Performance of an irreversible Diesel cycle under variable stroke length and compression ratio

Transcription

1 Marsland Press Journal of Amerian Siene 00;6():58-6 Performane of an irreversible iesel yle under variable stroke length and ompression ratio epartment of Agriulture Mahine Mehanis, Shahrekord University, P.O. Box 5, Shahrekord, Iran Abstrat: Finite-time thermodynami analysis of an air-standard internal-ombustion iesel yle is performed in this paper. he relations between the power output and the ompression ratio, between the power output and the thermal effiieny are derived by detailed. he maximum power output and the orresponding effiieny limit of the yle with onsiderations of heat transfer and frition like term losses are also found. etailed numerial examples are given. he results shows that if ompression ratio is less than ertain value, the power output inreases with inreasing stroke length, while if ompression ratio exeeds ertain value, the power output first inreases and then starts to derease with inreasing stroke length. With further inrease in ompression ratio, the inrease of stroke length results in dereasing the power output. he results obtained in the present study are of importane to provide good guidane for performane evaluation and improvement of pratial iesel engines. [Journal of Amerian Siene 00;6():58-6]. (ISSN: 55-00). Keywords: iesel yle; power output; thermal effiieny; irreversible; frition; stroke length. Introdution Signifiant ahievements have ensued sine finite-time thermodynamis was developed in order to analyze and optimize the performanes of real heat-engines (Mozurkewih and Berry, 98; Andersen and Band, 98; Sieniutyz and Shiner, 99; Chen et al., 998; Aragon-Gonzalez et al., 000; Chen et al., 00]. Hoffman et al. (985) used mathematial tehniques, developed for optimal-ontrol theory, to reveal the optimal motions of the pistons in iesel yle engine. Klein (99) studied the effet of heat transfer on the performane of the Otto and iesel yles. Blank and Wu (99) examined the effet of ombustion on the work or power optimised Otto, iesel and ual yles. hey derived the maximum work or power and the orresponding effiieny bounds. Orlov et al. (99) obtained the power and effiieny limits for internal ombustion engines. Chen et al. (996) derived the relations between the power output and the thermal effiieny for the iesel yle with the onsideration of the heat-transfer losses. Bhattaharyya (000) proposed a simplified irreversible model for an air-standard iesel yle by using the finite time thermodynami approah. In his study, global thermal and frition losses are lumped into an equivalent frition term, whih is linear in the piston veloity. Chen et al. (00) modelled the diesel yle with frition-like term loss during a finite time and studied the effet of frition-like term loss on the yle performane. Burzler (00) determined the optimum piston trajetory that yielded maximum power output and effiieny of the diesel yle with different losses when the yle period, fuel intake per yle, fuel air mixture omposition, and ompression ratio are taken as onstants. Roha-Martinez et al. (00) investigated the effet of variable speifi-heats on the Otto and iesel yle performane. Chen et al. (00) modeled the behaviors of iesel yle, with frition losses, over a finite period. Qin et al. (00) and Ge et al. (005a) derived the performane harateristis of the diesel yle with heat transfer and frition like term losses when the maximum temperature of the yle was not fixed. Wang and Hou (005) studied the performane analysis and omparison of an Atkinson yle oupled to variable temperature heat reservoirs under maximum power and maximum power density onditions, assuming a onstant speifi heat, too. heir results showed an engine design based on maximum power density is better than that based on maximum power onditions, from the view points of engine size and thermal effiieny. Ge et al. (005b) onsidered the effet of variable speifi heats on the yle proess and studied the performane harateristis of endoreversible and irreversible Otto yles when variable speifi heats of working fluid are linear funtions of the temperature. Ozsoysal (006) gave the valid ranges of the heat transfer loss parameters of the Otto and diesel yles with onsideration of the heat loss as a perentage of the 58

2 Performane of an irreversible iesel yle fuel s energy. Zhao and Chen (006) performed analysis and parametri optimum riteria of an irreversible Atkinson heat engine using finite time thermodynami. Al-Sarkhi et al. (006) studied the effets of variable speifi heats of the working fluid on the performanes of the iesel and Miller yles. Ge et al. (007) studied the effets of variable speifi heats of the working fluid on the performanes of the iesel yle. Ge et al. (008a, 008b) analyzed the performane of an air standard Otto and iesel yles. In the irreversible yle model, the non-linear relation between the speifi heat of the working fluid and its temperature, the frition loss omputed aording to the mean veloity of the piston, the internal irreversibility desribed by using the ompression and expansion effiienies, and the heat transfer loss are onsidered. Ebrahimi (009) studied the effets of the temperature dependent speifi heat ratio of the working fluid on the performane of the diesel yle. As an be seen in the relevant literature, the investigation of the effet of stroke length on performane of iesel yle does not appear to have been published. herefore, the objetive of this study is to examine the effet of stroke length on performane of air standard iesel yle.. hermodynami analysis he iesel yle shown in Fig. approximates the ompression stroke up to ignition with the adiabati reversible (isentropi) proess ; it assumes that the ombustion proess is represented by the reversible onstant pressure proess ; it approximates the power stroke with the isentropi expansion proess ; and it assumes that the heat-removing proess is the reversible onstant volume proess 5. In a real yle, the speifi heat ratio is generally modeled as the first and seond order equation of mean harge temperature (Gatowski et al., 98; Brunt and Emtage, 997; Ebrahimi, 006). hus, it an be supposed that the speifi heat ratio of the working fluid is funtion of temperature alone and has the seond order equation forms: γ = a + b + () Where γ is the speifi heat ratio and is the absolute temperature. a, b and are onstants. he heat added per seond in the isobari ( ) heat addition proess may be written as in nl p ( + + ) Q = M d = R a b M nl d = M nl R ( + () a + b + a + b a artg artg Where is defined as = a a b. R and p are gas onstant and speifi heat at onstant pressure for the working fluid, respetively. M is the molar number of the working fluid per seond. he heat rejeted per seond in the isohori heat rejetion proess ( ) may be written as R Qout = Mnl vd = Mnl d = a + b + () Mnl R a + b a artg artg where v is the molar speifi heat at onstant volume for the working fluid. emperature Q in Entropy Q out Figure. emperature-entropy ( S) diagram for the air standard iesel yle Sine p and v are dependent on temperature, the adiabati exponent γ = p v will vary with temperature as well. herefore, the equation often used in a reversible adiabati proess with onstant γ annot be used in a reversible adiabati proess with variable γ. However, aording to Refs. (Ebrahimi, 009a; Chen et al., 008), the equation for a reversible adiabati proess with variable an be written as follows: γ V ( d )( V dv ) γ = + + () From Eq. (), one gets S 59

3 Marsland Press Journal of Amerian Siene 00;6():58-6 j j ln ( ) ai + bi + ( ) ( j i) a + b + + b aj + b ai artg artg (5) ln / = ln ( Vj / Vi) he ompression, r, and ut-off, β, ratios are defined as r = V V and β = V V = (6) herefore, the equations for proesses ( ) and ( ) are shown, respetively, by the following: a + b + ln + ( ) a + b+ b a + b a+ b artg artg (7) ( ) ln ( / ) ( ) ln ( / ) ( r ) = ln / and a + b + ln + ( ) a5 + b + b a + b a artg artg (8) r = ln β For an ideal iesel yle model, there are no losses. However, for a real internal ombustion engine yle, heat transfer irreversibility between the working fluid and the ylinder wall is not negligible. One an assume that the heat loss through the ylinder wall is proportional to the average temperature of both the working fluid and the ylinder wall and that the wall temperature is onstant at 0. If the released heat by ombustion for one molar working fluid is A, and the heat leakage oeffiient of the ylinder wall is B, one has the heat added to the working fluid per seond by ombustion as the following linear relation (Chen et al. 006). + Qin = Mnl A B 0 = (9) + M nl A + B 0 = Mnl A+ B( + ) where A = A + B 0 and B = B / are two onstants related to ombustion and heat transfer. aking into aount the frition loss of the piston, as dedued by Al-Sarkhi et al. (006) for the iesel yle, and a dissipation term represented by a frition fore whih in a linear funtion of the veloity gives dx fμ = μv = μ dt (0) where μ is the oeffiient of frition, whih takes into aount the global losses, x is the piston s displaement and v is the piston s veloity. herefore, the lost power due to frition is dwμ dx Pμ = = μ = μv dt dt () Running at N yles per seond, the mean veloity of the piston is v = LN () where L is the total distane the piston travels per yle. hus, the power output of the iesel yle engine an be written as Mnl R Pout = Qin Qout Pμ = ( ) + a + b a + b artg + artg () a + b a artg artg 6μ ( LN ) he effiieny of the iesel yle engine is expressed by Qin Qout Pμ ηot = = Q a + b a + b artg + artg a + b a artg artg + ( ) 6μ ( LN) in () a + b a + artg artg When r and are given, an be obtained from equation (7), then, substituting equation () into equation (9) yields, and the last, an be worked out by equation (8). Substituting,, and into equations () and (), respetively, the power output and thermal effiieny of the iesel yle engine an be obtained. herefore, the relations between the power output, the thermal effiieny and the ompression ratio an be derived.. Results and disussion 60

4 Performane of an irreversible iesel yle he following onstants and parameters have been used in this exerise: = 00 K, A = Jmol., β =.5,.mol K 8 B = 8 J, a = K, 5 b = K, =.5, r = , L = 0 0 mm, M nl =. 0 NL kmols, μ =.9 Nsm and N = 500rpm (Chen et al., 006; Ghatak and Chakraborty, 007; Ge et al., 007; Ebrahimi, 009b). Using the above onstants and range of parameters, the power output versus ompression ratio harateristi and the power output versus effiieny harateristi with varying the stroke length an be plotted. Numerial examples are shown as follows. he variations in the temperatures, and with the ompression ratio are shown in figure. It is found that and inrease with the inrease of ompression ratio, and dereases with the inrease of ompression ratio. Figures - show the effets of the variable stroke length on the yle performane with heat resistane and irreversible frition losses. From these figures, it an be found that the stroke length plays important roles on the power output. It is learly seen that the effets of stroke length on the power output is related to ompression ratio. hey reflet the performane 500 harateristis of a real irreversible iesel yle engine. It should be noted that the heat added and the heat rejeted by the working fluid inrease with inreasing stroke length. (see equations. () and ()). Figure indiates the effets of the stroke length on the power output of the yle for different values of the ompression ratio. It an be seen that the power output versus ompression ratio harateristi is approximately paraboli like urves. In other word, the power output inreases with inreasing ompression ratio, reah their maximum values and then dereases with further inrease in ompression ratio. he maximum power output inreases with inreasing stroke length up to about 80 mm where it reahes its peak value then starts to deline as the stroke length inreases. his is onsistent with the pratial working stroke length of engines, whih are between 70 and 90 mm in general. he optimal ompression ratio orresponding to maximum power output point remains onstant with inrease of engine speed. he working range of the yle dereases as the stroke length inreases. he results shows that if ompression ratio is less than ertain value, the power output inreases with inreasing stroke length, while if ompression ratio exeeds ertain value, the power output first inreases 00 emperature (K) Compression ratio Figure. he temperature versus ompression ratio ( L = 70mm ) 6

5 Marsland Press Journal of Amerian Siene 00;6(): L = 80mm 6 Power output (kw) L = 00mm L = 60mm L = 0mm L = 0mm Compression ratio Figure. Effet of L on the P out r harateristi 60 8 L = 00mm L = 80mm L = 60mm 6 L = 0mm L = 0 mm Power output (kw) hermal effiieny (%) Figure 5. Effet of L on the P out η at harateristi 6

6 Performane of an irreversible iesel yle and then starts to derease with inreasing stroke length. With further inrease in ompression ratio, the inrease of stroke length results in dereasing the power output. Numerial alulation shows that for any same ompression ratio, the smallest power output is for L = 0mm when r 5. or r > 9. and is for L = 0mm when 5. < r 9. and also the largest power output is for L = 0mm when r.65 or. < r, is for L = 60mm when.65 < r < or 7. r. and is for L = 70mm when r < 7.. he influene of the stroke length on the power output versus thermal effiieny is displayed in figure. As an be seen from this figure, the power output versus thermal effiieny is loop shaped one. It an be seen that the power output at maximum thermal effiieny improves with inreasing stroke length from 0 to around 70 mm. With further inrease in stroke length, the power output at maximum thermal effiieny dereases. he thermal effiieny at maximum power dereases with inrease of stroke length from 0 to 0 mm. Aording to above analysis, it an be found that the effets of the stroke length on the yle performane are obvious, and they should be onsidered in pratie yle analysis in order to make the yle model be more lose to pratie.. Conlusion An air-standard iesel-yle model, assuming a temperature-dependent speifi heat ratio of the working fluid, and heat resistane and fritional irreversible losses, has been investigated numerially. he performane harateristis of the yle with varying stroke lengths and ompression ratios were obtained by numerial examples. he results show that if ompression ratio is less than ertain value, the power output inreases with inreasing stroke length, while if ompression ratio exeeds ertain value, the power output first inreases and then starts to derease with inreasing stroke length. With further inrease in ompression ratio, the inrease of stroke length results in dereasing the power output. he results also show that the maximum power output inrease with inreasing stroke length. With further inrease in stroke length, the inrease of stroke length results in dereasing the maximum power output. he analysis helps us to understand the strong effet of stroke length on the performane of the iesel yle. herefore, the results are of great signifiane to provide good guidane for the performane evaluation and improvement of real iesel engines. Correspondene to: epartment of Agriulture Mahine Mehanis Shahrekord University, P.O. Box 5 Shahrekord, Iran el/fax: Rahim.Ebrahimi@gmail.om Referene [] Aizenbud BM, Band YB. Optimization of model internal ombustion engine. Journal of Applied Physis 98;6:77-8. [] Al-Sarkhi A, Jaber JO, Abu-Qudais M, Probert S. Effets of frition and temperature dependent speifi-heat of the working fluid on the performane of a diesel engine. Applied Energy 006;8():5 65. [] Aragon-Gonzalez G, Ganales-Palma A, Leon-Galiia A. Maximum irreversible work and effiieny in power yles. Journal of Physis : Applied Physis. 000;():0 09. [] Burzler MJ. Performane optimal for endoreversible systems. Ph hesis, University of Chemnitz, Germany, 00. [5] Bhattaharyya S. Optimising an irreversible iesel yle-fine tuning of ompression ratio and ut-off ratio. Energ Convers Manage 000;:87 5. [6] Blank, A, Wu C. he effets of ombustion on a power optimised endoreversible iesel yle. Energy Conver & Manage 99;:9 8. [7] Brunt MFJ, Rai H, Emtage AL. he alulation of heat release energy from engine ylinder pressure data. SAE Paper No [8] Chen L, Ge Y, Sun F. Unified thermodynami desription and optimization for a lass of irreversible reiproating heat engine yles, Pro. IMehE Part : J. Automobile Engineering, 008;: [9] Chen L, Ge Y, Sun F, Wu C. Effets of heat transfer, frition and variable speifi heats of working fluid on performane of an irreversible dual yle, Energy Conversion and Management 006;7: [0] Chen L, Sun F, Wu C. Optimal performane of an irreversible ual yle, Applied Energy 00;79():-. [] Chen L, Lin J, Luo J, Sun F, Wu C. Frition effets on the harateristi performane of iesel engines. Int J Energ Res 00;6(0): [] Chen L, Wu C, Sun F, Cao S. Heat transfer effets on the net work output and effiieny harateristis for an airstandard 6

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