THE NUMERICAL THERMODYNAMIC ANALYSIS OF OTTO-MILLER CYCLE (OMC) Mehmet Cakir 1*

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1 THE NUERIAL THERODYNAI ANALYSIS OF OTTO-ILLER YLE (O) ehmet air * Department of arine Engineering Operations, Yildiz Technical University, 449, Istanbul, Turey Abstract This paper presents a thermodynamic analysis for an irreversible Otto- iller ycle (O) by taing into consideration heat transfer effects and internal irreversibilities resulting from compression and expansion processes. In the analyses, the influences of the miller cycle ratio, combustion and heat loss constants and inlet temperature have been investigated relations with efficiency in dimensionless form. The dimensionless power output and power density and thermal efficiency relations have been computationally obtained versus the engine design parameters with respect to combustion and heat transfer constants. The results demonstrate that the heat transfer and combustion constants have considerable effects on the cycle thermodynamic performance. This situation theoretically verified for O. Key words: Otto-iller cycle; Thermodynamic optimization; Thermal efficiency.. Introduction Internal combustion engines are commonly used in the daily life. Air-standard power cycle models are employed by most of the researchers to investigate numerical thermodynamic analysis of the internal combustion engines. ozurewich and Berry [] studied the influences of the internal losses during the cycle processes of an Otto cycle and Hoffman et al. [2] conducted a similar study for diesel cycle. iller cycle is a strategy of shortening compression stroe relative to expansion stroe. iller cycle is more effective than Otto cycle and the heat transfer effects, friction and specific heat ratio on fuel efficiency are significant and must be observed in theoretical cycle analysis [ 8]. Wu et al. [9] analysed performance and optimization of a supercharged Otto-iller ycle engine. Klein [0] investigated a performance analysis for the purpose of investigate of the heat transfer effects through the engine walls of cylinder liner on the wor for Otto and Diesel ycles. Analogously, Lin et al. [] studied the performance of irreversible air standard iller ycle in a four-stroe free-piston engine using finite-time thermodynamic. Sahin et al. [2] optimized an air-standard dual cycle by virtue of the * orresponding author. Tel.: ; Fax: addresses: mecair@yildiz.edu.tr (.AKIR)

2 ecological objective function. They studied the optimum performance and design parameters at maximum ecological performance criterion. hen et al. [] performed a study in order to investigate the power output and thermal efficiency relations for an air standard reversible Otto ycle considering the heat transfer loss from the cylinder wall. Angulo-Brown et al. [4] have presented an irreversible model for the air-standard Otto ycle, considering the finite times for heat added and heat loss processes. They climaxed the power output, thermal efficiency and ecological functions related to the compression ratio and demonstrated that the optimum compression ratio values for practical Otto Engines. Ust et al. [5] proposed an irreversible model for on Otto heat engine and reported using thermodynamic analysis based on the maximum mean effective pressure, power and thermal efficiency. Gonca et al. [6] studied the power output and thermal efficiency analysis for an airstandard irreversible Dual-iller ycle (D). In this study, a thermodynamic performance analysis implemented for an irreversible Otto- iller ycle based on the investigation of power output, power density and thermal efficiency taing into the internal irreversibility arising from the compression and expansion processes. Furthermore, the various engine design parameters effects such as compression ratio, miller cycle ratio, inlet temperatures on the performance of the Otto-iller cycle have been analysed. 2. The Thermodynamic Analysis of the Irreversible O Fig. demonstrates P- and T-S diagrams of the irreversible air-standard O. While s stands for isentropic processes which does not tae into consideration the internal irreversibilities, the real heat input and output processes are 2 and 4 5 at constant volume; 5 at constant pressure. The total heat input and output given below: Q Q m ( T ) 2 () in 2 T Q Q Q m T T ) m ( T ) (2) out 45 5 ( 4 5 P 5 T where T, T2, T, T4 and T5 are temperatures at irreversible O cycle and m is the mass flow rate, and P are the specific heat capacities of the ideal air. The power output according to the first law thermodynamics can be referred: and the thermal efficiency is given as follows, W Q Q m T T ( T T ) ( T ) () in out 2) T W Q out ( T4 T5 ) ( T5 T ) (4) Q Q ( T T ) in The dimensionless power output and power density of the cycle could be given as: W W m T in in out (5) Q Q m T m T T ) ( T T ) ( T m T 2 T ) W T T T T T T W 2 ( 4 5) ( 5 ) d r T r (6) 2

3 Figure. P- and T-S diagrams for the irreversible Otto-iller ycle In this part, iller cycle ratio r [7] is used to define the difference between O and Otto ycle (O). We can define the compression ratio ( r ), miller ratio ( r ), stroe ratio ( ), pressure ratio ( ) and cycle temperature ratio ( )as follows [6]: r v v 2 (7) r v / T (8) 5 v T5 / r r v / v 5 2 (9) O equals to O if r. P (0) max P2 T T2 T T T T () The second law of thermodynamics requires that s2s s4s5 s5and the result is min T2 ST4 ST5 TT (2) Isentropic efficiency of the compression and expansion processes (-2 and -4) are written as [8]: T2 S T () T T and 2 T T4 E (4) T T By using Eqs. ()-(4) and re-ordering the design parameters of the O, the temperatures of the state 2 and 4 are written as following: and 4S r T2 T (5)

4 T 4 T E (6) Klein asserted that the heat input to the woring fluid at the constant volume processes could be given as [0]: Q a b( T T ) (7) 2 2 Where a and b are the heat release (combustion) and heat loss constants during the combustion processes respectively. T can be rewritten by using these constants as below: a T (8) b r b T By writing the Eq. (8) into Eq. (6), one can obtain r a b T T 4 E b (9) The relationship between T and T5 is: T 5 Tr (20) The dimensionless power output, power density and thermal efficiency of the cycle can be expressed by substituting Eqs. (5), (8), (9) and (20) into Eqs. (4), (5) and (6) as follows: r W r E (2) r E W d (22) r r r r Q Q out in E r r r (2) All equations have been written in Engineering Equation Solver (EES) [9] and numerical solutions and comparative figures have been obtained.. Results and Discussion The following parameters have been used in this analysis:. 4, 0.78J / gk, a J / g, b KJ / gk, r 4, T K, 0. 85, E 0.90 [5,,20]. Using the above constants and parameters, dimensionless power output and density versus thermal efficiency and compression ratio versus thermal efficiency could be plotted as in Figs

2- demonstrates the influence of a and b constants on the dimensionless power W, W d Blac, blue and red lines on the graph r (Otto), dimensionless power output for r 2 and r,

5 Figure 2.W, W d relation with variation of different a combustion constant for the irreversible Otto-iller cyclet 00K, b 0,4J / gk. Figure.W, relation with variation of different b heat transfer coefficients for the irreversible Otto-iller cyclet 00K, a 2500J / g. W d The Figs. 2- demonstrates the influence of a and b constants on the dimensionless power W, W d Blac, blue and red lines on the graph r (Otto), dimensionless power output for r 2 and r, respectively. In Fig. 2, the dimensionless power output and output, power density and thermal efficiency ( refers dimensionless power output for dimensionless power density for 2 density versus thermal efficiency increase with increasing a parameter. Increasing a causes an 5

. While the dimensionless power output and power density versus thermal efficiency increase with rise of a constant, they decrease with rise of b constant.

6 increase at the amount of heat added to the woring fluid due to combustion. Also, the thermal efficiency performance increases with increasing r and this situation holds for variation of b constant in Fig.. While the dimensionless power output and power density versus thermal efficiency increase with rise of a constant, they decrease with rise of b constant. This situation is similar to that of previous studies [,20,2]. Figure 4.W, W d relation with variation of different T temperatures for the irreversible Otto- iller cyclea 2500J / g, b 0.4J / gk. Figure 5.W, W d relation with variation of different r for the irreversible Otto-iller cycle T 00K, a 2500J / g, b 0.4J / gk. 6

The influence T on the performance is shown in the Fig. 4. olumetric efficiency of cycle reduces with increasing T. So, the mass of woring fluid reduces for cycle.

7 The influence T on the performance is shown in the Fig. 4. olumetric efficiency of cycle reduces with increasing T. So, the mass of woring fluid reduces for cycle. Hence, the performance decreases in all conditions with increasing T. Hou also [5] obtained similar results about the effect T on the performance of the dual cycle. Figure 6.W, W d r relation with variation of different r for the irreversible Otto-iller cycle T 00K, a 2500J / g, b 0.4J / gk. The dimensionless power output, power density and thermal efficiency relation is shown with variation of different r in Fig. 5. The loop curves of dimensionless power output, power density and thermal efficiency become bigger up to r 2 and then begin to decline when r increases. According to these curves, the ideal miller ratio is r 2 value. In Fig. 6, the dimensionless power output, power density and compression ration relation is shown with variation of different r. Here, maximum dimensionless power outputs approximately are r 0 value for all of r values. This situation holds for dimensionless power density. The maximum dimensionless power output is similar for miller ratio.5 and 2. After this point, if miller ratio increases, the dimensionless power output decreases. The dimensionless power density is maximum for r. 5. After this point, the higher miller ratio, the dimensionless power density gradually decreases. The thermal efficiency and compression ratio relation is shown with variation of different r in Fig. 7. Here, the maximum thermal efficiencies corresponding compression ratios could be observed for various r values. As it can be seen, the cycle thermodynamic performance increases to a certain value and then begins to reduce with increasing compression ratio. It could be observed that maximum thermal efficiency and corresponding compression ratio is similar for r. 5 and r 2. But, as Fig. 5 can be observed, idealist loop curve of dimensionless power out is r 2 value. 7

8 4. onclusion Figure 7. r relation with variation of different r for the irreversible Otto-iller cycle T 00K, a 2500J / g, b 0.4J / gk. This paper analyses the optimum cycle thermodynamic performance. The results obtained from this paper can be used to determine engine design parameters. Therefore, It is analysed the influences different miller cycle ratio ( r ), inlet temperature ( T ), combustion and heat loss constants ( a, b ) on the dimensionless power output, power density and thermal efficiency. By considering the internal irreversibilities and heat transfer influences, the relevance between the dimensionless power output and power density with respect to thermal efficiency have been shown. The results prove that the combustion and heat transfer constants have considerable effects on the cycle thermodynamic performance. This situation theoretically demonstrated for Otto iller ycle (O). The Theoretical Otto ycle thermodynamic performance rises with increase in the miller cycle ratio and combustion constant ( a ) with the reduction in the inlet temperature and heat transfer constant (b ). onsequently, optimum miller ratio attempted to be determining for irreversible Otto-iller ycle. Using these graphs, the future studies can be investigated in combustion engine conditions for Otto-iller ycle. Nomenclature a b E P Q r combustion constant at constant volume process (J/g) heat transfer constant at constant volume process (J/g.K) compression efficiency Expansion efficiency isentropic exponent specific heat at constant pressure (J/g.K) specific heat at constant volume (J/g.K) heat rate (W) compression ratio 8

9 r miller cycle ratio P pressure (Pa) s entropy (J/K) T temperature (K) v specific volume (m /g) volume (m ) W power output (W) pressure ratio (T /T 2 ) thermal efficiency cycle temperature ratio stroe ratio Superscripts. time-dependent condition non-dimensional References [] ozurewich,., Berry, R.S., Optimal Paths for Thermodynamic Systems: The Ideal Otto ycle, J Appl Phys., (982), 5(), [2] Hoffman, K.H., Watowich, S.J., Berry R.S., Optimal Paths for Thermodynamic Systems: The Ideal Diesel ycle, J Appl Phys, (985), 58(6), [] Ge, Y., hen, L., Sun, F., Wu,., Thermodynamic simulation of performance of an Otto cycle with heat transfer and variable specific heats for the woring fluid, Int. J. Therm. Sci., 44 (2005), 5, pp [4] Ge, Y., hen, L., Sun, F., Wu,., Finite-time thermodynamic modelling and analysis of an irreversible Otto-cycle, Appl. Energy, 85 (2007), pp [5] Hou, S.S., Heat transfer effects on the performance of an air standard dual cycle, Energy onvers. anage., 45 (2004), 8 9, pp [6] Ozsoysal, O.A., Heat Loss as a Percentage of the Fuel s Energy in Air-standard Otto and Diesel ycles, Energy onvers. anage., 47 (2006), 7 8, pp [7] Al-Sarhi, A., Jaber, J.O., Probert, S.D., Efficiency of a iller engine, Appl Energ, 8 (2006), pp [8] Li, T., Gao, Y., Wang, J., hen, Z., The iller cycle effects on improvement of fuel economy in a highly boosted, high compression ratio, direct-injection gasoline engine: EI vs. LI, Energy onversion and anagement, 79 (204), pp [9] Wu,., Puzinausas P.., Tsai J.S., Performance analysis and optimization of a supercharged 9

10 iller cycle Otto engine, Appl. Therm. Eng., 2 (200), 5, pp [0] Klein, S.A., An explanation for observed compression ratios in internal-combustion engines. Trans ASE J. Eng. Gas Turb Pow., (99), 4, pp [] Lin, J., Xu, Z., hang, S., Yan, H., Finite-time thermodynamic modeling and analysis of an irreversible iller cycle woring on a four-stroe engine, Int. ommunications in Heat and ass Transfer, 54 (204), pp [2] Sahin, B., Ozsoysal, O.A., Sogut, O.S., A omparative Performance Analysis of Endoreversible Dual-ycle under aximum Ecological Function and aximum Power onditions, Exergy, Int. J, 2 (2002), pp [] hen, L., Wu,., Sun, F., Wu,., Heat-Transfer Effects on the Net Wor-Output and Efficiency haracteristics for an Air Standard Otto ycle, Energy onvers gmt, 9 (998), 7, pp [4] Angulo-Brown, F., Rocha-artinez, J.A., Navarrete-Gonzalez, T.D., A Non-Endoreversible Otto ycle odel: Improving Power Output and Efficiency, J Phys:D Appl Phys, 29 (996), pp [5] Ust, Y., Sahin, B., Safa, A., The Effects of ycle Temperature and ycle Pressure Ratios on the Performance of an Irreversible Otto ycle, Acta Physica Polonica A, 20 (20),, pp [6] Gonca, G., Sahin, B., Ust, Y., Performance maps for an air-standard irreversible D with LI version, Energy, 54 (20), pp [7] Wang, Y., Lin, L., Rosilly, A.P., Zeng, S., Huang, J., He, Y., An analytic study of applying iller cycle to reduce NO X emission from petrol engine, Appl Therm Eng., 27 (2007), pp [8] Ge, Y., hen, L., Sun, F., Finite-time thermodynamic modeling and analysis for an irreversible dual cycle, athematical and omputer odelling, 50 (2009), pp [9] EES Academic Professional Edition.9.70-D, USA, F-hart Software, 202. [20] Ust, Y., Gonca, G., Kayadelen, H.K., Heat Transfer Effects on the Performance of An Air- Standard Irreversible Otto ycle,. Int ombust Symp., July 24-27, (200) Sarajevo, Bosnia. [2] Ust, Y., Sahin, B., Kayadelen, H.K., Gonca, G., Heat Transfer Effects on the Performance of an Air-standard Irreversible Dual ycle, Int. J. ehicle Design, 6 (20),, pp

HEAT TRANSFER EFFECTS ON THE PERFORMANCE OF AN AIR STANDARD OTTO CYCLE. Havva Demirpolat, Ali Ates, S.Orkun Demirpolat, Ali Kahraman

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