A Two-Zone Multigrid Model for SI Engine Combustion Simulation Using Detailed Chemistry

12 Pages·6.516 MB·English

by  Ge H-W. et al.

HindawiPublishingCorporation
JournalofCombustion
Volume2010,ArticleID201780,12pages
doi:10.1155/2010/201780
Research Article
A Two-Zone Multigrid Model for SI Engine Combustion
Simulation Using Detailed Chemistry
Hai-WenGe,1HarmitJuneja,2YuShi,1ShiyouYang,1andRolfD.Reitz1
1EngineResearchCenter,UniversityofWisconsin-Madison,Madison,WI53706,USA
2WisconsinEngineResearchConsultants,LLC,3983PlymouthDr.,Madison,WI53705,USA
CorrespondenceshouldbeaddressedtoHai-WenGe,[email protected]
Received26December2009;Revised19May2010;Accepted14June2010
AcademicEditor:IshwarPuri
Copyright©2010Hai-WenGeetal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Anefficientmultigrid(MG)modelwasimplementedforspark-ignited(SI)enginecombustionmodelingusingdetailedchemistry.
Themodelisdesignedtobecoupledwithalevel-set-G-equationmodelforflamepropagation(GAMUTcombustionmodel)for
highlyefficientenginesimulation.Themodelwasexploredforagasolinedirect-injectionSIenginewithknockingcombustion.
ThenumericalresultsusingtheMGmodelwerecomparedwiththeresultsoftheoriginalGAMUTcombustionmodel.Asimpler
one-zoneMGmodelwasfoundtobeunabletoreproducetheresultsoftheoriginalGAMUTmodel.However,atwo-zoneMG
model,whichtreatstheburnedandunburnedregionsseparately,wasfoundtoprovidemuchbetteraccuracyandefficiencythan
theone-zoneMGmodel.Withoutlossinaccuracy,anorderofmagnitudespeedupwasachievedintermsofCPUandwalltimes.
ToreproducetheresultsoftheoriginalGAMUTcombustionmodel,eitheralowsearchingleveloraproceduretoexcludehigh-
temperature computational cells from the grouping should be applied to the unburned region, which was found to be more
sensitivetothecombustionmodeldetails.
1.Introduction Advanced engine design concepts, including homogeneous
chargecompressionignition(HCCI),premixedchargecom-
CFD-based engine development is widely used in the pression ignition (PCCI), and modulated-kinetics (MK),
automotive industry due to its much lower cost compared areallchemicalkinetics-controlled,andsimulationofthese
to experiment-based engine development [1]. Addition- combustion processes requires detailed chemistry. Detailed
ally, computer simulation provides more insight about the chemistryisoftenimplementedintoCFDsoftwarethrough
complex engine combustion process which is inaccessible coupling with the CHEMKIN package. For example, Kong
or costly using current measurement techniques. Improved and Reitz [4] developed a KIVA-CHEMKIN model which
accuracy and efficiency in numerical models and rapidly implemented the CHEMKIN II solver [5] into the KIVA
advancing computer capabilities makes CFD-based engine code [6]. The KIVA-CHEMKIN model assumes that each
development more feasible than ever. Thus, traditional cell is a perfectly stirred reactor (PSR) and that species
empirical hardware-based optimization is being replaced conversion rates can be modeled using the CHEMKIN
withCFD-basedoptimization.Asaresult,thedevelopment solver. The KIVA-CHEMKIN model has been proven to
timeofavehicleintheautomotiveindustryhasbeenreduced be a very reliable tool for diesel engine simulation and
fromaverage60monthstwentyyearsagoto18monthstoday thus widely used in industry and academia. However,
[2]. even with a relatively simple detailed mechanism, such
Detailed chemistry is necessary to reproduce kinetics- as the ERC reduced n-heptane mechanism (34 species,
controlled processes, for instance, the processes of auto- 74 reactions) [7], computational time is increased by 1
ignition and pollutant emissions [3]. Understanding such to 2 order(s) of magnitude compared with conventional
processes is essential for improving engine performance, simplified combustion models, such as the Characteristic
especially when considering strict emissions regulations. TimeCombustion(CTC)model[8].Therefore,efficiencyis
2 JournalofCombustion
solver,whichisthemosttime-consumingpartofsimulation
whendetailedchemistryisused.TheMGmodelgroupsther-
modynamically similar cells via a mapping procedure into
one“groupedcell”fortheCHEMKINcalculation,followed
by a procedure to redistribute the group information back
onto the individual cells using remapping. The grouping
region (searching level) is either fixed [13] or determined
adaptively [15] accounting for the local inhomogeneities in
thethermodynamicconditionstodealwiththenonuniform
spatial distribution of thermochemistry properties. The
conceptofanadaptiveneighborsearchisfurtherillustrated
in Figure1 using a 2D schematic mesh. It can be seen
that the first level search only covers the four adjacent cells
Center Thirdlevelneighbors (six if 3D mesh) of the reference cell. If the in-cylinder
Firstlevelneighbors Fourthlevelneighbors
temperatureinhomogeneityisbelowprespecifiedvalues,the
Secondlevelneighbors
search can then be expanded to a second level or higher.
Figure1:Schematicofadaptivemultigridgroupingprocedure. In this study, the maximum search level was limited to
four, where a maximum of 129 cells can be reached using
the fourth level search in a 3D block structural mesh.
ofvitalinherentwhenapplyingdetailedchemistrytoengine The fifth searching level is a global search, which means
simulations, especially when used in engine optimization that grouping is not limited to neighbor cells and all the
studies.Dependingonthetotalnumberofdesignparameters computationalcellsareconsideredforgrouping.Themodel
considered in the optimization, hundreds or thousands of offers in total seven options: no MG, fixed first level, fixed
individualsimulationsarerequiredforoneoptimizationtask second level; fixed third level, fixed fourth level, fixed fifth
[9,10].Thus,manyeffortshavebeendevotedtoreducethe level,andfinallytheadaptivelevel.Whenadaptivesearching
computational time spent in solving the high-dimensional is used, the searching level at each time step is determined
and stiff ordinary differential equations (ODEs) that arise considering the inhomogeneity of all the computational
from the inclusion of detailed chemistry. Strategies for this cells. The grouping criteria considered in the present work
purposecanbecategorizedintothefollowingclasses: include the cell temperature and progress equivalence ratio
[13, 15]. In the present work, a difference in temperature
(1)reduce the number of species and reactions in the of 20K and a difference in equivalence ratio of 10% were
mechanism:forexample,[3];
used to determine if cells are thermodynamically “similar”
(2)dynamically reduce the size of the Jacobian matrix [15]. Temperature inhomogeneities of 400K, 350K, 300K,
in the CHEMKIN solver by lumping or assuming 250K,and50Kwereusedtodeterminethefirstthroughfifth
equilibrium species and/or reactions that have little (global)searchinglevels,respectively[15].
impact on the global reaction system: for example, After the calculation of chemical reactions of all the
QSSA, ILDM, CSP, partial equilibrium [3, 11], and grouped cells, the mass fractions of each species were
dynamicadaptivechemistry(DAC)scheme[12]; remappedbackontotheoriginalcells.Agradient-preserving
(3)reducethefrequencyofcallingtheCHEMKINsolver: remapping method [13, 15] was used to preserve temper-
for example, multizone models [13], dynamic cell ature and species composition gradients. Firstly, before the
clustering [14], and adaptive multigrid chemistry mappingprocedure,anewquantity,ch,isdefinedusingthe
(AMC)[15]; numberofCandHatomsofallparticipatingspecies,except
thecombustionproducts,CO andH O,where
(4)solve the ODEs using alternative faster numerical 2 2
schemes:forexample,[16]. H#
ch=2C# + −H2O. (1)
In the present paper, a one-zone and a two-zone −CO2 2
multigrid (MG) models were implemented into the level-
Thechnumberisanindicatorofreactivityofamixture
set-G-equationmodelforSIenginesimulation.Themodels
anddefinedbasedontheequivalentnumberofOatomsthat
were validated using comparisons with the full chemistry
are required to form final products, CO and H O. Thus,
2 2
solverforagasolinedirect-injection(GDI)enginecase.The
CO andH Ointhemixtureareexcludedinthedefinition
computational efficiency and accuracy of the models are 2 2
of the ch number. The ch number of a group is the sum of
discussed, and it is concluded that speedup techniques that
thechnumberofallcellsinthatgroup.Afterthechemistry
havepreviouslybeendevelopedfordieselenginesimulations
calculation, all species, except CO , H O, O , and N , are
2 2 2 2
aresuccessfulalsoformodelingspark-ignitionengines.
assigned back to the group’s cells based on ch. In this case,
the mass of species k in an individual cell is obtained from
2.MathematicalModels theratio:
ch
2.1. Multigrid Model. The multigrid (MG) model [13] is m =m cell . (2)
k,cell k,groupch
designed to reduce the frequency of calling the CHEMKIN group
JournalofCombustion 3
andtheflamepropagationprocessismodeledbytrackingthe
Φ<1 locationofthissurface.Thetransportequationoftheiso-G
surfaceis[19]
O2,O,NO··· ρ∂G +ρ−→U ·∇G=ρs |∇G|, (3)
∂t L
Diffusion
and it is solved using a level-set method. The second
term, on the left-hand side, is the convective term. The
Φ≈1
term on the right-hand side is the propagation term which
CO2,H2O,CO,NO··· accountsforthechemicalpropertiesofthemixture.Stretch
effects on the flame are reflected in the curvature of the G
Diffusion
surface. Therefore, turbulence-combustion interactions are
Φ>1 CH4,CO,H,H2··· amlseoshdeessucrsiebdedinbeyngthineeGco-edqeus,attihoenm. Coodnelseiddeerqinugattiohnesmfoorvitnhge
Favre-averagedGarewrittenas[20]
Fueldroplets ∂G(cid:2) +(cid:3)−→U(cid:2) −−→U (cid:4)·∇G(cid:2)= ρus0(cid:5)(cid:5)(cid:5)∇G(cid:2)(cid:5)(cid:5)(cid:5)−D κ(cid:2) (cid:5)(cid:5)(cid:5)∇G(cid:2)(cid:5)(cid:5)(cid:5).
∂t bf vertex ρ T T M
(4)
End-gaszone Flamezone Post-flamezone
front The computational domain is separated into three parts:
the region ahead of the flame front (unburned region,
CHEMKIN G < 0), the region on the flame front (G = 0), and
CHEMKIN
the regions behind the flame front (burned region, G >
Level-setG-equation 0). To consider autoignition ahead of the flame front
(e.g., leading to “knocking” combustion) and stratification
Figure 2: GAMUT combustion model for partially premixed
combustion. behind the flame front, the cells ahead and behind the
flame front are treated as PSRs and their thermochemical
states are computed using the CHEMKIN solver. With this
consideration, the model is then capable of modeling of
Inthiswaythemassofeachspeciesinthegroupisalso
both turbulent premixed and nonpremixed combustion.
conserved.Consequently,somecellscanhavemoreorfewer
CorHatomsthanbeforethemappingprocess,andthusthe Thus, the model is also referred to as the G-equation for
AllMixtures, a UniversalTurbulent (GAMUT) combustion
restofthecellsinthegroupneedtobeadjustedtomaintain
model[20].Figure2showstheschematicflamestructureof
the total number of C and H atoms in that group. After
apartiallypremixedflameandthecorrespondingmodeling
that O is distributed to maintain the total number of O
2 strategies for the different regimes. Computational cells in
atoms in each cell and, finally, adjustment of N is used to
2
theunburnedregionwithtemperaturesgreaterthan1100K
conserve the mass of each cell if necessary. Since after the
and a fraction of combustion products greater than certain
remappingprocessthemassfractionofeachspeciesineach
amount are regarded as autoignition sites. As soon as an
cell is known, the change of the specific internal energy of
each cell can be obtained from the difference between the ignitionkernelisformedbyeitherthesparkplugmodelor
autoignition,theflamepropagationmodelisactivated.
internal energy of formation of the species present in the
In the present, the discrete particle ignition kernel
cellbeforethegroupingprocessandthataftertheremapping
(DPIK)modelbyFanandReitz[21]wasusedformodeling
process. The cell temperature can be computed from the
of spark ignition. Once the characteristic length of the
updated specific internal energy and the mass fraction of
ignition kernel region is larger than the averaged turbulent
species.
Asmentionedearlier,themultigridchemistrymodelhas integral length scale, a G surface is initialized. The cells on
the flame front are assumed to be in chemical equilibrium;
been successfully used for DI engine simulations [15] and
foroptimizationofdieselenginesoperatingunderdifferent thatis,completecombustionisassumedtooccuracrossthe
flame. The change of composition in a computational cell
engine loads [1, 17]. It has also been successfully coupled
containing the flame front is determined from the swept
withtheDACschemeandparallelizedusingaloadbalancing
volumeofthepropagatingflame:
scheme [18]. It was found in these studies that significant
amountsofcomputationaltimeweresavedwiththeadaptive (cid:6) (cid:7)
dY A
multigridchemistrymodel. i = Yu−Yb s0, (5)
dt i i V T
2.2. Level-Set-G-Equation Model. The present level-set G- where A and V are the flame surface area and volume of
equation model is a turbulent combustion model which the computational cell, respectively. Y is the mass fraction
i
tracks flame propagation. The flame front propagation is of the ith species. The superscripts “u” and “b” refer to the
representedbyaniso-scalesurface(usuallythescalarG=0), valuesintheunburned(G<0)andburned(G>0)regions,
4 JournalofCombustion
respectively. The turbulent burning velocity in (4) and (5) The GAMUT combustion model has been developed
is related to the laminar burning velocity and turbulence and implemented into the KIVA-3V code by Tan and
intensityaswellastheDamko¨hlernumber[19]: Reitz [20, 23]. It has been extensively used to simulate
s0t =s0l +v(cid:5)⎧⎪⎨⎪⎩−a24bb32Da+⎡⎣(cid:14)a24bb32Da(cid:15)2+a4b32Da⎤⎦1/2⎫⎪⎬⎪⎭. cc[2oo0mm,bb2uu3–sstt2iioo8nn].iIpntrhosapcsaersaskls-oiigssnuaictecsdetsrgsafatuisfiloleylidnbeepeernnemgaipnixpeelside,dinctoowmshbiimuchsutlitaohtnee
1 1 diesel/natural-gasdual-fuelCIengines[29,30]andconven-
(6) tionaldieselengines[30–33].YangandReitz[28]havemade
improvements to the combustion submodels for modeling
Here, s0l is the laminar burn(cid:21)ing velocity, and v(cid:5) is SI combustion with the level set G-equation method and
the turbulence intensity, equal to (2/3)k, where k is the detailed chemical kinetics, including a transport equation
turbulent kinetic energy. The model constants a4 = 0.78, residual model, modeling flame front quenching in highly
b1=2.0,andb3=1.0arederivedfromtheturbulencemodel stratifiedmixtures,andtheinclusionofarecentlydeveloped
[19].TheDamko¨hlernumberisdefinedas PRFmechanism[34].
s0l
Da= l t , (7) 2.3.Two-ZoneMultigridModel. WhentheGAMUTcombus-
v(cid:5)l
F tionmodelisused,chemicalreactionsinthecellsaheadand
where l is the turbulence integral length scale and l is the behind the flame front are computed using the CHEMKIN
t F
thicknessoftheflame: solver. Thus, similar to the KIVA-CHEMKIN model, the
GAMUT combustion model spends the most CPU time in
l = (λ/Cp)0. (8) theCHEMKINsolver.SinceadditionalCPUtimeisneeded
F (ρs0) to solve the G-equation, the GAMUT combustion model
l u
usuallyrequiresmoreCPUtimethantheKIVA-CHEMKIN
The heat conductivity, λ, and heat capacity, Cp, are model. This motivated integration of the MG model into
evaluated at the inner layer temperature. The laminar the level-set-G-equation model for higher computational
burning velocity, s0, is determined from an experimental efficiency. If the original MG model is directly applied to
l
correlation, for example, that of Metghalchi and Keck [22] the GAMUT combustion model, the process of searching
iswidelyused: andgroupingthermodynamicallysimilarcellscoversallthe
(cid:14) (cid:15) (cid:14) (cid:15) computational cells, the “one-zone MG model”. However,
T γ p β theburntandunburnedregionshaveverydifferentthermo-
s0=s0 u u (1−2.1Y ), (9)
l l,ref T p dil chemical conditions in both temperature and composition.
u,ref u,ref
The burnt region usually has much higher temperatures,
where Tu,ref = 298K, pu,ref = 1atm, and Ydil is the mass more combustion products, and less reactants than the
fraction of diluents present in the fuel-air mixture. The unburned region. These two regions are separated by the
subscript“u”indicatestheunburnedgas,andthereference flame front, which is numerically represented by the iso-
laminarburningvelocityis surfaceofG = 0.Thus,itislogicaltoapplytheMGmodel
separately to the burnt and unburned regions, the “two-
s0l,ref=BM+B2(φ2−φM)2 (10) zone MG model”. The mapping and remapping procedures
in the burnt and unburned regions are independent, and
with BM = 26.32cm/s, B2 = −84.72cm/s, and φM = 1.13. thusdifferentsearchinglevelscanbeusedforthetworegions
Theexponentsγandβaregivenas
according to their local conditions. Both the one-zone and
(cid:22) (cid:23) two-zone MG models were implemented into the KIVA3v
γ=2.18−0.8 φ−1 ,
codeforcomparison.
(cid:22) (cid:23) (11)
β=−0.16+0.22 φ−1 ,
2.4. Adaptive Load-Balancing Algorithm for Parallelization.
whereφistheequivalenceratio. In the present work a load balancing scheme was also used
The flame surface from the G-equation describes the to parallelize the CHEMKIN computations, which are the
meanpositionoftheflamebrush,whichhasathicknesson most time-consuming part of the code. The parallelization
theorderofacomputationalcell.Thechemicalreactionrate isbasedonthemessagepassinginterface(MPI).Beforethe
foreachspeciesiscalculatedineachtimestepas CHEMKINsolveriscalled,allcellsthatneedtobecomputed
(cid:6) (cid:7) usingCHEMKINarelisted.Attheinitialstep,thosecellsare
∂Y A
k = Yu−Yb s0, (12) evenlyassignedtotheavailableprocessors.Then,thespeed
∂t k k V t
ofeachprocessorcanbedefinedastheratioofthenumber
where Yu and Yb are the mass fractions of species i in the ofcellscomputedbythisprocessorandtheCPUtimetaken
k k intheprevioustimestep:
unburntandburntgasesoneithersideoftheflamesurface.
Yb aredeterminedbyassumingchemicalequilibriuminthe
k Nn
burntgases.V isthevolumeofthecomputationalcellandA Pn+1= ckcell,i, (13)
isthetotalareaoftheflamefrontinthecell. i tin
JournalofCombustion 5
Intakeport/runner
Exhaustport
Intakevalve
Sparkplug Injectorboss
Exhaustvalve
∼238,000cells Topviewofno-valuemesh
(a) (b)
Figure3:ComputationalmeshforthesinglecylinderhomogeneousGDIengine.
wherethesuperscriptndenotesthetimestepandsubscripti Table1:Enginespecificationsandselectedoperatingconditions.
indicatestheithprocessor.Startingfromthenexttimestep,
Bore×Stroke(mm) 99.6×92.0
the cells are assigned based on the speed of the processor
Pn+1: ConnectingRodlength(mm) 154.9
i
CompressionRatio 11:1
Pn+1 EngineSpeed(rev/min) 1600
Nn+1 = (cid:24) i N , (14)
ckcell,i NcpuPn+1 ck MAP wide-openthrottle(WOT)
i=1 i
Air-FuelRatio 12:1
in which Nck is the total number of cells required in the InjectorType 6-holeInjector
CHEMKIN computation. In this way, a dynamic balance
FuelInjected(mg) 60
between the processors is achieved. To smooth the process, StartofInjection(degATDC) −243
arelaxationfactor,α,isintroducedin(12)as
SparkTiming(degATDC) −6.0
Nn
Pn+1=αPn+(1−α) ckcell,i. (15)
i i tn
i
autoignitionoccursinthisenginecase[35].Thus,thiscase
This algorithm has been validated on diesel engine is a critical case for validation of the MG and GAMUT
simulationsandhasproventobeveryefficient[18,34]. combustion models. The GAMUT combustion model has
Other models used in the KIVA code are described in been validated in [35] by comparing with available exper-
detail in [28]. A recently developed PRF mechanism [34], imental data, including pressure trace and knock intensity.
which consists of 41 species and 130 elementary reactions, Excellent agreement with the measured data was obtained.
wasusedinthepresentpaper. Thepresentpaperfocusesontheefficiencyandaccuracyof
the new MG model. Thus, the numerical results from the
3.ResultsandDiscussion originalGAMUTcombustionmodelaretakenasareference
for model validation. The calculation in the present paper
Themodelswereappliedtoanexperimentalsinglecylinder starts at −6.3deg ATDC and ends at 70deg ATDC. At this
homogeneous gasoline direct injection (GDI) engine [35]. moment, all the liquid fuel has vaporized. All cases were
This engine features a wedge type combustion chamber calculated using the parallel code on 4 nodes. Each node is
and a shallow piston bowl. A full mesh was created using equipped with an Intel Pentium 3.0GHz CPU and 2.0GB
WERC’sin-housegridgenerationtoolcapableofproducing RAMmemory.
structuredgrids.Figure3showsasnapshotofthecomputa- The GDI case was first simulated using the one-zone
tionalmeshwithamaximumgridsizeof238,000cells.The MG model. Figure4 shows the in-cylinder pressure and
direct-injection(DI)systememploysanoutboardsidespark heat release rate (HRR) of the GDI engine predicted
location and an intake-side-mounted multihole injector. using the different models, including the original GAMUT
The specifications of the engine and the selected operating combustion model (without MG model) and the GAMUT
conditions are listed in Table1. Experiments showed that combustionmodelwiththeMGmodel.Differentsearching
6 JournalofCombustion
×1013
6.5 4
6
5.5
3
5
MPa) 4.5 deg)
ess( 4 (erg/ 2
Pr RR
3.5 H
3 1
2.5
2
0
−5 0 5 10 15 20 25 30 35 40 45 50 55 60 10 12 14 16 18 20 22
Crank(degrees) Crankangel(degatdc)
w/oMG MG-global w/oMG MG-global
MG3 MG-adaptive MG3 MG-adaptive
MG4 MG4
(a) (b)
Figure4:PressureandHRRofSIenginesimulatedusingone-zoneMGmodelwithdifferentsearchinglevels.
Table2:Computationaltimeofone-zoneMGmodelwithdifferent Table3:Computationaltimeoftwo-zoneMGmodelwithdifferent
searchinglevels(CA=−6.3to70). combinationofsearchinglevels(CA=−6.3to70).
Case w/oMG MG3 MG4 MG-global MG-adaptive Case w/oMG MG0+5 MG1+5 MG2+5
CPUtime[hrs] 173.3 55.3 45.6 5.5 52.6 CPUtime[hrs] 173.3 35.7 27.4 13.7
Walltime[hrs] 48.6 18.4 16.5 5.5 17.9 Walltime[hrs] 48.6 13.1 11.1 7.2
Speedup[−] 3.6 9.4 10.5 31.5 9.7 Speedup[−] 3.6 13.2 15.6 24.1
levels were tested: fixed three level (MG3), fixed four level of different searching levels in the burnt and unburned
(MG4), fixed global level (MG-global), and the adaptive regions.Theunburnedregionhashigherchemicalpotential
search (MG-adaptive). The corresponding computational and therefore is more sensitive to the combustion model
timesofthedifferentsolutionmethodsarelistedinTable2. details.Applyingahighersearchinglevelcanleadtofailure
ThespeedupdatainthetablereferstotheCPUtimeofthe inaccuratelypredictingautoignitionintheunburnedregion.
originalcombustionmodelandwallclocktimeofeachcase. The mixture in the burnt region is usually close to
Itcanbeseenthattheparallelcodeworkswell.Threefoldor the state of chemical equilibrium. Thus, it is safe to apply
morespeedupwasachievedforallcases,exceptforthefixed globalsearch,whichresultsinthemostaggressivegrouping
global adaptive search case, in which the CPU time spent and significantly reduces computational cost. Simulations
on the chemistry solver is very low and thus the efficiency with global search in the burnt region (5) and different
of the parallel scheme is low. Combined with the MG searchinglevel(0to2,labeledas“MG0+5”,“MG1+5”,and
model, the computational time was reduced by at least one “MG2+5”, resp.) in the unburned region were conducted
order of magnitude. With the fixed global search, the total on the same case. Table3 lists the computational times of
computationaltimewasreducedfrom173hoursto5hours. these simulations. The predicted pressure and HRR using
With other searching levels, around a 10-fold speedup was the two-zone MG model were compared with the original
achieved. The computational cost of the adaptive searching GAMUT combustion model, as illustrated in Figure5. It
level is similar to the one of the third searching level. can be seen from Figure5 that the two-zone MG model
However, the predicted pressure and HRR using the one- givesmuchbetterpredictionsthantheone-zoneMGmodel.
zone MG model are not good. As seen in Figure4, none of Only when the searching level in the unburned region is
them can accurately reproduce the HRR curve. All of them greater than or equal to 2, do the curves of pressure and
predictedanearliermaincombustioneventthantheoriginal HRR deviate from the results predicted using the original
GAMUTcombustionmodel. GAMUT combustion model. Figure6 shows total mole of
The two-zone MG model was then used to simulate in-cylinder NOx (NO , NO, and N O) computed using
2 2
the same case. The two-zone MG model enables the use the original GAMUT combustion model and the multigrid
JournalofCombustion 7
×1013
6.5 4
6
5.5
3
5
Press(MPa) 4.45 RR(erg/deg) 2
3.5 H
3 1
2.5
2
0
−5 0 5 10 15 20 25 30 35 40 45 50 55 60 10 12 14 16 18 20 22
Crank(degrees) Crankangel(degatdc)
w/oMG MG1+5 w/oMG MG1+5
MG0+5 MG2+5 MG0+5 MG2+5
(a) (b)
Figure5:PressureandHRRofSIenginesimulatedusingtwo-zoneMGmodelwithdifferentsearchinglevels.
×10−4 at CA = 3 and 18deg ATDC. Figure8 shows iso-surface
8 of the flame front on the same cut plane with contour
plot of NOx at CA = 18deg ATDC. Autoignition at
7
CA = 18deg ATDC is predicted by all the models. Before
autoignition event (e.g., CA = 3deg ATDC), the multigrid
6
modelsgiveverysimilarresultscomparingtotheonefrom
5 original GAMUT combustion model. It can be seen that
e)
ol usingsearchinglevelof2overpredictedthehotspotsinthe
m
( 4 unburnt region and consequently overpredicted the NOx
x
O in the corresponding regions. When searching level is set
N 3
to 1, the predicted temperature and NOx distributions are
2 veryclosetotheresultsoftheoriginalGAMUTcombustion
model.Inoverall,applyingaglobalsearchintheburntregion
1 isveryreliable,andthepredictionaccuracymainlydepends
onthesearchinglevelintheunburnedregion.
0
Although more conservative searching levels were
0 10 20 30 40 50 60 70
appliedtotheunburnedregion,itcanbeseenfromTable3
Crank(degrees)
that more savings in computational time were obtained.
w/oAMC AMC1+5 Even when the MG model is not used in the unburned
AMC0+5 AMC2+5 region (searching level = 0), about 5 times speedup in
Figure6: Total moleof NOx emissionsimulatedusingtwo-zone computational time was achieved, which is better than
MGmodelwithdifferentsearchinglevels. all the one-zone MG models except for the global search
in terms of its computational efficiency. If the searching
level in the unburned region is one, the model is able to
reproduce the results of the original GAMUT combustion
model.Thenumericalresultsofthemultigridmodelarevery modelsatisfactorily.Inthiscase,morethan6timesspeedup
closetotheoneoftheoriginalGAMUTcombustionmodel incomputationaltimewasachieved,correspondingtomore
beforecrankangleof30degATDC.Duetoearlierpredicted than15timesspeedupintermsofwalltime.
main combustion event when searching level is set to 2, Asshownabove,theunburnedgasregionisverysensitive
NOx formation is slightly earlier than others. After crank tothedetailsofthecombustionsolutiontechnique.Therisk
angle of 30deg ATDC, the multigrid model consistently of using the MG model is that it may artificially enhance
predicts slightly higher NOx emission. Figure7 shows iso- species and temperature mixing. When the one-zone MG
surface of the propagating flame front with contour plot model is employed, all the computational cells near the
of temperature on a cut plane right below the fire deck propagating flame front may be grouped. The cells in the
8 JournalofCombustion
WithoutMG MG1+5 MG2+5
2500
K
1000
(a)
WithoutMG MG1+5 MG2+5
2500
K
1000
(b)
Figure7:Iso-surfaceofflamefrontandtemperaturedistributionatCA=3(a)and18(b)degATDC.
WithoutMG MG1+5 MG2+5
500
)
3m
g/
(
0
Figure8:Iso-surfaceofflamefront(blackline)andNOxdistributionatCA=18degATDC.
unburned region have lower temperature than those in high-temperature computational cells during the mapping
the burnt region that will then have higher temperature. procedure, that is, to avoid allowing ignition-sensitive cells
Consequently, this can lead to a faster flame propagation tobegrouped.
speed and even autoignition. The two-zone MG model Asatestofthisconcept,atemperaturecriterionwasset
avoids such artificially enhanced mixing in temperature to 800K. In this case, cells are skipped if the temperature
between the burnt and unburned regions. Thus, it gives exceeds 800K. Again, different searching levels for the
much better prediction in terms of pressure and HRR. unburned region were tested. The corresponding predicted
However, as shown in Figure5, the use of too aggressive pressureandHRRareplottedinFigure9andthecomputa-
searching level in the unburned region will result in faster tionaltimesarelistedinTable4.ItcanbeseenfromFigure9
flamepropagationspeedduringthemaincombustionstage, thatbyexcludingthehigh-temperaturecells,theMGmodel
atleastforthecurrentstratifiedGDIenginecase.Usingalow with almost all the searching levels gives close enough
searching level is one option. Another option is to skip the predictionstotheoriginalGAMUTcombustionmodel.Only
JournalofCombustion 9
×1013
6.5 4
6
5.5
3
5
MPa) 4.5 deg)
ess( 4 (erg/ 2
Pr RR
3.5 H
3 1
2.5
2
0
−5 0 5 10 15 20 25 30 35 40 45 50 55 60 10 12 14 16 18 20 22
Crank(degrees) Crankangel(degatdc)
w/oMG MG4+5 w/oMG MG4+5
MG2+5 MG5+5 MG2+5 MG5+5
MG3+5 MG3+5
(a) (b)
Figure9:PressureandHRRofSIenginesimulatedusingtwo-zoneMGmodelwithdifferentsearchinglevelsandskippinghigh-temperature
cells(T>800K)intheunburnedregion.
×10−4 Table4:Computationaltimeoftwo-zoneMGmodelwithdifferent
8 combination of searching levels and skipping high-temperature
cells(T>800K)intheunburnedregion(CA=−6.3to70).
7
Case woMG MG2+5 MG3+5 MG4+5 MG5+5
6
CPUtime[hrs] 173.3 29.3 29.2 28.3 27.4
Walltime[hrs] 48.6 11.9 11.6 11 10.5
e) 5
ol Speedup 3.6 14.6 14.9 15.8 16.5
m
( 4
x
O
N
3
computed using the original GAMUT combustion model
2 and the multigrid model. Similar to Figure6, the NOx
emission predicted by original GAMUT combustion model
1 andmultigridmodelsveryclosebeforecrankangleof30deg
ATDC.Slightdifferencesbetweenthemshowupaftercrank
0
angle of 30deg ATDC. Figure11 shows iso-surface of the
0 10 20 30 40 50 60 70
propagatingflamefrontwithcontourplotoftemperatureon
Crank(degrees)
a cut plane right below the fire deck at CA = 3 and 18deg
w/oAMC AMC4+5 ATDC.Figure12showsiso-surfaceoftheflamefrontonthe
AMC3+5 AMC5+5 same cut plane with contour plot of NOx at CA = 18deg
ATDC.Whenglobalsearchingisused,thehotspotsandNOx
Figure10:TotalmoleofNOxemissionofSIenginesimulatedusing
two-zone MG model with different searching levels and skipping emissionintheunburntregionareslightlyoverpredicted.
high-temperaturecells(T>800K)intheunburnedregion. A higher criterion temperature, 900K, was also tested.
However, the performance results were worse than those of
800Kandthereforewerenotpursued.
whenglobalsearchingwasappliedintheunburnedregion,
does the predicted main combustion occur slightly earlier 4.Conclusions
thantheonepredictedbyGAMUTmodel.Asacompromise,
fewercellsweregroupedsincethehigh-temperaturecellsare In the present paper a multigrid model was implemented
excluded.Thespeedupincomputationaltimesissimilarto together with a level-set-G-equation model for spark igni-
the ones in Table3, even though more aggressive searching tion engine combustion modeling using detailed chemistry
wasused.Figure10showsthecorrespondingNOxemissions (GAMUT combustion model). The model was validated
10 JournalofCombustion
WithoutMG MG1+5 MG2+5
2500
K
1000
(a)
WithoutMG MG1+5 MG2+5
2500
K
1000
(b)
Figure11:Iso-surfaceofflamefrontandtemperaturedistributionatCA=3(a)and18(b)degATDCsimulatedusingtwo-zoneMGmodel
withdifferentsearchinglevelsandskippinghigh-temperaturecells(T>800K)intheunburnedregion.
WithoutMG MG1+5 MG2+5
500
)
3m
g/
(
0
Figure12:Iso-surfaceofflamefront(blackline)andNOxdistributionatCA=18degATDCsimulatedusingtwo-zoneMGmodelwith
differentsearchinglevelsandskippinghigh-temperaturecells(T>800K)intheunburnedregion.
against the numerical results of the original GAMUT com- (iii)The burnt region is insensitive to the combustion
bustionmodel.Thefollowingconclusionscanbedrawn. model because the mixture in the burnt region is
closetochemicalequilibrium.Thus,globalsearching
(i)A one-zone MG model was unable to accurately can be applied to the burnt region to maximize the
reproduce the main combustion event predicted by computationalefficiencywithoutlossinaccuracy.
theoriginalGAMUTcombustionmodel.
(iv)The unburned region is very sensitive to the details
(ii) A two-zone MG model, which treats the unburned of the combustion model implementation. Either
and burnt regions separately, was able to reproduce using a low searching level or excluding high-
the results of the original GAMUT combustion temperature computational cells from the grouping
modelandlargereductionincomputertimewasseen in the unburned region was found to provide accu-
(1to2order(s)ofmagnitude). rateandefficientpredictions.