Vol. 132 (2017) ACTA PHYSICA POLONICA A No. 4 Performance Analysis of an Atkinson Cycle Engine under Effective Power and Effective Power Density Conditions G. Gonca∗ Yildiz Technical University, Naval Arch. and Marine Eng. Depart., Besiktas, Istanbul, Turkey (Received November 16, 2016; in final form May 20, 2017) This study presents performance optimization of an Atkinson cycle engine using criteria named as effective power and effective power density conditions. The effects of design and operating parameters such as compression ratio, cycle pressure ratio, cycle temperature ratio, equivalence ratio, bore/stroke ratio, inlet temperature, inlet pressure, engine speed, friction coefficient, mean piston speed and stroke length, on the performance characteristics have been examined. Moreover, the energy losses have been determined as fuel energy and they have been classified as incomplete combustion losses, friction losses, heat transfer losses, and exhaust output losses. Realistic values of specific heats have been used depending on temperature of working fluid. The results of the study can be assessed as an engineering tool by the Atkinson cycle engine designers. DOI: 10.12693/APhysPolA.132.1306 PACS/topics: gasoline engine, Atkinson cycle, engine performance, power density, finite-time thermodynamics 1. Introduction on artificial neural network technique. Gahruei et al. [28] compared the performances of dual Diesel cycle and dual In the recent years, the researchers carried out several AC based on the FTT by considering irreversible energy studies [1–21] on the Miller cycle (MC) engine to dimin- losses. It was observed from the results that the perfor- ish NOx emissions by reducing the maximum combus- mance of dual AC are higher than that of dual Diesel tion temperatures of the engines. However, the Atkinson cycle. Zhao and Xu [29] designed an AC engine in order cycle (AC) engine can provide more cycle work than the to maximize fuel economy at partial load running con- Otto cycle (OC) engine and the Miller cycle (MC) engine ditions based on genetic algorithm and power simulation at the same maximum combustion temperatures due to models. The results showed that the fuel economy could higher expansion ratio. Therefore, so many works have be improved up to 7.67%. been performed about AC engines in the recent years. Mozaffari et al. [30] conducted an optimization work Wang and Hou [22] analyzed the performance of an AC for the AC engine using mutable smart bee algorithm engine using maximum power and maximum power den- and adaptive neuro-fuzzy inference system. Capaldi [31] sity criteria. Ge et al. [23] determined the performance of designed a novel Atkinson–Miller cycle engine for a mi- an AC engine with considerations of heat transfer losses, cro cogeneration plant to increase thermal efficiency of friction losses and temperature dependent specific-heats the plant and to abate the pollutant emissions released of the working fluid. Lin and Hou [24] conducted an in- from the plant. Gonca and Sahin [32] carried out a vestigation about the effects of heat loss, friction loss, thermo-ecological performance optimization for a dual and temperature dependent specific heats on the perfor- AC engine. Gonca [33, 34] performed a couple of in- mance of an air-standard AC engine under the restricted vestigation studies on the dual AC engine considering maximum cycle temperatures. friction, heat transfer and temperature-dependent spe- Benajes et al. [25] investigated the potential of the AC cific heats based on classical thermodynamics and FTT and exhaust gas recirculation (EGR) applications on re- methods. Ebrahimi [35–37] carried out thermodynamic ducing of exhaust emissions in a heavy duty diesel engine. performance analyses for the dual cycle [35], MC [36] and It was pointed out that AC can remarkably decrease ni- AC [37] engines. trous oxides but soot emissions increase. Ebrahimi [26] In this study, the influences of the design and running examined the influences of the equivalence ratio, average parameters on the efficiency, power and power density of piston speed and temperature of cylinder wall on the per- an AC engine have been examined by using simulation formance of an AC engine using a finite–time thermody- model based on the FTT. In this comprehensive report, namics (FTT) model. Zhao et al. [27] performed an opti- performance conditions have been evaluated based on the mization work for geometrical compression ratio and op- effective efficiency (EE), effective power (EP), and effec- erating parameters of an AC spark ignition engine based tive power density (EPD) for an AC engine. This study has a noticeable novelty. Presented results can be as- sessed by engine designers and manufacturers to obtain optimum performance conditions for the AC engines. ∗e-mail: [email protected] (1306) Performance Analysis of an Atkinson Cycle Engine. 1307 2. Theoretical model of friction which considers the global losses, s¯P is mean piston velocity which is given as In this study, AC engine is analyzed by using FTT model. The AC is shown in Fig. 1. The parameters and s¯P = L × N=30; (5) engine specifications used in the analysis are inlet pres- where L and N are stroke length [m] and engine speed _ sure P1, inlet temperature T1, engine speed N, stroke L, [rpm]. Qf is the total heat potential of the injected fuel bore d, residual gas fraction (RGF) friction coefficient µ, and it is given as below cylinder wall temperature TW , cycle temperature ratio α Q_ f =m _ f Hu; (6) and their standard values are given as follows: 100 kPa, where Hu is lower heat value (LHV). m_ f is time- 300 K, 3600 rpm, 0.072 m, 0.062 m, 0.05, 12.9 N s/m, dependent fuel mass and it can be expressed as follows: 400 K, 8, respectively. In the present model, the EE, EP, m_ f = mf N=120; (7) where mf is fuel mass per cycle [kg]. Q_ f;c is heat released by combustion, Q_ ht is the heat loss by heat transfer into cylinder wall and they are given as below Q_ f;c = ηcm_ f Hu; (8) Q_ ht = htrAcyl(Tme − TW ) = htrAcyl(T2 + T3 − 2TW )=2; (9) Where, ηc is combustion efficiency. It can be written as below [7, 8, 26]: 2 ηc = −1:44738 + 4:18581/φ − 1:86876/φ : (10) Fig. 1. P −V and T −S diagram for the irreversible φ is equivalence ratio and it can be written as below Atkinson cyclediagram for the irreversible Atkinson cy- cle. φ = (mf =ma)=Fst; (11) where m is air mass per cycle [kg]. F is stoichiometric and EPD are given as below [19, 20, 33, 38]: a st fuel-air ratio and they are given as follows: P ef _ _ EE = ηef = ; EP = Pef = Qin − Qout − Pl; ma = ρaVa = ρa (VT − Vrg) ; (12) Q_ f VT = Vs + Vc = Vsr=(r − 1); (13) Pef EP D = P = ; (1) 2 d VT πd L VT V = = ; (14) c r 4(r − 1) where the total heat addition Q_ in at constant volume Fst = "(12:01α + 1:008β + 16γ + 14:01δ)=28:85; (15) (2–3), the total heat rejection Q_ out at constant pres- ρa = f(T1;P1); (16) sure (4–1) and loss power by friction (Pl) [10, 39] could where VT , Va, Vrg, Vs, and Vc are volume of total cylin- be written as below: der, air, residual gas, stroke and clearance. Q_ in = Q_ f;c − Q_ ht = ρrg is density of residual gas which is given as below Z T3 ρ = f(T ;P ): (17) m_ C dT =m _ 0:835 × 10−11T 3 rg mix 1 T V T T is average temperature of air-steam mixture. They T2 mix +0:5816 × 10−7T 2:5 − 2:123 × 10−7T 2 are given as below m_ aT1Ra +m _ rgT1Rrg −5 1:5 4 −0:5 Tmix = : (18) +2:108 × 10 T + 1:0433T + 2:024 × 10 T m_ aRa +m _ rgRrg T3 Ra and Rrg are gas constants of air and residual gas. −3:063 × 105T −1 + 1:106 × 107T −2 ; (2) Their values are taken as 0.287 kJ/(kg K). T2 The compression ratio r is given as Z T4 _ −11 3 Qout =m _ T CP dT =m _ T 0:835 × 10 T r = V1=V2; (19) T1 −7 2:5 −7 2 where f stands for function. The functional statements +0:5816 × 10 T − 2:123 × 10 T are acquired by using EES software [40]. The fuel type used in the model is gasoline and its chemical formula is +2:108 × 10−5T 1:5 + 1:3303T + 2:024 × 104T −0:5 given as C7H17 [41]. T3 5 −1 7 −2 α; β; γ; δ are atomic numbers of carbon, hydrogen, oxy- −3:063 × 10 T + 1:106 × 10 T ; (3) T2 gen, nitrogen in fuel, respectively. " is molar fuel-air ra- ¯2 ¯2 tio [42]: Pl = µSP = Z + 0:048N + 0:4SP VsN=1200; (4) γ β where Z is a constant relation to friction [10] and its " = 0:21=(α − 2 + 4 ); (20) minimum value is taken as 75, where µ is a coefficient where htr is heat transfer coefficient and it is stated 1308 G. Gonca as [42]: pression and expansion processes, respectively. In this −0:06 0:8 0:4 0:8 study, the other dimensionless engine design parameters htr = 130V P1 Tmix(¯sP + 1:4) ; (21) T used in the analysis are cycle temperature ratio (α) and where m_ T ; m_ a; m_ rg and Acyl are flow rate of total charge [kg/s], air [kg/s], residual gas [kg/s] and total heat trans- cycle pressure ratio (λ).