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This article was downloaded by: [Beijing University of Technology] On: 10 June 2011 Access details: Access Details: [subscription number 932491352] Publisher Taylor & Francis Informa Ltd Registered

1 This article was downloaded by: [Beijing University of Technology] On: 10 June 2011 Access details: Access Details: [subscription number ] Publisher Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK International Journal of Ambient Energy Publication details, including instructions for authors and subscription information: The power and efficiency characteristics for an irreversible Otto cycle L. Chen a ; T. Zheng a ; F. Sun a ; C. Wu b a Faculty 306, Naval University of Engineering, Wuhan, People's Republic of China b Mechanical Engineering Department, U.S. Naval Academy, Annapolis, MD, USA Online publication date: 30 March 2011 To cite this Article Chen, L., Zheng, T., Sun, F. and Wu, C.(2003) 'The power and efficiency characteristics for an irreversible Otto cycle', International Journal of Ambient Energy, 24: 4, To link to this Article: DOI: / URL: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

International Journal of Ambient Energy, Volume 24, Number 4 October 2003 The power and efficiency characteristics for an irreversible Otto cycle L. Chen*, T. Zheng**, F. Sun*** and C.

2 International Journal of Ambient Energy, Volume 24, Number 4 October 2003 The power and efficiency characteristics for an irreversible Otto cycle L. Chen*, T. Zheng**, F. Sun*** and C. Wut ' Lingen Chen, Faculty 306. Naval University of Engineering, Wuhan , People's Republic of China (To whom all correspondence should be addressed - address: Igchenna@public.wh.hb.cn ). " Tong Zheng, Faculty 306. Naval University of Engineering, Wuhan People's Republic of China. "' Fengrui Sun. Faculty 306. Naval University of Engineering, Wuhan People's Republic of China. t Chih Wu, Mechanical Engineering Department. U.S. Naval Academy, Annapolis, MD USA. O Ambient Press Limited 2003 SYNOPSIS The performance of an air-standard Otto cycle with heat transfer and friction-like term losses is analysed and optimised using finite-time thermodynamics. The relationship between the power output and the compression ratio, and between the thermal efficiency and the compression ratio of the cycle are derived. Moreover, the effects of heat transfer and global losses, lumped in a friction-like term on the performance of the cycle, are investigated by detailed numerical examples. INTRODUCTION Finite-time thermodynamics [I-31 is a powerful tool for the performance analysis and optimisation of real engineering cycles. Several authors have examined the finite-time thermodynamic (FTT) performance of internal combustion engines. Mozurkewich and Berry [4] and Hoffman et a/. [5] used mathematical techniques from optimalcontrol theory to determine the optimal motion of the piston in an Otto and Diesel engine. Aizenbud and Band [6] and Chen et a/. [7] determined the optimal motion of a piston fitted to a cylinder containing a gas pumped with a given heating rate and coupled to a heat bath during finite time. Orlov and Berry [8] obtained the power and efficiency limits from finite-time thermodynamics for internal combustion engines. Angulo-Brown et a/. [9] and Chen et a/. [lo] optimised the power of the Otto and Diesel engines with friction loss during finite time. KIein [I 11 studied the effect of heat transfer through a cylinder wall on work output of the Otto and Diesel cycles. Chen et a/. [12, 131 derived the relationships between net power output and efficiency of Diesel and Otto cycles with consideration of heat transfer through the cylinder wall. On the basis of these research works, the relationship governing net power output and the efficiency for the Otto cycle with consideration of heat transfer loss and friction-like term loss during finite time are derived in this paper. CYCLES ANALYSIS An ideal air-standard Otto cycle is shown in Figure 1. The compression process ignition is isentropic 1-2; the combustion is modelled by a reversible constant volume process 2-3; the expansion process is isentropic 3-4; and the heat rejection is a reversible constant volume process 4-1. As is usual in FTT-heat engine models we assume instantaneous adiabats. For the isochoric branches (2-3 and 4-1) in Figure 1, we assume that heating from state 2 to state 3 and cooling from state 4 to state 1 proceed according to constant temperature rates; i.e. dt - I (for 2-3), and dt -- l (for4-1) (1) dt K, dt K,

3 average temperature of both working fluid and cylinder wall and that the wall temperature is a constant. The heat added to the working fluid by combustion is given in the following linear relation [ll - 131: where a and /3 are two constants related to combustion and heat transfer. Combining Equations (6) and (7) gives: Figure 1 T-s diagram for the Otto cycle. where T is the absolute temperature and t is time, K, and K, are constants. Equation (1) may be considered as average temperature rates. Integrating Equation (1) yields: where t,, and t2, are the heating and cooling times, respectively. Then, the cycle period is: The work output is: where C, is the heat capacity at constant volume, i.e. the product of mass flow rate and specific heat. Thus, the power output is: For processes 1-2 and 3-4, we have: where y = V1/V2 is the compression ratio, k is the ratio of specific heats, k = C,/C,, C, is the heat capacity at constant pressure, i. e., the product of mass flow rate and specific heat. Substituting Equations (8)-(10) into Equation (5) yields: p =-= 1 W C, [a(1- + 2P (1- y k-l) TI] z (K, + KP yl-k) (a- 2py k-l TI) (1 1) Equation (1 1) gives a parabola function of y. Taking into account the friction loss of the piston as recommended by Angulo-Brown et a/. 191 and Chen et a/. [lo] for the Otto cycle and Diesel cycle and assuming a dissipation term represented by a friction force which is a linear function of the velocity gives: where p is a coefficient of friction which takes into account global losses and x is the piston displacement. Then, the lost power is: The piston mean velocity is: The heat added to the working fluid during process 2-3 is: For an ideal Otto cycle, there are no irreversible losses. However, for a real Otto cycle, heat transfer irreversibility between the working fluid and the cylinder wall and friction-like term loss are not negligible. We assume that the heat loss through the cylinder wall is proportional to the where x, is the piston position at minimum volume and At,, is the time spent in the power stroke. Thus, the resulting power output is: - 'V la(' -Y'-~) + 2P -~"')~11-b(y-1)2 (15) (K, + K, (a - 2Py k-l TI)

4 where: The thermal efficiency of the cycle is: P q=- (QiJz) - - b (y - (K, + K, yl-k) (a - 2Py k-l TI) (1 7) NUMERICAL EXAMPLES To illustrate the preceding analysis, we consider the same Otto engine parameters reported by Angulo-Brown et a/. [9] and Klein [I 1). Using the same values of temperatures, the cycle time, isochoric mole heat capacitance and for the number of moles of gas in the power stroke given in these references, we have z = ms, C, = kj/k and C, = kj/k. Taking equal heating and cooling times (t,, = t, = 2/2 = 16.6 ms), the constant temperature rates K, and K, are estimated as K, = x s/k and K, = x s/k. We consider p = 7'0 with o = 12.9 kg/s where o is the friction coefficient of the exhaust and compression strokes. Taking the same values of x, and At,, as in the Mozurkewich paper [4] and following the same procedure to determine the losses for the full cycle, we obtain b = 32.5 kw. The maximum cycle temperature ratio is 2 = 2742/329 = The typical parameter ranges of the three parameters are a = kj, f3 = kj/k and T, = K [Ill. Figures 2-4 show, respectively, the power output versus compression ratio curve, the efficiency versus compression ratio curve and the power output versus efficiency curve for a = 3500 kj, P = 1.0 kj/k and T, = 350 K. If the global losses lumped in a friction-like term are negligible, the power output versus compression ratio character is similar to a parabola, the efficiency increases monotonically with the increase of compression ratio, and the power versus efficiency curve exhibits a parabola. With heat transfer loss and global losses lumped in a friction-like term, the power output versus compression ratio character and the efficiency versus compression ratio character are similar to a parabola, while the power output versus efficiency curve is loop-shaped. For the specified parameter ranges and b = 32.5 kw (solid line), there is a maximum power output P,,, = kw with the corresponding optimum compression ratio y, = and efficiency qp = ; and there is also a maximum efficiency qmax = with the corresponding optimum compression ratio y,, = and power output P, = kw. Suppose we maintain the same data as in the preceding calculations and change only the losses to b = 54 kw, both the power output and the efficiency would decrease as shown in Figures 2, 3 and 4. The effect of f3 on the power output versus Figure 2 Effect of b on P - y

5 Figure 3 Effect of b on q - y Figure 4 Effect of b on P - q efficiency curve with a = 3500 kj, TI = 350 K and b = 32.5 kw is shown in Figure 5. The effect of a on the power output versus efficiency curve with p = 1.0 kj/k, b = 32.5 kw and TI = 350 K is shown in Figure 6. The effect of T, on the power output versus efficiency curve with a = 3500 kj, p = 1.O kj/k and b = 32.5 kw is shown in Figure 7. Figures 5-7 show that the maximum power output and the corresponding efficiency increase with a decrease of p and T, and an increase of a. Because the finite-time thermodynamic optimisation emphasises the compromise between power output and efficiency, the parameter selection range should be between the maximum power point and the maximum efficiency. CONCLUSION In this paper, the effects of cylinder wall heattransfer and global losses lumped in a friction-like term on the performance of the Otto cycle during finite time are investigated. The relationship between power output and compression ratio, and between thermal efficiency and compression ratio of the cycle are derived. The maximum power output and corresponding efficiency, and the maximum efficiency and corresponding power

6 Figure 5 Effect of P on P - q Figure 6 Effect of a on P - q output are also calculated. The detailed effect analyses are shown by numerical examples. The results provide significant guidance for the performance evaluation and improvement of real Otto engines. ACKNOWLEDGEMENTS This paper is supported by The Foundation for the Author of National Excellent Doctoral Dissertation of the People's Republic of China (Project No ) and The National Key Basic Research and Development Program of the People's Republic of China (Project No. G ). REFERENCES 1. Sieniutycz, S. and Shiner, J. S. "Thermodynamics of irreversible processes and its relation to chemical engineer: Second law analyses and finite time thermodynamics". Journal of Non-Equilibrium Thermodynamics, Vol. 19, NO. 4, 1994, pp Bejan, A. "Entropy generation minimization: The new thermodynamics of finite-size device and finite-time processes". Journal of Applied Physics, Vol. 79, No. 3, 1996, pp Chen, L., Wu, C. and Sun, F. "Finite time thermodynamic optimization or entropy

7 Figure 7 Effect of T, on P - q generation minimization of energy systems". Journal of Non-Equilibrium Thermodynamics, Vol. 24, NO. 4, 1999, pp Mozurkewich, M. and Berry, R. S. "Optimal paths for thermodynamic systems: the ideal Otto cycle". Journal of Applied Physics, Vol. 53, NO. 1, 1982, pp Hoffman, K. H., Watowich, S. J. and Berry, R. S. "Optimal paths for thermodynamic systems: The ideal Diesel cycle". Journal of Applied Physics, Vol. 58, No. 6, 1985, pp Aizenbud, B. M., Band, Y. B. and Kafri, 0. "Optimization of a model internal combustion engine". Journal of Applied Physics, Vol. 53, NO. 3, 1982, pp Chen, L., Sun, F. and Wu, C. "Optimal expansion of a heated working fluid with phenomenological heat transfer". Energy Conversion Management, Vol. 39, Nos. 3/4, 1998, pp Orlov, V. N. and Berry, R. S. "Power and efficiency limits for internal combustion engines via methods of finite-time thermodynamics". Jounal of Applied Physics, Vol. 74, NO. 10, 1993, pp Angulo-Brown, F., Fernandez-Betanzos, J. and Diaz-Pico, C. A. "Compression ratio of an optimized Otto-cycle model". European Journal of Physics, Vol. 15, No. 1, 1994, pp Chen, L., Lin, J., Lou, J., Sun, F. and Wu, C. "Friction effect of on the characteristic performance of Diesel engines". International Journal of Energy Research, Vol. 26, No. 11, 2002, pp Klein, S. A. "An explanation for observed compression ratios in internal combustion engines". Transactions of ASME Jounal Engineering: Gas Turbine Power, Vol. 113, NO. 4, 1991, pp Chen, L., Zen. F., Sun, F. and Wu, C. "Heat transfer effects on the net work output and power as function of efficiency for air standard Diesel cycle". The International Journal of Energy, Vol. 21, No. 12, 1996, pp Chen, L., Wu. C., Sun, F. and Wu, C. "Heat transfer effects on the net work output and efficiency characteristics for an air standard Otto cycle". Energy Conversion Management, Vol. 39, NO. 7, 1998, pp

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Online publication date: 01 March 2010 PLEASE SCROLL DOWN FOR ARTICLE This article was downloaded by: [2007-2008-2009 Pohang University of Science and Technology (POSTECH)] On: 2 March 2010 Access details: Access Details: [subscription number 907486221] Publisher Taylor