S. M. A. Ibrahim!, K. A. Abed1, M. El Bayoumyl and M. S.Gad1. 1Department of MechaniCal Engineering,Al- Azahar University, Nasr City, Egypt. 2Department of ...
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, Journal
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of AI Azhar Universi~y Engineering
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Vol. 9, No. 30, January, 2014, 113·122
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1 HEORETICAL INVESTIGATION OF THE PERFORMANCE OF DIESEL ENGINE FUELED BY BIODIESEL S. M. A. Ibrahim!, K. A. Abed1, M. El Bayoumyl and M. S.Gad1 1 Department of MechaniCal Engineering,Al- Azahar University, Nasr City, Egypt 2Department of Mechanical Engineering, National Research Center, Dokki, Egypt
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ABSTRACT A q~asi dimensional two zone compression ignition engine cycle model is used to predict the C) c1e'perforinance of a diesel engine for the cases of using diesel fuel, B5, B20, B40, B70 and B i 00; The apparent fuel burning rate could be expressed as the sum of two components, one [f.; I ating 't6 premixed and the ~ther to diffusion burning. Governing equations of the mathematical m:)del mainly consist of first order differential equations derived for cylinder pressure, te nperature, cumulative work done, specific fuel consumption and thermal efficiency. A c(mputer code for the cycle model has been prepared by Matlab to perform numerical c, lculations at different engine loads for verification of the model. An experimental investigation h, s been carried out on a diesel engine fuelled withB20, BIOOand diesel fuels. It was observed that there is agood agreement betw~en simulated and experimental results, these results indicate that the a.ssul11pti,onsof the model are reasonable. It is shown that specific fuel consumption v,··!uesfor diesef: biodiesel blends (B20, B40, B70 and B100) were slightly higher them diesel ft,el by about from 2.5% to .13% respectively, the thermal efficiency for biodiesel-diesel blends U '20, B40., B70 and B 100) were lower than that of diesel fuel by about from 0.05% to 0.22% rnpectively.
i"" 1\ EYWORDS: Jatropha
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oil, Biodiesel, Specific fuel consumption, Thermal efficiency, Simulation.
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1 INTRODUCTION " C )mputer ~imulation has contributed enormously towards new evaluation in the field of internai ) ;, C( 1mbustion engines. Mathematical tools have become very popular in recent years owing to the C( iI1tinuously increasing improvement in computational power. Diesel engine simulation models rl duce the number of experiments, decrease complexity and computer system requirements. ( l}mputer simulations reduce time and costs for the development of new engines. Computer SJ mulations of in~ernal combustion engine cycles are desirable because of the aid they provide in d.!sign stu'qies,' predicting trends, serving as diagnostic tools, giving more data, less time and cost tl an are normally obtainable from experiments, and helping to understand the complex process thllt (I ;cur in the combustion chatnb,yr" Computer models of engine processes are valuable tools for analyzing eng,ine performance, exha).,lstemissions prediction and allow exploration of many engine d':sign alternatives in an inexpensive fashion, [1]. .
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THEORETICAL
INVESTIGATION
OF THE PERFORMANCE
OF DIESEL ENGINE FUELED BY BIODIESEL
M'1thematical engine simulation models are divided into two main groups. The first is fluid dynamics be,sed models and the second is thermodynamics based models. The former models are called multi d i nensional models which are based on the conservation of mass, and energy at any location within tll : engirie'"cylinder. The latter models are based on the thermodynamic analysis of the cylinder c( ntetl,tsduring the engine, qptfrating, cycle ..piesel engine. simulation models can be classified into th 'ee ((~t~gories, zero dimerisidha1,'single:.zo,il,~ piodels; ,qiIasi dimensional, multi zone :models and m dtidimensional models. Zero dimensional; single zone ~odeWassume that the cylinder~;charge is LIt iform in both composition and temperature, at all time 'durin.g the cycle. It has,beenshown that c;:,(ibrated and validated single zone models are capable of predicting engine perf0~.p~~ ~d fuel et,lnomy accurately and with high computational efficiency. However, single zone,rhodeIg:6lifinot be L1' ed to account for fuel spray evolution and spatial variation in mixture composition and te nperature, which are essential to predict exhaust emissions. On the other hand, multidimensional m )dels, like KIVA resolve the space the cylinder on afine grid, thus providing a formidable amount o I special information. , i' , . A ; an intermediate step between zero dimenSional and multi dimensional models, quasi dimensional, m llti zone models can be effectively used to model diesel engine combustion systems. The quasi d i nensional models combine ;some of the advantages of zero dimensional models and multi d i nensional models. They solve mass, energy equations, bui do not explicitly solve the momentum e( uation. These models can provide the spatial information requiredito predict emission products and re luire significantly less computirig resources compared to multi dimensional models. Quasi di nensional combustion modeling could be considered an active area of research, [2]. o fer the years, numerous models have been developed to predict engine combustion )-\'i* m,ore than 01 e zone, Within those multi zone spray combustion models, the level of ,detail, 'fidelity and ,v( lidation embedded in individual sub modelS have varied considerably. Furthermore, only;a subset "oJ these models has aimed at predicting emissions, especially,NO apd soot. A number 'of multi zone UJ' )dels have tracked the mixing of gaseous jets :with air and subs~quel1t combustion, without cc nsidering the fuel spray dYn.aJnicS,[3]'. . 'I,
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,2; MATHEMATICAL MODE;L FORMULATION' .' . :,,", :' J n·the present· work;-,a,quasi dimensiona] two. zone thermodyn?mic. model i,8,c}j.'q~el1 td: ~iri1ulate ,Jour stroke cycles; (int~ke, cOl11pression,expansion, and exbaust). 9rcompre,~,si9n, ~gnition engine ,,fl):::lledwith various types of alternative fuels,;such as diesel,: bi:oqies~La:iid their blends. This Hodel predicts engiri~' perform¥n'ce paramete'rs;'The combustion wodel was chosen to give a t'nsonable aCCWc;lyY with fast computation. The,;unbOmed 'l11ixtU1;e,forcompression,'ignition er gine during intake and compressioll strokes 'consists of air, and previoUSly burned gases. The c! mposition of the unburned mixture does not change significantly during intake and c(,mpression strokes. It is sufficiently accurate to assume the composition is frozen [3, 4J. T Ie combustion products or burned mixture gases are close to thermodynamic equilibrium during th; combustion process and much of the expansion process. In this model, the cylinder charge is a~sumed to be uniform in both temperature 'and;composition ..The burned gases are considered to b! in chemical equilibrium whereas the unburned gases are assumed to be frozen. The firsUaw of th::rmodynamics, equation of state, conservation of mass and volume are applied to the unburned ,ai;d burned gases. A system of first order ordinary differential equations can be oi;>tained,fo~ the pl,essure, mass, volume. and temperature of the' unburned and burned gases. The first law of thertnodynami~s is'. used to' c~dculate the pressure, "heat release rate and the mass fraction of b i (med gases as a 'function oJ ~tank angle, [5].' . , , " , this approach the comb4stion models, such as Wiebe model, Watson model and Whitbhbuse model, ,are' .~valuated ''based' on the comparison of the computational results 'with e; ,periroental da~a ;:I.S ,tp check, reliabi lhy and feasibility of mode1.sin predicting working process . o· d'i~sel engit:Ie. TfW comparison shows .'that above mentioned three models can be used for the " engineering p,uxpqs,eto predict. performance characteristics of the engines operated with diesel. ... ,.' -
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THEORETICAL
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1e heat addition for compre~sion ignition engine may be a function of crank angle. Watson et al oposed that the apparent ftiel burning rate could be expressed as the sum of two components, Ie relating to premixed and the other t6 diffusion burning.Among these models, the predicting suits with Watson model agree best with the experimental data, so Watson model is sekcted. \l' atson model consists of two functions which are superimposed. The first function simulate~ the p emixed combustion and the second simulates the diffusion combustion. A weighting factor P is u ;ed to determine how much emphasis is given to each of the function, [6, 7, 8].
dmb dB
= dmp
+ dmd
dB
dB
(1)
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(2) ., '"
(3)
(4) (5)
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(6) m
¢0.35
r = m" = 1- 0.875 ID _____!:_
(7)
0.375
(8) (2
= 5000
(9) (10)
T
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'4 -.
0 79K
3
(11)
0.25
Where: m mb mp md
)
T I
mass of fuel - air mixture in kg, fuel mass burned in kg, fuel mass b,~rned in premixed phase in kg, fuel burned in diffusion phase in kg, P Weighting factor, cD Fuel - air equivalence ratio, ID ;Ignitidn eelay in millisecond, N Engine speed in rpm, . . KJ ,K2,K3, and K4 shape factors for premixed and diffusion burning phases,
mass
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Sign ~S
start angle of heat release (combustion start angle), the duration of heat release (combustion duration from Xb=Oto Xb=l) is given by 100 Crank Angle as a datum value which needs to be large "; i, enough to complete combustion arid ';i',; 'Xb mass fraction burned. In the present model, the engine fuelled with some fuels such as diesel, biodiesel, mixture of diesel and biodiesel. The molecular formula used for diesel is taken as CIOH20,whereas for jatropha biodiesel, it is taken as C.18H3402. . . 2.1 Heat Transfer Heat transfer has become inevitable in any internal combustion engine so as to maintain cylinder walls, cylinder heads and pistons at secure in service temperatures. Heat is transferred from or to the working fluid during every part of each cycle. The primary heat transfer from the cylinder gases to the wall is convection and only 5% for radiation. The heat transfer is giv,en by the following equation, [9, 10].
Qht = hA(T - Tw) + et;(T4 - Tw4)
(12)
Where: h A Tw
the heat transfer coefficient in W/m2.K, the combustion chamber surface area in m2, the wall temperature in K, E emissivity (E =0.69 W/m2.K4) and S Stefan Boltzman constant =5.67xlO"'-8 W/m2.K4• Woschni accounts for the increase in gas velocity in the cylinder during combustion. The average cylinder gas velocity U for a four stroke engine without swirl determined by Woschni is, [11]: The heat transfer coefficient given by Woschni is: ..
h(B) = 3.2f(b-o.2)(pO,8)(T-0.5S)((CIUp +C2(;~
)(P- Pm))0.8)
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(13)
r r
Where: b P T
the cylinder bore in m, the cylinder pressure in atm, the cylinder temperature in Kelvin, the displacement volume in m3, Vd the motoring pressure in atm, Pm mean piston speed in mlsec, up u the average cylinder gas velocity in m/sec, engine compression ratio, the atmospheric pressure (Pat =1 atm), are constants, compression (CJ=2.28, C2=0), induction ~nd exhaust (C1=6.18, C2=O) and combustion and expansion (Cj=2.28,C2=O ..00324). the reference temperature, pressure, ~nd volume respectively that we take them the initial conditions for compression stroke. ~ ] .2 Ign ition Delay .. . i;nition delay is the time period between the star(Qf i~J~ction of fuel (tinj) and the start of lombustion (tign).The start of injection is usually taken ,as the tiine when the injeCtor needle lifts ( ff its seat. It is a complicated function of mixture temperature, pressure, equivalence ratio and t le fuel properties. It is best defined from the change in slope of the heat release rate versus time :.
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THEORETICAL
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cur" e which occurs at ignition. The Wolfer's empirical relation is used to determine the ignition deja y, [11, 12]. I') = AP-nexp (EI RT) " (14) Nhere:
IJ .
the ignition delay in milli second, apparent activation energy for the fuel autoignition process, Joule
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universal gas constant, 287 J/kg.K, the gas pressure in atm, the gas temperature in K, and f\ ,n are constants depend on the fuel, injection and air characteristics. R P 1
3 FORMULATION OF THE MODEL Tie differential first law of thermodynamics for this model for a small crank angle change de ]':
= dU
dQ-dYf(
l
T
(15)
The ideal gas equation of state as:
PV
= mRgasT
(16)
Where: the gas constant (Rgas=0.287 kJ/kg.K), P the cylinder pressure in Pa, V the cylinder volume in m3 and T the mean gas temperature in Kelvin. T Ie total volume of the engine cylinder and the rate of its change as follow: Rgas
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V
V=(_d
V
r -1
dV dB R
=
(17)
2
= (Vd(sin(B)))(l + (cos(B»(R2
~
(sin(B)))-O.5)
(18)
2 21 L
where: Vd L b I R dP de
.
)+(~)(R+l-cos(B)-(R2-(sin(B»)2)O.5)
=
(19)
),
the swept volume of the engine in cubic meter, the engine stroke in meter, the engine bore in meter. the engine connecting rod length in meter and the ratio of connecting rod length to cral1k radius.
(k-l)(CdQ)_C!!:i)(T_T V de 6N
W
»~(kP)(dV) V de
(20)
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