Fuel 89 (2010) 2323–2330

Contents lists available at ScienceDirect

Fuel

journal homepage: www.elsevier .com/locate / fuel

Detailed approach for apparent heat release analysis in HCCI engines

Morteza Fathi a,1, R. Khoshbakhti Saray a,*, M. David Checkel b

a Faculty of Mechanical Engineering, Sahand University of Technology, Tabriz, Iranb Mechanical Engineering Department, University of Alberta, Edmonton, AB, Canada T6G 2G8

a r t i c l e i n f o a b s t r a c t

Article history:Received 15 September 2009Received in revised form 21 April 2010Accepted 22 April 2010Available online 5 May 2010

Keywords:Apparent heat releaseHCCIFirst lawSpecific heat ratioTemperature correction

0016-2361/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.fuel.2010.04.030

* Corresponding author. Tel./fax: +98 412 3459065E-mail addresses: morteza.fathi@yahoo.com (M.

(R. Khoshbakhti Saray), dave.checkel@ualberta.ca (M.1 Tel.: +98 912 230 5837.

Homogeneous charge compression ignition (HCCI) combustion is a spontaneous multi-site auto-ignitionof a lean premixed fuel–air mixture, which has high heat release rate, short combustion duration and noevidence of flame propagation. In HCCI engines, there is no direct control method for the time of auto-ignition. Auto-ignition timing should be controlled in order to make heat release process take place atthe appropriate time in the engine cycle. Heat release analysis is a diagnostic tool which aids engineexperimenters. It facilitates the endeavors being conducted in obtaining a control method by investigat-ing heat release rate and also cumulative heat release. This study can be divided into two parts. First, tra-ditional first law heat release model which is widely used in engine combustion analysis was presentedand the applicability of this model in HCCI engines was investigated. Second, a new heat release modelbased on the first law of thermodynamics accompanying with a temperature solver was developed andassessed. The model was applied in four test conditions with different operating conditions and a varietyof fuel compositions, including i-octane, n-heptane, pure NG, and at last, a dual fueled case of NG andn-heptane. Results of this work indicate that utilizing the modified first law heat release model togetherwith a solver for temperature correction will guarantee obtaining a well-behaved and accurate apparentheat release trend and magnitude in HCCI combustion engines.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction Since achieving HCCI combustion is generally difficult, it seems

Homogeneous charge compression ignition (HCCI) combustionmode proposed by Onishi et al. [1] is a reliable method that hasbeen found to produce low NOx levels, near zero soot and improvedCO2 emissions. It provides equal or greater fuel conversion efficien-cies compared to that of conventional DI diesel combustion [2–4].

The advantages of HCCI combustion are commonly associatedwith its nature being a spontaneous multi-site combustion of avery lean and premixed fuel–air mixture which has high heat re-lease rate (HRR) and no evidence of flame propagation [4,5]. Thehigh efficiency is due to the ability of operating with high compres-sion ratios, lack of throttling losses at part load, lean combustion,and close to constant volume ideal Otto cycle heat release.

There are some deficiencies intrinsic to HCCI combustion whichshould be overcome [4,5]: first, the lack of any direct control meth-od for combustion timing – in contrast to control actions like sparkignition or fuel injection in SI or CI engines, respectively; second,producing high levels of HC and CO emissions; third, obtainingan appropriate fueling rate for achieving high engine loads undermechanical limitations of engine.

ll rights reserved.

.Fathi), khoshbakhti@sut.ac.irDavid Checkel).

that heat release analysis is required for a manageable HCCI com-bustion as it relies on auto-ignition. Identifying early stages of heatrelease, timing of the main heat release, and maximum rate of heatrelease are necessary for a successful control strategy for HCCIcombustion engine. Due to these facts and other benefits of heatrelease analysis [6–13], development of a suitable model for pre-dicting apparent heat release, being able to be applied easily whileeliminating erroneous assumptions, is quite necessary.

To date, numerous researchers have studied heat release analy-sis in both SI and CI engines. One of the earliest simple attemptswas done by Rasswieler and Withrow [14] in the 1930’s. R–Wmethod was a simple but yet efficient method based on correlationbetween pressure trace and burnt/unburnt fraction of air/fuel mix-ture using combustion chamber pictures. The method takes the dif-ference between measured pressure and predicted pressure fromthe polytropic compression/expansion to be proportional to theamount of fuel burned.

Heat release models for both SI and CI engines were presentedby Krieger and Borman [15]. Also, their work included the effect ofdissociation of the product species. Their models as stated byGatowski et al. [7] strive for accuracy in representing the thermo-dynamic properties of the in-cylinder charge and involve substan-tial computations.

Gatowski et al. [7] presented a model as they claimed being thefirst to give a full description of a heat release model which is

Nomenclature

A area, energy ODE constantcv specific heat at constant volumeheight instantaneous cylinder heighth enthalpy, step sizehc convective heat transfer coefficientn polytropic indexN engine speed in rpmm mass_m mass flow rate

p pressurepm motoring pressureQ heatR specific gas constantT temperatureU internal energyu specific internal energyup mean piston speedV volumeVd displacement volumew work or characteristic velocitydQgross gross cumulative heat release

Greek symbolsc specific heat ratioh crank angle

Subscriptsc corrected or convectionf formationht heat transfer integeri position or eventP productsr referenceR reactantss sensible

AbbreviationsAHRR apparent heat release rateaTDC after top dead centerbBDC before bottom dead centerCAD crank angle degreeEEOC estimated end of combustionEVO exhaust valve openESOC estimated start of combustionHCCI homogeneous charge compression ignitionHRR heat release rateIVC inlet valve closureMFB mass fraction burnedMFLHR modified first law heat releaseSFLHR simplified first law heat release

Table 1Engine specifications.

Parameter Specification

Engine model Waukesha CFREngine type Water cooled, single cylinderCombustion chamber Disk cylinder head, flat-top pistonThrottle Fully openBore 82.6 mmStroke 114.3 mmDisplacement 612 ccIVC 34 CAD, aTDCEVO 40 CAD, bBDC

2324 M. Fathi et al. / Fuel 89 (2010) 2323–2330

simple in approach and accounts for all major loss mechanismswhile keeping the calculation method simple, as a single zone heatrelease analysis procedure. In their study, the thermodynamicproperties of the chamber contents were approximated by specify-ing that the ratio of specific heats is a linear function of tempera-ture. They argued that accuracy of the calculations based on thisassumption is consistent with the accuracy intrinsic to the use ofthe single zone model. This model, being almost the basic modelfor single zone heat release analysis, is presented and discussed la-ter in the paper to be compared with the modified first law model.

Other researchers also developed this kind of modeling, buttheir works were to optimize existing models in terms of, forexample, the correlations used. These correlations were namelycorrelations for heat transfer, specific heat ratio, etc. For instance,Chun and Heywood [16] argued that better results could beachieved if the assumption of linearity with temperature for the ra-tio of specific heats was studied in more details.

Brunt et al. [17] and Brunt and Platts [8] developed two modi-fied single zone models, one for SI engines and one for CI engines,respectively, to cater for heat transfer.

Reviewing the literature, few researches can be found beingconducted directly on heat release analysis in HCCI engines. In2005, Hampson [4] developed a simple engine design tool basedon thermodynamics, allowing engine designers to begin with thepeak pressure limit of engine, desired IMEP, and limitations onpressure rise rate and thus generate an idealized wire-frame cylin-der pressure cycle. He used this tool to identify the ideal HRR forHCCI combustion. He claimed that for low IMEP, this is a singlemode HRR centered at TDC, and for medium and high loads, a sec-ond mode of combustion is required to achieve maximum effi-ciency and retain the benefits of HCCI combustion. Thus, thisstudy developed a design method not a heat release model, andhis work is included here, because of proposing a target heat re-lease for HCCI combustion to shoot for.

In this study, due to the lack of a reliable work on heat releaseanalysis in HCCI engines, the focus is on investigating the applica-bility of simplified first law heat release (SFLHR) model in inter-

preting HCCI combustion. Due to the simplifying assumptions,this model cannot well predict heat release trend in such engines.Thus, a modified first law heat release (MFLHR) model which putsaside erroneous assumptions together with a solver for tempera-ture correction, which calculates the heat released from combus-tion more accurately, has been developed and will be presented.

2. Experimental setup

Experimental data was obtained from University of Alberta en-gine research facility. All experiments were performed using aWaukesha CFR (Cooperative Fuel Research) single cylinder re-search engine coupled to a DC motoring dynamometer. The basicengine specifications for the current study are shown in Table 1.

Table 2 indicates the CFR engine operating conditions used inthese experiments. The engine was maintained at two constantspeeds of 700 and 800 rpm and ran with an open throttle. The in-take system included a 2.4 kW heater with a PID temperature con-troller to preheat intake air when required. A port liquid fuelinjector was installed a short distance upstream of the intake valveto ensure proper mixing. The lubricating oil was maintained at aconstant temperature using a heater.

Un-cooled EGR was circulated through an external line to enterthe intake plenum between the air heater and the fuel injectors.

Table 2CFR engine operating conditions for four considered cases.

Case 1 Case 2 Case 3 Case 4

Fuel i-Octane n-Heptane NG n-Heptane + NGCompression ratio 13.5:1 11.5:1 17.25:1 13.8:1Speed (rpm) 700 700 800 800Intake temperature

(�C)140 100 140 120

PRF mass flow rate(mg/s)

78.51 79.78 0 36.45

NG mass flow rate(mg/s)

0 0 82.32 21.76

Air mass flow rate(g/s)

2.377 2.598 4.46 2.50

Pmax location(CAD, aTDC)

8.8 �2.2 2.5 3.4

0

20

40

60

80

100

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

Pres

sure

[bar

]

Case 1

Case 2

Case 3

Case 4

Fig. 1. Average cylinder pressure for 100 consecutive cycles for four cases.

M. Fathi et al. / Fuel 89 (2010) 2323–2330 2325

For these steady-state experiments, the EGR rate was manuallycontrolled with a butterfly valve.

A BEI rotary incremental encoder with a resolution of 0.1 CADwas used to monitor engine rotational speed and coordinate thepressure trace with respect to crank position. Cylinder pressurewas measured with a Kistler 6043A water cooled pressure trans-ducer in combination with a Kistler 507 charge amplifier. The pres-sure transducer was mounted in the cylinder wall close to thecylinder head.

Experimental data were acquired using a personal computerrunning custom Labview software and using three high samplingrate NI PCI-MIO-16E1 data acquisition cards.

The pressure trace signal was referenced to the intake pressureat the time of IVC. Proper digital filter was applied to the pressuretrace signal rejecting the high frequency noise.

Four separate experimental conditions were examined. Onewith isooctane as fuel, referred to as case 1, a case with normalheptane as fuel, which has its peak pressure location fallen beforeTDC, referred to as case 2, the other with pure NG as fuel, and atlast a dual fueled case with normal heptane and NG. The operatingconditions for each case are shown in Table 2. The coolant temper-ature for all cases was set to 100 �C. To reduce the effects of cyclicvariations, the pressure traces of all cases are the average of 100consecutive cycles. These average cylinder pressure traces areshown in Fig. 1.

3. Heat release model

The simple zero dimensional single zone models for apparentheat release rate (AHRR) analysis are usually used in preference

to multi-zone models which can probably be more accurate, dueto the fact that they are numerically more efficient, have less com-plexity and thus are less time-consuming meanwhile commonlyyielding similar results. Such models do not include spatialvariations.

The accuracy results from a heat release model is dependent onmany factors, among which are, the accuracy of the measured in-cylinder pressure data, the accuracy of determining TDC location,and the assumptions adopted in and applied to the model. Investi-gating the last factor mentioned is the main subject of this study. Itwill be shown that in special cases such as HCCI engines havingshort combustion duration, some assumptions utilized in previ-ously developed SFLHR model are sources of errors. Therefore, inthis study, two approaches in first law heat release analyses willbe investigated and compared.

3.1. Simplified first law heat release model

The SFLHR model, or basic first law heat release model as Bruntet al. [17] named, is the result of applying first law of thermody-namics to the engine combustion chamber charge. This modelwas first fully developed by Gatowski et al. [7] by considering fuelinjection and all the major loss mechanisms including heat transferand crevice flows.

The energy balance for a single zone model for an incrementalcrank angle interval is [7]:

dQ gross ¼ dUs þ dW þX

hidmi þ dQ ht ð1Þ

where dW is the work due to piston motion which equals to pdV andPhidmi is the mass exchanges across the system boundary.By ignoring all mass exchanges including valve leakages (which

is true for this and many other studies which analyze the systemduring closed part of the cycle or nonflow period i.e. from IVC toEVO), fuel injection (which is true, since it was assumed that thefuel is premixed), blowby, and crevice effects, and taking into ac-count the later-mentioned assumptions, the heat release modelcommonly used in the literature is obtained.

dQ gross ¼c

c� 1pdV þ 1

c� 1Vdpþ dQht ð2Þ

Eq. (2), gives the apparent gross heat release on the intervals. Byomitting the last term in the right hand side, Eq. (2) gives the netapparent heat release, which is not an exact one. There are a num-ber of assumptions in developing Eq. (2):

1. The state of the cylinder contents is defined as average proper-ties of the uniform charge.

2. The change in sensible internal energy is assumed to be a func-tion of mean charge temperature only:

Us ¼ muðTÞ ð3Þ

By considering the nonflow period:

dUs ¼ mcvðTÞdT ð4Þ

where cv is the mass average specific heat at constant volumeand is assumed to be a function of temperature only.

3. The mean charge temperature is determined by the ideal gaslaw:

T ¼ pVmR

ð5Þ

4. The specific gas constant is assumed to be constant and thisassumption has its root in that the molecular weights of thereactants and products are nearly identical [7]. With thisassumption:

2326 M. Fathi et al. / Fuel 89 (2010) 2323–2330

dT ¼ dðpVÞmR

ð6Þ

It is clear from thermodynamics that:

cv

R¼ 1

c� 1ð7Þ

By substituting Eqs. (4), (6), and (7) into Eq. (1), the SFLHR model,i.e. Eq. (2) will be obtained.

3.1.1. Mass fraction burnedMass fraction burned (MFB) is calculated from the analysis of

measured in-cylinder pressure data. Brunt and Emtage [18] com-pared the performance of five MFB models proposed in the litera-ture in accordance with their accuracy in burn angles prediction.As a result, the model developed by Rasswieler and Withrow[14] became the preferred model. Also, here in this study, thisMFB model was employed which is obtained by:

MFBh ¼Ph

i¼ESOCDpc;iPEEOCi¼ESOCDpc;i

ð8Þ

where MFBh is the mass fraction burned at crank angle h, Dpc is thecorrected pressure rise due to combustion and Dpc; is calculated bytaking the difference between the firing and motoring pressuresand then referenced to the cylinder volume at TDC:

Dpc;i ¼ pi � pi�1ðVi�1=ViÞn� �

ðVi�1 Vr= Þ ð9Þ

3.1.2. Specific heat ratio modelIn applying traditional SFLHR model, the specific heat ratio is the

most important thermodynamic property, which depends on tem-perature and composition and to a lesser extent on pressure. Thereare a number of functions proposed in the literature for this prop-erty. Gatowski et al. [7] proposed a straight line fit for cðTÞ. Bruntet al. [17] used a second order correlation between gamma andtemperature. Egnell [19] in his multi-zone model, proposed anexponential function of temperature for the specific heat ratio.Other researchers [10,20] also developed models for calculating thisproperty, but the work of Ceviz and Kaymaz [21] was more general.They evaluated the specific heat ratio functions and compared themwith their own function derived from the equilibrium combustionmodel being dependent on both mean charge temperature andair–fuel ratio. The results of their work showed that taking into ac-count this dependency of specific heat ratio on temperature andair–fuel ratio notably optimized heat release analysis.

Here in this study, the equilibrium combustion model of Olikaraand Borman [22] was fully incorporated with the model to evalu-ate the specific heat ratio and internal energy, using the thermody-namic data of JANAF table. The equilibrium combustion model wasimplemented by considering the products being composed of 11species.

3.1.3. Heat transfer correlationOne of the most important submodels which must be fed into

the heat release model is the model for evaluating heat lost dueto heat transfer. There are a number of models proposed in the lit-erature for this loss term.

In this study, the well-known expression proposed by Woschni[23] with modifications which made it be appropriate for HCCI en-gines has been used [24]. In this work, the radiative heat loss hasbeen ignored. The expression used to calculate the heat flux of con-vective heat transfer is obtained by:

dQ ht ¼ hc � A� ðTcharge � TwallÞ ð10Þ

where Tcharge is the mean charge temperature and Twall is the tem-perature of the wall.

The heat transfer coefficient is approximated by:

hc ¼ 3:4� height�0:2p0:8T�0:73w0:8 ð11Þ

where height is the effective height of the chamber which is equalto V/A [24], instead of bore which was used in the originalexpression.

The characteristic velocity is obtained as follows:

w ¼ C1up þ C2VdTr

prVrðp� pmÞ ð12Þ

where C1 = 2.28 and C2 = 0 for compression and 5.4 � 10–4 for com-bustion and expansion.

It is seen that in order to make Woschni model a viable one inHCCI combustion modeling, some modifications such as in temper-ature exponent (0.73), height, and C2 should be applied.

3.2. Modified first law heat release model

The MFLHR model is achieved by applying the energy conserva-tion equation to the cylinder contents and not utilizing erroneousassumptions. By starting with the first law of thermodynamics forthe cylinder charge during closed valve interval and ignoring massleakages, it yields:

dU ¼ �dW � dQ ht ð13Þ

where U is the absolute internal energy of the cylinder contents. Byconsidering the in-cylinder charge to be a homogeneous mixture ofreactants (denoted by the R index) and products (denoted by P in-dex) which are supposed to be ideal gases (it should be noted herethat Gatowski et al. [7] also used this procedure, but there, the con-tents were fuel vapor and products and the internal energy was as-sumed to be a function of temperature only):

m ¼ mR þmP ð14ÞdmP ¼ �dmR ð15ÞU ¼ mRuR þmPuP ¼ mRðus;R þ uf ;RÞ þmPðus;P þ uf ;PÞ ð16Þ

By differentiating Eq. (16), the equation for internal energy changeis obtained:

dU ¼ ðuf ;R � uf ;PÞdmR þ ðus;R � us;PÞdmR þmRdðus;R � us;PÞ þmdus;P

ð17Þ

Substituting Eq. (17) and the work term into Eq. (13) yields:

ðuf ;R � uf ;PÞdmR þ ðus;R � us;PÞdmR þmRdðus;R � us;PÞ þmdus;P

¼ �pdV � dQ ht ð18Þ

ðuf ;R � uf ;PÞ is the difference in internal energy of formation betweenthe reactants and products. The gross heat release for an incremen-tal crank angle interval, which is the energy released due to com-bustion, is:

dQ gross ¼ ðuf ;P � uf ;RÞdmR ð19Þ

Substitution of Eq. (19) into Eq. (18) yields the MFLHR model:

dQgross ¼ ðus;R � us;PÞdmR þmRdðus;R � us;PÞ þmdus;P þ pdV þ dQht

ð20Þ

In this equation for the MFLHR model, mR is the mass of reactants atany instant and equals to:

mR ¼ ð1�MFBÞ:m ð21Þ

and dmR, is the change in mass of the reactant component due tocombustion and is equal to:

dmR ¼ �m � dMFB ð22Þ

M. Fathi et al. / Fuel 89 (2010) 2323–2330 2327

Here in this model, it is not only assumed the change in sensibleinternal energy being a function of temperature but also a functionof composition, too. The difference between this model and theSFLHR model developed (Eq. (2)), is that in the SFLHR model itwas first assumed that the change in the internal energy is a func-tion of temperature only to obtain Eq. (2) to be the governing equa-tion of SFLHR model. Then, for refining the results, it was assumedthat the gamma term is a function of composition and tempera-ture. By contrast, here the dependency of internal energy on com-position and temperature was applied into the model itself.

Also another assumption which needs to be considered morecarefully is the ideal gas law used for temperature determinationwhich is the subject of next section.

3.2.1. Solver for temperature correctionUsing the ideal gas law for temperature calculation, the cumu-

lative gross heat release trend will be at fault, even when utilizingMFLHR model. Investigating these errors, a solver was developedfor the mean charge temperature.

The internal energy of the homogeneous charge including reac-tants, i.e. fuel vapor and air, and products which were supposed tobe composed of 11 species, namely, CO2, H2O, CO, N2, O2, H2, OH,NO, O, H, N, according to the model of Olikara and Borman [22],was evaluated using the thermodynamic data of JANAF table.

The correction of the temperature was achieved by solving theinitial value problem of ordinary differential equation (ODE) of en-ergy by the aid of fourth-order Runge–Kutta method. The approachwas:

a - case 1

-10

10

30

50

70

90

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

Gro

ss H

RR

[J

/ Deg

]

SFLHR without T correction

SFLHR with T correction

MFLHR without T correction

MFLHR with T correction

c - case 3

-12

8

28

48

68

88

108

Gro

ss H

RR

[J

/ Deg

]

Fig. 2. HRR obtained from differe

1. First, the energy Eq. (20) should be rewritten to produce a func-tion of temperature, species composition and time:

ðuR � uPÞdmR

dtþmR

ddtðus;R � us;PÞ þm

dus;P

dt

þ pdVdtþ hAðT � TwallÞ ¼ 0 ð23Þ

By replacing the thermodynamic properties and specific heats ofeach species with polynomial functions fitted from the JANAFtable,

�cv i¼ Ruða1 � 1þ a2T þ a3T2 þ a4T3 þ a5T4Þ ð24Þ

�ui ¼ Ru ða1 � 1ÞT þ a2

2T2 þ a3

3T3 þ a4

4T4 þ a5

5T5 þ a6

h ið25Þ

And the ODE of energy equation, by applying the aforemen-tioned replacement and arrangement, will take the following fi-nal form:

dTdt¼ A5T5 þ A4T4 þ A3T3 þ A2T2 þ A1T þ A6 ð26Þ

where A1 to A6 are instantaneous constants of the equationwhich are themselves functions of temperature, pressure andspecies mole fractions at any instant, obtained from arrange-ment of polynomial coefficients of overall 14 species togetherwith their mole fractions and production rates.

2. This produced equation was used to determine the correctedtemperature by fourth-order Runge–Kutta method:

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

b - case 2

-10

10

30

50

70

90

110

130

Gro

ss H

RR

[J

/ Deg

]

d - case 4

-10

10

30

50

70

90

Gro

ss H

RR

[J

/ Deg

]

nt models for different cases.

-

1

2

3

4

Gro

ss c

umul

ativ

e he

at r

elea

se [

J]

-

9

1

2

3

4

Gro

ss c

umul

ativ

e he

at r

elea

se [

J]

2328 M. Fathi et al. / Fuel 89 (2010) 2323–2330

dTdt¼ fcnðt; TÞ and T0 ¼ set point temperature ¼ TIVC

ð27Þ

where the step size equals to:

h ¼ 0:16N

ð28Þ

This procedure was applied to the model from IVC to EVO. It can beseen from the results, that this corrected temperature gives accept-able results. It is also worth mentioning here, that the CPU timerequired for the model to be executed was less than 30 s.

4. Results and discussion

Fig. 2a shows the HRR and Fig. 3a illustrates the correspondingcumulative gross heat release for case 1. It can be seen from thesefigures that applying the traditional SFLHR model to HCCI engines,which have short combustion durations approximately centered atTDC, produces large errors. It is well known that the gross HRRshould not be negative after the completion of combustion, andconsequently the cumulative gross heat release should not de-crease following the end of combustion. But as can be seen in thesefigures, there are negative heat release gradients following the endof combustion, not only when applying SFLHR model but also inthe case of utilizing MFLHR model without temperature correction,which is obviously wrong. These figures indicate that there is noevidence of negative heat release gradient after the completion ofcombustion when applying MFLHR model together with the tem-perature correction solver. Thus, it is guaranteed that applyingthe developed model to HCCI engines which have very short com-

a - case 1

20

80

80

80

80

80

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

c - case 3

10

0

90

90

90

90

CAD, aTDC

-40 -30 -20 -10 0 10 20 30

SFLHR without T correction

SFLHR with T correction

MFLHR without T correction

MFLHR with T correction

Fig. 3. Gross cumulative heat release obtained

bustion durations, results in the correct trend and magnitude inthe heat release diagrams for this case.

In Fig. 2b, the HRR and in Fig. 3b, the corresponding cumulativegross heat release for case 2 is shown. The two-phase nature of n-heptane combustion can be seen in these diagrams. Again, it can beseen that the correct trend can be obtained, only when the MFLHRmodel accompanying with the temperature correction procedure isused. These figures and also Figs. 2a and 3a show that applying thewrong model for apparent heat release gives erroneous results notonly in diagrams trend, but also in the low magnitude of peak heatrelease rate and cumulative heat release in these cases.

Figs. 2c and 3c show the HRR and cumulative gross heat releasefor case 3, respectively. The above mentioned results can be seen inthese two figures, too. But, in this case, the magnitude of peak HRRand cumulative heat release has been lowered due to applyingtemperature correction. Also, it can be seen that applying MFLHRmodel together with the temperature correction solver has dimin-ished the negative temperature combustion trend which shouldnot be seen in the combustion of NG.

The diagrams for HRR and cumulative heat release are shown inFigs. 2d and 3d, respectively, for the fourth case. Again, it is obviousthat MFLHR model when accompanied with the temperature cor-rection procedure, gives acceptable results, both in terms of shapeand magnitude.

The comparison between mean charge temperatures calculatedfrom ideal gas law and temperature correction procedure are dem-onstrated in Fig. 4. It can be seen that the correction procedure fortemperature has smoothen the temperature diagram, lowered itspeak temperature, and increased its post combustion temperature,for case 1. For cases 2 and 4, this procedure has increased both thepeak and post combustion temperature. Applying temperature cor-rection procedure has totally lowered the temperature for case 3.

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

b - case 2

-10

90

190

290

390

490

Gro

ss c

umul

ativ

e he

at r

elea

se [

J]

d - case 4

-10

40

90

140

190

240

290

340

390

440

490

Gro

ss c

umul

ativ

e he

at r

elea

se [

J]

from different models for different cases.

a - case 1

c - case 1

400

600

800

1000

1200

1400

1600

1800

Tem

pera

ture

[K

]

Uncorrected Temperature

Corrected Temperature

400

600

800

1000

1200

1400

1600

1800

Tem

pera

ture

[K

]

b - case 2

300

500

700

900

1100

1300

1500

1700

Tem

pera

ture

[K

]

d - case 4

400

600

800

1000

1200

1400

1600

Tem

pera

ture

[K

]

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

-40 -30 -20 -10 0 10 20 30

CAD, aTDC

Fig. 4. The comparison between temperatures calculated from ideal gas law and temperature correction procedure for different cases.

M. Fathi et al. / Fuel 89 (2010) 2323–2330 2329

5. Conclusions

In this study, the applicability and accuracy of traditional SFLHRmodel applied to HCCI engines have been investigated. To achievethis assessment, several specific heat ratio models proposed in theliterature were applied to this model and the results of the mostaccurate are shown in the results, and four cases were evaluated.Results show that this model cannot well and fully predict theaccurate apparent cumulative gross heat release trend and magni-tude. To overcome this deficiency, the MFLHR model accompany-ing with a solver for correction of temperature was proposed andinvestigated. The results from this model, for all the various work-ing conditions and fuel compositions of evaluated cases, showgood agreement with the concept that states there should not beany indication of negative gradient in gross heat release.

These results indicate that in HCCI engines, utilizing traditionalSFLHR model results in erroneous results. However, applyingMFLHR model together with temperature correction procedure en-sures obtaining more accurate results.

Future work – in this paper, the main goal was to present amodel that well predicts the gross heat released from combustionof in-cylinder contents in HCCI engines. In spite of presenting thismodel, research is being conducted by the authors to develop amore accurate and simpler model taking into account more detailsabout combustion phenomena in HCCI engines. Also, the authorsare trying to correctly incorporate exhaust gas recirculation inthe model, and investigate its effects on HCCI combustion.

References

[1] Onishi S, Jo SH, Shoda K, Jo PD, Kato S. Active thermo-atmosphere combustion(ATAC) a new combustion process for internal combustion engines. SAE paperno. 790501; 1979.

[2] Duret P, Gatellier B, Monteiro L, Miche M, Zima P, Maroteaux D, et al. Progressin diesel HCCI combustion within the European SPACE LIGHT project. SAEpaper no. 2004-01-1904; 2004.

[3] Sjoberg M, Dec JE. An investigation of the relationship between measuredintake temperature, BDC temperature, and combustion phasing for premixedand DI HCCI engines. SAE paper no. 2004-01-1900; 2004.

[4] Hampson GJ. Heat release design method for HCCI in diesel engines. SAE paperno. 2005-01-3728; 2005.

[5] Hosseini V, Checkel MD. Using reformer gas to enhance HCCI combustion ofNG in a CFR engine. SAE paper no. 2006-01-3247; 2006.

[6] Heywood JB. Internal combustion engine fundamentals. New York: McGraw-Hill; 1988.

[7] Gatowski JA, Balles EN, Chun KM, Nelson FE, Ekchian JA, Heywood JB. Heatrelease analysis of engine pressure data. SAE paper no. 841359; 1984.

[8] Brunt MFJ, Platts KC. Calculation of heat release in direct injection dieselengines. SAE paper no. 1999-01-0187; 1999.

[9] Sastry GVJ, Chandra H. A three-zone heat release model for DI diesel engines.SAE paper no. 940671; 1994.

[10] Lanzafame R, Messina M. ICE gross heat release strongly influenced by specificheat ratio values. Int J Automot Technol 2003;4:125–33.

[11] Arregle J, Lopez JJ, Garcia JM, Fenollosa C. Development of a zero-dimensionaldiesel combustion model. Part 1: analysis of the quasi-steady diffusioncombustion phase. Appl Therm Eng 2003;23:1301–17.

[12] Egnell R. The influence of EGR on heat release rate and NO formation in a DIdiesel engine. SAE paper no. 2000-01-1807; 2000.

[13] Asad U, Zheng M. Fast heat release characterization of a diesel engine. Int JTherm Sci 2008;47:1688–700.

[14] Rasswieler GM, Withrow L. Motion pictures of engine flames correlated withpressure cards. SAE Trans 1938;42:185–204 [Reprinted SAE paper no. 800131;1980].

[15] Krieger RB, Borman GL. The computation of apparent heat release for internalcombustion engines. ASME paper no. 66-WA/DGP-4; 1966.

[16] Chun KM, Heywood JB. Estimating heat-release and mass-of-mixture burnedfrom spark-ignition engine pressure data. Combust Sci Technol1987;54:133–43.

[17] Brunt MFJ, Rai H, Emtage AL. The calculation of heat release energy fromengine cylinder pressure data. SAE paper no. 981052; 1998.

[18] Brunt MFJ, Emtage AL. Evaluation of burn rate routines and analysis errors. SAEpaper no. 970037; 1997.

[19] Egnell R. Combustion diagnostics by means of multi-zone heat release analysisand NO calculation. SAE paper no. 981424; 1998.

2330 M. Fathi et al. / Fuel 89 (2010) 2323–2330

[20] Klein M, Eriksson L. A specific heat ratio model for single-zone heat releasemodels. SAE paper no. 2004-01-1464; 2004.

[21] Ceviz MA, Kaymaz I. Temperature and air–fuel ratio dependent specific heatratio functions for lean burned and unburned mixture. Energy ConversManage 2005;46:2387–404.

[22] Olikara C, Borman G. A computer program for calculating properties ofequilibrium combustion products with some applications on IC engines. SAEpaper no. 750468; 1975.

[23] Woschni G. A universally applicable equation for the instantaneous heattransfer coefficient in the internal combustion engine. SAE paper no. 670931;1967.

[24] Filipi ZS, Chang J, Guralp OA, Assanis DN, Kuo T-W, Najt PM, et al. New heattransfer correlation for an HCCI engine derived from measurements ofinstantaneous surface heat flux. SAE paper no. 2004-01-2996; 2004.