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Combustion and Flame 143 (2005) 11–26www.elsevier.com/locate/combustflam

Development and application of a comprehensive soomodel for 3D CFD reacting flow studies in a diesel eng

Sangjin Honga, Margaret S. Wooldridgea,∗, Hong G. Ima,Dennis N. Assanisa, Heinz Pitschb

a Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48109-2125, USAb Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

Received 14 July 2004; received in revised form 2 March 2005; accepted 9 April 2005

Available online 1 August 2005

Abstract

A three-dimensional reacting flow modeling approach is presented for diesel engine studies that can bepredictions of trends in soot emissions for a wide range of operating conditions. The modeling framework eskeletal chemistry forn-heptane for ignition and combustion, and links acetylene chemistry to the soot nuclprocess. The soot model is based on integration and modification of existing submodels for soot nucleaglomeration, oxidation, and surface growth. With the optimized modeling parameters, the simulations agwith results of high-pressure shock tube studies of richn-heptane mixtures, reproducing the trends for soot mover a range of temperature and pressure conditions (T = 1550–2050 K,P = 20, 40, and 80 MPa). Engine simultion results for soot mass are in excellent agreement with diesel engine smoke number measurements ovof injection timings (−11◦ ATDC–2.4◦ ATDC) and two exhaust gas recirculation levels (16 and 26–27%).model results demonstrate that correct description of the soot formation, as well as the soot transport procritical for achieving reliable predictive capabilities in engine simulations. 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Soot emissions modeling; Computational engine simulations

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1. Introduction

Despite the highly competitive thermal efficienof the direct-injection diesel engine, the perennNOx-soot emissions trade-off challenges its comance with ever more stringent emissions regulatioIn order to improve our understanding of the pollutaformation and destruction mechanisms, and to m

* Corresponding author. Fax: +1 734 647 3170.E-mail address: [email protected]

(M.S. Wooldridge).

0010-2180/$ – see front matter 2005 The Combustion Institutdoi:10.1016/j.combustflame.2005.04.007

the demand for rapid design and development tuaround, three-dimensional computational fluid dnamic (CFD) models of reacting flow in enginare seeing increasing use. Engine soot modelsranged in complexity from phenomenological to dtailed physico-chemical models. NOx emissions aretypically modeled using variants of the extended Zdovich mechanism.

Among the empirical soot models, the two-stmodel of Hiroyasu and Kadota[1] and its variants[2–8] have been used in a number of engine sties owing to its simplicity of implementation in CFcodes. This model is based on two empirical r

e. Published by Elsevier Inc. All rights reserved.

http://www.elsevier.com/locate/combustflame

mailto:[email protected]

http://dx.doi.org/10.1016/j.combustflame.2005.04.007

12 S. Hong et al. / Combustion and Flame 143 (2005) 11–26

Nomenclature

A Preexponential factor in rate coefficientexpression (units of cm3, mol, s)

AC Correction factor for nucleation rate ex-pression

Ck Coagulation rate forkth soot momentdm Average soot diameter (nm)D Sum of the turbulent soot diffusivity and

the velocity slip diffusivity (m2/s)E Activation energy (kcal/mol)Gk Growth rate forkth soot momentIk Nucleation rate forkth soot momentkX Per-site rate coefficient (cm3/site/mol/s)mCsoot Soot mass (g)Mk kth mean soot momentn Power of temperature in rate coefficient

expressionn(v, t) Soot particle-size distribution (a log-

normal distribution is assumed)ni, nj Number densities of soot particles of

volume (size)i or j per unit volume(1/cm3 cm3)

N0 Avogadro’s number (1/mol)R Universal gas constant (kcal/mol/K)

Si Surface area ofith soot particle (cm2)˙Sk Source/sink term for thekth momentt Time (s)T Temperature (K)v Soot volume (cm3)vi, vk Volume of soot particle of sizei or k

(cm3)vg Average soot volume (cm3)v1 Volume of one carbon atom�v Flow velocity vector (m/s)X Species designation[X] Molar concentration of speciesX

(mol/cm3)

Greek symbols

α Fraction of surface sites availableβ(vi , vj ) Collision frequency between soot parti-

cles of volume (size)i andj (m3/s)χS Number density of surface sites(2.3 ×

1015 cm−2)

σ Standard deviationω Reaction rate (mol/cm3)

c-delootdtsod-nsofns

ofte

ikincalrti-ess,heyar-reeeonal

ndan-n-nerd-

tthety-

ricss-dy-

calde-mes

hasu-

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or-theable

isroletorss-

equations, formation and oxidation, which are funtions of the major reactant concentrations. The modoes not take into account particle growth and sdynamics, its prediction of soot formation is linkeexplicitly to fuel concentration, and rate coefficienused in the empirical reactions often have to be mified when engine geometry or operating conditioare changed. This approach limits the applicabilitythe model as a predictive design tool to conditiowhere the model has been previously validated.

Tesner et al.[9] introduced an improved classmodels by postulating formation of an intermediaspecies responsible for particle nucleation. Surov[10] assumed that the formation and growth of radinuclei and the formation and growth of soot pacle nuclei are different stages of the same procpartially superimposed on one another, but that toccur through different mechanisms. Hence, the pticle formation process is assumed to consist of thstages: (i) the formation of radical nuclei, (ii) thgrowth of the radical nuclei and their conversion upreaching a critical diameter into nuclei with a physicsurface, and (iii) the further growth of the nuclei atheir transformation into carbon particles. The stdard KIVA-3V [11] soot model is primarily based othat of Surovikin[10], while the oxidation of soot particles follows the procedure of Haynes and Wag[12] with rate constants from Nagle and Stricklan

Constable[13]. Following the framework of Tesner eal. [9], a number of other researchers have linkedintermediate species for particle nucleation to acelene[14,15], while others have introduced a genesoot precursor radical[16,17]. Nevertheless, this clasof models still considerably oversimplifies the gaphase combustion chemistry and neglects particlenamics.

At the other extreme, detailed, multistep chemimodels of soot formation and oxidation have beenveloped for canonical systems such as laminar fla[18–22], counterflow diffusion flames[23–26], andturbulent diffusion flames[27]. Application of a mod-eling framework derived from these approachesbeen attempted in a few closed-cycle engine simlations [28,29], including the work of Kitamura eal. [30]. However, the extensive use of existing, dtailed kinetic models in multidimensional simulatiois still cost prohibitive and quantitative agreemewith experimental data remains a challenge. Thefore, there is strong motivation to develop a soot fmation model for practical fuels that can captureessential physico-chemical processes, yet is amento large-scale simulations.

In addition to the soot physical chemistry, itrecognized that soot transport can play a largein the soot emissions from engines and combus[31,32]. However, the sensitivity of particulate emi

S. Hong et al. / Combustion and Flame 143 (2005) 11–26 13

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sions to the soot transport dynamics and the methused to model soot transport are often not well domented.

Based on the needs identified above, the obtive of the current work is to develop a model thincludes the broad scope of the physical and chemmechanisms important in soot processes and is sciently simplified such that the soot model can betegrated into KIVA simulations of diesel combustioThe modeling approach is based on integrationmodification (as necessary) of existing submodelssoot nucleation, agglomeration, oxidation, and sface growth. In addition, when appropriate, the moshould account for soot particle transport which is dferent from that of gas-phase species. A key goathe modeling effort is accurate predictions of trenin soot emissions for a wide range of operating contions. The results of well-controlled shock tube stuies by Kellerer et al.[33] are therefore used to caibrate the model and to develop confidence inpredictive capabilities. In the following sections, tsubmodels are described, comparisons with the eximental results are presented, and the sensitivity osoot model to the input parameters of the componsubmodels is investigated. The work concludes wa comparison of KIVA simulation results with expeimental data obtained from diesel engine studies.

2. Modeling approach

The modeling approach adopted in this studybased on our previous work on soot emissions ofural gas engines[34,35], where various submodels aincorporated and modified as necessary to repreeach of the physical and chemical mechanisms csidered important in soot modeling for engine studThe basic framework of the soot modeling is the mment method, which has been used previously[18,36] to describe soot properties with reasonable acracy and computational costs. In the moment meththe evolution of the soot properties is determinedthe first three moments representing the soot nber density(M0), soot volume fraction(M1), andthe deviation from the average volume(M2), usinga presumed particle-size distribution. Specificallylog-normal size distribution,

(1)n(v, t) = 1

3√

2π lnσexp

[− ln2(v/vg)

18 ln2 σ

]1

v,

is used in this study. In Eq.(1), n is the numberdensity of soot particles of volumev (where spher-ical particles are assumed throughout this work),vgis average particle volume, and theσ is the standarddeviation of the volume distribution. The assumptiof a log-normal size distribution for soot particl

is supported by experimental observations in engstudies[12,37,38]. Note that because a particle-sidistribution is assumed, higher moments need nocalculated and significant computational savingsrealized.

With a presumed log-normal size distribution, tfirst three soot moments are sufficient to resolvesoot properties using the relations

(2)Mk = M0vkg exp

(9

2k2 ln2 σ

),

(3)vg = M21

M3/20 M

1/22

,

(4)ln2 σ = 1

9ln

(M0M2

M21

).

The transient features of the soot moments aretermined via

(5)∂M0

∂t= I0 − C0,

(6)∂M1

∂t= I1 + G1,

(7)∂M2

∂t= I2 + G2 + C2,

where Ik is the nucleation rate,Gk is the combinedgrowth and oxidation rates, andCk is the coagulationrate for thek = 0, 1, and 2 moments. The source asink terms represented in Eqs.(1)–(3) are developedbased on the detailed physical and chemical submels for the soot processes. The submodels includskeletal reaction chemistry to represent ignition, cobustion, and the formation of soot precursor spec(b) nucleation of soot primary particles coupled toreaction kinetics; (c) soot coagulation based on cosion theory; (d) soot oxidation by O2 and OH; and (e)soot surface growth using a modified HACA mechnism.

2.1. Reaction chemistry

Because diesel engine combustion is the sysof interest in the current work,n-heptane chemistry iused as a surrogate fuel to model the ignition, cobustion, and soot nucleation chemical kinetics. Treaction mechanism employed in this study is pvided in Liu et al.[39]. The mechanism is a skeltal form of a detailed mechanism forn-heptane[40],which is similar to the skeletal mechanisms by Pitsand Peters[41] and Bollig et al. [42]. Comparedwith these previous mechanisms, the new mechanhas been enhanced and updated with the kineticdata provided by Baulch et al.[43,44] and othersThe mechanism has been validated by comparwith ignition delay times from shock-tube[45] and


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rapid compression machine experiments[46] at var-ious temperatures, pressures, and equivalence raspecies measurements from lean and rich plug flreactor (PFR) experiments[47]; temperature measurements from PFR experiments for various initemperatures[48] at elevated pressure; and specmeasurements in ann-heptane/air counterflow diffusion flame experiment[49]. Most importantly for thepresent study, all the major species and the acetymass fraction for the latter experiments are well pdicted. The validation studies are documented in mdetail in Liu et al.[39].

2.2. Nucleation of soot primary particles

The nucleation of soot primary particles is cosidered the least well-understood step in the sootmation process[50]. Although a unique soot precusor has not been identified, many species, incing acetylene (C2H2), polyacetylene, benzene, anpolycyclic aromatic hydrocarbon (PAH), have besuggested as important in the nucleation of sootmary particles[19,36]. Frenklach and Wang[19] esti-mated soot nucleation rates using collision procesof higher PAH compounds, which are only formedthe presence of acetylene. The use of PAH as aprecursor, however, requires a relatively large retion mechanism, resulting in increased computatiocosts and possibly a larger degree of empiricism, ifsupporting chemistry is unknown. Thus, an altertive approach that does not involve PAH compounis sought. Among the other compounds suggesabove, acetylene has been proposed as an essspecies in soot formation[51] and it is believed to participate in the PAH growth[50]. Because acetyleneconsidered a primary contributor to soot nucleatand its detailed kinetics are well represented inskeletaln-heptane mechanism described above,cleation of soot monomers was symbolized byreaction:

C2H2 ⇒ 2Csoot+ H2. (R1)

Here, 2Csoot represents a soot monomer that is coposed of two carbon atoms. In this work, the rconstant for(R1) is an empirical global rate constafor soot formation, which is discussed further beloOnce the soot monomers are formed, it is assumthat they immediately consolidate to form soot pmary particles. It is then necessary to determinetotal number of carbon atoms that constitute the sprimary particle. After investigating the effect of thprimary particle size on the overall soot model (dcussed in Section3), the soot primary particles werassumed to consist of 32 carbon atoms. Thus, 16monomers are required to form one soot primary pticle, which is formed instantaneously from the so

;

l

monomers. When less than 16 soot monomersavailable (i.e., when the number of monomers isevenly divisible by 16), the monomers are consodated to form a smaller soot primary particle to pserve conservation of carbon atoms. The stipulathat the primary particle consists of 32 carbon atois based on the work by Appel et al.[22] where theprimary soot particles are formed by the collisiontwo pyrenes consisting of 16 C atoms each.

The average diameter,dm, of the soot primary particles was determined by calculating the combinmass of the 32 carbon atoms, using a soot denof ρsoot= 1.8 g/cm3 [18], and assuming that the 3carbon atoms combine to form a spherical partinamely

(8)πd3

m6

= mCsoot

ρsoot.

The form of the rate coefficient for reaction(R1)is based on the fundamental assumption that theof production of the soot primary particles followthe rate of production of the important gas-phaspecies—acetylene. The soot nucleation rate expsion considered is that proposed by Leung et al.[52],

ωnucleation= 1.0× 104 exp

[−21,100

T

]

(9)× [C2H2] [mol/cm3],which was developed to represent direct formationsoot primary particles from acetylene.

The nucleation rate is incorporated into the mment model via

(10)Ik = ACvk1ωnucleationN0,

whereAC is a correction factor,v1 is the specific vol-ume of the soot primary particle raised to the powof the kth moment, andN0 is Avogadro’s numberThe correction factor in Eq.(10) is adjusted to in-vestigate the sensitivity of the overall soot modelthe nucleation submodel and to optimize the ovall soot model performance under benchmark eximental conditions. The correction factor is set atfixed value determined in the benchmarking studfor all subsequent engine modeling studies. The ssitivity analysis, model benchmarking, and validatiprocesses are discussed further below.

2.3. Surface growth and oxidation

The reaction mechanism used in the current stfor soot growth by surface reaction and soot oxidatis shown inTable 1, which is taken from Kitamura eal. [30] with one modification. In this mechanism, thsurface growth model is based on the HACA meanism[18,36] with the addition of several reactio


ra et al.

Table 1The soot surface growth and oxidation mechanism of Kitamura et al.[30] used in the current work

Reaction k = Aexp(−E/RT )

A (cm3/mol s) E (kcal/mol)

G1f Csoot-H + H → Csoot• + H2 2.5× 1014 12.0G1b Csoot• + H2 → Csoot-H + H 4.0× 1011 7.0G2f Csoot• + H → Csoot-H 2.2× 1014 −G2b Csoot-H → Csoot• + H 2.0× 1017 109.0G3a Csoot• → C2H2 + products 3.0× 1012 62.0G4f Csoot• + C2H2 → CsootCHCH• 2.0× 1012 4.0G4b CsootCHCH• → Csoot• + C2H2 5.0× 1013 38.0G5 CsootCHCH• → Csoot-H + H 5.0× 1010 −G6 Csoot• + O2 → products 2.2× 1012 7.5G7 CsootCHCH• + O2 → products 2.2× 1010 7.5G8 Csoot-H + OH → products Reaction probability= 0.13

a The preexponential factor listed for reaction G3 has been reduced from the original expression provided in Kitamu[30] by a factor of 0.01.

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paths suggested by Colket and Hall[53]. The surfacegrowth mechanism includes possible acetylene eination from the soot radical (reaction G3) and serates the acetylene addition process into a reversformation of the radical adduct (reactions G4f aG4b) and a cyclization reaction (reaction G5). Trates for soot oxidation by O2 and OH are taken fromAppel et al.[22] and Neoh et al.[54], respectively.The modification of the preexponential factor for raction G3 is based on the results of the sensitivityvalidation studies. Details are presented below.

The contributions of soot growth and oxidationthe soot moment equations are calculated usingreaction mechanism inTable 1, along with the expression

(11)GXk =

∞∫0

vki kX[X]αχSSini dvi,

wherekX is the per-site rate coefficient,[X] is theconcentration of the gaseous species involved insurface reactions,α is the fraction of surface siteavailable for reaction,χS is the number density of suface sites,Si is the surface area of theith soot particle,andni is the particle size distribution function defineby the log-normal size distribution.

2.4. Particle growth by coagulation

Soot particle growth by collision is modeled usiSmoluchowski’s equation[55],

Ck =∞∫

0

vki

1

2

vi∫0

β(vj , vk)nj nk dvj dvi

(12)−∞∫

vini

∞∫β(vj , vi)nj dvj dvi,

0 0

whereβ(vj , vi) is the collision frequency betweesoot particles,ni and nj are the number densitieof soot particles of volume (size)i and j , respec-tively, andvi andvj are the volumes of soot particleof size i and j , respectively. Soot exhausted froautomotive engines is known to be in the transitregion between the free molecular and the conuum regimes[12,17,55]. The coagulation rate in thtransition regime is typically determined using anterpolation formula. Here we use a continuum meapproximation[56],

(13)Ck = CgkCf

k

Cgk

+ Cfk

,

whereCk is the coagulation rate for thekth soot mo-ment andCf

kand C

gk

represent the coagulation ratfor thekth soot moment in the free molecular regimand the gas-slip regime, respectively. As dictatedthe size of the soot particles, the collision frequencthe free molecular regime,βF, and the gas-slip regimβG [56] are determined using the following relation

(14)βF(vi , vj ) = KF

(1

vi+ 1

vj

)0.5(v

1/3i

+ v1/3j

)2,

βG(vi , vj ) = KG(v

1/3i

+ v1/3j

)(15)× (

C(vi)v−1/3i

+ C(vj )v−1/3j

).

In Eqs. (14) and (15), KF = (3/4π)1/6√6kBT/ρ,

KG = 2(kBT/3µ), andC(v) = 1 + 1.257Kn, whereKn is the Knudsen number.

2.5. Soot particle transport

Although soot transport does not play a role inmodel optimization and validation studies presenin the next section, the soot particle transport has b


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identified as a key component to accurate soot moing in engine studies[34]. Therefore, a brief description of the representation of the soot particle transpis provided here. Additional details are providedHong [35]. The soot transport model is used in susequent engine simulation tests discussed in asection of this work.

When soot particles are in the transition regibetween continuum and free molecular flow, adtional soot transport equations are required due tovelocity slip between the soot particles and themedium. The soot particle transport equation ispressed as

(16)∂Mk

∂t+ �∇ · (�vMk

) = �∇(D �∇Mk

) ˙Sk,

where Mk is the kth mean soot moment,�v is theflow velocity vector,D is the sum of the turbulensoot diffusivity and the diffusivity due to velocit

slip, and ˙Sk represents the various source and sterms for thekth moment (e.g., nucleation, oxidtion, etc.). The turbulent soot diffusivity dependsparticle size and appropriate expressions for themolecular and transition regimes are used[57]. Ther-mophoretic forces on the soot particles are includethe soot transport modeling via calculation of a thmophoretic velocity after the approach describedHinds[55].

3. Model calibration

The following procedure was used to calibratesoot model and to validate the model beyond theibration conditions. The experimental results of tshock-tube study by Kellerer et al.[33] were used tooptimize the soot model in terms of three key paramters: the correction factor,AC, used in the nucleatiomodel (Eq.(10)), the rate coefficient of the surfacreaction G3 (Table 1), and the size of the primarsoot particles. The optimization of these paramewas determined via a detailed sensitivity analysisthe soot model. Once the optimal values weretermined, the parameters were fixed at these vafor the remainder of the model validation and engstudies.

In the shock-tube study by Kellerer et al.[33], timehistories of soot carbon yield (defined as the ratiothe total carbon present in the soot particles tototal carbon available in the mixture, Csoot/Ctotal),soot number density, and mean soot particle diamwere determined for richn-heptane mixtures, highldilute in argon. These time-resolved measuremeare presented by Kellerer et al. for one set of expimental conditions (P = 25 MPa,T = 1750 K,[C] =7.89 mol/m3, and φ = 5). As we found no othe

time-resolved soot data available in the literaturen-heptane, these conditions were used as the basoptimizing the transient behavior of the soot modThe temperature dependence of the soot modelcalibrated using the overall measurements of syield presented in the same work. The soot yield msurements were obtained at conditions 1.5 ms athe passage of the reflected shock wave and thesults span the temperature rangeT = 1600–2000 Kand three pressures (20, 40, and 80 MPa). For theperature calibration of the soot model, only the resof theP = 40 MPa conditions were used. A descrtion of the sensitivity analysis, calibration proceduand validation results follows.

The soot model and the gas-phase reaction manism were implemented in a homogeneous exsion problem configuration for the model calibratiand validation. The initial conditions for the mixtucomposition were matched to the experimental indata. Throughout the reaction progress, adiabaticditions with constant volume were assumed.

After numerous parametric studies, it was fouthat the rate coefficient for the surface reaction Gthe size of the soot primary particles, and the nuation rate correction factorAC were the soot modecharacteristics that were both the most uncertainexhibited the strongest influence on the soot moing results at the calibration conditions. Although tsensitivity analysis showed that results of changthe values of these parameters are coupled, the efof the rate of the surface growth reaction G3 exhited the most dramatic influence on the temperadependence of the soot yield.

Fig. 1 shows the results of changing the preexnential factor(AG3) for reaction G3 for the temperature range 1300–2100 K. Physically, increasingvalue forAG3 reduces soot surface growth for exiing particles while simultaneously releasing acetylewhich can be used to nucleate new primary soot pticles. When the reaction was not included in the sface mechanism(AG3 = 0), the overall soot yield wasignificantly higher than the experimental data andmaximum soot yield was obtained atT > 2200 K.When the rate coefficient for G3 was set at the vaprovided by Kitamura et al.[30] (AG3 = 3 × 1014),the soot particles experienced such rapid eliminaof C2H2 and corresponding loss of surface growsites, that the overall soot yield was significanlower than the experimental values. In addition,AG3 = 3 × 1014, the maximum soot yield was obtained at a temperature lower than 1500 K. Basedthe two limiting results and further parametric stuies, it was found that reducingAG3 by a factor of0.01 (AG3 = 3 × 1012) resulted in reasonable quaitative agreement with the experimental data in terof temperature dependence and acceptable qua


t

Fig. 1. The effect of the soot surface reaction G3 on soot yield as a function of temperature (t = 1.5 ms,P = 4 MPa,AC = 0.01,and a primary soot particle size of 32C).

Fig. 2. Comparison of the experimental results of Kellerer et al.[33] and the modeling results (AG3 = 3× 1012) of the presenstudy for soot yield at conditions ofP = 2.5 MPa,T = 1750 K, [C] = 7.89 mol/m3, andφ = 5. Sensitivity of the modelingresults to the size of the primary soot particles is presented.

ee

ootheonootto-d intalicle

of

,

m-

avents.

ereotent

ientultstita-ticlearyiredform-

thel,

tive agreement in terms of the overall soot yield (sFig. 1).

After the temperature dependence of the smodel was optimized for soot yield at 40 MPa, teffects of the size of the primary soot particlesthe quantitative agreement with the soot yield, snumber density, and soot particle-size time hisries were investigated. The results are presenteFigs. 2–4, showing a comparison of the experimenand predicted results for soot yield, average partdiameter, and soot number density as a functiontime using the optimized value forAC (discussedbelow) andkG3 for conditions of 25 MPa, 1750 K[C] = 7.89 mol/m3, and an equivalence ratio,φ = 5.In the figures,t = 0 s represents the start of the si

ulation and the time when the reflected shock wpasses the measurement point in the experimeTwo primary soot particle sizes, 2C and 32C, wconsidered.Figs. 2–4show that the predicted soproperties are in reasonable qualitative agreemwith the experimental data, reproducing the transresponse of the system quite well. The model resalso indicate there is a trade-off among the quantive agreement among the soot yield, the soot pardiameter, and the number density. For smaller primsoot particles (2C), fewer soot monomers are requto form a primary soot particle. Consequently,an equivalent number of monomers, the soot nuber density for the 2C model is larger than that for32C model (seeFig. 4). Relative to the 32C mode


age

oot

Fig. 3. Comparison of the experimental results of Kellerer et al.[33] and the modeling results of the present study for aversoot particle diameter corresponding to the experimental and simulation conditions ofFig. 2.

Fig. 4. Comparison of the experimental results of Kellerer et al.[33] and the modeling results of the present study for snumber density corresponding to the experimental and simulation conditions ofFig. 2.

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the 2C model also results in a smaller averageticle size due to the abundance of smaller partic(seeFig. 3) and more soot surface area availablesurface interactions. The quantitative agreementtween the model predictions for soot yield andexperimental data is improved for the smaller 2C pticle size; however, this is at the expense of increadiscrepancies between the 2C model and experimtal results for the average soot particle diameterthe soot number density. Overall, a primary soot pacle size of 32C was chosen in subsequent calculatin favor of the physical basis for this primary parcle size (i.e., representing the collision of two pyremolecules) and as a compromise between the tsient soot properties under the calibration conditio

The sensitivity of the nucleation submodel corretion factor, AC, on the quantitative agreement withe soot yield, soot number density, and soot parti

size time histories was also investigated. Increasthe correction factor increases the nucleation ratthe soot primary particles, which in turn yields ancrease in the number density of soot particles andecrease in the average particle size. Similar toeffect of changing the size of the primary soot pacle, changingAC led to a trade-off in the agreemebetween the experimental and the modeling resSpecifically, increasing the correction factor ledimproved quantitative agreement with the soot yiebut degraded the quantitative agreement with the aage particle size and number density. Based on tparametric tests,AC = 0.01 was found to be an optmal compromise. ChangingAC had a minor effect onthe temperature dependence of the soot model.

Fig. 5provides the overall performance of the somodel under the calibration conditions over a widrange of temperatures. In the figure, the performa


Fig. 5. Comparison of the performance of the current soot model and the soot model developed by Kitamura et al.[30]. Theexperimental results of Kellerer et al.[58] are shown in the upper graph. The experimental results of Kellerer et al.[33] areshown in the lower graph. (Upper graph) Benzene oxidation withφ = 5, Ar = 99.5%, andP = 3 MPa (Fig. 8 of Kitamuraet al.[30]). (Lower graph)n-Heptane oxidation withφ = 5, [C] = 5.8 mol/m3, andP = 4 MPa.

ters-ce

meure-eults

, thebleetorst,ofothex-

ch-delis

ootzed

on

geare-sedera-thetedly

on-n-

ootted

ure-sure

nto-tryra-algh-thes,om-

of the current model using the optimized parame(i.e.,AC = 0.01,AG3 = 3× 1012, and a primary particle size of 32C) is compared with the performanof the soot model developed by Kitamura et al.[30].Note that the Kitamura model results for soot volufraction are compared with the experimental measments of Kellerer et al.[58] obtained from benzenoxidation shock-tube experiments. Benchmark resfrom the Kitamura model for soot formation fromn-heptane are not available. On an absolute basissoot model developed in this study is in reasonaquantitative agreement with then-heptane shock-tubstudies, and the model predictions are within a facof 5 for temperatures less than 1900 K. In contrathe Kitamura model results differ by over an ordermagnitude under some temperature conditions. Bmodels underpredict the soot levels relative to theperimentally determined values.

4. Model validation

Having calibrated the soot model under the benmark conditions, the performance of the soot mofor conditions outside the optimization boundsconsidered next. For the following results, the smodel parameters were fixed under the optimiconditions ofAC = 0.01, AG3 = 1 × 1012, and aprimary soot particle size of 32C. The simulati

and experimental results for soot yield for a ranof temperatures and pressures of 2 and 8 MPashown in Fig. 6. The simulations correctly reproduce the experimentally observed trend of increasoot formation with increased pressure. The tempture dependence is also well produced; however,maximum soot yield occurs at temperatures shifto slightly higher temperatures (by approximate100 K) than those observed experimentally. Csistent with the results under the calibration coditions (4 MPa), the model underpredicts the syield. These results demonstrate that the calibrasoot model has the predictive capability to captthe soot formation characteristics ofn-heptane combustion for a wide range of temperature and presconditions.

5. Engine simulation results

The calibrated soot model was integrated iKIVA-3V engine simulations ofn-heptane combustion. The simulation conditions and engine geomewere selected to match the experimental configution of a single-cylinder version of an Internation4.5L V6 diesel engine equipped with a Siemens hipressure common-rail injection system. Details onengine testing facility, the KIVA input parameterand the other submodels (such as the spray and c


redictionsdoes not

the effect

Fig. 6. Comparison of the results of the optimized soot model with the experimental results of Kellerer et al.[33] for soot yieldas a function of pressure and temperature for conditions ofP = 2 and 8 MPa,[C] = 5.8 mol/m3, andφ = 5.

(a) Start of injection vs EGR (b) Speed vs equivalence ratio

Fig. 7. Engine operating conditions considered for comparison of experimental soot measurements and numerical pfor soot emissions. Here, the equivalence ratio is defined based on the fuel-to-air ratio in the fresh-air charge only, andinclude the effect of EGR addition.

Table 2Engine simulation conditions

Case SOI (◦ ATDC) EGR (%, mass basis) Speed (rpm) φa

1 −11.1 26.90 1500 0.752 −7.0 25.00 1500 0.743 −3.4 25.77 1500 0.744 2.1 25.85 1500 0.735 2.4 16.41 1500 0.62

a Here, the equivalence ratio is defined based on the fuel-to-air ratio in the fresh-air charge only and does not includeof EGR addition.

tedd initedur-

tion

nd

edGR

ereonsions

bustion models) are provided in Hong et al.[59–61].The simulation conditions studied were selecbased on conditions that are frequently encounterethe Federal Testing Procedure defined by the UnStates Environmental Protection Agency for measing emissions for a mid-size truck[62]. The specificcases considered in terms of exhaust gas recircula

(EGR) loadings, injection timing, engine speed, aoverall equivalence ratio are shown inFig. 7 andTa-ble 2. For this work, all simulations were conductat the same engine speed (1500 rpm), while the Eloading, equivalence ratio, and start of injection wvaried. These engine settings include the conditithat are the highest contributors to the soot emiss


s 2 and 4.

Case 2

Case 4

Fig. 8. Comparison of experimental and predicted results for pressure as a function of crank angle degree (CA) for Case

id-

ionh isC).

e-ac-ix-edal.isy

e in,ula-

arere-

these

ryt

ntalDCandver aal.

ol-on-glere-the

for the engine considered when configured in a msized truck.

For the engine simulations, the diesel combustis represented by a newly developed model whicbased on a modified eddy dissipation concept (EDBriefly, the modified EDC model allows for more ralistic representation of the thin subgrid scale retion zone as well as the small-scale molecular ming processes. A detailed description of the modifiEDC modeling approach can be found in Hong et[59,61]. The soot model is directly integrated into thmodified KIVA 3V program, with no changes to anof the submodel (e.g., soot, NOx, or EDC combus-tion) parameters. The soot calculations are mada manner similar to the NOx emissions calculationsas a postprocessing procedure after the EDC calctions are completed at each time step.

The engine simulation results for pressurecompared with the experimental data for two rep

sentative conditions (Cases 2 and 4) inFig. 8. Thenet apparent heat release rates corresponding toconditions can be found in Hong et al.[59]. Cases 2and 4 are indicative of operating conditions with vedistinct ignition profiles due primarily to the differeninjection timings (−7.0◦ ATDC for Case 2 and 2.1◦ATDC for Case 4). As seen inFig. 8, the model pre-dictions are in good agreement with the experimedata for both test cases. Details of the modified Ecombustion model and a comparison of measuredpredicted cycle pressures and heat release rates owide range of conditions can be found in Hong et[59,61].

Fig. 9presents simulation results for the soot vume fraction with the corresponding temperature ctours and velocity vectors as a function of crank anfor conditions defined by Case 2. The simulationsults for the soot number density with overlays ofO2 contours are also provided inFig. 9. The fuel spray


injectionature.he figure

Fig. 9. Instantaneous simulation results as a function of crank angle obtained for Case 2 operating conditions (start of= −7◦ ATDC, 1500 rpm, EGR= 25%,φ = 0.74). The column on the left provides soot volume fraction data with tempercontour and velocity vector overlays. The column on the right provides soot number density data with O2 contour overlaysThe modeling results were obtained using the optimized input parameters. The scales provided on the far right of tapply to all images inFig. 9, where sm0= soot number density [1/cm3], sm1= soot volume fraction [dimensionless], temp=temperature [K], o2= O2 mass concentration [g/cm3].

rgeheid

s in

c-ng

nd

-thex-

wo

motion imparts momentum to the surrounding chain the cylinder, while the upward movement of tpiston amplifies the angular momentum of the flunear top dead center (TDC). As seen in the figurethe left column ofFig. 9, the interaction of the twoflows induces a vortex motion in the clockwise diretion. The vortex flow drives the soot particles alo

the piston bowl surface, and the particles grow aoxidize during transport.

In addition to the clockwise vortex flow, flow toward the squish region is an important motion incylinder affecting the soot formation, growth, and oidation processes. As seen inFig. 9, as the pistonmoves downward, the soot cloud is divided into t


f injectionature

ure apply

Fig. 10. Instantaneous simulation results as a function of crank angle obtained for Case 4 operating conditions (start o= 2.4◦ ATDC, 1500 rpm, EGR= 26%,φ = 0.73). The column on the left provides soot volume fraction data with tempercontour and velocity vector overlays. The column on the right provides soot number density data with O2 contour overlays. Themodeling results were obtained using the optimized input parameters. The scales provided on the far right of the figto all images inFig. 10, where sm0= soot number density [1/cm3], sm1 = soot volume fraction [dimensionless], temp=temperature [K], o2= O2 mass concentration [g/cm3].

texonot

owl

w-ionish

sections; one is transported by the clockwise vorflow and the other is transported by the flow motitoward the squish region. Initially, comparable sovolume fractions are predicted in the squish and b

regions of the cylinder. At later crank angles, hoever, the oxidation process is slow in the squish regand higher soot volume fractions exist in the squregion compared to the bowl region (Fig. 9d).


aximumaximum

Fig. 11. Comparison of experimental and predicted soot emissions. All “experiment” data are normalized by the mexperimental value of soot mass measured for Case 3 conditions, and all “prediction” data are normalized by the mpredicted value for soot mass calculated for Case 3 conditions.

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Fig. 10presents simulation results for conditiocorresponding to a later injection timing (Casecompared to theFig. 9simulation results (Case 2). Fothe late injection, high soot volume fractions are pdicted at later crank angles (seeFig. 10, CA = 22.5◦ATDC). The general features of the Case 4 simulatresults are similar to the early injection timing resuwith two regions of high soot number density affectby the vortex and squish flow motions. An importadifference between the results is the smaller regiohigh temperatures identified in the late injection tiing conditions (Figs. 10b and 10c). This is a key re-sult, asFigs. 9 and 10show that the high-temperaturegions (shown as contour overlays) always boundregions of high soot volume fraction. Although nshown for clarity, the OH contours also exhibit similcharacteristics, i.e., high OH levels bound the regiof high soot loadings. This result is in good quatative agreement with the experimental investigatby Dec and Tree[63], who also found that regions ohigh soot levels were enveloped by clouds of high Olevels.

As an indication of the computational costs assoated with this comprehensive level of soot modelithe simulation results shown inFig. 9 required ap-proximately 4–5 days of computational time usia Linux system, Intel Pentium 4 2.8 GHz proceswith 1 GB of RAM. Thus, parametric studies canconducted in a reasonable amount of time. In twork, the overall soot emissions (soot mass percle) were examined for a range of injection timin(−11–2.5◦ ATDC) and two exhaust gas recirculatio(EGR) levels (16, 26–27%) levels. Predictions ofgeneral combustion characteristics such as cylinpressure and heat release agreed very well with

experimental engine data for these parametric stu(for details, see Hong et al.[59,61]).

In Fig. 11, simulation and experimental results fthe particulate emissions are summarized. The eximental soot measurements are presented as noized soot mass based on the measured AVL smnumber, where the AVL correlation for convertinsmoke number to soot mass concentration has bused [64]. The simulation results are in excelleagreement with the qualitative trends observed indiesel engine study, demonstrating the predictivepability of the soot model in full-cycle engine simultions.

The results of more extensive engine simulatioand comparisons with experimental data can be foin Hong et al.[61]. This work includes additional engine operating conditions and soot and NOx emissiondata. Explanation of observed trends for the engstudies can also be found in Hong et al.[61].

6. Conclusions

The present work is an advance in modeling sformation within the framework of widely used egine simulations, such as KIVA-3V, using more reistic physical and chemical bases. The level of epiricism used in the model is significantly reducfrom that of previous engine soot modeling studiwhile simultaneously maintaining reasonable coputational costs. The soot modeling approach shgood ability to reproduce the transient featuresserved in shock-tube time histories of richn-heptanemixtures of soot carbon yield, particle diameter, anumber density. This ability to accurately model tra


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sient soot phenomena is critical for engine simutions, as demonstrated by the crank-angle-resodata presented in this work. The model also repduces the experimentally observed trends for syield in shock-tube studies as a function of tempature and pressure. The quantitative agreementtween the optimized soot model is substantially iproved over the previous breakthrough work by Kimura et al.[30], which uses a similar soot modelinapproach.

Application of the soot model to engine simultion studies has been successfully demonstratedcomparisons of the computational predictions for nmalized soot mass are in excellent agreement wexperimentally observed trends in smoke numbThe engine simulation results also confirm the cical need to accurately account for particle transpin soot modeling studies. Because the soot modebased on the fundamental phenomena importansoot formation, this model has considerable potenas a powerful new tool to lend insight into the phycal and chemical mechanisms limiting soot emissiin diesel engines.

Acknowledgments

The authors sincerely thank Dr. Eric Kurtzthe Ford Motor Company for providing the engismoke data. This work has been supported and funthrough an Agreement (Simulation Based DesignDemonstration of Next Generation Advanced DieTechnology, Contract No. DAAE07-01-3-0005) btween TACOM (U.S. Army Tank-Automotive and Amaments Command), Ford Motor Company, Univsity of Michigan, and International Truck and EngiCorporation.

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