Iran. J. Chem. Chem. Eng. Research Article Vol. 39, No. 1, 2020 Archive of SID Thermodynamic Assessment and Optimization of Performance of Irreversible Atkinson Cycle Ahmadi, Mohammad Hossein*+ Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, I.R. IRAN Pourkiaei, Seyed Mohsen; Ghazvini, Mahyar, Pourfayaz, Fathollah*+ Department of Renewable Energies and Environmental, Faculty of New Sciences and Technologies, University of Tehran, Tehran, I.R. IRAN ABSTRACT: Although various investigations of Atkinson cycle have been carried out, distinct output power and thermal efficiencies of the engine have been achieved. In this regard, thermal efficiency, Ecological Coefficient of Performance (ECOP), and Ecological function (ECF) are optimized with the help of NSGA-II method and thermodynamic study. The Pareto optimal frontier which provides an ultimate optimum solution is chosen utilizing various decision- making approaches, containing fuzzy Bellman-Zadeh, LINMAP, and TOPSIS. With the help of the results, interpreting the performances of Atkinson cycles and their optimization is enhanced. Error analysis has also been performed for verification of optimization and determining the deviation in the study. KEYWORDS: Atkinson cycle; Thermodynamic analysis; Power; Ecological Coefficient of Performance; Thermal efficiency; Entropy generation. INTRODUCTION The main purpose of designing the cycle is to present of combining with an increment stroke and/or decreased the performance of the system by the mean of input volume of the combustion chamber, causes the ratio of power. In the Atkinson cycle, the intake, compression, expansion to outstrip the ratio of compression, throughout power, and exhaust strokes of the four-step take place the time of maintaining a regular compression pressure. by one piston sweep. In the Atkinson cycle, the compression So, it is favorable for enhanced cost efficiency, since ratio is less than the expansion ratio, due to the linkage, in a spark-ignition engine, the octane rating ratio limits which results in higher efficiency related to the engines the compression. So, a longer power stroke is the result utilizing the alternative Otto cycle. Also, four-stroke of a high expansion ratio, provides higher expansion ratios, engines are referred to as the Atkinson cycle. In these followed by the reduction of heat associated with arrangements, the intake step takes longer time to fill the waste in the exhaust [1]. the intake manifold with fresh air. Its result is the reduction A growing number of thermodynamic investigations of efficient compression ratio, and on the condition has focused on determining the limits of performance * To whom correspondence should be addressed. + E-mail: [email protected] , [email protected], [email protected] 1021 -9986/2020/1/267-280 14/$/6.04 Research Article 267 www.SID.ir Iran. J. Chem. Chem. Eng. Ahmadi M.H. et al. Vol. 39, No. 1, 2020 Archive of SID in thermal systems as well as optimizing thermodynamic interchanges in the objective function area. With respect cycles and processes containing finite-rate, finite-time, to this, multi-objective optimization of various processes and finite-size constraints [2-7]. Also, The performance has been examined in plenty of researches [43-83]. analysis for internal combustion engine cycles by using In the present research, an irreversible Atkinson cycle finite time thermodynamics were also performed by other is optimized in line with performance improvement papers [8-12]. Recently, abundant performance of the system. In this scenario, for maximizing the thermal evaluations of the Atkinson heat engine have been carried efficiency, ECOP and ECF parameters, a multi-objective out founded on irreversible, endo-reversible, and optimization solution is applied. For the sake of reversible cycle arrangements with utilizing various evaluating eventual answers’ precision in different objective functions including power output, the generated decision-making approaches, error analysis is carried out. power and performance, etc [13-25]. The engine sizes’ effect associated with the investment cost is not taken Cycle model and analysis into account in the analyses of performance contributed Fig. 1 shows an air standard Atkinson cycle diagram. to the mentioned optimization criteria. In this way, The working fluid of the most cycle models Sahin et al. [26,27] presented a novel optimization is considered to be as an ideal gas with the characteristic criteria named the maximum power density examination of fixed specific heats. However, this presumption could for the sake of including the engine size’s effects. be authentic only on the condition of small temperature Optimum operational states of reversible [26] and difference. So, in practical cycle, in which there is large irreversible [27] non-regenerative Joule-Brayton cycle temperature difference, the mentioned presumption have been studied by utilizing the maximum power cannot be implemented. As ref. [84] indicated, under density (MPD) criterion. In the study, the power density the condition of temperature range between 200-1000 K, has been maximized and model elements at MPD states the specific heat capacity with fixed pressure is as follows: have been found. These conditions lead to more efficient 4 and smaller setups. Many investigations have been performed C(..TP 3 56839 6 788729 10 (1) the MPD method to various models of heat engines 1.T.T 5537 106 2 3 29937 10 12 3 [28-38]. 15 4 466. 395 10 T )Rg Added to this, Chen et al. [39] and Wang and Hou [40] performed the technique of MPD to the Atkinson For temperatures between 1000 and 6000 K, the Cp cycle. They presented that the MPD efficiency is higher is calculated as: than the MP efficiency. Also, Wang and Hou [40] 4 investigated an Atkinson cycle linked to a variable C(..TP 3 08793 12 4597 10 (2) temperature heat source at MP and MPD. The analysis 0.T.T 42372 106 2 67 4775 10 12 3 revealed that an engine which is designed for MPD 15 4 3. 97077 10 T )Rg conditions, has smaller size than a MP design based engine. For temperatures between 200 and 600k, Eqs. (1) For the sake of unraveling enigma of this general and (2) can be used which the rage is too wide category, during the whole of the mid-eighties, for the temperature range (300-3500 K) of pragmatic engine. Evolutionary Algorithms (EA) were basically utilized Thus, for describing the specific heat model a single [41]. Determining a cluster of answers, each of which equation has been utilized. The presumption associated implements the objectives on the condition of a gratifying with this is air must be an ideal gas. degree without being overshadowed by any other answers 11 2 7 1. 5 C(.T.TP 2 506 10 1 454 10 (3) is a pragmatic answer to a multi-objective puzzle [42]. 7 5 0. 5 Issues contributed to multi-objective optimization 0.T.T. 4246 10 3 162 10 1 3303 regularly perform as an achievably innumerable group 1.T.T.T) 512 104 1. 5 3 063 10 5 2 2 212 10 7 3 of answers which is called Pareto frontier, where investigated vectors indicate primary feasible CCRV P g (4) 268 Research Article www.SID.ir Iran. J. Chem. Chem. Eng. Thermodynamic Assessment and Optimization of Performance ... Vol. 39, No. 1, 2020 Archive of SID T TT43 e (9) TT43s 3 Cv c And e can present the internal irreversibility 2S 2 of the procedures. Due to the dependency of CP and CV 4 4S on temperature, adiabatic element k C C varies Cp PV 1 by the changes of temperature. Thus, Eq. (10) is not valid for adiabatic stages. Nonetheless, regarding to refs. [90-101], a proper estimation for reversible adiabatic procedure S with k can be carried out, i.e. this procedure can be split to many infinitesimally small stages that each k is Fig. 1: Schematic of an Atkinson cycle diagram. considered fixed. For instance, between states i and j, every reversible adiabatic process could be considered as containing plentiful infinitesimally small processes with According to Eq (4) the C at fixed volume is v fixed k. On the condition of volume dV of the working determined as follows: fluid takes place, and an infinitesimally small change 11 2 7 1. 5 in temperature dT, for any of these processes, the equation C(.T.TV 2 506 10 1 454 10 (5) for reversible adiabatic process with variable k 0.T.T 4246 107 3 162 10 5 0. 5 can be presented as follows. 1..T 0433 1 512 104 1. 5 TVkk11 (T dT)(V dV) (10) 3.T.T) 063 105 2 2 212 10 7 3 The heat added in constant-volume process The received heat by the working fluid in through is calculated as follows: 2 → 3 is: Qin C(T V j T) i TS i j TClnTT V j i . So T3 12 3 Qin M C V dT M(8 . 353 10 T 5 (6) T one has T (T T ) ln(j ) , where T is the equivalent T2 ji Ti 8 2.. 5 7 2 5 1 5 .T.T.T816 10 2 123 10 2 108 10 temperature of the procedure. When CV is the subordinate 4 0. 5 1.T.T 0433 3 024 10 of temperature, the CV (T) could be considered as mean 3.T.T) 063 105 1 1 106 2 T3 specific heat of fixed volume. T2 From eq. (10), one gets The rejected heat is calculated as follows: T V C ln(j ) R ln(i ) (11) T4 Vg 12 3 TVij Qout M C P dT M(8 . 353 10 T (7) T1 The temperature in CV calculation is logarithmic 8 2. 5 7 2 5.T.T 816 10 2 123 10 Tj 5 1.