A Fully Coupled Computational Fluid Dynamics and Multi-zone Model With Detailed Chemical Kinetics...

8/10/2019 A Fully Coupled Computational Fluid Dynamics and Multi-zone Model With Detailed Chemical Kinetics for the Simu

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SPECIAL ISSUE PAPER 497

A fully coupled computational fluid dynamics andmulti-zone model with detailed chemical kinetics forthe simulation of premixed charge compression ignitionengines

A Babajimopoulos1*, D N Assanis

1, D L Flowers

2, S M Aceves

2,andR P Hessel

3

1Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA

2Lawrence Livermore National Laboratory, Livermore, California, USA

3Engine Research Center, University of Wisconsin, Madison, Wisconsin, USA

The manuscript was accepted after revision for publication on 19 April 2005.

DOI: 10.1243/146808705X30503

Abstract: Modelling the premixed charge compression ignition (PCCI) engine requires abalanced approach that captures both fluid motion as well as low- and high-temperature fueloxidation. A fully integrated computational fluid dynamics (CFD) and chemistry scheme (i.e.detailed chemical kinetics solved in every cell of the CFD grid) would be the ideal PCCI modellingapproach, but is computationally very expensive. As a result, modelling assumptions arerequired in order to develop tools that are computationally efficient, yet maintain an acceptabledegree of accuracy. Multi-zone models have been previously shown accurately to capturegeometry-dependent processes in homogeneous charge compression ignition (HCCI) engines.In the presented work, KIVA-3V is fully coupled with a multi-zone model with detailed chemicalkinetics. Computational efficiency is achieved by utilizing a low-resolution discretization to

solve detailed chemical kinetics in the multi-zone model compared with a relatively high-resolution CFD solution. The multi-zone model communicates with KIVA-3V at each compu-tational timestep, as in the ideal fully integrated case. The composition of the cells, however,is mapped back and forth between KIVA-3V and the multi-zone model, introducing significantcomputational time savings. The methodology uses a novel re-mapping technique that canaccount for both temperature and composition non-uniformities in the cylinder. Validationcases were developed by solving the detailed chemistry in every cell of a KIVA-3V grid. Thenew methodology shows very good agreement with the detailed solutions in terms of ignitiontiming, burn duration, and emissions.

Keywords: HCCI, PCCI, computer modelling, combustion processes, computational fluiddynamics, chemical kinetics, emissions

1 INTRODUCTION conversion efficiency, accompanied by low nitrogenoxides (NO

x) and soot emissions, particularly at part-

load, where its counterparts suffer significantly [13].1.1 HCCI and PCCISeveral technical issues must, however, be resolved

Homogeneous charge compression ignition (HCCI)before the concept finds an application in pro-

has emerged in the last couple of decades as aduction engines. HCCI engines suffer from high

promising alternative to the well-established tech- unburned hydrocarbon (HC) and carbon monoxidenologies of diesel and spark-ignited (SI) engines. (CO) emissions. High rates of heat release, and theHCCI has the potential to deliver diesel-like fuel resulting steep pressure rise rates and high-peak

pressures, limit the HCCI operating range (low specific* Corresponding author: Mechanical Engineering, The University power output). The main obstacle to date is the lackof Michigan, 2032 Walter E Lay Automotive Laboratory, 1231 Beal of any direct means of controlling the ignition timing,

Avenue, Ann Arbor, MI 48109-2133, USA. email: ababajim@ such as the spark or late injection event available incurrent production engines [4].umich.edu

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498 A Babajimopoulos, D N Assanis, D L Flowers, S M Aceves, and R P Hessel

The control issue has prompted the investigation of kinetics calculations makes such a model impracticaleven for todays fastest computers. For now, CFDvarious control strategies, including direct injection

(DI) [5] and variable valve actuation (VVA), the latter calculations with detailed chemistry in each cell

are limited to small chemical mechanisms (~100as a means of retaining large levels of residual gasesin the cylinder [69]. Both of these strategies can species) and coarse grids (~1000 cells). Recent

publications [20,21] have reported good resultsresult in a mixture with significant composition and

temperature stratification. During gas exchange and using this approach.In order to obtain some of the resolution affordedcompression the actual time for mixing of the fresh

air, fuel, and the residuals is limited and, as a con- by CFD models and yet reduce the computational

time required by chemical kinetics calculations,sequence, there are potential inhomogeneities inthe mixture [10]. This composition stratification Aceves et al. introduced a sequential multi-zone

modelling approach [2224]. This multi-zone modelmay be desirable, because it can help in controlling

the phasing of combustion, extending the low load of HCCI combustion assumes a decoupling of theturbulent mixing process and chemistry prior to andoperating range, and lengthening the burn duration

at higher loads [11,12]. This partially stratified HCCI during the main heat release. The approach uses aCFD code, KIVA-3V [25], and a multi-zone chemicalcan be better described with the less restrictive term

premixed charge combustion ignition (PCCI), which kinetics solver, in a sequential fashion. KIVA-3V isrun over part of the engine cycle, typically fromwill be the focus of the presented work.intake valve closing (IVC) until a transition point

before top dead centre (BTDC). At this point, cells1.2 Multi-zone modelling overview

with similar pressure and temperature histories aregrouped into a relatively small number of zonesIt is widely accepted that HCCI is essentially con-

trolled by chemical kinetics, with little direct effect (10100). The chemical kinetics solver is then applied

to this small number of zones, instead of the largeof turbulence. During the main heat release, thechemical kinetic processes occur on such short time number of cells used in the CFD code, offering a

great advantage in computational time comparedscales that turbulence is too slow to influence the

process. Although there is still some debate about with a full integration of a chemical kinetics code

and a CFD code. The multi-zone model has beenthe influence of turbulence on HCCI combustion[1314], spectroscopic and imaging investigations of successful in the prediction of combustion process

parameters, such as peak cylinder pressure and burnHCCI verify that simultaneous multi-point ignitionoccurs with no flame propagation [1518], support- duration. HC emissions are predicted reasonably well,

but CO is typically underpredicted by an order ofing the hypothesis that heat release is dominated by

chemical kinetics. Recent modelling work by Sankaran magnitude.The limitation of the sequential method is thatand Im [19] studied the influence of dissipation rate

and mixture inhomogeneities on the auto-ignition of once the chemistry calculation begins, the detailedinformation from the CFD code is lost and there ismixtures on an opposed flow configuration, where a

premixed fuel/air stream mixed with hot exhaust no mixing between the zones. Flowers et al. [26]

modified the multi-zone model to include mixinggases. It was found that, although dissipation rate

and mixture inhomogeneity can have a significant effects, by introducing a coupled CFD/multi-zonemodel. Instead of a one-way mapping of the CFD tem-effect on auto-ignition at lower mixing rates and

higher pressures [conditions typically observed near perature distribution onto the multi-zone chemicalkinetics solver, their method was modified to havetop dead centre (TDC) in an HCCI engine], chemical

kinetics dominate the auto-ignition process and mapping back and forth throughout the cycle. The

advantage is that the fluid mechanical processesdiffusion has little effect on the propagation of thereaction front. are still calculated on a high-resolution grid, while

the computationally intensive chemical kineticsIn theory, accurate analysis of PCCI combustion

could be achieved by fully integrating a computational processes can be solved within a small number ofzones. The goal of the study was to investigate thefluid dynamics (CFD) code with a detailed chemical

kinetics code, which would solve the chemistry in mixing of cold gases from the crevices and the

boundary layer with the hot gases in the core duringeach computational cell. Such a model would requiregrids fine enough (on the order of 104to 105cells) to the post main heat release oxidation. It was found

that there is diffusion of CO and fuel from the lowestresolve adequately the temperature distribution inthe cylinder. The combination of these large numbers temperature regions into the hotter gases in the

core and that the fuel continues to react during theof cells with computationally intensive chemical

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parameters and run conditions are listed in Table 1. solutions improved as the fuelO2

equivalence ratiodistribution was made less steep and as the RGF wasThe KIVA-3V grid used for the analysis was a 2D

axisymmetric grid with 10 200 cells at bottom reduced.

The running time for a fully integrated solution ondead centre (Fig. 1). The fuel was methane and thechemical mechanism used in the analysis was GRI- a 2.8 GHz PC operating on Linux was around 30 h.

The corresponding running time for a multi-zoneMech 3.0 [31]. The equivalence ratio and the residual

gas fraction were varied and several initial fuelair solution was approximately 3.5 h. This is a significanttime gain, which is not accompanied by major lossand residual gas fraction (RGF) distributions at IVC

were used. These distributions were linear and were in accuracy, as will be demonstrated in the following

sections. It should be noted that the multi-zoneimposed as only a function of the cylinder radius andnot a function of the axial position along the cylinder. model would have a considerably greater advantage

in running time for higher-resolution grids. TheThe initial fuel and RGF distributions for one of

the solved cases are shown in Fig. 1. This is a case time for running the multi-zone model is largelyindependent of the grid resolution, since chemistry,with a global equivalence ratio of 0.4 and 35 per cent

RGF. The initial fuelO2equivalence ratio distribution which is the most time-consuming part of the calcu-

lation, is always solved for the same number of zonesis quite steep, with values ranging from 0 to 1.1.

This was one of the most extreme cases that were (~100). On the other hand, the running time for thefully integrated solution increases rapidly with theexamined and the results presented in the followingsections correspond to this sample case. Agreement number of KIVA-3V cells, since chemistry is solved

for every cell in the grid.between the multi-zone and the fully integrated

Table 1 Engine parameters and operatingconditions 3 DEFINITIONS OF EQUIVALENCE RATIO FOR

COMPOSITION MAPPING AND REMAPPINGParameter Value

Engine speed 2007 r/min A key to the new model is finding an appropriateCompression ratio 10.5:1

composition marker to guide the correct mappingStroke 13.5 cm

Bore 11.41 cm and remapping of the cells composition betweenConnecting rod length 21.6 cm KIVA-3V and the multi-zone model. In previous workDisplacement 1378 cm3

by the authors present [29,30], when the multi-zoneFuel MethaneChemical kinetic mechanism GRI-Mech 3.0 [31] code was used sequentially with KIVA-3V, the group-Start of calculation (IVC) 155

ing of the cells into temperature (T)equivalencePressure at IVC 3.18 bar

ratio (W) zones took place only once during the cycle,Temperature at IVC 565 K Average equivalence ratio 0.30.4 before any reactions had occurred, and thus theResidual gas fraction 235%

fuelO2

equivalence ratio was an obvious choice. In

Fig. 1 Grid and sample distributions of CH4and EGR (represented by CO

2) at IVC for validation

runs



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501A ful ly cou pled CFD and mul ti- zone mod el

the proposed methodology, however, the equivalence Cck

Hhk

Ook

Nnk

is a generic formula for species k,where c

k, h

k, o

k, and n

k are the numbers of atomsratio must provide more information about the com-

position and how combustion has progressed in the (carbon, hydrogen, oxygen, and nitrogen, respect-

ively) that constitute the molecule of species k.cell. Before proceeding with the formulation of themodel, some definitions of equivalence ratio that will Knowing the mixture composition at each point

during the combustion process, the total numberbe used in the following sections are introduced.

HCCI applications concern mainly lean or near of C atoms in the mixture, C#, isstoichiometric combustion with high levels of residual

C#= K

k=1

Nkck=

K

k=1

xkN

totck=N

tot K

k=1

xkck

(6)gases. For W1 and no RGF, the complete com-bustion of a general oxygenated fuel of average

where Nk

is the number of molecules of species kmolecular composition Cx

Hy

Oz

with air can beand N

tot is the total number of molecules in thewritten as

mixture. Similar expressions can be written for the

total number of atoms of oxygen (O#) and hydrogenWC

xH

yO

z+Ax+

y

4z

2B (O2+3.76N2) (H#). After some manipulation, an equation for theglobal equivalence ratio, W, can be derived

xWCO

2+

y

2WH

2

O

W= 2C#+H

#/2zC

#

O#zC# (7)

+Ax+y

4z

2B [(1W)O2+3.76N2] (1) where z=z/x. The symbol used for the globalequivalence ratio is the same as for the traditional

In equation (1), W is the traditionally defined fuelair equivalence ratio [equation (2)]. The reasonfuelair equivalence ratio [32] is that, for a fuelair mixture that has not reacted,

the two definitions are equivalent. The fundamental

difference between the two definitions is that theW=(fuel/air)

a(fuel/air)

s

(2)global equivalence ratio takes into account the

instantaneous atomic composition of the mixture,where the subscript a denotes the actual fuelair

while the traditional definition is based on the massratio and the subscript s the stoichiometric ratio. fractions of the species. In a closed reactor, since theWhen operating lean, the residual gas may containmass and the total number of atoms of each elementa significant amount of excess oxygen. With highare conserved, the global equivalence ratio is con-levels of RGF a more appropriate equivalence ratiostant and is independent of whether combustion hasis the fuelO

2equivalence ratio, W*

not started (reactants only), is already completed

(products only), or is at some intermediate stage.W*=

(fuel/O2

)a

(fuel/O2

)s

(3)It should be noted that the calculation ofW with

equation (7) resembles the method used to estimateEquations (1) to (3) only relate to the composition the operating equivalence ratio of an engine fromof the reactant and product species and do not the measured exhaust gas composition [32]. Intake into account the complex process by which

addition, the global equivalence ratio W as definedcombustion proceeds. At any stage during the com- in equation (7), is similar to the conserved scalar Z*bustion process, the molecular composition is the that Bilger uses in [33] to study the structure of non-result of a global reaction of the form premixed flames.

An alternative definition for the equivalence ratioXCWCxHyOz+Ax+

y

4z

2B (O2+3.76N2)D (referred to as progress equivalence ratio, Q) can beobtained if the number of C, H, and O atoms thatbelong to the complete combustion products CO

2 K

k=1

xk

Cck

Hhk

Ook

Nnk

(4)and H

2O are excluded from the calculation in

equation (7)whereK is the total number of species included in

the reaction mechanism,xkis the molecular fraction

Q=2C#CO2

+(H#H2O

/2)zC#CO2

O#CO2H2O

zC#CO2

(8)of species k in the mixture, and X is a normalizing

factor such thatWis directly related to the oxygen ratio V introducedby Mueller et al. in [34]. Mueller et al. used the oxygen

K

k=1

xk=1 (5)

ratio to measure the instantaneous stoichiometry of



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a mixture accounting for the number of C, H, and O started at 90 BTDC, the initial pressure was 1.8 bar,and the initial temperature was adjusted so that theatoms that belonged to fuel or oxidizer, and fuel-

plus-oxidizer reactant species. main heat release occurred after TDC (ATDC). As

already mentioned, the global equivalence ratio isFor a closed reactor, the value of the progressequivalence ratio can range from W (reactants only) constant throughout the whole process. The initial

value of the fuelO2

and the progress equivalenceto 0 (complete combustion products), depending

on the progress of combustion. The differences ratio is the same and slightly lower thanW. This isattributed to the 5 per cent RGF that includes excessbetween the fuelO

2equivalence ratio (W*), the global

equivalence ratio (W), and the progress equivalence O2

, which lowers the value ofW* compared with W,

and CO2

and H2O, whose atoms are not used in theratio (Q) are illustrated in Fig. 2. Figure 2 shows

the evolution of temperature and the equivalence calculation ofQ.W* andQ are equivalent, when there

are no intermediate combustion products present.ratios during the combustion of four different fuels

(iso-octane [35], propane [36], methane [31], and As it can be seen in Fig. 2, the value of W* startsdropping well before the main heat release event,dimethyl ether (DME) [37]). The calculations were

performed with an adiabatic variable volume reactor as the fuel breaks down into smaller-chain hydro-carbons and radicals. This is more evident for iso-code, based on CHEMKIN [38].

The initial global equivalence ratio for all cases octane, which is the largest molecule, and less formethane, which has only one carbon atom. On thewas W=0.4 and the RGF, including only completecombustion products, was 5 per cent. Calculations other hand, the evolution of Q corresponds much

Fig. 2 Equivalence ratio and temperature evolution during combustion for various fuels, ascalculated using an adiabatic variable volume reactor simulation (the numbers in thesquare brackets are the references for the chemical mechanisms used). The initial globalequivalence ratio for all cases was W=0.4 and the residual gas fraction was 5 per cent



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better with the heat release and the subsequent riseof the temperature in the cylinder for all fuels thanW* does, owing to the fact that the main heat release

occurs when CO2

and H2O are formed. It is, there-

fore, apparent that the progress equivalence ratio, Q,

is the most appropriate choice for identifying cells

with similar composition and it will be used in thefollowing sections for grouping cells into T Qzones.

4 MODEL FORMULATION

4.1 Coupled KIVA-3V and multi-zone model

KIVA-3V [25] provides the CFD framework for theproposed methodology. KIVA-3V handles the fluid

mechanical processes on a highly resolved grid, while

the computationally intensive chemical kinetics aresolved only for a relatively small number of zones.

The equations pertinent to chemical reactions that

need to be addressed by the multi-zone code are thecontinuity and energy equations. The continuity

equation is

qrk

qt+V(r

ku)=VCrDkVA

rkrBD+ rck+ rsdkl (9)

Fig. 3 Procedure for mapping between KIVA-3V andwhererk

is the mass density of species k, rthe totalmulti-zone chemical kinetics solver

mass density, and u the fluid velocity vector. Fickslaw is used for diffusion with a single coefficientD

k.

some thermodynamic state (temperature, pressure,The terms rck

and rs indicate source terms resultingand composition). These cells are grouped into zones,from chemistry and spray, respectively. Species l isaccording to an algorithm that considers the tem-the species of which the spray droplets are composedperature and progress equivalence ratio of the cellsandd

kl is the Dirac delta function.

and is presented in the following section. Each zoneThe internal energy equation iscontains a fraction of the mass in the cylinder. Thus,each zone becomes representative of a group of cellsq(rI)

qt +V(ruI)=rVu+(1A

o)s:VuVJ

throughout the cylinder. The averages of temper-

ature, pressure, and composition for the cells in a+Aore+Qc+Qs (10)

zone are determined to specify the thermodynamicstate of the mixture in that zone.where I is the specific internal energy exclusive of

chemical energy, p is the pressure, s :Vu indicates The chemical process for each zone is handled byCHEMKIN [38]. Each zone is allowed to react fromthe double-dot product between the surface tension

and velocity gradient tensor, Jis the sum of the con- timetto timet+Dtin an adiabatic constant volumereactor. The adiabatic reactor is used only to deter-tributions owing to heat conduction and enthalpy

diffusion, e is the dissipation rate of the turbulent mine the change in composition and an amount of

heat release for each zone. The constant volumekinetic energy, and Qcand Qsare source terms caused

by chemical heat release and spray interaction. assumption may introduce some error, but the time-steps used (on the order of 1ms) are sufficientlyWhat KIVA-3V requires from the chemistry solver

at each timestep is the composition change (rck

) small to make it negligible [24]. Moreover, heat

transfer, convection, and diffusion between the cellsand the heat release due to chemical reactions (Qc)for each cell. Figure 3 shows schematically the pro- (and thus the zones) are calculated by KIVA-3V. After

the chemistry calculation, the new zone compositioncedure for the application of the current multi-zonemodel to the calculation of PCCI combustion. At and the heat release are mapped back onto all the

cells within the zone. As will be shown in the nexteach discrete time, t, every cell in KIVA-3V is at



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Table 2 Mass fractions in temperature zonessections, the way this remapping is performed iscritical for the quality of the solution. The KIVA-3V

Zone (1=coldest, 5=hottest) 1 2 3 4 5code subsequently proceeds to determine convection

Mass fraction in zone, % 5 10 20 30 35and diffusion processes over the same timestep.

4.2 Grouping of cells intoTQzones

At each timestep, the grouping of the KIVA-3V 2. The cells in each temperature zone are sorted from

lowest to highest Q. Starting from the cell withcells into zones must be performed in a way

which guarantees that the grouped cells have similar the lowest Q, the cells of the temperature zone aredivided into as many zones as needed, so that thethermodynamic and chemical properties. Temper-

ature is the most representative variable of the maximum Q range in each zone is DQmax

=0.02.Figure 4 shows an illustrative example ofTQzonethermodynamic state of a cell. In addition, as already

shown in section 3, the progress equivalence ratio Q generation for the sample case presented in Fig. 1.

The left side of Fig. 4 shows the temperature andprovides information about the composition and

how far combustion has progressed in the cell. These the progress equivalence ratio distributions in thecylinder at 20 BTDC, as obtained from KIVA-3V.two variables are, therefore, selected and the cells are

grouped intoTQ zones. The right side of Fig. 4 shows the cells that belong in the third temperature zone, divided into QIn previous work by the present authors [27] it was

shown that, when there is significant temperature zones.

3. The last step is to take anyTQzones that containand composition stratification in the cylinder, the

part of the charge that ignites and burns fastest is more than 1 per cent of the cylinder mass, sortthe cells in these zones by temperature, and dividenot necessarily the hottest one, but rather one that

has a combination of relatively high temperature and them into smaller temperature zones so that, inthe end, the mass fraction in each zone does notfuelO

2equivalence ratio. Temperature, however, is

still the dominant factor that determines ignition exceed 1 per cent.

timing and the equivalence ratio plays a secondaryThis zone generation process yields a total number

role, especially for the high-octane-number fuels

of zones just over 100 (the mass fraction in sometypically used in PCCI engines. Taking this into con- zones can actually be less than 1 per cent). Once thesideration, the steps for grouping the cells into zones

averages of temperature, pressure, and compositionare as follows.

for the cells in a zone are determined, the zone is

allowed to react from time tto time t+Dt. After the1. All cells in the cylinder are sorted from lowest tohighest temperature and are divided into five tem- chemistry calculation, the change in the zone com-

position and the energy released owing to chemicalperature zones. Each zone contains a prescribed

fraction of the mass within the cylinder, given in reactions are mapped back onto the cells within thezone. The next step is to remap the species from theTable 2.

Fig. 4 Schematic ofTQzone generation. The temperature and progress equivalence ratio fieldsare used to divide the cells first into Tzones, which are then divided into smaller Qzones.The figure on the right shows the geometric shape of the third temperature zone, whichcontains 20 per cent of the mass (between 15 and 35 per cent of the mass when rankedaccording to temperature)



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chemical kinetic zones onto the KIVA-3V cells. Two the higher-temperature cells. This pattern would beapproaches to handling remapping will be discussed less prominent if a higher-resolution grid had beenin the following sections. used. Figure 6 compares the TW cloud evolution

for the multi-zone model with average remapping4.3 Remapping using average values (black points) against the detailed solution (grey

points) at four times: the transition point at whichThe simplest procedure to map zones back onto the the multi-zone model is called for the first timecells consists of assigning the average composition

and is defined as the time at which the temperatureof the zone to each cell. This means that all the cells

of the hottest cell in the cylinder exceeds 900 Kin a particular zone will have the same composition.

(~41 BTDC), five timesteps after the transitionThe energy per unit mass released owing to chemicalpoint (Dt=1ms), 40 BTDC, and TDC.reactions, De, as computed by the chemistry calcu-

The effect of grouping into zones and remappinglation, is mapped onto the cells in the zone as athe average zone composition onto the cells ischange in the specific internal energy. The new cellevident. Early in the process bands of cells withtemperature is then computed using the updatedthe same global equivalence ratio are formed. Thisspecific internal energy and the remapped averageintroduces large artificial composition gradientscomposition. This simple remapping process is

in KIVA-3V, which significantly enhance diffusionreferred to as average remapping.between neighbouring cells that belong to differentFigure 5 compares the solution obtained with thezones [equation (9)]. Remapping the average zonemulti-zone model with average remapping againstcomposition in each cell essentially increases thethe detailed solution with full chemistry in each celleffective grid size from the dimension of one cell tofor the sample case shown in Fig. 1. The variablesthe dimension of one zone, thus introducing largecompared are cylinder pressure, mean temperature,numerical diffusion. Only 1 crank angle degree (CAD)and maximum temperature in the cylinder. Theafter the transition point, the shape of the TWcloudcylinder pressure and mean temperature are infor the multi-zone has changed significantly and itsgood agreement, but the maximum temperature isedges have disappeared. By TDC, the cloud hasunderpredicted with the multi-zone model.almost collapsed to a straight line and all the cells inIn order to understand the discrepancy in the

the cylinder have the same global equivalence ratio.maximum temperature prediction, it is useful to lookThe temperature distribution, however, has beenat what happens in the temperature and compositionmaintained to a large degree, because the energydistributions in the cylinder during combustion.released owing to chemical reactions is mapped ontoA way to do this is to plot the TW distributionthe cells in the zone as a change in the specificin the cylinder at different times. These plots areinternal energy, thus preserving the original temper-essentially scatter plots of the temperature and globalature distribution throughout the zone. This meansequivalence ratio of all the computational cells in thethat the multi-zone model with average remappingcylinder and resemble clouds [29]. The linear patternis effectively solving a different problem with all cellsof these plots is a result of heat transfer and the tem-having the same average composition rather than theperature distribution in the cylinder. The layer ofinitially specified distribution. This also explains whycells closest to the cylinder wall is the coldest, whilethe maximum temperature in the cylinder is under-the cells closer to the centre of the cylinder have apredicted, since the combustion temperature is lowermore uniform temperature (see Fig. 4). As a result,

the low-temperature cells are further apart than for lower equivalence ratios.

Fig. 5 Comparison of simulation results of multi-zone solution with average remapping againstthe detailed solution



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zones cells based on ch. The mass of species k in C and H atoms in the zone remains constant. For themost part, however, there is still a shortage of C andeach cell will be

H atoms in each cell. The only remaining species

containing C is CO2

, which is distributed to the zonesmk,cell

=ch

cellch

zone

mk,zone

(12)cells, filling up the missing C atoms (M

k is the

molecular mass of species k)Equation (12) guarantees that the mass of eachindividual species in the zone is conserved. This

k

mk,cellM

k

ck+m

CO2,cellM

CO2

=C#cell

(13)interpolation may actually increase slightly the

number of C or H atoms in some cells. If thishappens, then the total number of C or H atoms that Similarly to CO

2, H

2O can be distributed to the

zones cells to maintain the number of H atoms inthe remaining cells in the zone are allowed to haveis adjusted accordingly, so that the total number of each cell. Having done this the only species that have

Fig. 7 Comparison of simulation results of multi-zone solution with improved remappingagainst the detailed solution

Fig. 8 TWcloud evolution for the detailed solution and the multi-zone solution with improvedremapping



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not been distributed are O2and N

2. O

2is distributed multi-zone model with improved remapping and

the detailed solution are compared at different timesto maintain the total number of O atoms in each

cell. Finally, N2

is used as a filler, to bring each cell in Figs 8 and 9. Figure 8 compares theTWclouds at

40 BTDC, TDC, 5 ATDC and 15 ATDC. Up to TDC,to its original mass. In the last step, the changein the specific internal energy of each cell is calcu- which is before any significant heat release has

occurred, the two clouds are identical. At 5

ATDC,lated accounting for the internal energy of formation

of the species present in the cell before grouping the heat release has just started for the detailed

solution, with the multi-zone solution followingthe cells into zones and after the chemistry calcu-

lation and the remapping have been performed. The closely. As already mentioned, it is the cells with high

temperature and equivalence ratio (top-right cornernew cell temperature is then computed using the

updated specific internal energy and the remapped of the cloud) that burn first. At 15 ATDC, the mainheat release event is over and the TW cloud of thecomposition.

Figure 7 compares the solution obtained using the multi-zone code with the improved remapping has

caught up and is very similar to the detailed solution.multi-zone model with the improved remapping

against the detailed solution with full chemistry in The effect that combustion has had on the shape of

theTWcloud is raising the temperature of the cells,each cell for the sample case shown in Fig. 1. The

agreement between the two solutions for pressure moving the cloud along theTaxis. The compositionof the cells has of course changed, but the globaland mean temperature is excellent and the maxi-

mum temperature prediction has improved as well, equivalence ratio remains the same as reactants are

converted to combustion products.compared with the average remapping.

The benefits of the improved remapping can be Figure 9 compares the TQclouds at TDC, 5ATDC,and 15 ATDC. As with the TW clouds, up to TDCseen more clearly if the TW and TQ clouds for the

Fig. 9 TQcloud evolution for the detailed solution and the multi-zone solution with improvedremapping



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there are no differences between the multi-zone cells have not burned completely and are the sourceof unburned HC and CO emissions.solution with improved remapping and the detailed

solution. At 5 ATDC, the shape of the cloud for the So far, the two remapping methods the averageand the improved have been compared with thedetailed solution starts changing significantly as the

progress equivalence ratio of the cells that have detailed solution only in terms of pressure and

temperature predictions and TW cloud evolution.started burning goes to 0 and their temperature

increases. After the end of the main heat release Figure 10 compares the evolution of the massfractions of six species in the cylinder (CH

4, CO

2,event, at 15 ATDC, the progress equivalence ratio of

most cells is almost 0. There are, however, still cells CO, NO, OH, and H2O

2) for the two remapping

methods with the detailed solution. The improvedwith high Q and relatively low temperature. These

Fig. 10 Comparison of the evolution of the mass fraction of selected species using the multi-zone model with the two different remapping options (average and improved) againstthe detailed solution



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remapping performs significantly better than the 3. Two methods for mapping the new zone com-

average remapping for all species, especially later position back onto the KIVA-3V cells were exam-

in the expansion stroke (50 ATDC), when the com- ined. In the first approach (average remapping),position in the cylinder begins to become frozen. the average composition of the zones is mapped

More specifically, the average remapping method onto the cells of each zone. It was found thatoverpredicts the formation of CO

2 (combustion this approach introduces significant artificial

efficiency), while it underpredicts the final CO mass composition gradients in the cylinder resultingfraction. In addition, the average remapping signifi- in non-physical increased diffusion and mixing.

cantly underpredicts the formation of NO, which is The second remapping approach (improveddirectly related to the underestimated in-cylinder remapping) uses an algorithm that attempts to

peak temperature. Overall, the improved remapping maintain the total number of C, H, O, and Ndoes an excellent job in tracking down the evolution atoms in each cell constant. It was shown that the

of all the species in the cylinder. Any large discrep- non-physical diffusion is avoided with improved

ancy with the detailed solution is short lived and only remapping and predictions of pressure, temper-

during the period of high heat release rate, when ature, and species mass fractions match very

temperature and composition change rapidly in each closely the solution of chemistry in every cell.

cell. By the end of combustion, however, the final 4. Overall, the proposed methodology off

ers a com-predictions of the improved remapping method are putationally efficient alternative to the CFD with

very close to the detailed solution. detailed chemistry in every cell approach, while

maintaining good agreement with the detailed

solution. The fully coupled KIVA-3V and multi-

zone model can provide a useful tool for the5 CONCLUSIONS fundamental understanding of PCCI combustion,

the effects of temperature and composition strati-A multi-zone model with detailed chemical kinetics fication on ignition and burn duration, and thehas been fully coupled with KIVA-3V for the simu- sources of emissions.lation of PCCI engines. The main conclusions of this

study are outlined below.

1. The computational time with the multi-zone modelREFERENCESreduced the simulation time by almost 90 per cent

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A Fully Coupled Computational Fluid Dynamics and Multi-zone Model With Detailed Chemical Kinetics...

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