research article comparative numerical study of four...

Research ArticleComparative Numerical Study of Four Biodiesel Surrogates forApplication on Diesel 0D Phenomenological Modeling

Claude Valery Ngayihi Abbe12 Raidandi Danwe13 and Robert Nzengwa12

1National Advanced School of Engineering University of Yaounde PO Box 337 Yaounde Cameroon2Faculty of Industrial Engineering University of Douala PO Box 2701 Douala Cameroon3Higher Institute of the Sahel University of Maroua PO Box 46 Maroua Cameroon

Correspondence should be addressed to Claude Valery Ngayihi Abbe ngayihiclaudeyahoofr

Received 19 November 2015 Revised 1 February 2016 Accepted 2 February 2016

Academic Editor Yiguang Ju

Copyright copy 2016 Claude Valery Ngayihi Abbe et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

To meet more stringent norms and standards concerning engine performances and emissions engine manufacturers need todevelop new technologies enhancing the nonpolluting properties of the fuels In that sense the testing and development ofalternative fuels such as biodiesel are of great importance Fuel testing is nowadays a matter of experimental and numerical workResearches on diesel enginersquos fuel involve the use of surrogates for which the combustionmechanisms are well known and relativelysimilar to the investigated fuel Biodiesel due to its complex molecular configuration is still the subject of numerous investigationsin that area This study presents the comparison of four biodiesel surrogates methyl-butanoate ethyl-butyrate methyl-decanoateand methyl-9-decenoate in a 0D phenomenological combustion model They were investigated for in-cylinder pressure thermalefficiency andNO

119909emissions Experiments were performed on a six-cylinder turbochargedDI diesel engine fuelled bymethyl ester

(MEB) and ethyl ester (EEB) biodiesel from wasted frying oil Results showed that among the four surrogates methyl butanoatepresented better results for all the studied parameters In-cylinder pressure and thermal efficiency were predicted with goodaccuracy by the four surrogates NO

119909emissionswere well predicted formethyl butanoate but for the other three gave approximation

errors over 50

1 Introduction

Extensive studies regarding biodiesel combustion as an alter-native for conventional diesel fuel have been performedrecently [1 2] Experimental studies are more and moreaccompanied by numerical studies to better understand thephysical phenomena involved in the combustion process indiesel engines when fuelled by biodiesel [3ndash5] Numericalstudies in diesel combustion are often performed usingsurrogates forwhich combustion kineticmechanisms arewellestablished and are comparable to those of investigated fuels[6ndash9]

Biodiesel combustion is often found difficult to modeldue to the diversity of its sources and also the complexitymolecular structure of biodiesel components which consistof saturated and unsaturated fatty acid [10] This makes themodeling procedure for such type of fuel complex It is widely

accepted that numerical simulations provide a useful tool forengine conception and optimization It is therefore importantto identify suitable biodiesel surrogates that can be used forsimulation purpose

Most of the numerical works in literature present theuse of methyl butanoate and methyl decanoate [11ndash14] assurrogates for biodiesel fuel These works are mostly about1D and 3D CFD detailed combustion kinetic modeling As itwas stated in previous researches CFDmodeling presents thedisadvantage of a high computer cost [15] This is where 0Dphenomenologicalmodeling can be effective because it is lesstime-consuming

Investigations on different biodiesel surrogates for 0Dmodeling are somehow scarce Galle et al [16] performed anumerical analysis of a simplified spray model for differentbiodiesel surrogatesTheir work showed that the choice of thesurrogates is of high importance and the fuel properties are

Hindawi Publishing CorporationJournal of CombustionVolume 2016 Article ID 3714913 11 pageshttpdxdoiorg10115520163714913

2 Journal of Combustion

highly influencing the model performance Stagni et al [17]proposed a reduced kinetic model for biodiesel fuel for appli-cation on 0DmodelThey showed that the mechanism whenapplied permits a considerable time saving in computation

Som et al [18] performed four different chemical kineticmodels for 0D and 3D simulation the kinetic models weremainly based on mixture of two different set of surrogates(a) methyl decanoate methyl 9 decenoate and n-heptaneand (b) methyl butanoate and n-heptane Only species molefraction simulations were performed using 0D modeling Allthe mechanisms performed very well against experimentaldata but at the expense of computer cost

Theobjective of this study is to compare 4 differentmethyland ethyl ester surrogates in strictly 0D phenomenologicalmodeling for biodiesel combustion simulation purpose Thesurrogates will be compared according to computed maxi-mum pressure NO

119909emission and thermal efficiency

2 Material and Methods

21 0D Model Governing Equations The model used inthis study was validated in a previous study [15] we arepresenting here some fundamental relationships for a betterunderstanding of the computing methodology

211 Spray Submodel Injection and spray are modeled usingthe theory described by Lyshevsky and Razleytsev [19ndash22]The diesel jet is assumed to be constituted of two phasesan initial and a base which are separated by a transitorycharacteristic length which is computed as follows

119871119887= 119862119878119889119899119882119890

025

11987204

120588119897

minus06

(1)

where 119905119887

= 119897119887

2

119861119904is the characteristic time (s) 119862

119904is a

weighing coefficient 119889119899is injector nozzle diameter 119882

119890is the

Webber number and119872 is an a dimensional criterion [22]Webber number is computed by

119882119890=

1198802

0120588119891119889119888

120590119891

(2)

where 1198800is the spray initial velocity given by

1198800=

24119902119888119877119875119872

0751205881198911205871198892119888119894119888120593inj

(3)

119902119888is the fuel mass flow rate in Kgcycle 120588

119891is the fuel density

kgm3 119889119888is the injector nozzle diameter in mm 120593inj is the

injection duration in crank angle degrees 119894119888is the number of

injector holes

212 Evaporation Submodel The injected fuel is scatteredinto fine droplets after the transition length these droplet areevaporating at a given rate which is proportional to their size[20 21] The fuel spray is divided in two zones In the firstzone droplets are concentrated behind the front flame areaIn the second zone droplets have reached the front flame andthe evaporation is turbulent

The size of the pulverized droplets is evaluated for eachzone using the Sauter mean diameter calculated by

11988932

= 1711988911989911987200733

(119882119890 sdot 120588)minus0266

(4)

where 120588 = 120588119886120588119897is the ratio of density between air and liquid

fuelDroplets are assumed to evaporate following the 119889

2 law[23] for which the evaporation rate for a given droplet is

1198892

119894= 1198892

0minus 119870119905 (5)

where 1198890represents the droplet diameter after breakup (see

(4)) and 119889119894the diameter of the same droplet at time 119905119870 is the

evaporation constant

119870 = 106

sdot

4119873119906119863119901119901119904

120588119897

(6)

where 119873119906is the Nusselt number for diffusion processes 119863

119901

is the diffusion constant for fuel vapor and 119901119904is the fuel

saturated vapor pressureCombustion duration which is going to be used as an

entry data for heat release rate calculation is calculated inseconds by

120591ev =119860119911

(11988711989411990512058206)

(7)

where 119887119894119905

= 1198701198892

32is the relative evaporation constant and 120582

the excess air coefficient 119860119911is a fitting weighing coefficient

where its value varies from 4 to 12 [21]

213 Ignition Delay and Heat Release Submodels Ignitiondelay is computed using the following correlation [24]

ID = [036 + 022119880119901] exp[119864

119886sdot (

1

119877119879im120576119899119888minus1minus

1

17190)

+ (212

119875im120576119899119888 minus 124)

063

]

(8)

where 119864119886is the fuel activation energy which is computed by

119864119886

= 1310000(CN + 25) CN is the fuel cetane number119880119901is the engine piston speed 119879im and 119875im are respectively

the temperature and pressure at the intake manifold 120576 is theenginersquos compression ratio and 119899

119888is the polytropic exponent

for compressionThe fuel burnt ratio at any crank angle 119909 = 119891(120593) is

computed using a double Wiebe function [25 26] by

119909 = 120573119909119901+ (1 minus 120573) 119909

119889 (9)

where 119909119901and 119909

119889represent the fuel burnt ratio for premixed

and diffusion combustion phases and 120573 represents the frac-tion of injected fuel during premixed phase

For each combustion phase we can write

119909119894= 1 minus exp[minus119886

119894(120593 minus 120593comb

Δ120593)

119898119894+1

] (10)

Journal of Combustion 3

where 119886119894and119898

119894are Wiebe weighing coefficients 120593comb is the

start of ignition corresponding angle Δ120593 is the combustionduration in degrees of rotation

The heat release rate is computed by derivation of 119909 about120593

214 Thermodynamic Combustion Modeling The governingchemical reaction used in the study is given by

(1 minus 119910119903)

1 + 120576120601 + 120603[120576120601 C

119886H119887O119888N119889+ 119891 (H

2O) + 021 sdotO

2

+ 079 sdotN2+ 120603H

2O] + 119910

119903[1199101015840

1CO2+ 1199101015840

2H2O

+ 1199101015840

3N2+ 1199101015840

4O2+ 1199101015840

5CO + 119910

1015840

6H2+ 1199101015840

7H + 119910

1015840

8O

+ 1199101015840

9OH + 119910

1015840

10NO] 997888rarr V

1CO2+ V2H2O + V3N2

+ V4O2+ V5CO + V

6H2+ V7H + V

8O + V9OH

+ V10NO

(11)

The mass fraction of each species is calculated based onequilibrium assumption [27] The following equations wereexploited to determine the thermodynamic state of eachsurrogate of chemical formula C

119886H119887O119888N119889 such as specific

heat enthalpy and entropy depending on the temperature ofthe combusting mixture Consider

119888119901

119877= 1198861+ 1198862119879 + 11988631198792

+ 11988641198793

+ 1198865

1

1198792

ℎ

119877119879= 1198861+

1198862

2119879 +

1198863

41198792

+1198864

41198793

+1198865

5

1

1198792+ 1198866

1

119879

119904

119877= 1198861ln119879 + 119886

2119879 +

1198863

21198792

+1198864

31198793

+1198865

4

1

1198792+ 1198867

(12)

Thefitting coefficients 1198861to 1198867are the first sevenChemkin

NASA coefficients of specific species in the thermdatChemkin file The reduced thermodynamic data are incor-porated into the code and are in compliance with thetemperature range that our study is covering

The thermodynamic tables used for air properties abouttemperature are taken from the Chemkin data base fortemperature range of 300 to 5000K [28]

The thermodynamic state of the burning mixture iscalculated at each time step as a function of each species massfraction issued from combustion products

The molar enthalpy of the mixture is then calculated by

ℎ = sum119910119894ℎ119894+ ℎ119891119910119891 (kJkmol) (13)

its molar entropy is calculated by

119904 = (119904119891minus ln119910

119891) 119910119891+ sum(119904

119894minus ln119910

119894) 119910119894 kJkmolK (14)

the heat capacity of the mixture is given by

119888119901= 119888119901119891

119910119891+ sum119888

119901119894119910119894 (15)

Specific volume and internal energy of the mixture arecomputed by

119906 = ℎ minus 119877119879

V = 119877119879

119875

(16)

where 119877 is the universal gas constant and ℎ119891 119904119891 119888119901119891

arerespectively the enthalpy entropy and specific of the fuel(surrogate) involved in reaction (11)

The above determined parameters with equilibriumhypothesis permit the determination of in-cylinder burn-ing mixture pressure and temperature The following threeequations give relationships for the internal energy specificvolume entropy enthalpy and specific heat with temperatureand pressure as functions of the crank angle [24 25]

119889119906

119889120579= (119888119875minus

119901V119879

120597 ln V120597 ln119879

)119889119879

119889120593

minus (V(120597 ln V120597 ln119879

+120597 ln V120597 ln119875

))119889119901

119889120593

(17)

119889V119889120579

=V119879

120597 ln V120597 ln119879

119889119879

119889120593minus

V119901

120597 ln V120597 ln119901

119889119901

119889120593 (18)

119889119904

119889120579= (

119888119875

119879)

119889119879

119889120593minus

V119879

120597 ln V120597 ln119879

119889119901

119889120593 (19)

with (120597ℎ120597119879)119875= 119888119875

Considering the in-cylinder burning gases made of twozones (unburned and burned) variations of in-cylinderpressure and temperature about the crank angle for unburnedand burned gases are given by the following relations

119889119901

119889120593=

119860 + 119861 + 119862

119863 + 119864 (20)

119889119879119887

119889120593=

minusℎ (1205871198872

2 + 4119881119887) 11990912

119879119887minus 119879119908

V119898119888119875119887

119909

+V119887

119888119875119887

(120597 ln V119887

120597 ln119879119887

)(119889119901

119889120593)

+ℎ119888119906

minus ℎ119888119887

119909119888119875119887

[119889119909

119889120593minus 119909 minus 119909

2119862

120596]

(21)

119889119879119906

119889120593=

minusℎ (1205871198872

2 + 4119881119887) 11990912

119879119906minus 119879119908

V119898119888119875119906

119909

+V119906

119888119875119906

(120597 ln V119906

120597 ln119879119906

)(119889119901

119889120593)

+ℎ119888119906

minus ℎ119888119887

119909119888119906

[119889119909

119889120593minus 119909 minus 119909

2119862

120596]

(22)


with

119860 =1

119898(119889119881

119889120593+

119881119862blowby

120596)

119861 = ℎ

(119889119881119889120593 + 119881119862blowby120596)

120596119898[V119887

119888119875119887

120597 ln V119887

120597 ln119879119887

11990912

sdot119879119887minus 119879119908

119879119887

+V119906

119888119875119906

120597 ln V119906

120597 ln119879119906

(1 minus 11990912

)119879119906minus 119879119908

119879119906

]

119862 = minusV119887minus V119906

119889119909

119889120593minus V119887

120597 ln V119887

120597 ln119879119887

ℎ119888119906

minus ℎ119888119887

119888119875119887

119879119887

[119889119909

119889120593

minus

(119909 minus 1199092

) 119862blowby

120596]

119863 = 119909[V2119887

119888119875119887

119879119887

(120597 ln V119906

120597 ln119879119906

)

2

+V119887

119875

120597 ln V119887

120597 ln119875]

119864 = 1 minus 119909[V2119906

119888119875119906

119879119906

(120597 ln V119906

120597 ln119879119906

)

2

+V119906

119901

120597 ln V119906

120597 ln119901]

(23)

where ℎ119888119887

and ℎ119888119906

are heat transfer coefficients to the wallrespectively for burned and unburned zones [29] 119909 is thefraction of burned fuel 119898 is the fuel mass V is the specificvolume120596 is the engine speed in rads and119862blowby is the blowby coefficient

Nonlinear equations (17)ndash(22) are simultaneously solvedusing Runge-Kutta method (Dormand-Prince)

215 Nitric Oxides Emission Submodels NO119909emissions are

computed using the extended Zeldovich [30 31] where NO119909

formation rate is computed as

119889 [NO]

119889119905=

21198621[1 minus ([NO] [NO]

119890)]

1 + [[NO] [NO]119890] 1198622

(24)

where 1198621= 1198701198911

[O]119890[N2]119890and

1198622=

1198621

1198701199032

[NO]119890[O]1198901198701199033

[NO]119890[H]119890

(25)

[119883] is the concentration of a given species 119883 and [119883]119890the

concentration of the same species at equilibrium 119870119891119894

and1198701199032 respectively represent the forward and reverse rate of

each reaction involved in the NO119909formation mechanism

22 Biodiesel Surrogates The surrogates used in this studyare respectively methyl butanoate ethyl butyrate methyldecanoate and methyl 9 decenoate These four surrogateswere chosen firstly because of the high amount of work ontheir combustion kinetics and study as biodiesel surrogates[33ndash36] and secondly for the wildly availability of theirvalidated reduced mechanisms data The thermodynamicdata for each surrogate were taken respectively from thework of Liu et al [37] formethyl butanoate Herbinet et al formethyl decanoate [38] Luo et al [39] for methyl 9 decenoateand the work of Goos et al [40] for methyl butyrate

Table 1 Engine specification [32]

Engine 6 liters Ford cargoType Direct injection turbochargedNumber of cylinders 6Bore times stroke (mm) 1040ndash1149Compression ratio 164 1Maximum power (kW) 136 at 2400 rpmMaximum brake torque (Nm) 650 at 1400 rpmInjection pump In-line typeInjection opening pressure 197 bar

Table 2 Fuel properties [32]

Property Methyl ester biodiesel Ethyl ester biodieselDensity (15∘C) 8843 kgm3 8834 kgm3

Viscosity (40∘C) 45mm2s 49mm2sLower heating value 3733 kJkg 37550 kJkgCetane number 549 535

Table 3 Values of start of injection angle [32]

Fuel Start of injection (BTDC ∘CA)1100 rpm 1400 rpm 1700 rpm

Methyl ester biodiesel 14 13 12Ethyl ester biodiesel 14 1325 1225

23 Engine Specification and Characteristic of the BiodieselThe experimental analysis against which our study is aboutwas performed by Sanli et al [32] Combustion and emis-sion characteristics of a six-cylinder turbocharged DI dieselengine were investigated for methyl ester biodiesel and ethylester biodiesel from wasted frying oil The characteristics ofthe engine are given in Table 1 and that of biodiesel fuels isgiven in Table 2

The numerical study was performed for three differentengine speeds for each surrogate 1100 rpm 1400 rpm and1700 rpm The injection timing for each biodiesel was inaccordance with the measured start of injection angle duringexperimental setup the values are given in Table 3 Themeasured crank angle at which the fuel line reached theinjector needle opening pressure was taken as the injectiontiming angle or start of injection (SOI)

The biodiesel surrogates were numerically investigatedfor three parameters

(i) Maximum pressure(ii) NO

119909emission

(iii) Thermal efficiency

3 Results and Discussions

31 Evaluation of Thermodynamic Properties of Biodiesel Sur-rogates A first evaluation was performed for each surrogateaccording to (12) Equations (13) to (15) permit the compu-tation of the mixture enthalpy specific heat and entropy asa function of the surrogate used These values are used for


Table 4 Comparative experimental and simulated results for methyl ester biodiesel and each surrogate at 1100 rpm

RPM MEB1100 119875max (Mpa) Error NO

119909(ppm) Error Thermal eff Error

Experimental 968 1400 3900(1) Methyl butanoate 979 115 1408 057 3806 0241(2) Ethyl butyrate 910 597 1012 9277 3307 1521(3) Methyl decanoate 958 098 532 6200 3487 1059(4) Methyl 9 decenoate 914 551 1422 8984 3343 1428









the computation of the in-cylinder pressure and temperature(21) and (22) show that in-cylinder temperature for each zoneis linearly proportional to the mixture enthalpy and inverselyproportional to the mixture specific heat The variation ofthe mixturersquos entropy (19) is a nonlinear function of thetemperature variation as well as the variation of in-cylinderpressure Thus the variation of surrogatersquos properties valuessuch as enthalpy entropy and specific heat as a function oftemperature could be a good indicator of its suitability for our0D modeling

Figure 1 presents the variation of enthalpy against temper-ature for each surrogateThe curve shapes are similar and theresidual values are higher for methyl butanoate and methyl9 decenoate with maximum difference of 3659 kJkmolConcerning entropy and specific heat (Figures 2 and 3)we also notice a similar curve shape with higher residualvalues between methyl butanoate and methyl decanoatemaximum values which are respectively of 112 kJkmolKand 501 kJkmolK for entropy and specific heat The resid-uals presented in the plots are the differences betweeneach computed parameter for each surrogate for a giventemperature The plot presents the higher residual valuesThese results show that some notable differences shall beexpected in terms of thermodynamic computed values ofcombusting species during the simulation for each surro-gate which is the subject of the discussion in the nextsections

hR (methyl butanoate)

hR (methyl butyrate)hR (methyl 9 decenoate)

0

(K)500 1000 1500 2000 2500 3000 3500

minus400E + 01

minus350E + 01

minus300E + 01

minus250E + 01

minus200E + 01

minus150E + 01

minus100E + 01

minus500E + 00

000E + 00

minus150

minus100

minus50

0

50

100

(kJk

mol

)

Max residualhR (methyl decanoate)

Figure 1 Variation of enthalpy against temperature for biodieselsurrogates

32 Biodiesel Surrogates Numerical Investigation Maximumpressure thermal and efficiency and NO

119909emission were

computed for methyl ester biodiesel and ethyl ester biodieselfromwaste fried oilThe four mentioned biodiesel surrogatesthermodynamic data were used in the simulation at 11001400 and 1700 rpm Results of simulations and subsequenterror evaluations are displayed in Tables 4 5 6 7 8 and 9respectively at 1100 1400 and 1700 rpm Errors are evaluatedas relative errors between measured and computed values


Table 7 Comparative experimental and simulated results for ethyl ester biodiesel and each surrogate at 1100 rpm

RPM EEB1100 119875max (Mpa) Error NO











sR (methyl butanoate) sR (methyl butyrate)sR (methyl decanoate) sR (methyl 9 decenoate)Max residual

000

5000

10000

15000

20000

25000

minus400E + 01

minus350E + 01

minus300E + 01

minus250E + 01

minus200E + 01

minus150E + 01

minus100E + 01

minus500E + 00

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500

Figure 2 Variation of entropy against temperature for biodieselsurrogates

321 Methyl Ester Biodiesel Numerical Investigation

Maximum in-Cylinder Pressure Maximum pressure is fairlywell predicted for each surrogate However methyl butanoateshows a better prediction rate of an average of 127 accuracyacross the different rpmTheother surrogates present an aver-age accuracy of 653 156 and 607 for ethyl butyratemethyl decanoate and methyl 9 decenoate respectively InFigure 4 it can be seen that experimental and simulated

Max residual

0002000400060008000

1000012000

minus600E + 01

minus500E + 01

minus400E + 01

minus300E + 01

minus200E + 01

minus100E + 01

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500

cpR (methyl decanoate)cpR (methyl butanoate) cpR (methyl butyrate)

cpR (methyl 9 decenoate)

Figure 3 Variation of specific against temperature for biodieselsurrogates

pressure traces closely match for each biodiesel surrogatescompared toMEB experimental data Better pressure simula-tions are achieved bymethyl butanoate andmethyl decanoatecompared to the other two

Thermal Efficiency Thermal efficiency provides a goodinsight of fuel heat input to mechanical energy output duringcombustion cycle especially when evaluating alternative fuel[41 42] The simulation results show that methyl butanoate


0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)

(a) Methyl 9 decenoate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(b) Methyl butanoate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(d) Methyl decanoate

Figure 4 Experimental and simulated pressure trace at 1700 RPM for MEB for each surrogate

gives the better approximationwith an average error of 146Ethyl butyrate methyl decanoate and methyl 9 decenoatepresent average errors below 15 which are acceptable forengine simulation Methyl decanoate presents an approxi-mation of average 856 followed by methyl 9 decenoate at1276 and ethyl butyrate at 1376

119873119874119909Emissions NO

119909emissions are simulated using the

extended Zeldovich mechanism [30 43] the simulationresults present a good agreement with experimental resultsfrommethyl butanoate with an average of 665 error acrossthe three regimesMethyl decanoatemethyl 9 decenoate andethyl butyrate however poorly predict NO

119909emissions with

respective average errors of 599 9246 and 8949

322 Ethyl Ester Biodiesel Numerical Investigation

Maximum in-Cylinder Pressure Maximum pressure was cal-culated through simulation in the 0D phenomenologicalmodel as well as in the case of methyl ester biodiesel

Maximum pressure is also fairly well predicted for eachsurrogate Methyl butanoate shows a better prediction rateof an average of 094 accuracy across the different rpmwhich is slightly better than during the methyl ester biodieselsimulation Simulations present an average accuracy of459 187 and 410 for ethyl butyrate methyl decanoateand methyl 9 decenoate respectively Figure 5 shows thatexperimental and simulated pressure traces closely match foreach biodiesel surrogate compared to EEB experimental dataBetter pressure simulations are achieved bymethyl butanoateand methyl decanoate compared to the other two just as inthe case of MEB

Thermal Efficiency The simulation results present a betterapproximation for methyl butanoate with an average errorof 355 Ethyl butyrate methyl decanoate and methyl 9decenoate present average errors close and over 15 whichis below acceptable for engine simulation Methyl decanoatepresents an approximation of average 1225 followed bymethyl 9 decenoate at 1621 and ethyl butyrate at 1711


0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


Figure 5 Experimental and simulated pressure trace at 1700 RPM for EEB for each surrogate

119873119874119909Emissions As it was the case for MEB the simulation

results present a good agreement with experimental resultsfrommethyl butanoate with an average of 384 error acrossthe three regimes which is an improvement compared toMEB simulation Methyl decanoate methyl 9 decenoate andethyl butyrate just as it was the case for MEB poorly predictNO119909emissions with respective average errors of 5356

8759 and 9117

33 Discussion The approximations results are similarwhether we are investigating methyl ester biodiesel or ethylester biodiesel For each case pressure trace and thermalefficiency are fairly well predicted Ethyl butyrate and methyl9 decenoate present the worst results in terms of simulationprecision

The overall trend observed from the various simulationresults is that methyl butanoate gives better predictions ofengine parameters compared to other surrogates this is inaccordance with its high rate of usage as a surrogate forbiodiesel in 3D and 1D simulation studies [4 5 44] However

this result is somehow contradictory with comments fromBrakora et al [45] and Hakka et al [33] that say thatmethyl butanoate is not a particular good surrogate forbiodiesel While this was explained by the fact that methylbutanoate possesses a short alkylic chain and therefore cannotadequately capture ignition delay and species history itshould be noted that most of these findings were doneunder 3D or experimental investigations Our 0D modelonly uses Chemkin Nasa coefficients to compute in-cylinderthermodynamic parameters the ignition delay is computedas a function of the investigated biodiesel cetane numberThereaction kinetic in our model is therefore independent of thesurrogate thermodynamic data

The three other surrogates present overall good approxi-mation for thermal efficiency andmaximumpressureMethyldecanoate presents better simulation approximation errorsthan ethyl butyrate and methyl 9 decenoate that trend isinteresting since one would have expected a closer approx-imation value for ethyl butyrate since its enthalpy heatcapacity and entropy curves are closer to the ones for methyl


butanoate However it has been noticed in the literature thatmethyl decanoate has been extensively used as a surrogatefor biodiesel combustion simulation as compared to ethylbutyrate and methyl 9 decanoate [13 46 47]

Another trend observed is the poorly predicted NO119909

emission simulation for methyl decanoate ethyl butyrateand methyl 9 decenoate For these three surrogates NO

119909

emissions are underpredicted compared to experimentalresults An earlier study performed on Kiva-2 showed thatsurrogates with lesser content of oxygen tend to predict lowerNO119909emission concentration [48] In our case each surrogate

presents 2 atoms of oxygen in its formula methyl butanoatepresents a chemical formula of C

5H10O2 ethyl butyrate of

C6H12O2 methyl decanoate of C

11H22O2 and methyl 9

decenoate C11H20O2 The stoichiometric airfuel ratio which

is calculated by 119871 = ((83)119886+8sdot119887minus119888)0232 for each surrogateof formula C

119886H119887O119888N119889will be respectively 8788 94928

1137 and 1124 According to experimental parameters thesame mass of injected fuel was considered for each surrogatein the simulation The model takes into account the molarfraction of each species contained in the surrogate Thecomposition of the burningmixturewill therefore be depend-able of the surrogate composition The model will thereforepredict a richer mixture during combustion for methylbutanoate while others will be leaner That could influencethe calculation of oxygen content in the burning mixtureand therefore will impact the computation of NO

119909emission

through the extended Zeldovichmechanism Another area ofinvestigation could be the extension of the thermodynamicdata for each surrogate by integration ofmore chain reactionsinto the reduced chemical mechanical mechanism Thatcould lead to an increase of computation time

4 Conclusion

Four biodiesel surrogates were investigated for their perfor-mance in 0D phenomenological combustion modeling Thesurrogated thermodynamic data were those of butanoateethyl butyrate methyl decanoate and methyl 9 decenoateSimulations were compared against experimental data gath-ered from the combustion of ethyl ester and methyl esterbiodiesel from waste cooking oil in a 6-cylinder DI dieselengine at engine speed varying to 1100 1400 and 1700 rpmEach biodiesel surrogate was investigated for in-cylinderpressure maximum pressure thermal efficiency and NO

119909

emissions After the analysis of the simulation the followingconclusions could be derived

(i) Enthalpy entropy and heat capacity of the surrogatesfollow similar curve shapes the highest differenceswere identified for methyl butanoate and methyldecanoate concerning entropy and heat capacity andbetweenmethyl butanoate andmethyl 9 decenoate forenthalpy

(ii) Each surrogate fairly well predicted maximum pres-sure and thermal efficiency for each engine regimeand each biodiesel

(iii) Methyl butanoate showed the best accuracy for allthree simulated parameters 127 and 094 for

maximum pressure 146 and 355 for thermalefficiency and 665 and 384 for NO

119909emissions

for MEB and EEB respectively followed by methyldecanoate methyl 9 decenoate and ethyl butyrate

(iv) Out of the four surrogates only methyl butanoatecould well predict NO

119909emissions at 665 and

384 for MEB and EEB respectively the other threesurrogates presented heavy average errors higher than50

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the Ministry of Higher Educationof Cameroon for financing this research

References

[1] S A Basha K R Gopal and S Jebaraj ldquoA review on biodieselproduction combustion emissions and performancerdquo Renew-able and Sustainable Energy Reviews vol 13 no 6-7 pp 1628ndash1634 2009

[2] N Usta E Ozturk O Can et al ldquoCombustion of bioDiesel fuelproduced from hazelnut soapstockwaste sunflower oil mixturein aDiesel enginerdquoEnergy Conversion andManagement vol 46no 5 pp 741ndash755 2005

[3] X Wang K Li and W Su ldquoExperimental and numericalinvestigations on internal flow characteristics of diesel nozzleunder real fuel injection conditionsrdquo ExperimentalThermal andFluid Science vol 42 pp 204ndash211 2012

[4] J Yang M Johansson C Naik et al ldquo3D CFD modeling ofa biodiesel-fueled diesel engine based on a detailed chemicalmechanismrdquo SAE Technical Paper 2012-01-0151 SAE Interna-tional 2012

[5] S Som and D E Longman ldquoNumerical study comparingthe combustion and emission characteristics of biodiesel topetrodieselrdquo Energy and Fuels vol 25 no 4 pp 1373ndash1386 2011

[6] N Samec B Kegl and R W Dibble ldquoNumerical and experi-mental study of wateroil emulsified fuel combustion in a dieselenginerdquo Fuel vol 81 no 16 pp 2035ndash2044 2002

[7] H J Curran P Gaffuri W J Pitz and C K WestbrookldquoA comprehensive modeling study of n-heptane oxidationrdquoCombustion and Flame vol 114 no 1-2 pp 149ndash177 1998

[8] S Hong M S Wooldridge H G Im D N Assanis and HPitsch ldquoDevelopment and application of a comprehensive sootmodel for 3D CFD reacting flow studies in a diesel enginerdquoCombustion and Flame vol 143 no 1-2 pp 11ndash26 2005

[9] G Vourliotakis D I Kolaitis and M A Founti ldquoDevelopmentand parametric evaluation of a tabulated chemistry tool forthe simulation of n-heptane low-temperature oxidation andautoignition phenomenardquo Journal of Combustion vol 2014Article ID 237049 13 pages 2014

[10] L Coniglio H Bennadji P A Glaude O Herbinet andF Billaud ldquoCombustion chemical kinetics of biodiesel andrelated compounds (methyl and ethyl esters) experiments


and modelingmdashadvances and future refinementsrdquo Progress inEnergy andCombustion Science vol 39 no 4 pp 340ndash382 2013

[11] S Um and S W Park ldquoModeling effect of the biodieselmixing ratio on combustion and emission characteristics usinga reduced mechanism of methyl butanoaterdquo Fuel vol 89 no 7pp 1415ndash1421 2010

[12] J Y W Lai K C Lin and A Violi ldquoBiodiesel combustionadvances in chemical kinetic modelingrdquo Progress in Energy andCombustion Science vol 37 no 1 pp 1ndash14 2011

[13] P Dievart S H Won S Dooley F L Dryer and Y Ju ldquoAkinetic model for methyl decanoate combustionrdquo Combustionand Flame vol 159 no 5 pp 1793ndash1805 2012

[14] V I Golovitchev and J Yang ldquoConstruction of combustionmodels for rapeseed methyl ester bio-diesel fuel for internalcombustion engine applicationsrdquo Biotechnology Advances vol27 no 5 pp 641ndash655 2009

[15] C VNgayihi Abbe R Nzengwa R Danwe ZMAyissi andMObonou ldquoA study on the 0Dphenomenologicalmodel for dieselengine simulation application to combustion of Neem methylesther biodieselrdquo Energy Conversion and Management vol 89pp 568ndash576 2015

[16] J Galle R Verschaeren and S Verhelst ldquoThe behavior ofa simplified spray model for different diesel and bio-dieselsurrogatesrdquo SAE Technical Paper 2015-01-0950 2015

[17] A Stagni C Saggese M Bissoli et al ldquoReduced kineticmodel of biodiesel fuel combustionrdquo Chemical EngineeringTransactions vol 37 pp 877ndash882 2014

[18] S Som W Liu and D E Longman ldquoComparison of differentchemical kinetic models for biodiesel combustionrdquo in Proceed-ings of the Internal Combustion Engine Division Fall TechnicalConference (ASME rsquo13) American Society of Mechanical Engi-neers Dearborn Mich USA October 2013

[19] A S Lyshevsky Fuel Atomization in Marine Diesels MachgizLeningrad Russia 1971 (Russian)

[20] N F Razleytsev Combustion Simulation and Optimization inDiesels Vischa Shkola Kharkiv Ukraine 1980 (Russian)

[21] F I Abramchuk A P Marchenko N F Razlejtsev and E ITretiak Modern Diesel Engines Increase of Fuel Economy andDurability Technika Kiev Ukraine 1992

[22] A S Kuleshov ldquoMulti-zone DI diesel spray combustion modelfor thermodynamic simulation of engine with PCCI and highEGR levelrdquo SAE International Journal of Engines vol 2 no 1pp 1811ndash1834 2009

[23] D B Spalding ldquoThe combustion of liquid fuelsrdquo in Proceed-ings of the Fourth Symposium (International) on Combustionand Detonation Waves The Combustion Institute CambridgeMass USA 1953

[24] Y Aghav V Thatte M Kumar et al ldquoPredicting ignition delayand HC emission for DI diesel engine encompassing EGR andoxygenated fuelsrdquo SAE Technical Paper 2008-28-0050 SAE2008

[25] N Watson A Pilley and M Marzouk ldquoA combustion correla-tion for diesel engine simulationrdquo SAE Technical Paper 8000291980

[26] OGrondinModelisation dumoteur a allumage par compressiondans la perspective du controle et du diagnostic [PhD thesis]Universite de Rouen Rouen France 2004

[27] C R Ferguson and T K Allan Internal Combustion EnginesAppliedThermosciences JohnWileyamp SonsHobokenNJ USA2nd edition 2000

[28] R J Kee F M Rupley and J A Miller ldquoThe chemkin thermo-dynamic data baserdquo Tech Rep 1990

[29] G Woschni ldquoA universally applicable equation for the instan-taneous heat transfer coefficient in the internal conbustionenginerdquo SAE Technical Paper 670931 1967

[30] J B Heywood Internal Combustion Engine FundamentalsMcGraw-Hill New York NY USA 1988

[31] G A Lavoie J B Heywood and J C Keck ldquoExperimentaland theoretical study of nitric oxide formation in internalcombustion enginesrdquo Combustion Science and Technology vol1 no 4 pp 313ndash326 1970

[32] H Sanli M Canakcib E Alptekinb A Turkcanb and AN Ozsezenb ldquoEffects of waste frying oil based methyl andethyl ester biodiesel fuels on the performance combustion andemission characteristics of a DI diesel enginerdquo Fuel vol 159 pp179ndash187 2015

[33] M H Hakka P-A Glaude O Herbinet and F Battin-LeclercldquoExperimental study of the oxidation of large surrogates fordiesel and biodiesel fuelsrdquo Combustion and Flame vol 156 no11 pp 2129ndash2144 2009

[34] W Wang and M A Oehlschlaeger ldquoA shock tube study ofmethyl decanoate autoignition at elevated pressuresrdquo Combus-tion and Flame vol 159 no 2 pp 476ndash481 2012

[35] S Zhang L J Broadbelt I P Androulakis andM G Ierapetri-tou ldquoComparison of biodiesel performance based on HCCIengine simulation using detailed mechanism with on-the-flyreductionrdquo Energy amp Fuels vol 26 no 2 pp 976ndash983 2012

[36] A M El-Nahas M V Navarro J M Simmie et al ldquoEnthalpiesof formation bond dissociation energies and reaction pathsfor the decomposition of model biofuels ethyl propanoate andmethyl butanoaterdquoThe Journal of Physical Chemistry A vol 111no 19 pp 3727ndash3739 2007

[37] W Liu R Sivaramakrishnan M J Davis S Som D ELongman and T F Lu ldquoDevelopment of a reduced biodieselsurrogate model for compression ignition engine modelingrdquoProceedings of the Combustion Institute vol 34 no 1 pp 401ndash409 2013

[38] OHerbinetW J Pitz andC KWestbrook ldquoDetailed chemicalkinetic mechanism for the oxidation of biodiesel fuels blendsurrogaterdquo Combustion and Flame vol 157 no 5 pp 893ndash9082010

[39] Z Luo M Plomer T Lu et al ldquoA reduced mechanism forbiodiesel surrogates for compression ignition engine applica-tionsrdquo Fuel vol 99 pp 143ndash153 2012

[40] E Goos A Burcat and B Ruscic ldquoTransfer of extended thirdmillennium ideal gas and condensed phase thermochemicaldatabaserdquo in Extended Third Millennium Ideal Gas and Con-densed Phase Thermochemical Database Engineering FOAHaifa Israel 2009

[41] G Labeckas and S Slavinskas ldquoThe effect of rapeseed oil methylester on direct injectionDiesel engine performance and exhaustemissionsrdquo Energy Conversion and Management vol 47 no 13-14 pp 1954ndash1967 2006

[42] C D Rakopoulos K A Antonopoulos D C Rakopoulos DT Hountalas and E G Giakoumis ldquoComparative performanceand emissions study of a direct injection Diesel engine usingblends of Diesel fuel with vegetable oils or bio-diesels of variousoriginsrdquo Energy Conversion and Management vol 47 no 18-19pp 3272ndash3287 2006

[43] G A Lavoie and P N Blumberg ldquoA Fundamental model forpredicting fuel consumption NO

119909and HC emissions of the


conventional spark-ignition enginerdquo Combustion Science andTechnology vol 21 no 5-6 pp 225ndash258 1980

[44] I Uryga-Bugajska M Pourkashanian D Borman E Cata-lanotti and C W Wilson ldquoTheoretical investigation of theperformance of alternative aviation fuels in an aero-enginecombustion chamberrdquo Proceedings of the Institution of Mechani-cal Engineers Part G Journal of Aerospace Engineering vol 225no 8 pp 874ndash885 2011

[45] J L Brakora Y Ra and R D Reitz ldquoCombustion model forbiodiesel-fueled engine simulations using realistic chemistryand physical propertiesrdquo SAE International Journal of Enginesvol 4 no 1 pp 931ndash947 2011

[46] K Seshadri T Lu O Herbinet et al ldquoExperimental and kineticmodeling study of extinction and ignition of methyl decanoatein laminar non-premixed flowsrdquo Proceedings of the CombustionInstitute vol 32 no 1 pp 1067ndash1074 2009

[47] S M Sarathy M J Thomson W J Pitz and T Lu ldquoAnexperimental and kinetic modeling study of methyl decanoatecombustionrdquoProceedings of the Combustion Institute vol 33 no1 pp 399ndash405 2011

[48] C Y Choi and R D Reitz ldquoModeling the effects of oxygenatedfuels and split injections on DI diesel engine performance andemissionsrdquo Combustion Science and Technology vol 159 no 1pp 169ndash198 2000

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



highly influencing the model performance Stagni et al [17]proposed a reduced kinetic model for biodiesel fuel for appli-cation on 0DmodelThey showed that the mechanism whenapplied permits a considerable time saving in computation

Som et al [18] performed four different chemical kineticmodels for 0D and 3D simulation the kinetic models weremainly based on mixture of two different set of surrogates(a) methyl decanoate methyl 9 decenoate and n-heptaneand (b) methyl butanoate and n-heptane Only species molefraction simulations were performed using 0D modeling Allthe mechanisms performed very well against experimentaldata but at the expense of computer cost

Theobjective of this study is to compare 4 differentmethyland ethyl ester surrogates in strictly 0D phenomenologicalmodeling for biodiesel combustion simulation purpose Thesurrogates will be compared according to computed maxi-mum pressure NO

119909emission and thermal efficiency

2 Material and Methods

21 0D Model Governing Equations The model used inthis study was validated in a previous study [15] we arepresenting here some fundamental relationships for a betterunderstanding of the computing methodology

211 Spray Submodel Injection and spray are modeled usingthe theory described by Lyshevsky and Razleytsev [19ndash22]The diesel jet is assumed to be constituted of two phasesan initial and a base which are separated by a transitorycharacteristic length which is computed as follows

119871119887= 119862119878119889119899119882119890

025

11987204

120588119897

minus06

(1)

where 119905119887

= 119897119887

2

119861119904is the characteristic time (s) 119862

119904is a

weighing coefficient 119889119899is injector nozzle diameter 119882

119890is the

Webber number and119872 is an a dimensional criterion [22]Webber number is computed by

119882119890=

1198802

0120588119891119889119888

120590119891

(2)

where 1198800is the spray initial velocity given by

1198800=

24119902119888119877119875119872

0751205881198911205871198892119888119894119888120593inj

(3)

119902119888is the fuel mass flow rate in Kgcycle 120588

119891is the fuel density

kgm3 119889119888is the injector nozzle diameter in mm 120593inj is the

injection duration in crank angle degrees 119894119888is the number of

injector holes

212 Evaporation Submodel The injected fuel is scatteredinto fine droplets after the transition length these droplet areevaporating at a given rate which is proportional to their size[20 21] The fuel spray is divided in two zones In the firstzone droplets are concentrated behind the front flame areaIn the second zone droplets have reached the front flame andthe evaporation is turbulent

The size of the pulverized droplets is evaluated for eachzone using the Sauter mean diameter calculated by

11988932

= 1711988911989911987200733

(119882119890 sdot 120588)minus0266

(4)

where 120588 = 120588119886120588119897is the ratio of density between air and liquid

fuelDroplets are assumed to evaporate following the 119889

2 law[23] for which the evaporation rate for a given droplet is

1198892

119894= 1198892

0minus 119870119905 (5)

where 1198890represents the droplet diameter after breakup (see

(4)) and 119889119894the diameter of the same droplet at time 119905119870 is the

evaporation constant

119870 = 106

sdot

4119873119906119863119901119901119904

120588119897

(6)

where 119873119906is the Nusselt number for diffusion processes 119863

119901

is the diffusion constant for fuel vapor and 119901119904is the fuel

saturated vapor pressureCombustion duration which is going to be used as an

entry data for heat release rate calculation is calculated inseconds by

120591ev =119860119911

(11988711989411990512058206)

(7)

where 119887119894119905

= 1198701198892

32is the relative evaporation constant and 120582

the excess air coefficient 119860119911is a fitting weighing coefficient

where its value varies from 4 to 12 [21]

213 Ignition Delay and Heat Release Submodels Ignitiondelay is computed using the following correlation [24]

ID = [036 + 022119880119901] exp[119864

119886sdot (

1

119877119879im120576119899119888minus1minus

1

17190)

+ (212

119875im120576119899119888 minus 124)

063

]

(8)

where 119864119886is the fuel activation energy which is computed by

119864119886

= 1310000(CN + 25) CN is the fuel cetane number119880119901is the engine piston speed 119879im and 119875im are respectively

the temperature and pressure at the intake manifold 120576 is theenginersquos compression ratio and 119899

119888is the polytropic exponent

for compressionThe fuel burnt ratio at any crank angle 119909 = 119891(120593) is

computed using a double Wiebe function [25 26] by

119909 = 120573119909119901+ (1 minus 120573) 119909

119889 (9)

where 119909119901and 119909

119889represent the fuel burnt ratio for premixed

and diffusion combustion phases and 120573 represents the frac-tion of injected fuel during premixed phase

For each combustion phase we can write

119909119894= 1 minus exp[minus119886

119894(120593 minus 120593comb

Δ120593)

119898119894+1

] (10)


where 119886119894and119898





(1 minus 119910119903)

1 + 120576120601 + 120603[120576120601 C

119886H119887O119888N119889+ 119891 (H

2O) + 021 sdotO

2

+ 079 sdotN2+ 120603H

2O] + 119910

119903[1199101015840

1CO2+ 1199101015840

2H2O

+ 1199101015840

3N2+ 1199101015840

4O2+ 1199101015840

5CO + 119910

1015840

6H2+ 1199101015840

7H + 119910

1015840

8O

+ 1199101015840

9OH + 119910

1015840

10NO] 997888rarr V

1CO2+ V2H2O + V3N2

+ V4O2+ V5CO + V

6H2+ V7H + V

8O + V9OH

+ V10NO

(11)




119888119901

119877= 1198861+ 1198862119879 + 11988631198792

+ 11988641198793

+ 1198865

1

1198792

ℎ

119877119879= 1198861+

1198862

2119879 +

1198863

41198792

+1198864

41198793

+1198865

5

1

1198792+ 1198866

1

119879

119904

119877= 1198861ln119879 + 119886

2119879 +

1198863

21198792

+1198864

31198793

+1198865

4

1

1198792+ 1198867

(12)






ℎ = sum119910119894ℎ119894+ ℎ119891119910119891 (kJkmol) (13)


119904 = (119904119891minus ln119910

119891) 119910119891+ sum(119904

119894minus ln119910

119894) 119910119894 kJkmolK (14)


119888119901= 119888119901119891

119910119891+ sum119888

119901119894119910119894 (15)


119906 = ℎ minus 119877119879

V = 119877119879

119875

(16)




119889119906

119889120579= (119888119875minus

119901V119879

120597 ln V120597 ln119879

)119889119879

119889120593

minus (V(120597 ln V120597 ln119879

+120597 ln V120597 ln119875

))119889119901

119889120593

(17)

119889V119889120579

=V119879

120597 ln V120597 ln119879

119889119879

119889120593minus

V119901

120597 ln V120597 ln119901

119889119901

119889120593 (18)

119889119904

119889120579= (

119888119875

119879)

119889119879

119889120593minus

V119879

120597 ln V120597 ln119879

119889119901

119889120593 (19)

with (120597ℎ120597119879)119875= 119888119875


119889119901

119889120593=

119860 + 119861 + 119862

119863 + 119864 (20)

119889119879119887

119889120593=

minusℎ (1205871198872

2 + 4119881119887) 11990912

119879119887minus 119879119908

V119898119888119875119887

119909

+V119887

119888119875119887

(120597 ln V119887

120597 ln119879119887

)(119889119901

119889120593)

+ℎ119888119906

minus ℎ119888119887

119909119888119875119887

[119889119909

119889120593minus 119909 minus 119909

2119862

120596]

(21)

119889119879119906

119889120593=

minusℎ (1205871198872

2 + 4119881119887) 11990912

119879119906minus 119879119908

V119898119888119875119906

119909

+V119906

119888119875119906

(120597 ln V119906

120597 ln119879119906

)(119889119901

119889120593)

+ℎ119888119906

minus ℎ119888119887

119909119888119906

[119889119909

119889120593minus 119909 minus 119909

2119862

120596]

(22)


with

119860 =1

119898(119889119881

119889120593+

119881119862blowby

120596)

119861 = ℎ

(119889119881119889120593 + 119881119862blowby120596)

120596119898[V119887

119888119875119887

120597 ln V119887

120597 ln119879119887

11990912

sdot119879119887minus 119879119908

119879119887

+V119906

119888119875119906

120597 ln V119906

120597 ln119879119906

(1 minus 11990912

)119879119906minus 119879119908

119879119906

]

119862 = minusV119887minus V119906

119889119909

119889120593minus V119887

120597 ln V119887

120597 ln119879119887

ℎ119888119906

minus ℎ119888119887

119888119875119887

119879119887

[119889119909

119889120593

minus

(119909 minus 1199092

) 119862blowby

120596]

119863 = 119909[V2119887

119888119875119887

119879119887

(120597 ln V119906

120597 ln119879119906

)

2

+V119887

119875

120597 ln V119887

120597 ln119875]

119864 = 1 minus 119909[V2119906

119888119875119906

119879119906

(120597 ln V119906

120597 ln119879119906

)

2

+V119906

119901

120597 ln V119906

120597 ln119901]

(23)

where ℎ119888119887

and ℎ119888119906






119889 [NO]

119889119905=

21198621[1 minus ([NO] [NO]

119890)]

1 + [[NO] [NO]119890] 1198622

(24)

where 1198621= 1198701198911

[O]119890[N2]119890and

1198622=

1198621

1198701199032

[NO]119890[O]1198901198701199033

[NO]119890[H]119890

(25)


















119909emission





















0

(K)500 1000 1500 2000 2500 3000 3500

minus400E + 01

minus350E + 01

minus300E + 01

minus250E + 01

minus200E + 01

minus150E + 01

minus100E + 01

minus500E + 00

000E + 00

minus150

minus100

minus50

0

50

100

(kJk

mol

)




119909emission were
















000

5000

10000

15000

20000

25000

minus400E + 01

minus350E + 01

minus300E + 01

minus250E + 01

minus200E + 01

minus150E + 01

minus100E + 01

minus500E + 00

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500




Max residual

0002000400060008000

1000012000

minus600E + 01

minus500E + 01

minus400E + 01

minus300E + 01

minus200E + 01

minus100E + 01

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500







0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)




119873119874119909Emissions NO










0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)





8759 and 9117









119909










119909emission


4 Conclusion


119909






119909emissions







Acknowledgment


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










where 119886119894and119898





(1 minus 119910119903)

1 + 120576120601 + 120603[120576120601 C

119886H119887O119888N119889+ 119891 (H

2O) + 021 sdotO

2

+ 079 sdotN2+ 120603H

2O] + 119910

119903[1199101015840

1CO2+ 1199101015840

2H2O

+ 1199101015840

3N2+ 1199101015840

4O2+ 1199101015840

5CO + 119910

1015840

6H2+ 1199101015840

7H + 119910

1015840

8O

+ 1199101015840

9OH + 119910

1015840

10NO] 997888rarr V

1CO2+ V2H2O + V3N2

+ V4O2+ V5CO + V

6H2+ V7H + V

8O + V9OH

+ V10NO

(11)




119888119901

119877= 1198861+ 1198862119879 + 11988631198792

+ 11988641198793

+ 1198865

1

1198792

ℎ

119877119879= 1198861+

1198862

2119879 +

1198863

41198792

+1198864

41198793

+1198865

5

1

1198792+ 1198866

1

119879

119904

119877= 1198861ln119879 + 119886

2119879 +

1198863

21198792

+1198864

31198793

+1198865

4

1

1198792+ 1198867

(12)






ℎ = sum119910119894ℎ119894+ ℎ119891119910119891 (kJkmol) (13)


119904 = (119904119891minus ln119910

119891) 119910119891+ sum(119904

119894minus ln119910

119894) 119910119894 kJkmolK (14)


119888119901= 119888119901119891

119910119891+ sum119888

119901119894119910119894 (15)


119906 = ℎ minus 119877119879

V = 119877119879

119875

(16)




119889119906

119889120579= (119888119875minus

119901V119879

120597 ln V120597 ln119879

)119889119879

119889120593

minus (V(120597 ln V120597 ln119879

+120597 ln V120597 ln119875

))119889119901

119889120593

(17)

119889V119889120579

=V119879

120597 ln V120597 ln119879

119889119879

119889120593minus

V119901

120597 ln V120597 ln119901

119889119901

119889120593 (18)

119889119904

119889120579= (

119888119875

119879)

119889119879

119889120593minus

V119879

120597 ln V120597 ln119879

119889119901

119889120593 (19)

with (120597ℎ120597119879)119875= 119888119875


119889119901

119889120593=

119860 + 119861 + 119862

119863 + 119864 (20)

119889119879119887

119889120593=

minusℎ (1205871198872

2 + 4119881119887) 11990912

119879119887minus 119879119908

V119898119888119875119887

119909

+V119887

119888119875119887

(120597 ln V119887

120597 ln119879119887

)(119889119901

119889120593)

+ℎ119888119906

minus ℎ119888119887

119909119888119875119887

[119889119909

119889120593minus 119909 minus 119909

2119862

120596]

(21)

119889119879119906

119889120593=

minusℎ (1205871198872

2 + 4119881119887) 11990912

119879119906minus 119879119908

V119898119888119875119906

119909

+V119906

119888119875119906

(120597 ln V119906

120597 ln119879119906

)(119889119901

119889120593)

+ℎ119888119906

minus ℎ119888119887

119909119888119906

[119889119909

119889120593minus 119909 minus 119909

2119862

120596]

(22)


with

119860 =1

119898(119889119881

119889120593+

119881119862blowby

120596)

119861 = ℎ

(119889119881119889120593 + 119881119862blowby120596)

120596119898[V119887

119888119875119887

120597 ln V119887

120597 ln119879119887

11990912

sdot119879119887minus 119879119908

119879119887

+V119906

119888119875119906

120597 ln V119906

120597 ln119879119906

(1 minus 11990912

)119879119906minus 119879119908

119879119906

]

119862 = minusV119887minus V119906

119889119909

119889120593minus V119887

120597 ln V119887

120597 ln119879119887

ℎ119888119906

minus ℎ119888119887

119888119875119887

119879119887

[119889119909

119889120593

minus

(119909 minus 1199092

) 119862blowby

120596]

119863 = 119909[V2119887

119888119875119887

119879119887

(120597 ln V119906

120597 ln119879119906

)

2

+V119887

119875

120597 ln V119887

120597 ln119875]

119864 = 1 minus 119909[V2119906

119888119875119906

119879119906

(120597 ln V119906

120597 ln119879119906

)

2

+V119906

119901

120597 ln V119906

120597 ln119901]

(23)

where ℎ119888119887

and ℎ119888119906






119889 [NO]

119889119905=

21198621[1 minus ([NO] [NO]

119890)]

1 + [[NO] [NO]119890] 1198622

(24)

where 1198621= 1198701198911

[O]119890[N2]119890and

1198622=

1198621

1198701199032

[NO]119890[O]1198901198701199033

[NO]119890[H]119890

(25)


















119909emission





















0

(K)500 1000 1500 2000 2500 3000 3500

minus400E + 01

minus350E + 01

minus300E + 01

minus250E + 01

minus200E + 01

minus150E + 01

minus100E + 01

minus500E + 00

000E + 00

minus150

minus100

minus50

0

50

100

(kJk

mol

)




119909emission were
















000

5000

10000

15000

20000

25000

minus400E + 01

minus350E + 01

minus300E + 01

minus250E + 01

minus200E + 01

minus150E + 01

minus100E + 01

minus500E + 00

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500




Max residual

0002000400060008000

1000012000

minus600E + 01

minus500E + 01

minus400E + 01

minus300E + 01

minus200E + 01

minus100E + 01

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500







0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)




119873119874119909Emissions NO










0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)





8759 and 9117









119909










119909emission


4 Conclusion


119909






119909emissions







Acknowledgment


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










with

119860 =1

119898(119889119881

119889120593+

119881119862blowby

120596)

119861 = ℎ

(119889119881119889120593 + 119881119862blowby120596)

120596119898[V119887

119888119875119887

120597 ln V119887

120597 ln119879119887

11990912

sdot119879119887minus 119879119908

119879119887

+V119906

119888119875119906

120597 ln V119906

120597 ln119879119906

(1 minus 11990912

)119879119906minus 119879119908

119879119906

]

119862 = minusV119887minus V119906

119889119909

119889120593minus V119887

120597 ln V119887

120597 ln119879119887

ℎ119888119906

minus ℎ119888119887

119888119875119887

119879119887

[119889119909

119889120593

minus

(119909 minus 1199092

) 119862blowby

120596]

119863 = 119909[V2119887

119888119875119887

119879119887

(120597 ln V119906

120597 ln119879119906

)

2

+V119887

119875

120597 ln V119887

120597 ln119875]

119864 = 1 minus 119909[V2119906

119888119875119906

119879119906

(120597 ln V119906

120597 ln119879119906

)

2

+V119906

119901

120597 ln V119906

120597 ln119901]

(23)

where ℎ119888119887

and ℎ119888119906






119889 [NO]

119889119905=

21198621[1 minus ([NO] [NO]

119890)]

1 + [[NO] [NO]119890] 1198622

(24)

where 1198621= 1198701198911

[O]119890[N2]119890and

1198622=

1198621

1198701199032

[NO]119890[O]1198901198701199033

[NO]119890[H]119890

(25)


















119909emission





















0

(K)500 1000 1500 2000 2500 3000 3500

minus400E + 01

minus350E + 01

minus300E + 01

minus250E + 01

minus200E + 01

minus150E + 01

minus100E + 01

minus500E + 00

000E + 00

minus150

minus100

minus50

0

50

100

(kJk

mol

)




119909emission were
















000

5000

10000

15000

20000

25000

minus400E + 01

minus350E + 01

minus300E + 01

minus250E + 01

minus200E + 01

minus150E + 01

minus100E + 01

minus500E + 00

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500




Max residual

0002000400060008000

1000012000

minus600E + 01

minus500E + 01

minus400E + 01

minus300E + 01

minus200E + 01

minus100E + 01

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500







0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)




119873119874119909Emissions NO










0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)





8759 and 9117









119909










119909emission


4 Conclusion


119909






119909emissions







Acknowledgment


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























0

(K)500 1000 1500 2000 2500 3000 3500

minus400E + 01

minus350E + 01

minus300E + 01

minus250E + 01

minus200E + 01

minus150E + 01

minus100E + 01

minus500E + 00

000E + 00

minus150

minus100

minus50

0

50

100

(kJk

mol

)




119909emission were
















000

5000

10000

15000

20000

25000

minus400E + 01

minus350E + 01

minus300E + 01

minus250E + 01

minus200E + 01

minus150E + 01

minus100E + 01

minus500E + 00

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500




Max residual

0002000400060008000

1000012000

minus600E + 01

minus500E + 01

minus400E + 01

minus300E + 01

minus200E + 01

minus100E + 01

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500







0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)




119873119874119909Emissions NO










0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)





8759 and 9117









119909










119909emission


4 Conclusion


119909






119909emissions







Acknowledgment


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























000

5000

10000

15000

20000

25000

minus400E + 01

minus350E + 01

minus300E + 01

minus250E + 01

minus200E + 01

minus150E + 01

minus100E + 01

minus500E + 00

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500




Max residual

0002000400060008000

1000012000

minus600E + 01

minus500E + 01

minus400E + 01

minus300E + 01

minus200E + 01

minus100E + 01

000E + 00

0

(K)500 1000 1500 2000 2500 3000 3500







0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)




119873119874119909Emissions NO










0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)





8759 and 9117









119909










119909emission


4 Conclusion


119909






119909emissions







Acknowledgment


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)




119873119874119909Emissions NO










0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)





8759 and 9117









119909










119909emission


4 Conclusion


119909






119909emissions







Acknowledgment


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0Crank angle (deg)

5

6

7

8

9

10Pr

essu

re (M

Pa)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)


0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)

(c) Ethyl butyrate

0Crank angle (deg)

5

6

7

8

9

10

Pres

sure

(MPa

)





8759 and 9117









119909










119909emission


4 Conclusion


119909






119909emissions







Acknowledgment


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119909










119909emission


4 Conclusion


119909






119909emissions







Acknowledgment


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article comparative numerical study of four...

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