.; Chen, J. Optimum performance analysis of an irreversible Diesel heat engine affected by variable heat capacities of working fluid. Energy Convers. Manag.
**2007**, 48, 2595–2603. [Google Scholar] [CrossRef] - He, J.; Lin, J. Effect of multi-irreversibilities on the performance characteristics of an irreversible air-standard Diesel heat engine. In Proceedings of the 2010 Asia-Pacific Power and Energy Engineering Conference, Chengdu, China, 28–31 March 2010; pp. 1–4.
- Ge, Y.L.; Chen, L.G.; Sun, F.R. Finite time thermodynamic modeling and analysis for an irreversible Diesel cycle. Proc. IMechE Part D
**2008**, 222, 887–894. [Google Scholar] [CrossRef] - Aithal, S.M. Impact of EGR fraction on diesel engine performance considering heat loss and temperature-dependent properties of the working fluid. Int. J. Energy Res.
**2009**, 33, 415–430. [Google Scholar] [CrossRef] - Aithal, S.M. Effect of EGR fraction on Diesel engine cycle efficiency considering thermophysical properties of the gas mixture. Int. J. Therm. Sci.
**2016**. submitted for publication. [Google Scholar] - Açıkkalp, E.; Yamık, H. Modeling and optimization of maximum available work for irreversible gas power cycles with temperature dependent specific heat. J. Non-Equilib. Thermodyn.
**2015**, 40, 25–39. [Google Scholar] [CrossRef] - Ebrahimi, R. Effects of variable specific heat ratio of working fluid on performance of an endoreversible Diesel cycle. J. Energy Inst.
**2010**, 83, 1–5. [Google Scholar] [CrossRef] - Ebrahimi, R.; Chen, L.G. Effects of variable specific heat ratio of working fluid on performance of an irreversible Diesel cycle. Int. J. Ambient Energy
**2010**, 31, 101–108. [Google Scholar] [CrossRef] - Sakhrieh, A.; Abu-Nada, E.; Akash, B.; Al-Hinti, I.; Al-Ghandoor, A. Performance of a Diesel engine using a gas mixture with variable specific heats model. J. Energy Inst.
**2010**, 83, 217–224. [Google Scholar] [CrossRef] - Wang, P.Y.; Hou, S.S. Performance analysis and comparison of an Atkinson cycle coupled to variable temperature heat reservoirs under maximum power and maximum power density conditions. Energy Convers. Manag.
**2005**, 46, 2637–2655. [Google Scholar] [CrossRef] - Zhao, Y.; Chen, J. Performance analysis and parametric optimum criteria of an irreversible Atkinson heat-engine. Appl. Energy
**2006**, 83, 789–800. [Google Scholar] [CrossRef] - Ust, Y. A comparative performance analysis and optimization of irreversible Atkinson cycle under maximum power density and maximum power conditions. Int. J. Thermophys.
**2009**, 30, 1001–1013. [Google Scholar] [CrossRef] - Ebrahimi, R. Thermodynamic modeling of an Atkinson cycle with respect to relative air-fuel ratio, fuel mass flow rate and residual gases. Acta Phys. Pol. A
**2013**, 124, 29–34. [Google Scholar] [CrossRef] - Patodi, K.; Maheshwari, G. Performance analysis of an Atkinson cycle with variable specific-heats of the working fluid under maximum efficient power conditions. Int. J. Low-Carbon Technol.
**2013**, 8, 289–294. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Performance of an endoreversible Atkinson cycle. J. Energy Inst.
**2007**, 80, 52–54. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Performance of Atkinson cycle with heat transfer, friction and variable specific heats of working fluid. Appl. Energy
**2006**, 83, 1210–1221. [Google Scholar] [CrossRef] - Lin, J.C.; Hou, S.S. Influence of heat loss on the performance of an air-standard Atkinson cycle. Appl. Energy
**2007**, 84, 904–920. [Google Scholar] [CrossRef] - Al-Sarkhi, A.; Akash, B.; Abu-Nada, E.; Al-Hinti, I. Efficiency of Atkinson engine at maximum power density using temperature dependent specific heats. Jordan J. Mech. Ind. Eng.
**2008**, 2, 71–75. [Google Scholar] - Ye, X.; Liu, J. Optimum performance of an irreversible Atkinson heat engine with the working substance having temperature-dependent heat capacities. J. Yunnan Univ. Nat. Sci. Edit.
**2010**, 32, 542–546. (In Chinese) [Google Scholar] - Ge, Y.L.; Chen, L.G.; Sun, F.R. Finite time thermodynamic modeling and analysis for an irreversible Atkinson cycle. Therm. Sci.
**2010**, 14, 887–896. [Google Scholar] [CrossRef] - Ebrahimi, R. Performance of an endoreversible Atkinson cycle with variable specific heat ratio of working fluid. J. Am. Sci.
**2010**, 6, 12–17. [Google Scholar] - Ebrahimi, R. Effects of mean piston speed, equivalence ratio and cylinder wall temperature on performance of an Atkinson engine. Math. Comput. Model.
**2011**, 53, 1289–1297. [Google Scholar] [CrossRef] - Ebrahimi, R. Performance analysis of irreversible Atkinson cycle with consideration of stroke length and volumetric efficiency. J. Energy Inst.
**2011**, 84, 38–43. [Google Scholar] [CrossRef] - Wu, C.; Kiang, R.L. Work and power optimization of a finite-time Brayton cycle. Int. J. Ambient Energy
**1990**, 1, 129–136. [Google Scholar] [CrossRef] - Chen, L.G.; Sun, F.R.; Yu, J. Effect of heat resistance on the performance of closed gas turbine regenerated cycle. J. Eng. Thermophys.
**1995**, 16, 401–404. (In Chinese) [Google Scholar] - Chen, L.G.; Zheng, J.L.; Sun, F.R.; Wu, C. Power density analysis and optimization of a regenerated closed variable-temperature heat reservoir Brayton cycle. J. Phys. D
**2001**, 34, 1727–1739. [Google Scholar] [CrossRef] - Chen, L.G.; Zheng, J.L.; Sun, F.R.; Wu, C. Power density analysis for a regenerated closed Brayton cycle. Open Sys. Inf. Dyn.
**2001**, 8, 377–391. [Google Scholar] [CrossRef] - Chen, L.G.; Sun, F.R.; Wu, C. Power optimization of a regenerated closed variable -temperature heat reservoir Brayton cycle. Int. J. Sustan. Energy
**2007**, 26, 1–17. [Google Scholar] [CrossRef] - Chen, L.G.; Wang, J.H.; Sun, F.R. Power density analysis and optimization of an irreversible closed intercooled regenerated Brayton cycle. Math. Comput. Model.
**2008**, 48, 527–540. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Performance of a reciprocating endoreversible Brayton cycle with variable specific heats of working fluid. Termotehnica
**2008**, 12, 19–23. [Google Scholar] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Performance of reciprocating Brayton cycle with heat transfer, friction and variable specific heats of working fluid. Int. J. Ambient Energy
**2008**, 29, 65–75. [Google Scholar] [CrossRef] - Sahin, B.; Kesgin, U.; Kodal, A.; Vardar, N. Performance optimization of a new combined power cycle based on power density analysis of the Dual cycle. Energy Convers. Manag.
**2002**, 43, 2019–2031. [Google Scholar] [CrossRef] - Atmaca, M.; Gumus, M.; Demir, A. Comparative thermodynamic analysis of Dual cycle under alternative conditions. Therm. Sci.
**2011**, 15, 953–960. [Google Scholar] [CrossRef] - Blank, D.A.; Wu, C. The effects of combustion on a power-optimized endoreversible Dual cycle. Energy Convers. Manag.
**1994**, 14, 98–103. [Google Scholar] - Lin, J.X.; Chen, L.G.; Wu, C.; Sun, F. Finite-time thermodynamic performance of Dual cycle. Int. J. Energy Res.
**1999**, 23, 765–772. [Google Scholar] [CrossRef] - Hou, S.S. Heat transfer effects on the performance of an air standard Dual cycle. Energy Convers. Manag.
**2004**, 45, 3003–3015. [Google Scholar] [CrossRef] - Qiu, W. Performance limits for international combustion engine cycle within temperature and pressure restraints. Chin. Intern. Combust. Engine Eng.
**2004**, 25, 66–68. (In Chinese) [Google Scholar] - Qin, J. Study on FTT of Dual cycle in internal-combustion engine. Intern. Combust. Engines
**2007**, 4, 12–13. (In Chinese) [Google Scholar] - Ebrahim, R.; Mahbobian, K.; Gandomkari, F.T. Effects of cut-off ratio on performance of an endoreversible Dual cycle. Appl. Mech. Mater.
**2011**, 110–116, 2847–2853. [Google Scholar] [CrossRef] - Rashidi, M.M.; Hajipour, A.; Fahimirad, A. First and second-laws analysis of an air-standard Dual cycle with heat loss consideration. Int. J. Mech. Electr. Comput. Technol.
**2014**, 4, 315–332. [Google Scholar] - Wang, W.H.; Chen, L.G.; Sun, F.R.; Wu, C. The effects of friction on the performance of an air stand Dual cycle. Exergy Int. J.
**2002**, 2, 340–344. [Google Scholar] [CrossRef] - Zheng, T.; Chen, L.G.; Sun, F.R. The Power and Efficiency Characteristics for Irreversible Dual Cycles. Trans. CSICE
**2002**, 20, 408–412. (In Chinese) [Google Scholar] - Parlak, A.; Sahin, B.; Yasar, H. Performance optimization of an irreversible Dual cycle with respect to pressure ratio and temperature ratio-experimental results of a ceramic coated IDI Diesel engine. Energy Convers. Manag.
**2004**, 45, 1219–1232. [Google Scholar] [CrossRef] - Ebrahimi, R. Effects of specific heat ratio on the power output and efficiency characteristics for an irreversible Dual cycle. J. Am. Sci.
**2010**, 6, 181–184. [Google Scholar] - Nejad, R.M.; Alaei, P. Effects of irreversible different parameters on performance of air standard dual-cycle. J. Am. Sci.
**2011**, 7, 608–613. [Google Scholar] - Parlak, A.; Sahin, B. Performance optimisation of reciprocating heat engine cycles with internal irreversibility. J. Energy Inst.
**2006**, 79, 241–245. [Google Scholar] [CrossRef] - Zhao, Y.; Chen, J. An irreversible heat engine model including three typical thermodynamic cycles and their optimum performance analysis. Int. J. Therm. Sci.
**2007**, 46, 605–613. [Google Scholar] [CrossRef] - Ozsoysal, O.A. Effects of combustion efficiency on a Dual cycle. Energy Convers. Manag.
**2009**, 50, 2400–2406. [Google Scholar] [CrossRef] - Ozsoysal, O.A. Waste energy depending on the maximum temperature and the excess air coefficient in an irreversible Dual cycle. ASCE J. Energy Eng.
**2016**. submitted for publication. [Google Scholar] - Ebrahimi, R. Effects of equivalence ratio and mean piston speed on performance of an irreversible Dual cycle. Acta Phys. Pol. A
**2011**, 120, 384–389. [Google Scholar] [CrossRef] - Gonca, G.; Sahin, B.; Ust, Y. Performance maps for an air-standard irreversible Dual–Miller cycle (DMC) with late inlet valve closing (LIVC) version. Energy
**2013**, 54, 285–290. [Google Scholar] [CrossRef] - Ust, Y.; Sahin, B.; Kayadelen, H.K.; Gonca, G. Heat transfer effects on the performance of an air-standard irreversible dual cycle. Int. J. Veh. Des.
**2013**, 63, 102–116. [Google Scholar] [CrossRef] - Nejad, R.M. Power output and efficiency of international combustion engine based on the FTT theory. Life Sci. J.
**2012**, 9, 387–390. [Google Scholar] - Chen, L.G.; Ge, Y.L.; Sun, F.R.; Wu, C. Effects of heat transfer, friction and variable specific heats of working fluid on performance of an irreversible Dual cycle. Energy Convers. Manag.
**2006**, 47, 3224–3234. [Google Scholar] [CrossRef] - Wang, F.; Huang, Y.; Gao, W. The effect of variable specific heats of working fluid on the power density characteristic of Dual cycle. Energy Environ.
**2010**, 2, 4–6. (In Chinese) [Google Scholar] - Wang, F. Thermodynamics Optimization Sudy for Dual Cycle. Master’s Thesis, Donghua University, Shanghai, China, 2010. [Google Scholar]
- Ye, X. Performance characteristics of an irreversible Dual heat engine under the variable heat capacities. J. Zhangzhou Normal Univ. Nat. Sci.
**2011**, 24, 26–30. (In Chinese) [Google Scholar] - Lin, J.C.; Hou, S.S.; Li, S.J. The effects of temperature-dependent specific heats of the working fluid on the performance of a Dual cycle with heat loss and friction. In Proceedings of the 2011 International Conference on Consumer Electronics, Communications and Networks (CECNet), Xianning, China, 16–18 April 2011; pp. 5378–5381.
- Gahruei, M.H.; Jeshvaghani, H.S.; Vahidi, S.; Chen, L.G. Mathematical modeling and comparison of air standard Dual and Dual–Atkinson cycles with friction, heat transfer and variable specific-heats of the working fluid. Appl. Math. Model.
**2013**, 37, 7319–7329. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R. Finite time thermodynamic modeling and analysis for an irreversible Dual cycle. Comput. Math. Model.
**2009**, 50, 101–108. [Google Scholar] [CrossRef] - Ebrahimi, R. Thermodynamic modeling of an irreversible dual cycle: Effect of mean piston speed. Rep. Opin.
**2009**, 1, 25–30. [Google Scholar] - Ebrahim, R.; Sherafati, M. Thermodynamic simulation of performance of a Dual cycle with stroke length and volumetric efficiency. J. Therm. Anal. Calorim.
**2013**, 111, 951–957. [Google Scholar] [CrossRef] - Asghari, N.; Mousavi Seyedi, S.R. Performance of Dual cycle with variables heats capacity of working fluid. Int. Res. J. Appl. Basic Sci.
**2013**, 4, 2544–2552. [Google Scholar] - Ebrahimi, R. Thermodynamic simulation of performance of an endoreversible Dual cycle with variable specific heat ratio of working fluid. J. Am. Sci.
**2009**, 5, 175–180. [Google Scholar] - Ebrahimi, R. Effects of cut-off ratio on performance of an irreversible Dual cycle. J. Am. Sci.
**2009**, 5, 83–90. [Google Scholar] - Ebrahimi, R. Effects of pressure ratio on the net work output and efficiency characteristics for an endoreversible Dual cycle. J. Energy Inst.
**2011**, 84, 30–33. [Google Scholar] [CrossRef] - Ebrahimi, R. Performance analysis of a dual cycle engine with considerations of pressure ratio and cut-off ratio. Acta Phys. Pol. A
**2010**, 118, 534–539. [Google Scholar] [CrossRef] - Al-Sarkhi, A.; Akash, B.; Jaber, J.O.; Mohsen, M.S.; Abu-Nada, E. Efficiency of Miller engine at maximum power density. Int. Commun. Heat Mass Transf.
**2002**, 29, 1159–1157. [Google Scholar] [CrossRef] - Mousapour, A.; Rashidi, M.M. Performance evalution of an air-standard Miller cycle with consideration of heat losses. Int. J. Mechatron. Electr. Comput. Technol.
**2014**, 4, 1175–1191. [Google Scholar] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Effects of heat transfer and friction on the performance of an irreversible air-standard Miller cycle. Int. Commun. Heat Mass Transf.
**2005**, 32, 1045–1056. [Google Scholar] [CrossRef] - Zhao, Y.; Chen, J. Performance analysis of an irreversible Miller heat engine and its optimum criteria. Appl. Therm. Eng.
**2007**, 27, 2051–2058. [Google Scholar] [CrossRef] - Gonca, G.; Sahin, B.; Ust, Y.; Parlak, A. Comprehensive performance analyses and optimization of the irreversible thermodynamic cycle engines (TCE) under maximum power (MP) and maximum power density (MPD) conditions. Appl. Therm. Eng.
**2015**, 85, 9–20. [Google Scholar] [CrossRef] - Ebrahimi, R. Power optimization of a Miller thermal cycle with respect to residual gases and equivalence ratio. Acta Phys. Pol. A
**2013**, 124, 6–10. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Effects of heat transfer and variable specific heats of working fluid on performance of a Miller cycle. Int. J. Ambient Energy
**2005**, 26, 203–214. [Google Scholar] [CrossRef] - Al-Sarkhi, A.; Jaber, J.O.; Probert, S.D. Efficiency of a Miller engine. Appl. Energy
**2006**, 83, 343–351. [Google Scholar] [CrossRef] - Chen, L.G.; Ge, Y.L.; Sun, F.R.; Wu, C. The performance of a Miller cycle with heat transfer, friction and variable specific heats of working fluid. Termotehnica
**2010**, 14, 24–32. [Google Scholar] - Doric, J.Z.; Klinar, I.J. The realization and analysis of a novel thermodynamic cycle in internal combustion engine. Therm. Sci.
**2011**, 15, 961–974. [Google Scholar] [CrossRef] - Yang, B.; He, J. Performance optimization of a generalized irreversible Miller heat engine cycle. J. Nanchang Univ. Eng. Technol.
**2009**, 31, 135–138. (In Chinese) [Google Scholar] - Lin, J.C.; Hou, S.S. Performance analysis of an air standard Miller cycle with considerations of heat loss as a percentage of fuel’s energy, friction and variable specific heats of working fluid. Int. J. Therm. Sci.
**2008**, 47, 182–191. [Google Scholar] [CrossRef] - Liu, J. Influence of multi-irreversibilities on the performance of a Miller heat engine. J. Zhangzhou Normal Univ. Nat. Sci.
**2009**, 22, 48–52. (In Chinese) [Google Scholar] - Liu, J.; Chen, J. Optimum performance analysis of a class of typical irreversible heat engines with temperature-dependent heat capacities of the working substance. Int. J. Ambient Energy
**2010**, 31, 59–70. [Google Scholar] [CrossRef] - Ye, X.M. Effect of the variable heat capacities on the performance of an irreversible Miller heat engine. Frontiers Energy
**2012**, 6, 280–284. [Google Scholar] [CrossRef] - Lin, J.; Xu, Z.; Chang, S.; Hao, Y. Finite-time thermodynamic modeling and analysis of an irreversible Miller cycle working on a four-stroke engine. Int. Commun. Heat Mass Transf.
**2014**, 54, 54–59. [Google Scholar] [CrossRef] - Mousapour, A.; Rezapour, K. Effects of variable specific heats of the working fluid, internal irreversibility, heat transfer and friction on performance of a Miller cycle. Int. J. Mechatron. Electr. Comput. Technol.
**2014**, 4, 886–909. [Google Scholar] - Mousapour, A.; Hajipour, A.; Rashidi, M.M.; Freidoonimehr, N. Performance evaluation of an irreversible Miller cycle comparing finite-time thermodynamics analysis and ANN prediction. Energy
**2016**, 94, 100–109. [Google Scholar] [CrossRef] - Al-Sarkhi, A.; Al-Hinti, I.; Abu-Nada, E.; Akash, B. Performance evaluation of irreversible Miller engine under various specific heat models. Int. Commun. Heat Mass Transf.
**2007**, 34, 897–906. [Google Scholar] [CrossRef] - Chen, L.G.; Ge, Y.L.; Sun, F.R.; Wu, C. Finite time thermodynamic modeling and analysis for an irreversible Miller cycle. Int. J. Ambient Energy
**2011**, 32, 87–94. [Google Scholar] [CrossRef] - Ebrahimi, R. Effect of expansion-compression ratio on performance of the Miller cycle. Acta Phys. Pol. A
**2012**, 122, 645–649. [Google Scholar] [CrossRef] - Ebrahimi, R.; Hoseinpour, M. Performance analysis of irreversible Miller cycle under variable compression ratio. J. Thermophy. Heat Transf.
**2013**, 27, 542–548. [Google Scholar] [CrossRef] - Ebrahimi, R. Thermodynamic modeling of performance of a Miller cycle with engine speed and variable specific heat ratio of working fluid. Comput. Math. Appl.
**2011**, 62, 2169–2176. [Google Scholar] [CrossRef] - Liu, H.; Xie, M.; Chen, S. Finite-time thermodynamic analysis of porous medium combustion engine. J. Dalian Univ. Technol.
**2008**, 48, 14–18. (In Chinese) [Google Scholar] - Ge, Y.L.; Chen, L.G.; Sun, F.R. Thermodynamic modeling and parametric study for porous medium engine cycles. Termotehnica
**2009**, 13, 49–55. [Google Scholar] - Mozurkewich, M.; Berry, R.S. Finite-time thermodynamics: Engine performance improved by optimized piston motion. Proc. Natl. Acad. Sci. USA
**1981**, 78, 1986–1988. [Google Scholar] [CrossRef] [PubMed] - Mozurkewich, M.; Berry, R.S. Optimum paths for thermodynamic systems: The ideal Otto cycle. J. Appl. Phys.
**1982**, 53, 34–42. [Google Scholar] [CrossRef] - Hoffman, K.H.; Berry, R.S. Optimum paths for thermodynamic systems: The ideal Diesel cycle. J. Appl. Phys.
**1985**, 58, 2125–2134. [Google Scholar] [CrossRef] - Blaudeck, P.; Hoffman, K.H. Optimization of the power output for the compression and power stroke of the Diesel engine. In Proceedings of the International Conference ECOS ’95, Istanbul, Turkey, 11–14 July 1995; Volume 2, p. 754.
- Teh, K.Y.; Edwards, C.F. Optimizing piston velocity profile for maximum work output from an IC engine. In Proceedings of the ASME 2006 International Mechanical Engineering Congress and Exposition, Chicago, IL, USA, 5–10 November 2006.
- Teh, K.Y.; Miller, S.L.; Edwards, C.F. Thermodynamic requirements for maximum international combustion engine cycle efficiency Part 1: Optimum combustion strategy. Int. J. Engine Res.
**2008**, 9, 449–465. [Google Scholar] [CrossRef] - Teh, K.Y.; Miller, S.L.; Edwards, C.F. Thermodynamic requirements for maximum international combustion engine cycle efficiency Part 2: Work extraction and reactant preparation strategies. Int. J. Engine Res.
**2008**, 9, 467–481. [Google Scholar] [CrossRef] - Teh, K.Y.; Edwards, C.F. An optimum control approach to minimizing entropy generation in an adiabatic international combustion engine. J. Dyn. Sys. Meas. Control
**2008**, 130, 041008. [Google Scholar] [CrossRef] - Teh, K.Y.; Edwards, C.F. An optimum control approach to minimizing entropy generation in an adiabatic IC engine with fixed compression ratio. In Proceedings of the ASME 2006 International Mechanical Engineering Congress and Exposition, Chicago, IL, USA, 5–10 November 2006.
- Band, Y.B.; Kafri, O.; Salamon, P. Maximum work production from a heated gas in a cylinder with piston. Chem. Phys. Lett.
**1980**, 72, 127–130. [Google Scholar] [CrossRef] - Band, Y.B.; Kafri, O.; Salamon, P. Finite time thermodynamics: Optimum expansion of a heated working fluid. J. Appl. Phys.
**1982**, 53, 8–28. [Google Scholar] [CrossRef] - Salamon, P.; Band, Y.B.; Kafri, O. Maximum power from a cycling working fluid. J. Appl. Phys.
**1982**, 53, 197–202. [Google Scholar] [CrossRef] - Aizenbud, B.M.; Band, Y.B. Power considerations in the operation of a piston fitted inside a cylinder containing a dynamically heated working fluid. J. Appl. Phys.
**1981**, 52, 3742–3744. [Google Scholar] [CrossRef] - Aizenbud, B.M.; Band, Y.B.; Kafri, O. Optimization of a model international combustion engine. J. Appl. Phys.
**1982**, 53, 1277–1282. [Google Scholar] [CrossRef] - Band, Y.B.; Kafri, O.; Salamon, P. Optimization of a model external combustion engine. J. Appl. Phys.
**1982**, 53, 29–33. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R. Optimum paths of piston motion of irreversible Otto cycle heat engines for minimum entropy generation. Sci. China Ser. G Phys. Mech. Astron.
**2010**, 40, 1115–1129. (In Chinese) [Google Scholar] - Ge, Y.L.; Chen, L.G.; Sun, F.R. Optimum paths of piston motion of irreversible Diesel cycle for minimum entropy generation. Therm. Sci.
**2011**, 15, 975–993. [Google Scholar] [CrossRef] - Burzler, J.M. Performance Optima for Endoreversible Systems. Ph.D. Thesis, University of Chemnitz, Chemnitz, Germany, 2002. [Google Scholar]
- Burzler, J.M.; Hoffman, K.H. Optimum Piston Paths for Diesel Engines. In Thermodynamics of Energy Conversion and Transport; Sienuitycz, S., De vos, A., Eds.; Springer: New York, NY, USA, 2000. [Google Scholar]
- Xia, S.J.; Chen, L.G.; Sun, F.R. Optimum path of piston motion for Otto cycle with linear phenomenological heat transfer law. Sci. China Ser. G Phys. Mech. Astron.
**2009**, 52, 708–719. [Google Scholar] [CrossRef] - Xia, S.J.; Chen, L.G.; Sun, F.R. Engine performance improved by controlling piston motion: linear phenomenological law system Diesel cycle. Int. J. Therm. Sci.
**2012**, 51, 163–174. [Google Scholar] [CrossRef] - Chen, L.G.; Xia, S.J.; Sun, F.R. Optimizing piston velocity profile for maximum work output from a generalized radiative law Diesel engine. Math. Comput. Model.
**2011**, 54, 2051–2063. [Google Scholar] [CrossRef] - Chen, L.G.; Sun, F.R.; Wu, C. Optimum expansion of a heated working fluid with phenomenological heat transfer. Energy Convers. Manag.
**1998**, 39, 149–156. [Google Scholar] [CrossRef] - Song, H.J.; Chen, L.G.; Sun, F.R. Optimization of a model external combustion engine with linear phenomenological heat transfer law. J. Energy Inst.
**2009**, 82, 180–183. [Google Scholar] [CrossRef] - Chen, L.G.; Song, H.J.; Sun, F.R.; Wu, C. Optimization of a model ICE with linear phenomenological heat transfer law. Int. J. Ambient Energy
**2010**, 31, 13–22. [Google Scholar] [CrossRef] - Song, H.J.; Chen, L.G.; Sun, F.R. Optimum expansion of a heated working fluid for maximum work output with generalized radiative heat transfer law. J. Appl. Phys.
**2007**, 102, 94901. [Google Scholar] [CrossRef] - Ma, K.; Chen, L.G.; Sun, F.R. Optimum expansion of a heated gas under Dulong–Petit heat Transfer law. J. Eng. Therm. Energy Power
**2009**, 24, 447–451. (In Chinese) [Google Scholar] - Chen, L.G.; Song, H.J.; Sun, F.R.; Wu, C. Optimum expansion of a heated working fluid with convective-radiative heat transfer law. Int. J. Ambient Energy
**2010**, 31, 81–90. [Google Scholar] [CrossRef] - Ma, K. Optimum Configurations of Engine Piston Motions and Forced Cool-down Processes. Ph.D. Thesis, Naval University of Engineering, Wuhan, China, 2010. [Google Scholar]
- Ma, K.; Chen, L.G.; Sun, F.R. New solution to optimum expansion of heated gas under generalized radiative heat transfer law. Chin. J. Mech. Eng.
**2010**, 46, 149–157. (In Chinese) [Google Scholar] [CrossRef] - Ma, K.; Chen, L.G.; Sun, F.R. Optimization of a model external combustion engine for maximum work output with radiative heat transfer law. J. Eng. Therm. Energy Power
**2011**, 26, 533–537. (In Chinese) [Google Scholar] - Chen, L.G.; Ma, K.; Sun, F.R. Optimum expansion of a heated working fluid for maximum work output with time-dependent heat conductance and generalized radiative heat transfer law. J. Non-Equilib. Thermodyn.
**2011**, 36, 99–122. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R. The optimum path of piston motion of irreversible Otto cycle for minimum entropy generation with radiative heat transfer law. J. Energy Inst.
**2012**, 85, 140–149. [Google Scholar] [CrossRef] - Ge, Y.L.; Chen, L.G.; Sun, F.R. Optimum paths of piston motion of irreversible Diesel cycle heat engines for minimum entropy generation with linear phenomenological heat transfer law. In Proceedings of the Chinese Society of Engineering Thermophysics on Engineering Thermophysics and Energy Utility, Nanjing, China, 8–10 November 2010. (In Chinese)
- Orlov, V.N.; Berry, R.S. Power output from an irreversible heat engine with a non-uniform working fluid. Phys. Rev. A
**1990**, 42, 7230–7235. [Google Scholar] [CrossRef] [PubMed] - Orlov, V.N.; Berry, R.S. Analytical and numerical estimates of efficiency for an irreversible heat engine with distributed working fluid. Phys. Rev. A
**1992**, 45, 7202–7206. [Google Scholar] [CrossRef] [PubMed] - Orlov, V.N.; Berry, R.S. Power and efficiency limits for international combustion engines via methods of FTT. J. Appl. Phys
**1993**, 74, 4317–4322. [Google Scholar] [CrossRef] - Xia, S.J.; Chen, L.G.; Sun, F.R. Maximum power output of a class of irreversible non-regeneration heat engines with a non-uniform working fluid and linear phenomenological heat transfer law. Sci. China Ser. G Phys. Mech. Astron.
**2009**, 52, 1961–1970. [Google Scholar] [CrossRef] - Chen, L.G.; Xia, S.J.; Sun, F.R. Maximum efficiency of an irreversible heat engine with a distributed working fluid and linear phenomenological heat transfer law. Revista Mexicana de Física
**2010**, 56, 231–238. [Google Scholar] - Chen, L.G.; Xia, S.J.; Sun, F.R. Performance limits for a class of irreversible international combustion engines. Energy Fuels
**2010**, 24, 295–301. [Google Scholar] [CrossRef] - Descieux, D.; Feidt, M. Modelling of a spark ignition engine for power-heat production optimization. Oil Gas Sci. Technol.
**2011**, 66, 737–745. [Google Scholar] [CrossRef] - Descieux, D.; Feidt, M. One zone thermodynamic model simulation of an ignition compression engine. Appl. Therm. Eng.
**2007**, 27, 1457–1466. [Google Scholar] [CrossRef] - Curto-Risso, P.L.; Medina, A.; Hernández, A.C. Theoretical and simulated models for an irreversible Otto cycle. J. Appl. Phys.
**2008**, 104, 094911. [Google Scholar] [CrossRef] - Curto-Risso, P.L.; Medina, A.; Hernández, A.C. Optimizing the operation of a spark ignition engine: Simulation and theoretical tools. J. Appl. Phys.
**2009**, 105, 094904. [Google Scholar] [CrossRef] - Curto-Risso, P.L.; Medina, A.; Hernández, A.C. Thermodynamic optimization of a spark ignition engine. In Proceedings of the 22nd International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2009), Foz do Iguaçu, Brazil, 31 August–3 September 2009; pp. 1979–1987.
- Curto-Risso, P.L.; Medina, A.; Hernández, A.C. Optimizing the geometrical parameters of a spark ignition engine: simulation and theoretical tools. Appl. Therm. Eng.
**2011**, 31, 803–810. [Google Scholar] [CrossRef] - Georgiou, D.P.; Theodoropoulos, N.G.; Milidonis, K.F. Ideal thermodynamic cycle analysis for the Meletis–Georgiou vane rotary engine concept. J. Thermodyn.
**2010**, 2010, 130692. [Google Scholar] [CrossRef] - Liu, C. Finite Time Thermodynamic Analysis and Optimization for Meletis–Georgiou Cycle. Master’s Thesis, Naval University of Engineering, Wuhan, China, 2011. [Google Scholar]
- Liu, C.; Chen, L.G.; Sun, F.R. Performance analysis and optimization of an irreversible Meletis–Georgiou cycle. In Proceedings of the 7th National Academic Conference on Engineering Thermophysics in Higher Education Institutions, Daqing, China, 19–21 June 2011. (In Chinese)
- Liu, C.; Chen, L.G.; Sun, F.R. Endoreversible Meletis–Georgiou cycle. Int. J. Energy Environ.
**2012**, 3, 305–322. [Google Scholar] - Liu, C.; Chen, L.G.; Sun, F.R. Influence of variable specific heats of working fluid on performance of an endreversible Meletis–Georgiou cycle. Int. J. Ambient Energy
**2012**, 33, 9–22. [Google Scholar] [CrossRef] - Liu, C.; Chen, L.G.; Sun, F.R. Modelling and performance analysis for endreversible Meletis–Georgiou cycle with non-linear relation between specific heat of working fluid and its temperature. J. Energy Inst.
**2013**, 86, 49–59. [Google Scholar] [CrossRef] - Chen, L.G.; Liu, C.; Sun, F.R. Performance of irreversible Meletis–Georgiou vane rotary engine cycle with variable specific heats of working fluid. Int. J. Sustan. Energy
**2014**, 33, 76–95. [Google Scholar] [CrossRef] - Da Silva, M.F.F. Some considerations about thermodynamic cycles. Eur. J. Phys.
**2012**, 33, 13–42. [Google Scholar] [CrossRef] - Liu, X.; Chen, L.G.; Qin, X.Y.; Ge, Y.L.; Sun, F.R. Finite-time thermodynamic analysis for an endoreversible rectangular cycle. Energy Conserv.
**2013**, 32, 19–21. (In Chinese) [Google Scholar] - Liu, C.X.; Chen, L.G.; Ge, Y.L.; Sun, F.R. Power and efficiency characteristics for an irreversible rectangular cycle. Power Energy
**2013**, 34, 113–117. (In Chinese) [Google Scholar] - Wang, C.; Chen, L.G.; Ge, Y.L.; Sun, F.R. Effects of variable specific heats of working fluid on perfromace of irreversible rectangular cycle. Energy Conserv.
**2014**, 33, 18–22. (In Chinese) [Google Scholar] - Wang, C.; Chen, L.G.; Ge, Y.L.; Sun, F.R. Performance analysis of an endoreversible rectangular cycle considering non-linear variable specific heats of working fluid. Int. J. Energy Environ.
**2015**, 6, 73–80. [Google Scholar] - Wang, C.; Chen, L.G.; Ge, Y.L.; Sun, F.R. Performance analysis of an irreversible rectangular cycle considering non-linear variable specific heats of working fluid. In Proceedings of Chinese Society Engneering Thermophyscis on Engneering Thermdynamics & Energy Utility, Xian, China, 1–2 November 2014. (In Chinese)
- Wang, C.; Chen, L.G.; Ge, Y.L.; Sun, F.R. Performance analysis of an endoreversible rectangular cycle with heat transfer loss and variable specific heats of working fluid. Int. J. Energy Environ.
**2015**, 6, 73–80. [Google Scholar] - Lichty, C. Combustion Engine Processes; McGraw-Hill: New York, NY, USA, 1967. [Google Scholar]
- Georgiou, D.P. Useful work and the thermal efficiency in the ideal Lenoir with regenerative preheating. J. Appl. Phys.
**2008**, 88, 5981–5986. [Google Scholar] [CrossRef] - Gong, S.W.; Chen, L.G.; Sun, F.R. Performance analysis and optimization of endoreversible Lenoir cycle with polytropic process. Energy Conserv.
**2013**, 32, 22–26. (In Chinese) [Google Scholar] - Zhang, Z.Y.; Chen, L.G.; Qin, X.Y.; Sun, F.R. Effects of variable specific heats of working fluid on perfromace of endoreversible Lenori cycle. Energy Conserv.
**2013**, 32, 14–19. (In Chinese) [Google Scholar] - Zhou, J.L.; Chen, L.G.; Sun, F.R. Thermodynamic analysis of an air-standard Lenoir cycle with linear variable specific heats of working fluid. Power Energy
**2014**, 35, 678–682. (In Chinese) [Google Scholar] - Zhou, J.L.; Chen, L.G.; Sun, F.R. Performance analysis of an air-standard Lenoir cycle with non-linear variable specific heats of working fluid. Energy Conserv.
**2015**, 34, 19–23. (In Chinese) [Google Scholar] - Gonca, G. 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 Convers. Manag.
**2016**, 111, 205–216. [Google Scholar] [CrossRef] - Gonca, G. Performance analysis and optimization of irreversible Dual–Atkinson cycle engine (DACE) with heat transfer effects under maximum power and maximum power density conditions. Appl. Math. Modell.
**2016**, in press. [Google Scholar] [CrossRef] - Ust, Y.; Arslan, F.; Ozsari, I.; Cakir, M. Thermodynamic performance analysis and optimization of DMC (Dual Miller Cycle) cogeneration system by considering exergetic performance coefficient and total exergy output criteria. Energy
**2015**, 90, 552–559. [Google Scholar] [CrossRef] - Wu, Z.X.; Chen, L.G.; Ge, Y.L.; Sun, F.R. Ecological objective function optimization of an irreversible Dual–Miller cycle with nonlinear variable specific heat ratio of the working fluid. Energy Conserv.
**2016**. in press (In Chinese) [Google Scholar] - Cakir, M. The numerical thermodynamic analysis of Otto–Miller cycle (OMC). Therm. Sci.
**2016**, 20, 363–369. [Google Scholar] [CrossRef]

**Figure 14.**OPM trajectories on the power stroke with different HTAs and OPBs. 1.MEF, Newton’s heat transfer law; 2. MEG, Newton’s heat transfer law; 3. MW, Newton’s heat transfer law; 4. MEF, linear phenomenological heat transfer law; 5. MEG, linear phenomenological heat transfer law; 6. MW, linear phenomenological heat transfer law; 7. MEF, radiative heat transfer law; 8. MEG, radiative heat transfer law.

**Figure 15.**Comparison of OPM trajectories with different HTAs and OPBs (velocity). 1. MEF, Newton’s heat transfer law; 2. MEG, Newton’s heat transfer law; 3. MW, Newton’s heat transfer law; 4. MEF, linear phenomenological heat transfer law; 5. MEG, linear phenomenological heat transfer law; 6. MW, linear phenomenological heat transfer law; 7. MEF, radiative heat transfer law; 8. MEG, radiative heat transfer law.

**Figure 16.**Comparison of OPM trajectories with different HTAs and OPBs (temperature). 1. MEF, Newton’s heat transfer law; 2. MEG, Newton’s heat transfer law; 3. MW, Newton’s heat transfer law; 4. MEF, linear phenomenological heat transfer law; 5. MEG, linear phenomenological heat transfer law; 6. MW, linear phenomenological heat transfer law; 7. MEF, radiative heat transfer law; 8. MEG, radiative heat transfer law.

**Figure 17.**Comparison of OPM trajectories with different HTAs and OPBs (displacement). 1. MEF, Newton’s heat transfer law; 2. MEG, Newton’s heat transfer law; 3. MW, Newton’s heat transfer law; 4. MEF, linear phenomenological heat transfer law; 5. MEG, linear phenomenological heat transfer law; 6. MW, linear phenomenological heat transfer law; 7. MEF, radiative heat transfer law; 8. MEG, radiative heat transfer law.

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Ge, Y.; Chen, L.; Sun, F.
Progress in Finite Time Thermodynamic Studies for Internal Combustion Engine Cycles. *Entropy* **2016**, *18*, 139.
https://doi.org/10.3390/e18040139

**AMA Style**

Ge Y, Chen L, Sun F.
Progress in Finite Time Thermodynamic Studies for Internal Combustion Engine Cycles. *Entropy*. 2016; 18(4):139.
https://doi.org/10.3390/e18040139

**Chicago/Turabian Style**

Ge, Yanlin, Lingen Chen, and Fengrui Sun.
2016. "Progress in Finite Time Thermodynamic Studies for Internal Combustion Engine Cycles" *Entropy* 18, no. 4: 139.
https://doi.org/10.3390/e18040139