Comparative analysis of the Atkinson and the Otto cycles with heat transfer, friction and variable specific heats of working fluid

Transcription

1 همایش ملي مهندسي مکانیک 9 خرداد 939 (3 May, 3) Comparative analysis of the Atkinson and the Otto cycles with heat transfer, friction and variable specific heats of working fluid Mohammad Mehdi Rashidi, Alireza Hajipour *, Afshin Fahimirad 3 Associate Professor at the Engineering Faculty of Bu-Ali Sina University, Department of Mechanical Engineering, Hamedan, Iran, mm_rashidi@yahoocom * Corresponding author: MSc of Mechanical Engineering, Young Researchers Club, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran, alirezahajipour@gmailcom 3 MSc of Mechanical Engineering, CHP System Project Manager, Iran Heavy Diesel Mfg Co (Desa), Amol, Iran, afahimirad@desair Abstract In this article, the performance of air standard Atkinson and Otto cycles with irreversibility factors, ie efficiencies of compression and expansion processes, heat transfer loss, friction-like term loss and variable specific heats of working fluid is analyzed using finite-time thermodynamics he relations between the power output and the compression ratio and between the thermal efficiency and the compression ratio of the cycle are derived by detailed numerical examples Moreover, the effects of heat transfer loss, the friction-like term loss and variable specific heats of working fluid on the cycle performance are analyzed he results show that the effects of heat transfer loss, friction and variable specific heats of working fluid on the irreversible cycle performance should be considered in cycle analysis Keywords: Finite-time thermodynamics; Atkinson cycle; Otto cycle; Irreversibly; Efficiency - Introduction here are some types of the four-stroke engines in which they are nearly associated to each other, with some differences in their design he internal combustion engines which we focused on this paper are the Atkinson cycle and the Otto cycle he Atkinson cycle engine was developed in by James Atkinson and the Otto cycle engine which was developed in 7 by Nikolaus August Otto is an idealized thermodynamic cycle Some authors have examined the finite-thermodynamic performance of the Atkinson and the Otto cycles Comparison of performances of air standard Atkinson and Otto cycles with heat transfer

2 همایش ملي مهندسي مکانیک 9 خرداد 939 (3 May, 3) considerations is done by Hou [] Efficiency of an Atkinson engine at maximum powerdensity and performance of an Atkinson cycle with heat transfer, friction effects and variable specific-heats of the working fluid and thermodynamic simulation of performance of an Otto cycle with heat transfer and variable specific heats of working fluid and reciprocating heatengine cycles is analyzed by Chen et al [-5] he universal power and efficiency characteristics for irreversible reciprocating heat engine cycles are studied by Qin et al [] When irreversibility factors considered to cycle s analyze, the analysis of cycle is closer than to the practical situation of cycle s performance and is a good benchmark for comparison and analyze for air-standard cycles progressive in internal combustion engines In this paper we will study the effects of variable specific-heats of working fluid on performance of an Atkinson and an Otto cycles with heat transfer and friction considerations - Cycle Model he -s diagrams of the air standard Atkinson and Otto cycles are shown in Figures -a and -b he adiabatic compression and expansion processes are the same in the Atkinson and Otto cycles he process ( s) and (3 4s) are the reversible adiabatic compression and expansion, while the process ( ) and (3 4) are the irreversible adiabatic process in which consider into the thermal irreversibility in the real compression and expansion process For the two adiabatic processes ( ) and (3 4), the compression and expansion efficiencies can be expressed as compression ( S ) c ( ) () expansion ( 4 3) e ( ) 4S 3 () In the Atkinson cycle the heat added in the isochoric process ( 3) and the heat rejected in the isobaric process (4 ) and in the Otto cycle the heat addition and rejection processes occur in the isochoric states ( 3), (4 ) In Fig, we can assume that heating from state to state 3 and cooling from state 4 to state proceed at to constant temperature-rates, ie d dt (for 3) and K d dt (for 4 ), (3) K where is the absolute temperature and t is the time; K and K are constants Integrating Eq (3) yields t K( 3 ) and t K ( 4 ), (4) where t and t are the heating and cooling times, respectively hen, the cycle period is

3 ( 3 ) ( 4 ) همایش ملي مهندسي مکانیک 9 خرداد 939 (3 May, 3) t t K K (5) In practical cycles, specific heats of working fluid are variable and these variations will have great influences on the performance of the cycle According to references [-5], it can be supposed that the specific heats of working fluid are dependent on the temperature alone and, over the temperature ranges generally encountered for gases in heat engines (3- K), the specific heat curve is nearly a straight line, which may be closely approximated by the following forms: C a k () pm p C b k (7) vm v, where a p, and are constant, C pn and C vm are molar specific heats with constant pressure and volume, respectively Accordingly, one has R Cpm Cvm ap bv, () where R is the gas constant of the working fluid For the Atkinson and the Otto cycles, the heat added to the working fluid during process ( 3) is 3 3 in, A, O vm v v 3 3 (9) Q M C d M ( b k ) d M b ( ) k ( ), where M is the molar number of the working fluid he heat rejected by the working fluid during process (4 ) for the Atkinson and the Otto cycles in a row are 4 4 out, A pm p p 4 4 () Q M C d M ( a k ) d M a ( ) k ( ), and 4 4 out, O vm v v 4 4 () Q M C d M ( b k ) d M b ( ) k ( ) he work output of the cycle is W Qin Qout () Since C pn and C vm are dependent on temperature, the adiabatic exponent k = C pn / C vm will vary with temperature as well herefore, the equation often used in reversible adiabatic processes with constant k cannot be used in reversible adiabatic process with variable k However, according to references [-5], a suitable engineering approximation for a reversible adiabatic process with variable k can be made, ie, this process can be broken up into

4 همایش ملي مهندسي مکانیک 9 خرداد 939 (3 May, 3) infinitesimally small process, and for each of these processes, the adiabatic exponent k can be regarded as a constant For example, any reversible adiabatic process between states i and j can be regarded as consisting of numerous infinitesimally small processes with constant k For any of these processes, when small changes in temperature d and in volume dv of the working fluid take place, the equation for a reversible adiabatic process with variable k can be written as follows: k k V ( d)( V dv ) (3) From Eq (3), one gets j Vj k ( j i ) bv ln ( ) Rln ( ) V (4) i i he compression ratio is defined as r c V V (5) herefore, equations for process ( ) for the Atkinson and the Otto cycles as follows k b R () S ( S ) vln ( ) ln rc For (3 4) process for the Atkinson cycle k b R R (7) 3 ( 3 4S) vln ( ) ln ( ) ln rc, 4S 4S and for (3 4) process for the Otto cycle k b R () 3 ( 3 4S) vln ( ) ln rc 4 S For the ideals Atkinson and Otto cycles models there are no losses However, for a real Atkinson cycle or Otto cycle, heat transfer irreversibilities between the working fluid and cylinder wall are not negligible One can assume that the heat loss through the cylinder wall is proportional to average temperature of both the working fluid and cylinder wall, the wall temperature is assumed constant he heat added to the working fluid by combustion process is given by the following relation [-5]: 3 Q M ( ), (9) in

5 همایش ملي مهندسي مکانیک 9 خرداد 939 (3 May, 3) where α and β are two constant related to the combustion and heat transfer We can assume a dissipation term represented by a friction force, which as a function of the velocity, so dx f v, () dt where μ is the coefficient of friction which takes into accounts the global losses and x is the piston displacement hen, the lost power is dw dx dx P v () dt dt dt he piston s mean velocity is v x x t x r c ( ), t () where x is piston s position at minimum volume and Δt is the time spent in the power stroke hus the lost power is: P b r (3) c ( ), where x b t (4) So, the output power is P W P (5) he efficiency of the cycle is P () Qin When r c and are given, S can be obtained from Eq () for the Atkinson and the Otto cycles We can obtain from Eq () hen, substituting Eq (9) into Eq (9) yields 3, and 4S can be worked out using Eq (7) for the Atkinson cycle and Eq () for the Otto cycle hen 4 can be obtaining from Eq () for both of cycles Substituting,, 3 and 4 into Eqs (5) and () yields the power and efficiency hen, the relations between the power

6 همایش ملي مهندسي مکانیک 9 خرداد 939 (3 May, 3) output and the compression ratio, between thermal efficiency and the compression ratio can be derived 3- Results and discussion According to references [-5], the following parameters are used in the calculations: α =,-7, J/mol, β = -3 J/molK, a p = -3 J/molK, = 9-3 J/molK, M = 57( -5 ) kmol, = 3 K, η c = η e = 95 and = J/molK he constant temperature rates K and K are estimated as K = ( - ) s/k and K = 7 ( - ) s/k In addition, b = -54 W is set Using the above constants and ranges of parameters, the characteristic curves of P versus r c, η versus r c can be plotted Figs - 9 show the effects of the variable specific heats of the working fluid on the performance of the cycle with heat resistance and friction losses One can see that the output power versus compression ratio characteristic and efficiency versus compression ratio characteristic are parabolic like curves hey reflect the performances characteristic of real irreversible Atkinson and Otto cycles From Eqs () and (7), one can see that when =, C pm = a p and C vm = hold It should be noted that a p and are constant specific heats of working fluid Because R = C pm - C vm = a p - = constant, a p and must change synchronously Figs 5 show the effects of a p and on the cycle performance One can see that the maximum power output, the maximum efficiency will decrease with increase of a p and he parameter reflects the variation degree of specific heat with temperature he is, the more acutely the specific heat varies with temperature Figs 9 show the effects of on the performances of cycles Figs 3 show the effects of friction loss on the cycle performance From Figs 3, one can see that when b increases, the maximum power output, the maximum efficiency as well as the compression ratio will decrease According to above analysis, the effects of the variable specific heats of working fluid on the Atkinson and Otto cycles performances are obvious, and they should be considered in practical cycle analysis in order to make the cycle model closer to practice 4- Conclusions In this paper, the air standard Atkinson and Otto cycles, with considerations of heat transfer loss, friction like term loss and the variable specific heats of working fluid, is presented he performances characteristic of these cycles were obtained by detailed numerical example he results show that the effects of variable specific heats of working fluid on the cycle performance are significant, and should be considered in practical cycle analysis he obtained results in this paper provide guidelines for the design of practical internal combustion engines

7 Power P (kw) Power P (kw) 5- Figures همایش ملي مهندسي مکانیک 9 خرداد 939 (3 May, 3) =9 J/molK = J/molK =3 J/molK 9 7 = J/mol = 5 J/molK = 544 J/molK b = 35( -3 ) kw Fig -a -s diagram for an Atkinson cycle Fig 3 Influence of and on the output power of Otto =9 J/molK, a p = J/molK = J/molK, a p =3 J/molK =3 J/molK, a p =3 J/molK Efficiency 3 = J/mol = 5 J/molK = 544 J/molK b = 35( -3 ) kw Fig -b -s diagram for an Otto cycle Fig 4 Influence of a p and on the efficiency of =9 J/molK, a p = J/molK = J/molK, a p =3 J/molK =3 J/molK, a p =3 J/molK =9 J/molK = J/molK =3 J/molK 9 = J/mol = 5 J/molK = 544 J/molK Efficiency 3 = J/mol = 5 J/molK = 544 J/molK 7 b = 35( -3 ) kw b = 35( -3 ) kw Fig Influence of a p and on the output power of Fig 5 Influence of on the efficiency of Otto

8 Power P (kw) Power P (kw) Power P (kw) Power P (kw) همایش ملي مهندسي مکانیک 9 خرداد 939 (3 May, 3) 4 =344 J/molK =544 J/molK =44 J/molK 5 5 =344 J/molK =544 J/molK =44 J/molK = J/mol = 5 J/molK Efficiency 35 3 = J/mol = 5 J/molK a p = J/molK b = 35( -3 ) kw = J/molK = J/molK b = 35( -3 ) kw Fig Influence of on the output power of Fig 9 Influence of on the efficiency of Otto 9 =344 J/molK =544 J/molK =44 J/molK 4 b = ( -3 ) kw b = 35 ( -3 ) kw b = 54 ( -3 ) kw = J/mol = 5 J/molK 7 b = 35( -3 ) kw = J/molK 4 = J/mol = 5 J/molK = 544 J/molK = J/molK a p = J/molK Fig 7 Influence of on the output power of Otto Fig Influence of b on the output power of =344 J/molK =544 J/molK =44 J/molK b = ( -3 ) kw b = 35 ( -3 ) kw b = 54 ( -3 ) kw Efficiency 3 = J/mol = 5 J/molK a p = J/molK = J/molK b = 35( -3 ) kw 4 = J/mol = 5 J/molK = 544 J/molK = J/molK Fig Influence of on the efficiency of Fig Influence of b on the output power of Otto

9 همایش ملي مهندسي مکانیک 9 خرداد 939 (3 May, 3) b = ( -3 ) kw b = ( -3 ) kw b = 35 ( -3 ) kw b = 54 ( -3 ) kw b = 35 ( -3 ) kw b = 54 ( -3 ) kw Efficiency 3 = J/mol Efficiency 3 = J/mol = 5 J/molK = 544 J/molK = 5 J/molK = 544 J/molK = J/molK a p = J/molK = J/molK Fig Influence of b on the efficiency of Fig 3 Influence of b on the efficiency of Otto References [] Hou, S (7) Comparison of performances of air standard Atkinson and Otto cycles with heat transfer considerations, Energy Conversion and Management, 4, pp 3-9 [] Chen, L Lin, J Sun, F Wu, C (99) Efficiency of an Atkinson engine at maximum power density, Energy Conversion Management, 39(3/4), pp [3] Chen, L Ge, Y Sun, F Wu, C () Performance of an Atkinson cycle with heat transfer, friction and variable specific heats of working fluid, Applied Energy, 3, pp - [4] Chen, L Ge, Y Sun, F Wu, C (5) hermodynamic simulation of performance of an Otto cycle with heat transfer and variable specific heats of working fluid, International Journal of hermal Sciences, 44, pp 5-5 [5] Chen, L Ge, Y Sun, F Wu, C (5) Reciprocating heat engine cycles, Applied Energy,, pp [] Qin, X Chen, L Sun, F (3) he universal power and efficiency characteristics for irreversible reciprocating heat engine cycles, Eur J Phys, 4(4), pp 359-3