Performance Analysis of an Atkinson Cycle Engine Under Effective Power

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 assessed 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 cycle. 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: Pef ˙ ˙ EE = ηef = ,EP = Pef = Qin − Qout − Pl, ma = ρaVa = ρa (VT − Vrg) , (12) Q˙ f VT = Vs + Vc = Vsr/(r − 1), (13) Pef EPD = 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 = ε(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. ε 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 ε = 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). They may be expressed respec- fer area [m2], respectively, they are given as: tively as k−1 Tmax T3 λ r − 1 m˙ T =m ˙ a +m ˙ f +m ˙ rg, (22) α = = = = 1 + , (35) Tmin T1 r ηC m˙ a = maN/120 =m ˙ f Fst/φ, (23) λ = Pmax/Pmin = P3/P1. (36) m˙ = m N/120 =m ˙ RGF, (24) rg rg a In this study, HTL, FL, ICL, and EOL are given as fol- 2 Acyl = πdLr/(r − 1) + πd /2, (25) lows: where m and m are air masses per cycle [kg]. RGF Q˙ Q˙ s rg L = ht × 100,L = out × 100, is the residual gas fraction. r and d are compression ht ex Q˙ fuel Q˙ fuel ratio and cylinder bore [m], respectively. TW and Tme Pu are cylinder wall temperature and average combustion Lfr = × 100,Lic = (1 − ηC ) × 100. (37) Q˙ fuel temperature and CV and CP are constant volume and constant pressure specific heats, they can be stated as 3. Results and discussion follows [38]: −11 2 −7 1.5 In this study, a finite time thermodynamic model has CP = 2.506 × 10 T + 1.454 × 10 T been used to evaluate EE, EP, and EDP of an AC engine. Parametrical studies have been performed to investigate −4.246 × 10−7T + 3.162 × 10−5T 0.5 + 1.3301 the engine design and running parameters on the perfor- −1.512 × 104T −1.5 + 3.063 × 105T −2 mance of AC engine. The engine properties are given in Table I. −2.212 × 107T −3, (26) Engine properties. TABLE I CV = CP − R. (27) The equations for reversible adiabatic processes (1–2s) Specification Value and (3–4s) are respectively as follows [43]: bore [mm] 72 T stroke [mm] 62 C × ln 2s = R ln |r| , V1 cylinder number 2 T1 stroke volume [dm3] 0.54 T4s 1 CV2 × ln = R × ln , (28) maximum power [kW] 15 T3 r where compression ratio 10.7 maximum speed [rpm] 3600 C = 2.506 × 10−11T 2 + 1.454 × 10−7T 1.5 V1 2s1 2s1 coolant water −7 −5 0.5 −4.246 × 10 T2s1 + 3.162 × 10 T2s1 + 1.0433 The variation of EE, EP, and EPD are demonstrated 4 −1.5 5 −2 −1.512 × 10 T2s1 + 3.063 × 10 T2s1 with respect to compression ratio (r) in the following figures. 7 −3 −2.212 × 10 T2s1, (29) −11 2 −7 1.5 CV2 = 2.506 × 10 T4s3 + 1.454 × 10 T4s3

−7 −5 0.5 −4.246 × 10 T4s3 + 3.162 × 10 T4s3 + 1.0433

4 −1.5 5 −2 −1.512 × 10 T4s3 + 3.063 × 10 T4s3

7 −3 −2.212 × 10 T4s3, (30) T2s − T1 T4s − T3 T2s1 = ,T4s3 = , (31) ln T2s/T1 ln T4s/T3

β = P3/P2 = T3/T2. (32) β is named as pressure ratio. For irreversible conditions, T2 and T4 could be written as below T2S + T1 (ηC − 1) T2 = , (33) Fig. 2. The variation of Pef −Pd−ηef with re- ηC spect to α. T4 = T3 + ηE (T4S − T3) , (34) Figure 2 shows the eﬀects of cycle temperature ratio on where ηC and ηE are isentropic eﬃciencies for the com- the performance parameters. The maximum EE, EP, and Performance Analysis of an Atkinson Cycle Engine. . . 1309

Fig. 3. The variation of Pef −Pd−ηef with re- Fig. 6. The variation of Pef −Pd−ηef with respect to µ. spect to L.

Fig. 4. The variation of Pef −Pd−ηef with respect to N.

Fig. 7. The variation of (a)Pef −Pd and (b) ηef with respect to N and λ.

EPD increase with increase of cycle temperature ratio owing to more energy input into cylinder. It is clear from the figure that the amplitude of power density is lower than that of effective power. Figure 3 demonstrates the effects of friction coefficient on the engine performance. The friction coefficient is directly related to lubrication oil and friction surfaces. Friction losses increase with increase of the friction coefficient, hence maximum EE, EP, and EPD decrease. Figure 4 illustrates the effects of engine speed on the performance characteristics. As expected, the EP and EPD raise with enhancing engine speed. However, the EE is lower at low engine speeds compared to that at Fig. 5. The variation of Pef −Pd−ηef with respect to S¯P at constant (a) N, (b) L. high engine speeds. At high engine speeds, there are 1310 G. Gonca

Fig. 8. The variation of Pef −Pd−ηef with respect to T 1 at constant (a) α and (b) Tmax. no considerable differences between maximum effective efficiencies as the friction losses rise with rising engine speeds. Increase ratio of fuel’s energy slightly is higher compared to that of the EP and EPD. Figure 5a and b illustrates the effects of average piston speed on the performance characteristics. In these fig- Fig. 9. The variation of (a) α, (b) Pef −Pd, (c) ηef and ures, two conditions are determined as constant engine (d) Pef −ηef with respect to r and φ. speed condition (the 1. condition) and constant stroke length condition (the 2. condition). It is clear that the EP, EPD, and EE increase together with rising average piston speed at the 1. condition since engine dimensions (stroke length and bore) enhance. However, while the EE decreases, the EP and EPD increase with increase of average piston speed at the 2. condition as engine speed increases. It is obvious that power density change of the 2. condition is grater compared to that of 1. condition since engine dimensions increase with increase of effective power. Figure 6 shows the effects of stroke length on the engine performance. It is clear from the figure that the EP increases while the EE and EPD decrease with increase of stroke length. The main reason of this result is that Fig. 10. The variation of Pef −Pd−ηef with re- the friction losses and engine dimensions increase with respect to φ. spect to stroke length. Although engine power increases, ratio has positive effect on the engine performance pa- engine dimensions more increase. Also, we can see that rameters. They increase with enhancing cycle pressure the ratio of power change is higher than that of power ratio. The engine power and power density increase with density. increase of engine speed. However, the EE rises to a spec- Figure 7a and b demonstrates the effects of cycle pres- ified value of engine speed and then decreases. It is clear sure ratio and engine speed on the engine performance that optimum engine speed which provides the maximum for constant compression ratio condition. Cycle pressure EE rises with enhancing cycle pressure ratio. Performance Analysis of an Atkinson Cycle Engine. . . 1311

Fig. 11. The variation of Pef −Pd−ηef with respect to TW .

Fig. 12. The variation of Pef −Pd−ηef with respect to P1.

Figure 8a and b shows the effects of intake tempera- Fig. 14. The effects of d/L on Pef −Pd−ηef variation ture on the engine performance. Two main conditions at constant (a) α and L, (b) φ and L, (c) φ and r. have been described as constant cycle temperature ratio condition (the 1. condition) and constant maximum com- minishes with enhancing air inlet temperature at the 2. bustion temperature condition (the 2. condition) in these condition as air mass in the cylinder minimizes. figures. At the 1. condition, the maximum EP, EPD, Figure 9a–d illustrates the influences of compression and EE increase while intake temperature increases since ratio and equivalence ratio on the cycle temperature ra- maximum combustion temperature and energy input in- tio and performance characteristics. As can be seen from crease. However, the maximum engine performance di- the figure, cycle temperature ratio, EP, EPD, and EE rise with enhancing compression ratio. However, they maximize to a determined value and then begin to abate with respect to rising equivalence ratios. There are optimum values of equivalence ratio which provides maximum cycle temperature ratio, EP, EPD, and EE. Their optimum values are attained at different equivalence ratios. The highest values of cycle temperature ratio, EP and EPD are between 1 and 1.2 of equivalence ratio while the maximum value of EE is between 0.8 and 1 of that. Figure 10 shows the influence of equivalence ratio on the performance characteristics. Similar to previous figures, the maximum EE, EP, and EPD increase to partic- ular values of equivalence ratio and then begin to abate. The maximum effective efficiency is seen when equivalence ratio is equal to 0.9 while the maximum effective Fig. 13. The variation of Pef −Pd−ηef with respect to d/L. power is seen when equivalence ratio happens 1.2. 1312 G. Gonca

temperature ratio condition (the 1. condition) and constant equivalence ratio condition (the 2. condition). In- complete combustion losses (Lic) and heat transfer losses (Lht) increase whilst exhaust energy losses (Lex) decrease and friction losses (Lfr) remain constant with rising compression ratio at the 1. condition. Total cylinder volume and equivalence ratio change with respect to changing of compression ratio at this condition. However, Lic and Lfr are constant, Lht increases and Lex minimizes with respect to rising compression ratio at the 2. condition. Lic does not change at constant equivalence ratio because combustion efficiency is constant. Total cylinder volume increases with increasing compression ratio, hence Lht increases and Lex diminishes. Lfr changes with respect to stroke length and engine speed which are constant at both of the conditions. Therefore, Lfr does not change at the 2. condition due to constant fuel energy input. At the 1. condition, it increases since fuel energy input decreases with increase of compression ratio. 4. Conclusion The influences of the design and running parameters on the performance characteristics of an AC engine are investigated by using a FTT model. A comprehensive parametrical study is conducted. The results showed that the EP, EPD, and EE rise with rising air inlet pressure, cycle Fig. 15. The variation of energy loss percentages with respect to r for constant (a) α and (b) φ. pressure and temperature ratios. The performance characteristics diminish with friction coefficient. However, the EP, EPD, and EE raise with rising average piston The effects of cylinder wall temperature on the per- speed for constant engine speed conditions, but, whilst formance characteristics is shown in Fig. 11. There are the EP and EPD rise, the EE minimizes with rising av- no considerable changes in maximum effective power and erage piston speed for constant stroke length conditions. power density depends on cylinder wall temperature. While the EP and EPD increase, the EE reduces with However, maximum effective efficiency increases with in- rising stroke length and engine speed. The EP, EPD, crease of cylinder wall temperature as heat transfer loss and EE increase up to a determined value and then be- decreases. gin to minimize with rising equivalence ratio and com- Figure 12 demonstrates the effect of air inlet pressure pression ratio. The incomplete combustion losses (ICL) on the performance characteristics. It is known that more and heat transfer losses (HTL) raise, as exhaust output air mass is introduced into the cylinder at higher pressure losses (EOL) decrease with augmenting compression ra- conditions. Therefore, the performance characteristics tio for constant cycle temperature ratio conditions. At rise with enhancing air inlet pressure. this condition, FL is constant. However, the FL and ICL The influence of bore/stroke ratio (d/L) on the engine are constant, while EOL diminishes and HTL increase performance characteristics is shown in Fig. 13. It is ob- at the constant equivalence ratio conditions. The results vious that the performance characteristics rise with rising have scientific value and they can be used as engineering d/L owing to enhancing dimension of the engine. approaches by engine designers. Figure 14 shows the effects of d/L on the engine performance at constant cylinder volume for different con- References ditions. In this figures, three conditions are determined as constant cycle temperature ratio and stroke length [1] Y.Ge, L. Chen, F. Sun, C. Wu, Int. Commun. Heat condition (the 1. condition), constant equivalence ratio Mass Transfer 32, 1045 (2005). and stroke length condition (the 2. condition), constant [2] Y. Ge, L. Chen, F. Sun, C. Wu, Int. J. Ambient equivalence ratio and compression ratio condition (the 3. Energy 26, 203 (2005). condition). At the 1. condition, the EP, EPD, and EE [3] L. Chen, Y. Ge, F. Sun, C. Wu, Termotehnica 14, 24 maximize to a specified value and then begin to abate (2010). with rising d/L. At the 2. and 3. conditions, the EP, [4] L. Chen, Y. Ge, F. Sun, C. Wu, Int. J. Ambient EPD and EE raise with enhancing d/L. Energy 32, 87 (2011). Figure 15 illustrates the effects of compression ratio on [5] A. Al-Sarkhi, B.A. Akash, J.O. Jaber, M.S. Mohsen, losses as fuel’s energy. In order to investigate the energy E. Abu-Nada, Int. Commun. Heat Mass 29, 1159 losses, two conditions are determined as constant cycle (2002). Performance Analysis of an Atkinson Cycle Engine. . . 1313

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