Research Article Comparing in Cylinder Pressure Modelling ...downloads.hindawi.com/archive/2014/534953.pdf · Research Article Comparing in Cylinder Pressure Modelling of a DI Diesel

Research ArticleComparing in Cylinder Pressure Modelling ofa DI Diesel Engine Fuelled on Alternative Fuel UsingTwo Tabulated Chemistry Approaches

Claude Valery Ngayihi Abbe12 Robert Nzengwa12 and Raidandi Danwe23

1 Faculty of Industrial Engineering PO Box 2701 University of Douala Douala Cameroon2National Advanced School of Engineering PO Box 337 University of Yaounde Yaounde Cameroon3Higher Institute of the Sahel PO Box 46 University of Maroua Maroua Cameroon

Correspondence should be addressed to Claude Valery Ngayihi Abbe ngayihiclaudeyahoofr

Received 9 April 2014 Accepted 1 August 2014 Published 29 October 2014

Academic Editor Xinqian Zheng

Copyright copy 2014 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

The present work presents the comparative simulation of a diesel engine fuelled on diesel fuel and biodiesel fuel Twomodels basedon tabulated chemistry were implemented for the simulation purpose and results were compared with experimental data obtainedfrom a single cylinder diesel engine The first model is a single zone model based on the Krieger and Bormann combustion modelwhile the secondmodel is a two-zonemodel based onOlikara and Bormann combustionmodel It was shown that bothmodels canpredict well the enginersquos in-cylinder pressure as well as its overall performances The second model showed a better accuracy thanthe first while the first model was easier to implement and faster to compute It was found that the first method was better suitedfor real time engine control and monitoring while the second one was better suited for engine design and emission prediction

1 Introduction

The modeling of internal combustion engines has beenlargely developed during past years For this purpose amultitude of industrial codes dedicated to the simulation ofthe engines is available on market (GT-Power Diesel-RKRicardo-Wave Fluent etc) These codes despite the factthat they can be useful for predicting engine performancesare expensive for third worldrsquos university laboratory andtheir source codes are practically impossible to modify toimplement new model or functions

When modeling compression engine differentapproaches can be used with different level of complexitysuch as thermodynamic 0D models quasi-dimensionalmultizone models and computational fluid dynamics (CFD)models [1 2]

For this study a quasi-dimensional approachwas selectedthese models allows to compute efficient economic and

fast calculations of engine performances as a function ofdifferent engine parameters Using these types of models wecan compute the different stages of a diesel engine cycle as incompression injection ignition delay and combustion andexhaust stage

The evaluated models in this study will be evaluated interms of accuracy and speed of calculation

2 Governing Equations

21 Fuel Injection and Vaporization Model For both modelsthe fuel spray characteristic is modeled using the phe-nomenological model of Razleytsev [3] and Lyshevsky [4]That model has been used and implemented in the so calledRK-model [5] and its results Themain aim of this part of themodel is to determine the finesse of the atomized fuel fromthe injector nozzleThefinesse of atomization is characterizedby the calculated Sauter mean diameter of fuel droplet The

Hindawi Publishing CorporationInternational Scholarly Research NoticesVolume 2014 Article ID 534953 7 pageshttpdxdoiorg1011552014534953

2 International Scholarly Research Notices

model is a simple sequence of calculated parameters and isstructured as follows

First the average outflow velocity of fuel from the injectoris calculated in ms by

1198800=

24119902119888RPM

0751205881198911205871198892119888119894119888120593inj

(1)

where 119902119888is the cyclic fuel supply in Kgcycle RPM is the

crankshaft rotational speed in rpm 120588119891is the density of the

fuel in kgm3 119889119888is the diameter of the injector hole in mm

120593inj is the duration of injection in degree of rotation of thecrankshaft

The criterion119872 characterizing the relationship betweenthe surface tension force inertia and viscosity is calculatedas follows

119872 =

1205832

119891

(119889119888120588119891120590119891)

(2)

where 120583119891is the coefficient of dynamic viscosity of the fuel at

a temperature of 323K in Pasdots 120590119891is the coefficient of surface

tension of the fuel at a temperature of 323K in NmWeber number characterizing the relationship between

surface tension force and inertia is determined as

119882119890=

1198802

0120588119891119889119888

120590119891

(3)

The density of the charge at the end of the compressionbefore the TDC is calculated as follows

120588air =120583air119872]

119881119888

(4)

where 120583air = 289KgKmole is the molecular mass of air 120588airis the density of air

We then determine the fuelair density ratio by

120588 =120588air120588119891

(5)

Finally the Sauter mean diameter of the atomized fuel iscalculated in micron by

11988932=1061198643211988911988811987200733

(120588119882119890)0266

(6)

where 11986432is an empirical factor depending on designs of the

injector whose recommended value is 17At this point the finesse of the pulverized fuel is deter-

mined and we can see it mainly depends on physical prop-erties of the fuel such as viscosity and density The next stepof the model is to determine the kinetic of combustion of theatomized fuel whose kinetic will be dependent of the earlierfound Sauter mean diameter

22 Model of the Kinetic of Combustion of the Atomized FuelThis part of the elaborated model will permit us to determineparameters of the process such as the evaporation rate ofthe atomized fuel its ignition delay and the duration ofcombustion

Pressure in the cylinder at the end of the compressionbefore the TDC is

119875119888= 1198750120576137 (7)

where 1198750is the reference pressure which in our case corre-

sponds to the inlet manifold pressureWe then determine the theoretical constant of evapora-

tion of the fuel by

119887it =119870

1198892

32

(8)

where 119870 = 1119875119888sdot 106 is the evaporation constant related to

cylinder pressure in m2s

120591119890V =

119860119911

(119887it12058206)

(9)

where 119860119911is a constant characterizing the duration of evap-

oration of large drops in diesel engine in 1s and its valueis given as 24 in [3] but Kuleshov [5] used it as weightcoefficient that can be varied in order to match experimentaldata 120582 is the coefficient of excess air

The full duration of combustion is then calculated as

120601119911= 120601inj minus ID + 6RPM120591

119890V (10)

with ID being the ignition delay computed using the formulaof Hardenberg and Hase [6] in both models

ID

= [036 + 022119880119901]

times exp[119864119886sdot (

1

119877119879im120576119899119888minus1minus

1

17190) + (

212

119875im120576119899119888 minus 124

)

063

]

(11)

The value of the apparent activation energy 119864119886in this

correlation is given by 119864119886= 618840(119862119873+25) however this

valuewas computed for the particular experiment reported in[6] and needs to be corrected in order to be used for differentexperimental conditions In order to match experimentalignition delay values especially for biodiesel fuel themethodproposed by Aghav et al [7] where the value 618840 can bevaried from the initial 618840 to higher values was used

23 Heat Release and Heat Transfer Laws For the twomodels we used a double Wiebe function [8] to model theheat release rate and the Woschni [9] law for heat transfersimulation

International Scholarly Research Notices 3

3 Combustion Models

31 Method 1 Combustion Model Based on Borman andKrieger [10] Thismethod is a single zonemodel based on thefirst law of thermodynamicsmass conservation and ideal gaslaws Following that we can write the governing equation forcalculating variation of in-cylinder pressure with respect tocrank angle as [11]

119889119876inj minus 119889119876loss

119889120579=

120574

120574 minus 1119875119889119881

119889120579+

1

120574 minus 1119881119889119875

119889120579 (12)

The Krieger and Bormann algorithm is based on polyno-mial fitting constant to compute the adiabatic index (ratioof specific heat) as function of crank angle The fittingcoefficients can be found in the Appendix

The internal energy of combustion products at equilib-rium for a reaction between air and a hydrocarbon CnH2n isgiven as

119906 =119860 minus 119861

120582 + 119906corr (13)

where

119860 = 1198861119879 + 11988621198792+ 11988631198793+ 11988641198794+ 11988651198795

119861 = 1198870+ 1198871119879 + 11988721198792+ 11988731198793+ 11988741198794

(14)

119906corr = 119888119906 exp(119863120582 + 119864120582 + 119865119875119879120582) is the correction factor for theinternal energy accounting for dissociation

119863120582= 1198890+ 1198891sdot 120582minus1+ 1198893120582minus3

119864120582=

(1198900+ 1198901120582minus1+ 1198903120582minus3)

119879

119865119875119879120582

= [1198910+ 1198911120582minus1+ 1198913120582minus3+

(1198914+ 1198915120582minus1)

119879] log (119891

6sdot 119875)

(15)

The gas constant is computed as

119877 = 0287 +0020

120582+ 119877corr (16)

with 119877corr = 119888119903 exp(1199030 log 120582 + ((1199031 + 1199032119879) + 1199033 log(1198916119875))120582)The adiabatic index (ratio of specific heat) is computed as

120574 = 1 +119877

119888V (17)

with 119888V = 120597119906120597119879

32 Method 2 Combustion Model Based on Olikara andBormann Method [12 13] This model is a two-zone ther-modynamic model where the thermodynamics properties of

combustion products and fuel are determined using polyno-mial curve fitted data from the Chemkin [14] or JANAF [15]tables and are given by

119888119901

119877= 1198861+ 1198862119879 + 11988631198792+ 11988641198793+ 11988651198794

ℎ

119877119879= 1198861+1198862

2119879 +

1198863

41198792+1198864

41198793+1198865

51198794+ 1198866

1

119879

119904

119877= 1198861ln119879 + 119886

2119879 +

1198863

21198792+1198864

31198793+1198865

41198794+ 1198867

(18)

The in-cylinder pressure and temperature of burnedand unburned gases derivative can be calculated followingFergusonrsquos algorithm [13 16] by

119889119875

119889120579=119860 + 119861 + 119862

119863 + 119864

119889119879119887

119889120579=

minusℎ (12058711988722 + 4119881119887) 119909

12119879119887minus 119879119908

V119898119888119875119887119909

+V119887

119888119875119887

(120597 ln V119887

120597 ln119879119887

)(119889119875

119889120579)

+ℎ119906minus ℎ119887

119909119888119875119887

[119889119909

119889120579minus 119909 minus 119909

2119862

120596]

119889119879119906

119889120579=

minusℎ (12058711988722 + 4119881119887) 119909

12119879119906minus 119879119908

V119898119888119875119906119909

+V119906

119888119875119906

(120597 ln V119906

120597 ln119879119906

)(119889119875

119889120579)

+ℎ119906minus ℎ119887

119909119888119906

[119889119909

119889120579minus 119909 minus 119909

2119862

120596]

(19)

where

119860 =1

119898(119889119881

119889120579+119881119862

120596)

119861 = ℎ(119889119881119889120579 + 119881119862120596)

120596119898

times [V119887

119888119875119887

120597 ln V119887

120597 ln119879119887

11990912119879119887 minus 119879119908

119879119887

+V119906

119888119875119906

120597 ln V119906

120597 ln119879119906

(1 minus 11990912)119879119906minus 119879119908

119879119906

]

119862 = minusV119887minus V119906

119889119909

119889120579minus V119887

120597 ln V119887

120597 ln119879119887

ℎ119906minus ℎ119887

119888119875119887119879119887

[119889119909

119889120579minus

(119909 minus 1199092) 119862

120596]

119863 = 119909[V2119887

119888119875119887119879119887

(120597 ln V119906

120597 ln119879119906

)

2

+V119887

119875

120597 ln V119887

120597 ln119875]

119864 = 1 minus 119909[V2119906

119888119875119906119879119906

(120597 ln V119906

120597 ln119879119906

)

2

+V119906

119875

120597 ln V119906

120597 ln119875]

(20)


Table 1 Olikara and Borman constants

119860 119861 119862 119863 119864

1198701199011

0432168 minus0112464 times 105 0267269 times 101 minus0745744 times 10minus4 0242484 times 10minus8

1198701199012


1198701199013

minus0141784 minus0213308 times 104 0853461 0355015 times 10minus4 minus0310227 times 10minus8

1198701199014

0150879 times 10minus1 minus0470959 times 104 0646096 0272805 times 10minus5 minus0154444 times 10minus8

1198701199015

minus0752364 0124210 times 105 minus0260286 times 101 0259556 times 10minus3 minus0162687 times 10minus7

1198701199016

minus0415302 times 10minus2 0148627 times 105 minus0475746 times 101 0124699 times 10minus3 minus0900227 times 10minus8

The equations of state of the mixture are given by

119889119906

119889120579= (119888119875minus119875V119879

120597 ln V120597 ln119879

)119889119879

119889120579minus (V(

120597 ln V120597 ln119879

+120597 ln V120597 ln119875

))119889119875

119889120579

119889V119889120579

=V119879

120597 ln V120597 ln119879

119889119879

119889120579minus

V119875

120597 ln V120597 ln119875

119889119875

119889120579

119889119904

119889120579= (

119888119875

119879)119889119879

119889120579minus

V119879

120597 ln V120597 ln119879

119889119875

119889120579

(21)

with (120597ℎ120597119879)119875= 119888119875

The combustion products are evaluated assuming thatthey are in equilibrium at a given temperature and pressureUsing Olikara and Borman [12] method we find combustionproducts mole fractions and we can then find the thermody-namic property of the mixture as in entropy specific volumeenthalpy and internal energy

Considering the combustion reaction of a hydrocarbon

C120572H120573O120574N120575+119886119904

120601(O2+ 376N

2)

997888rarr 1198991CO2+ 1198992H2O + 119899

3N2+ 1198994O2+ 1198995CO

+ 1198996H2+ 1198997H + 119899

8O + 119899

9OH + 119899

10NO

(22)

we then have

C 120572 = (1199101+ 1199105) 119879119898

H 120573 = (21199102+ 21199106+ 1199107+ 1199109) 119879119898

O 120574 +2119886119904

120601= (2119910

1+ 1199102+ 21199104+ 1199105+ 1199108+ 1199109+ 11991010) 119879119898

N 120575 +2 sdot 376119886

119904

120601= (2119910

3+ 11991010) 119879119898

(23)

119910119894is the mole fraction of the 119894th combustion specie at

equilibrium and 119879119898the total number of mole Following that

we can write sum10119894=1119910119894minus 1 = 0

The system of equation comprises 10 unknowns and 4equations we then need 6 complementary equations in order

to be able to solve the system For that we introduce six gasphase equilibrium reactions constant

1

2H2lArrrArr H 119870

1199011=119910711990112

11991012

6

1

2O2lArrrArr O 119870

1199012=119910811990112

11991012

4

1

2H2+1

2O2lArrrArr OH 119870

1199013=

1199109

11991012

411991012

6

1

2O2+1

2N2lArrrArr NO 119870

1199014=

11991010

11991012

411991014

3

H2+1

2O2lArrrArr H

2O 119870

1199015=

1199102

11991012

4119910611990112

CO +1

2O2lArrrArr CO

21198701199016=

1199101

11991012

4119910511990112

(24)

with 119901 representing the pressure at which the reaction occursin atmosphere The reactions constants are computed usingthe following expression

log119870119901119894= 119860 log(1198791000) + 119861119879 + 119862 +119863119879 + 1198641198792 with

the constants 119860 119861 119862119863 and 119864 given in Table 1

We find ourselves with a set of 11 nonlinear equationswith 11 unknowns which are solved using Newton Raphsoniteration A detailed description of the resolution algorithmcan be found in [13] The method was implemented usinga modified Matlab script provided by [16] to insert newsubroutines of the fuel injection andpulverization parametersas well as the biodiesel constant and the double Wiebefunction of heat release rate

4 Results and Discussion

For validation purposes the two models were implementedand comparedwith experimental results from [17] the enginecharacteristics are given inTable 2where fuel injection timingrefers to the actual crankshaft angle at which fuel startscoming out of the nozzle Two sets of calculation wereperformed one for diesel fuel and the second for biodieselfuelThe characteristics of diesel and biodiesel fuel were takenfrom [17 18] for method 1 To simulate biodiesel combustionfor method 2 we usedmethyl butanoate thermodynamic dataas surrogate [14]

The experimental imep (indicative mean effective pres-sure)was not given in the experimental work reported by [17]it was therefore evaluated using the experimental pressure


Table 2 Engine specifications

Number Particular Specifications1 Make Kirloskar oil engine2 Model DAF 83 Rated brake power (kW) 64 Rated speed (rpm) 15005 Number of cylinder 16 Bore times stroke (mm) 95 times 1107 Compression ratio 175 18 Fuel injection timing 23∘

minus60 minus40 minus20 0 20 40 60

1

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)

ExperimentalSimulation

In-cylinder pressure versus crank anglefor model 1 for biodiesel fuel

Figure 1 Comparison of computed and experimental pressure tracefor model 1 for biodiesel fuel

trace by integrating the area under the 119875-119881 diagram usingthe trapezoidal rule and the formula used was then

imep = int119881119891

119881119904

119875119889V119881119889

=

119899

sum

119894=1

(V119894+1minus V119894) (119875119894+ 119875119894+1)

2(25)

with 119881119889being the displaced volume of the engine in m3

Simulations were computed at rated engine speed and thepressure plot was made and compared with the experimentalresults (Figures 1 2 3 and 4) Both models evaluated thecombustion duration at 72 CAD and 87 CAD respectivelyfor diesel and biodiesel fuel This can be explained by the factthe viscosity and density of biodiesel are significantly higherthan that of conventional diesel which tends to generatepulverized droplets with higher mean diameter that tend toburn slower

The pressure traces obtained from the two model showthat they reproduce well the in cylinder pressure for bothtype of fuels in the given engine configuration It can beseen that the maximum pressure decreases when biodieselfuel is used for the two simulations which is equally the


1

0

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





1

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)

In-cylinder pressure versus crank anglefor model 1 for diesel fuel


Figure 3 Comparison of computed and experimental pressure tracefor model 1 for diesel fuel

trend observed experimentally and in other works such as[19ndash22] This was expected since biodiesel fuel has higheroxygen content the combustion coefficient tends to be higherin that case Another trend observed in the pressure trace isthat the cylinder pressure tends to be under predicted duringthe exhaust phase especially for biodiesel fuel this could beexplained by the experimental conditions uncertainty

The values of computed parameters are given in Table 3in terms of maximum pressure imep maximum pressureoccurrence and ignition delay In order to have an evaluation


Table 3 Comparison of simulated enginersquos combustion performances with experimental data

Diesel BiodieselModel 1 Model 2 Experiment Model 1 Model 2 Experiment

Max pressure (MPa) 7948 787 787 837 873 853Imep (MPa) 052 047 06 0522 06 07Maximum pressureoccurrence (CA after TDC) 4 3 58 3 3 5

Ignition delay (CAD) 869 869 85 437 437 43

Table 4 Krieger and Borman coefficients

0 1 2 3 4 5 6119886 0692 3917119890 minus 5 529119890 minus 8 minus229119890 minus 11 27758119890 minus 17

119887 304933 minus0057 minus95119890 minus 5 2153119890 minus 8 minus2119890 minus 12

119888119906

232584119888119903

0004186119889 1041066 785125 minus371257

119890 minus15001 minus15838 9613

119891 minus010329 minus038656 0154226 minus14763 11827 14503119903 minus02977 1198 minus25442 minus04354


1

0

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)



Figure 4 Comparison of computed and experimental pressuretrace for model 2 for diesel fuel

of the accuracy of both model the mean relative error wascalculated according to the four parameters given above itwas then observed that the first model gave a mean relativeerror of 18 while the second one had given a mean relativeerror of 11

5 Computation Speed

Another assessment made for the two models was thespeed of computation the first model was computed in 6

seconds while the second took about 40 to 45 second to runcompletely on 2Ghz dual core Pentium personal computer

With this assessment we can say that the firstmodel couldbe suitable for real time engine control while the second couldbe used for enginersquos design and also emission evaluation sinceit computes in cylinder pressure by determining combustionspecies states at each time step Another development thatcould be made for the second model can be the implemen-tation of the Zeldovich mechanism [1 11] to compute nitricoxide emissions

6 Conclusion

The aim of the present study was to develop and implementtwo different models for diesel engine fuelled on biodieselbased on tabulated chemistry The two models showedgood predictability of engine performance with the secondapproach giving a better accuracy The first approach wasfaster to compute the cylinder pressure than the second andwas found more suitable for engine monitoring and controlwhile the second one was found better suited for enginedesign and emission prediction

Appendix

For more details see Table 4

Conflict of Interests

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

References

[1] P A Lakshminarayanan and Y V Aghav Modelling DieselCombustion Springer Amsterdam The Netherlands 2010


[2] B Challen and R Baranescu Diesel Engine Reference BookButterworth-Heinemann Boston Mass USA 2nd edition1999

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

[4] A S Lyshevsky Fuel Atomization inMarineDiesels (In Russian)Leningrad 1971

[5] 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

[6] H O Hardenberg and F W Hase ldquoAn empirical formula forcomputing the pressure rise delay of a fuel from its cetanenumber and from the relevant parameters of direct-injectiondiesel enginesrdquo SAE 790493 1979

[7] Y Aghav V Thatte M Kumar et al ldquoPredicting ignition delayand HC emission for DI diesel engine encompassing EGR andoxygenated fuelsrdquo Tech Rep SAE International 2008

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

[9] G Woschni ldquoA universally applicable equation for the instan-taneous heat transfer coefficient in the internal combustionenginerdquo SAE Technical Paper no 670931 1967

[10] R B Borman and G L Krieger ldquoThe computation of apparentheat release for internal combustionrdquo in ASME 66-WADGP-4ASME 1966

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

[12] COlikara andG Borman ldquoA computer program for calculatingproperties of equilibrium combustion products with someapplications to IC enginesrdquo SAE Technical Paper 750468 SAEInternational 1975

[13] C R Ferguson and A T Kirkpatrick Internal CombustionEngines Applied Thermosciences Wiley New York NY USA2nd edition 2000

[14] E M Fisher W J Pitz H J Curran and C K WestbrookldquoDetailed chemical kinetic mechanisms for combustion ofoxygenated fuelsrdquo Proceedings of the Combustion Institute vol28 no 2 pp 1579ndash1586 2000

[15] NIST JANAFThermochemical Tables NSRDS-NBS 37 1971[16] D R Buttsworth ldquoSpark ignition internal combustion engine

modeling using Matlabrdquo Faculty of Engineering amp Survey-ing Technical Reports University of Southern QueenslandToowoomba Australia 2002

[17] P K Sahoo and L M Das ldquoCombustion analysis of JatrophaKaranja and Polanga based biodiesel as fuel in a diesel enginerdquoFuel vol 88 no 6 pp 994ndash999 2009

[18] X Wang H Zuohua A K Olawole Z Wu and N Keiya ldquoAnexperimental investigation on spray ignition and combustioncharacteristics of biodieselsrdquo Proceedings of the CombustionInstitute vol 11 pp 2071ndash2077 2011

[19] M Lapuerta O Armas and J Rodriguez-Fernandez ldquoEffect ofbiodiesel fuels on diesel engine emissionsrdquo Progress in Energyand Combustion Science vol 34 no 2 pp 198ndash223 2007

[20] G Knothe J V Gerpen and J Krahl The Biodiesel HandbookAOCS Press Champaign Ill USA 2005

[21] M N Azuwir M Z Abdulmuin and A H Adom ldquoModellingand validation of automotive engine fuelled with palm oilbiodieselrdquo International Journal of Engineering and Technologyvol 3 no 6 pp 582ndash586 2011

[22] B Tesfa R Mishra F Gu and A D Ball ldquoCombustioncharacteristics of CI engine running with biodiesel blendsrdquoin Proceedings of the International Conference on RenewableEnergies and Power Quality Environment and Power QualityEuropean Association for the Development of Renewable Ener-gies Las Palmas Spain 2011

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model is a simple sequence of calculated parameters and isstructured as follows

First the average outflow velocity of fuel from the injectoris calculated in ms by

1198800=

24119902119888RPM

0751205881198911205871198892119888119894119888120593inj

(1)

where 119902119888is the cyclic fuel supply in Kgcycle RPM is the

crankshaft rotational speed in rpm 120588119891is the density of the

fuel in kgm3 119889119888is the diameter of the injector hole in mm

120593inj is the duration of injection in degree of rotation of thecrankshaft

The criterion119872 characterizing the relationship betweenthe surface tension force inertia and viscosity is calculatedas follows

119872 =

1205832

119891

(119889119888120588119891120590119891)

(2)

where 120583119891is the coefficient of dynamic viscosity of the fuel at

a temperature of 323K in Pasdots 120590119891is the coefficient of surface

tension of the fuel at a temperature of 323K in NmWeber number characterizing the relationship between

surface tension force and inertia is determined as

119882119890=

1198802

0120588119891119889119888

120590119891

(3)

The density of the charge at the end of the compressionbefore the TDC is calculated as follows

120588air =120583air119872]

119881119888

(4)

where 120583air = 289KgKmole is the molecular mass of air 120588airis the density of air

We then determine the fuelair density ratio by

120588 =120588air120588119891

(5)

Finally the Sauter mean diameter of the atomized fuel iscalculated in micron by

11988932=1061198643211988911988811987200733

(120588119882119890)0266

(6)

where 11986432is an empirical factor depending on designs of the

injector whose recommended value is 17At this point the finesse of the pulverized fuel is deter-

mined and we can see it mainly depends on physical prop-erties of the fuel such as viscosity and density The next stepof the model is to determine the kinetic of combustion of theatomized fuel whose kinetic will be dependent of the earlierfound Sauter mean diameter

22 Model of the Kinetic of Combustion of the Atomized FuelThis part of the elaborated model will permit us to determineparameters of the process such as the evaporation rate ofthe atomized fuel its ignition delay and the duration ofcombustion

Pressure in the cylinder at the end of the compressionbefore the TDC is

119875119888= 1198750120576137 (7)

where 1198750is the reference pressure which in our case corre-

sponds to the inlet manifold pressureWe then determine the theoretical constant of evapora-

tion of the fuel by

119887it =119870

1198892

32

(8)

where 119870 = 1119875119888sdot 106 is the evaporation constant related to

cylinder pressure in m2s

120591119890V =

119860119911

(119887it12058206)

(9)

where 119860119911is a constant characterizing the duration of evap-

oration of large drops in diesel engine in 1s and its valueis given as 24 in [3] but Kuleshov [5] used it as weightcoefficient that can be varied in order to match experimentaldata 120582 is the coefficient of excess air

The full duration of combustion is then calculated as

120601119911= 120601inj minus ID + 6RPM120591

119890V (10)

with ID being the ignition delay computed using the formulaof Hardenberg and Hase [6] in both models

ID

= [036 + 022119880119901]

times exp[119864119886sdot (

1

119877119879im120576119899119888minus1minus

1

17190) + (

212

119875im120576119899119888 minus 124

)

063

]

(11)

The value of the apparent activation energy 119864119886in this

correlation is given by 119864119886= 618840(119862119873+25) however this

valuewas computed for the particular experiment reported in[6] and needs to be corrected in order to be used for differentexperimental conditions In order to match experimentalignition delay values especially for biodiesel fuel themethodproposed by Aghav et al [7] where the value 618840 can bevaried from the initial 618840 to higher values was used

23 Heat Release and Heat Transfer Laws For the twomodels we used a double Wiebe function [8] to model theheat release rate and the Woschni [9] law for heat transfersimulation


3 Combustion Models


119889119876inj minus 119889119876loss

119889120579=

120574

120574 minus 1119875119889119881

119889120579+

1

120574 minus 1119881119889119875

119889120579 (12)



119906 =119860 minus 119861

120582 + 119906corr (13)

where

119860 = 1198861119879 + 11988621198792+ 11988631198793+ 11988641198794+ 11988651198795

119861 = 1198870+ 1198871119879 + 11988721198792+ 11988731198793+ 11988741198794

(14)


119863120582= 1198890+ 1198891sdot 120582minus1+ 1198893120582minus3

119864120582=

(1198900+ 1198901120582minus1+ 1198903120582minus3)

119879

119865119875119879120582

= [1198910+ 1198911120582minus1+ 1198913120582minus3+

(1198914+ 1198915120582minus1)

119879] log (119891

6sdot 119875)

(15)


119877 = 0287 +0020

120582+ 119877corr (16)


120574 = 1 +119877

119888V (17)

with 119888V = 120597119906120597119879



119888119901

119877= 1198861+ 1198862119879 + 11988631198792+ 11988641198793+ 11988651198794

ℎ

119877119879= 1198861+1198862

2119879 +

1198863

41198792+1198864

41198793+1198865

51198794+ 1198866

1

119879

119904

119877= 1198861ln119879 + 119886

2119879 +

1198863

21198792+1198864

31198793+1198865

41198794+ 1198867

(18)


119889119875

119889120579=119860 + 119861 + 119862

119863 + 119864

119889119879119887

119889120579=

minusℎ (12058711988722 + 4119881119887) 119909

12119879119887minus 119879119908

V119898119888119875119887119909

+V119887

119888119875119887

(120597 ln V119887

120597 ln119879119887

)(119889119875

119889120579)

+ℎ119906minus ℎ119887

119909119888119875119887

[119889119909

119889120579minus 119909 minus 119909

2119862

120596]

119889119879119906

119889120579=

minusℎ (12058711988722 + 4119881119887) 119909

12119879119906minus 119879119908

V119898119888119875119906119909

+V119906

119888119875119906

(120597 ln V119906

120597 ln119879119906

)(119889119875

119889120579)

+ℎ119906minus ℎ119887

119909119888119906

[119889119909

119889120579minus 119909 minus 119909

2119862

120596]

(19)

where

119860 =1

119898(119889119881

119889120579+119881119862

120596)

119861 = ℎ(119889119881119889120579 + 119881119862120596)

120596119898

times [V119887

119888119875119887

120597 ln V119887

120597 ln119879119887

11990912119879119887 minus 119879119908

119879119887

+V119906

119888119875119906

120597 ln V119906

120597 ln119879119906

(1 minus 11990912)119879119906minus 119879119908

119879119906

]

119862 = minusV119887minus V119906

119889119909

119889120579minus V119887

120597 ln V119887

120597 ln119879119887

ℎ119906minus ℎ119887

119888119875119887119879119887

[119889119909

119889120579minus

(119909 minus 1199092) 119862

120596]

119863 = 119909[V2119887

119888119875119887119879119887

(120597 ln V119906

120597 ln119879119906

)

2

+V119887

119875

120597 ln V119887

120597 ln119875]

119864 = 1 minus 119909[V2119906

119888119875119906119879119906

(120597 ln V119906

120597 ln119879119906

)

2

+V119906

119875

120597 ln V119906

120597 ln119875]

(20)



119860 119861 119862 119863 119864

1198701199011


1198701199012


1198701199013


1198701199014


1198701199015


1198701199016



119889119906

119889120579= (119888119875minus119875V119879

120597 ln V120597 ln119879

)119889119879

119889120579minus (V(

120597 ln V120597 ln119879

+120597 ln V120597 ln119875

))119889119875

119889120579

119889V119889120579

=V119879

120597 ln V120597 ln119879

119889119879

119889120579minus

V119875

120597 ln V120597 ln119875

119889119875

119889120579

119889119904

119889120579= (

119888119875

119879)119889119879

119889120579minus

V119879

120597 ln V120597 ln119879

119889119875

119889120579

(21)

with (120597ℎ120597119879)119875= 119888119875



C120572H120573O120574N120575+119886119904

120601(O2+ 376N

2)

997888rarr 1198991CO2+ 1198992H2O + 119899

3N2+ 1198994O2+ 1198995CO

+ 1198996H2+ 1198997H + 119899

8O + 119899

9OH + 119899

10NO

(22)

we then have

C 120572 = (1199101+ 1199105) 119879119898

H 120573 = (21199102+ 21199106+ 1199107+ 1199109) 119879119898

O 120574 +2119886119904

120601= (2119910

1+ 1199102+ 21199104+ 1199105+ 1199108+ 1199109+ 11991010) 119879119898

N 120575 +2 sdot 376119886

119904

120601= (2119910

3+ 11991010) 119879119898

(23)






1


1199011=119910711990112

11991012

6

1


1199012=119910811990112

11991012

4

1

2H2+1


1199013=

1199109

11991012

411991012

6

1

2O2+1


1199014=

11991010

11991012

411991014

3

H2+1

2O2lArrrArr H

2O 119870

1199015=

1199102

11991012

4119910611990112

CO +1

2O2lArrrArr CO

21198701199016=

1199101

11991012

4119910511990112

(24)


log119870119901119894= 119860 log(1198791000) + 119861119879 + 119862 +119863119879 + 1198641198792 with










1

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





imep = int119881119891

119881119904

119875119889V119881119889

=

119899

sum

119894=1

(V119894+1minus V119894) (119875119894+ 119875119894+1)

2(25)





1

0

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





1

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)














119888119906

232584119888119903

0004186119889 1041066 785125 minus371257

119890 minus15001 minus15838 9613



1

0

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





5 Computation Speed




6 Conclusion


Appendix




References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










3 Combustion Models


119889119876inj minus 119889119876loss

119889120579=

120574

120574 minus 1119875119889119881

119889120579+

1

120574 minus 1119881119889119875

119889120579 (12)



119906 =119860 minus 119861

120582 + 119906corr (13)

where

119860 = 1198861119879 + 11988621198792+ 11988631198793+ 11988641198794+ 11988651198795

119861 = 1198870+ 1198871119879 + 11988721198792+ 11988731198793+ 11988741198794

(14)


119863120582= 1198890+ 1198891sdot 120582minus1+ 1198893120582minus3

119864120582=

(1198900+ 1198901120582minus1+ 1198903120582minus3)

119879

119865119875119879120582

= [1198910+ 1198911120582minus1+ 1198913120582minus3+

(1198914+ 1198915120582minus1)

119879] log (119891

6sdot 119875)

(15)


119877 = 0287 +0020

120582+ 119877corr (16)


120574 = 1 +119877

119888V (17)

with 119888V = 120597119906120597119879



119888119901

119877= 1198861+ 1198862119879 + 11988631198792+ 11988641198793+ 11988651198794

ℎ

119877119879= 1198861+1198862

2119879 +

1198863

41198792+1198864

41198793+1198865

51198794+ 1198866

1

119879

119904

119877= 1198861ln119879 + 119886

2119879 +

1198863

21198792+1198864

31198793+1198865

41198794+ 1198867

(18)


119889119875

119889120579=119860 + 119861 + 119862

119863 + 119864

119889119879119887

119889120579=

minusℎ (12058711988722 + 4119881119887) 119909

12119879119887minus 119879119908

V119898119888119875119887119909

+V119887

119888119875119887

(120597 ln V119887

120597 ln119879119887

)(119889119875

119889120579)

+ℎ119906minus ℎ119887

119909119888119875119887

[119889119909

119889120579minus 119909 minus 119909

2119862

120596]

119889119879119906

119889120579=

minusℎ (12058711988722 + 4119881119887) 119909

12119879119906minus 119879119908

V119898119888119875119906119909

+V119906

119888119875119906

(120597 ln V119906

120597 ln119879119906

)(119889119875

119889120579)

+ℎ119906minus ℎ119887

119909119888119906

[119889119909

119889120579minus 119909 minus 119909

2119862

120596]

(19)

where

119860 =1

119898(119889119881

119889120579+119881119862

120596)

119861 = ℎ(119889119881119889120579 + 119881119862120596)

120596119898

times [V119887

119888119875119887

120597 ln V119887

120597 ln119879119887

11990912119879119887 minus 119879119908

119879119887

+V119906

119888119875119906

120597 ln V119906

120597 ln119879119906

(1 minus 11990912)119879119906minus 119879119908

119879119906

]

119862 = minusV119887minus V119906

119889119909

119889120579minus V119887

120597 ln V119887

120597 ln119879119887

ℎ119906minus ℎ119887

119888119875119887119879119887

[119889119909

119889120579minus

(119909 minus 1199092) 119862

120596]

119863 = 119909[V2119887

119888119875119887119879119887

(120597 ln V119906

120597 ln119879119906

)

2

+V119887

119875

120597 ln V119887

120597 ln119875]

119864 = 1 minus 119909[V2119906

119888119875119906119879119906

(120597 ln V119906

120597 ln119879119906

)

2

+V119906

119875

120597 ln V119906

120597 ln119875]

(20)



119860 119861 119862 119863 119864

1198701199011


1198701199012


1198701199013


1198701199014


1198701199015


1198701199016



119889119906

119889120579= (119888119875minus119875V119879

120597 ln V120597 ln119879

)119889119879

119889120579minus (V(

120597 ln V120597 ln119879

+120597 ln V120597 ln119875

))119889119875

119889120579

119889V119889120579

=V119879

120597 ln V120597 ln119879

119889119879

119889120579minus

V119875

120597 ln V120597 ln119875

119889119875

119889120579

119889119904

119889120579= (

119888119875

119879)119889119879

119889120579minus

V119879

120597 ln V120597 ln119879

119889119875

119889120579

(21)

with (120597ℎ120597119879)119875= 119888119875



C120572H120573O120574N120575+119886119904

120601(O2+ 376N

2)

997888rarr 1198991CO2+ 1198992H2O + 119899

3N2+ 1198994O2+ 1198995CO

+ 1198996H2+ 1198997H + 119899

8O + 119899

9OH + 119899

10NO

(22)

we then have

C 120572 = (1199101+ 1199105) 119879119898

H 120573 = (21199102+ 21199106+ 1199107+ 1199109) 119879119898

O 120574 +2119886119904

120601= (2119910

1+ 1199102+ 21199104+ 1199105+ 1199108+ 1199109+ 11991010) 119879119898

N 120575 +2 sdot 376119886

119904

120601= (2119910

3+ 11991010) 119879119898

(23)






1


1199011=119910711990112

11991012

6

1


1199012=119910811990112

11991012

4

1

2H2+1


1199013=

1199109

11991012

411991012

6

1

2O2+1


1199014=

11991010

11991012

411991014

3

H2+1

2O2lArrrArr H

2O 119870

1199015=

1199102

11991012

4119910611990112

CO +1

2O2lArrrArr CO

21198701199016=

1199101

11991012

4119910511990112

(24)


log119870119901119894= 119860 log(1198791000) + 119861119879 + 119862 +119863119879 + 1198641198792 with










1

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





imep = int119881119891

119881119904

119875119889V119881119889

=

119899

sum

119894=1

(V119894+1minus V119894) (119875119894+ 119875119894+1)

2(25)





1

0

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





1

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)














119888119906

232584119888119903

0004186119889 1041066 785125 minus371257

119890 minus15001 minus15838 9613



1

0

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





5 Computation Speed




6 Conclusion


Appendix




References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119860 119861 119862 119863 119864

1198701199011


1198701199012


1198701199013


1198701199014


1198701199015


1198701199016



119889119906

119889120579= (119888119875minus119875V119879

120597 ln V120597 ln119879

)119889119879

119889120579minus (V(

120597 ln V120597 ln119879

+120597 ln V120597 ln119875

))119889119875

119889120579

119889V119889120579

=V119879

120597 ln V120597 ln119879

119889119879

119889120579minus

V119875

120597 ln V120597 ln119875

119889119875

119889120579

119889119904

119889120579= (

119888119875

119879)119889119879

119889120579minus

V119879

120597 ln V120597 ln119879

119889119875

119889120579

(21)

with (120597ℎ120597119879)119875= 119888119875



C120572H120573O120574N120575+119886119904

120601(O2+ 376N

2)

997888rarr 1198991CO2+ 1198992H2O + 119899

3N2+ 1198994O2+ 1198995CO

+ 1198996H2+ 1198997H + 119899

8O + 119899

9OH + 119899

10NO

(22)

we then have

C 120572 = (1199101+ 1199105) 119879119898

H 120573 = (21199102+ 21199106+ 1199107+ 1199109) 119879119898

O 120574 +2119886119904

120601= (2119910

1+ 1199102+ 21199104+ 1199105+ 1199108+ 1199109+ 11991010) 119879119898

N 120575 +2 sdot 376119886

119904

120601= (2119910

3+ 11991010) 119879119898

(23)






1


1199011=119910711990112

11991012

6

1


1199012=119910811990112

11991012

4

1

2H2+1


1199013=

1199109

11991012

411991012

6

1

2O2+1


1199014=

11991010

11991012

411991014

3

H2+1

2O2lArrrArr H

2O 119870

1199015=

1199102

11991012

4119910611990112

CO +1

2O2lArrrArr CO

21198701199016=

1199101

11991012

4119910511990112

(24)


log119870119901119894= 119860 log(1198791000) + 119861119879 + 119862 +119863119879 + 1198641198792 with










1

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





imep = int119881119891

119881119904

119875119889V119881119889

=

119899

sum

119894=1

(V119894+1minus V119894) (119875119894+ 119875119894+1)

2(25)





1

0

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





1

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)














119888119906

232584119888119903

0004186119889 1041066 785125 minus371257

119890 minus15001 minus15838 9613



1

0

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





5 Computation Speed




6 Conclusion


Appendix




References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













1

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





imep = int119881119891

119881119904

119875119889V119881119889

=

119899

sum

119894=1

(V119894+1minus V119894) (119875119894+ 119875119894+1)

2(25)





1

0

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





1

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)














119888119906

232584119888119903

0004186119889 1041066 785125 minus371257

119890 minus15001 minus15838 9613



1

0

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





5 Computation Speed




6 Conclusion


Appendix




References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















119888119906

232584119888119903

0004186119889 1041066 785125 minus371257

119890 minus15001 minus15838 9613



1

0

2

3

4

5

6

7

8

9

10

CAD (deg)

Pres

sure

(MPa

)





5 Computation Speed




6 Conclusion


Appendix




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











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Comparing in Cylinder Pressure Modelling ...downloads.hindawi.com/archive/2014/534953.pdf · Research Article Comparing in Cylinder Pressure Modelling of a DI Diesel