07NAPLES-90

Comparison of Combustion and Pollutant Emission Models forDI Diesel Engines

G. D’Errico, D. Ettorre, T. LucchiniPolitecnico di Milano, Dipartimento di Energetica - Milano, Italy

Copyright c© 2007 Society of Automotive Engineers, Inc.

ABSTRACT

The increasing interest in the Diesel engine technologyand the continuous demand of reducing fuel consumptionand emissions has motivated over the years thedevelopment of advanced numerical models, to providequalitatively predictive tools for the designers (injectionstrategy, flow optimization, EGR level, combustionand emission control) and investigation tools forthe researchers to complement optical diagnostics.Nevertheless, there is not a common agreementabout many fundamental phenomena which have beenextensively investigated (turbulence-chemistry and flame-wall interactions, pollutant formation, very lean and veryrich combustion) and each model has been implementedinto different codes and validated with respect to differentoperating conditions.

In this work two significant approaches with different levelof complexity for Diesel combustion modelling have beenanalyzed and implemented by the authors in the sameopensource code, OpenFOAM: the Eddy Dissipationmodel and the PaSR (Partially Stirred Reactor) model.For what regard the latter, the potentialities and accuracyof the ISAT (In-Situ Adaptive Tabulation) algorithm,recently implemented by the authors into OpenFOAM, toreduce significantly the required computational time wereevaluated. Similarly, different models to predict pollutantemissions are revised and tested, due to considering theneed to fulfil the future emission regulations imposingfurther reductions in NOx and soot.

The mentioned models were applied to simulatea selection of significant Constant-Volume DieselCombustion test-cases from the Engine CombustionNetwork database [1]. These data are particularly worthof interest since they have a public domain access,

providing a framework for collaborative comparisons,and they include detailed information about pressurerise, liquid penetration length, ignition delay, lift-offlength and soot distribution. The selected and simulatedconditions consider n-heptane as fuel and includedifferent oxygen concentrations and thermodynamicstates (ambient density and temperature). Finally a realengine configuration was considered and the obtainedresults were compared against cylinder pressure dataand pollutant concentrations.

INTRODUCTION

The development and assessment of a CFD methodologyand its implementation into a numerical simulation toolkitspecifically tailored for engine simulation represents avery challenging task. In particular Diesel enginemodelling requires to describe into details manysimultaneous interacting thermofluids and chemicalprocesses, which take place in a domain with a complexgeometry and moving boundaries. On the modellingfront, the task is to assemble a complete and accuratedescription of the involved physical process, while on thenumerical viewpoint, the challenge is the developmentof flexible and efficient algorithms with respect to theimplementation of the model equations and to thedescription of the engine geometry [2]. The objectiveto aim at is the definition of a reliable CFD code whichcan be used as a predictive tool from a qualitativeviewpoint in a design stage and as a diagnostic tool toachieve a deeper understanding of the occurring physicalphenomena. Within this context, in recent works [3, 4]Reitz et al. compared three different Diesel combustionmodels, all implemented into a modified version of theKIVA-3V code, underlying the importance of uniqueCFD tool to be used to simulate identical conditions bymeans of different approaches. Similarly, Venugopal and

Abraham [5] extensively reviewed different approaches tomodel flame lift-off, showing how at the moment noneof the available models may be completely adequate,but any simulation result is obviously dependent onthe code implementation and case set-up. Howeverthe implementation of a new model by a sequentialprogramming language is extremely time consuming,requiring significant modifications in numerous parts ofthe code.

The last and less obvious challenge to CFD simulation isthe availability of suitable experimental data to guide thedevelopment and assess the accuracy of the proposedmodels [2]. In this field, a significant contribution isrepresented by the Engine Combustion Network database[3], which aims at establishing “an internet library ofwell-documented experiments that are appropriate formodel validation and the advancement of scientificunderstanding of combustion at conditions specific toengines“.

On the basis of the above mentioned considerations, theauthors intend to contribute to develop a CFD platformfor the simulation of internal combustion engines, whosefundamental prerequisites are the following:

• to be written in an highly efficient object-orientedprogramming to allow an easy implementation andtesting of new models;

• to be opensource to allow collaborative studiesregarding both the model implementation andvalidation (any CFD result often depends on severalparameters whose set-up should be of public domainfor model assessment).

To these ends, the authors have contributed over the lastyears to the development and application of the multi-purpose CFD code OpenFOAM [6, 7]. In this paper,the state of the art of the code regarding Diesel enginemodelling is discussed, including recent enhancementintroduced by the authors, and an initial comparisonamong combustion and emission models of differentcomplexity, applied to simulate a selection of availableSandia vessel measurements [1] and some operatingpoints of a commercial Diesel engine.

In the following sections a brief overview of the adoptedphysical models to describe Diesel spray evolution,combustion and emission formation is given, discussingin some detail the different approaches to model theturbulence-chemistry interaction and the soot formation.Successively the class definition to model Dieselcombustion is presented, to illustrate the advantages ofobject orientation when complex and interacting physicalmodels need to be implemented.

DIESEL SPRAY MODEL

The Eulerian-Lagrangian approach is used [8, 9] tomodel the fuel-air mixture formation in direct-injectionengines. To calculate the evolution of the spray into the

gaseous atmosphere, two phases need to be described:the dispersed liquid and the continuous gas phase,which interact each other according to their exchangesof mass, momentum and energy. The gas phase isdescribed using the Navier-Stokes equations, while theLagrangian formulation describes the evolution of themulti-component liquid phase. The spray is representedby points, often referred to as parcels. These pointsare then assigned properties which may be as manyas desired, like location, velocity, diameter and fuelcomposition [9, 10]. Different sub-models are then usedto describe liquid fuel injection, primary and secondarybreakup, droplet evaporation, heat-exchange, collisionsand turbulent dispersion.

OpenFOAM has been recently used for Lagrangianspray modelling and further details about experimentalvalidations and implementation can be found in [9, 11,12, 13]. The code already includes most of the widelyused sub-models for spray breakup, fuel injection, dropletcollisions, evaporation and turbulent dispersion. In thiswork, a constant spray angle is assumed, while theinitial droplet diameter is derived by the injector diameterand its area contraction coefficient [9]. Both the Kelvin-Helmoltz and Rayleigh-Taylor mechanisms are accountedfor to model the spray breakup [14]. The Ranz-Marshallcorrelation [15] is used to model the droplet evaporation.Droplet to droplet interactions and turbulence dispersioneffects are neglected. The reader is also referred to [9] forfurther details.

COMBUSTION MODELS

The two different combustion models evaluated in thiswork will be now presented. The first one is basedon the Eddy Dissipation Model and it can be usedas a development tool since its limited computationaldemand. The second one is the Partially Stirred ReactorCombustion model [16] and uses complex chemistry tomodel ignition and mixed-controlled combustion. Forthese reasons, it requires higher computational time thanthe first approach and is more suitable for diagnosticpurposes. However, it provides a better insight of thecombustion process taking place during the ignition andcombustion phases. For both the approaches, the RNGk − ε is used to model turbulence as suggested in [4, 9].

MODIFIED EDDY DISSIPATION MODEL

In Diesel engine combustion, the fuel is injected into thehot, compressed air and auto-ignition plays an importantrole in the combustion and flame stabilization processes.After ignition, combustion is generally mixing-controlled[17]. For these reasons, the fuel reaction rate can beexpressed as:

ωF = (1 − α) ωF,ign + αωF,mix (1)

where α is used to switch from the auto-ignition (α =0) to the mixing-controlled combustion mode (α = 1).Expressions for both ωF,ign and ωF,mix are thus required.

Auto-ignition: When the fresh gases are ignited, all thefuel contained in a computational cell is burned. HenceωF,ign is equal to:

ωF,ign = YF /∆t (2)

where YF is the fuel mass fraction and ∆t is thecomputational time-step at the ignition time. Following theapproach of Pires De la Cruz [18], a self-ignition progressvariable YI monitors how close the fresh gases are fromigniting. The average value of the progress variable istransported through convection and diffusion inside thecombustion chamber according to the equation:

∂ρYI

∂t+

∂

∂xi

(ρuiYI

)=

∂

∂xi

(ρDt

∂YI

∂xi

)+ ωI (3)

The rate of growth of the progress variable YI isproportional to the amount of the fuel tracer YT,fu in themixed zone and is a function of the local self-ignitiondelay, which depends on the fresh gas thermodynamicconditions. The fuel tracer represents the amount of freshmixed fuel that would exist in the computational cell inabsence of chemical reactions. It is a passive scalarbecause, by definition, it is neither consumed nor createdby chemical reactions.

The rate of growth of YI is equal to [18]:

ωI = ρYT,FuF (τd) (4)

which is valid until YI < YT,Fu. From the definition ofthe progress variable, the self-ignition delay τd in thepreceding conditions is given by:

∫ τd

0

F (τd) = 1 (5)

F (τd) is defined as:

F (τd) =1

τd(6)

τd represents the ignition delay as a function of thelocal thermodynamic conditions in each cell (pressure,temperature, air/fuel ratio, . . . ).

The ignition delay in the computational cell is reachedwhen YI ≥ YT,Fu. After ignition, the fuel burns accordingto the Equation 2 and α is set to one since the combustionbecomes mixing-controlled.

The ignition delay τd is estimated according to anAhrrenius correlation [19]:

τd = Ap−nexp(Ea/RT ) (7)

The Eddy Dissipation Model (EDM) by Magnussenand Mjergarter [20] estimates the mixing-controlled fuelburning rate ωF,mix from fuel (YF ), oxidizer (YO) andproduct mean mass fractions (YP ) and depends on the

turbulent mixing time, estimated from integral lengthscales as τt = k/ε:

ρωF,mix = Cmagρε

kmin

(YF ,

YO

s, β

YP

(1 + s)

)(8)

where Cmag and β are two model constants. In Equation8, the reaction rate is limited by the deficient mean specie.When β is finite, this deficient species may be combustionproducts to take into account the existence of burnt gases,providing the energy required to ignite fresh reactants.

Coupling the Eddy Dissipation Model for mixing-controlledcombustion with an ignition treatment makes it possible topredict both ignition and flame stabilization since fuel andoxidizer do not immediately ignite as soon as they meet[17].

PARTIALLY STIRRED REACTOR MODEL

Chomiak, Golovichev et al. [16, 21, 22] applied detailedkinetics and the Partially Stirred Reactor concept (PaSR)to correctly describe the turbulence/chemistry interactionin Diesel spray combustion.

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C

κ

C 0 C 1

Figure 1: Conceptual picture of the Partially Stirred Reactor.

In the PaSR approach, a computational cell is split intotwo different zones: in one zone all reactions occur,while in the other one there are no reactions. Thus,the composition changes due to mass exchange withthe reacting zone. Furthermore, the reacting zone istreated as a Perfectly Stirred Reactor (PSR), in which thecomposition is homogeneous. According to the PaSRconcept, the concentration of each species i at the exitof reactor can be defined as:

ci1 = κ∗ci + (1 − κ∗) ci

0 (9)

where κ∗ is the mass fraction of the mixture which reacts.As shown in Figure 1, the model distinguishes betweenthree molar concentrations:

• ci0 is the averaged concentration in the feed of the

cell and may be considered as the initial averagedconcentration in the cell;

• ci is the unknown concentration in the reaction zoneon a sub-grid level in the unknown reactive fraction ofthe cell material;

• ci1 is the sought for, time-averaged exit concentration.

This is also the averaged concentration in the cell;

According to Equation (9), ci1 is a linear interpolation

between ci and ci0 and the whole combustion process can

be split in two sub-steps, proceeding in parallel (see alsoFigure 2):

1) The initial concentration in the reaction zone changesfrom ci

0 to ci;

2) The reactive mixture ci is mixed by turbulence with ci0

resulting in the averaged concentration ci1.

C0

C1

C

f(c)I

II

time

conc

entr

atio

n

τ τmix

Figure 2: The reaction/mixing step procedure.

Since ci1 is the initial value for the next time-step, the

time between ci0 an ci

1 must be the integration step, τ .The turbulence mixes c with ci

0, hence the time differencebetween ci and ci

1 must be the characteristic time forturbulence, τmix. Assuming that the slope of the curve inFigure 2 is equal to the reaction rate in the reaction zone,it results:

ci1 − ci

0

τ=

ci − ci1

τmix= f

(ci); κ∗ =

τ

τ + τmix(10)

f(ci)

is the reaction rate of the species i during the time-step τ which is calculated according to Equation 21. Toobtain c1, it is now necessary to eliminate c in Equation9. Using the Taylor expansion, the term f

(ci)

can beexpressed as:

f(ci)

= f(ci1

)+

∂f

∂c

∣∣∣c=ci

1

(ci − ci

1

)(11)

The term∂f∂c is assumed to be the reciprocal of a chemical

time scale:1

τc= −

∂f

cr(12)

and is calculated in this work as:

∂f

∂c

∣∣∣c=ci

1

=ω(ci1

)− ω

(ci0

)

ci1 − ci

0

(13)

where ω(ci1

)and ω

(ci0

)are the reaction rate expressions

of the species i calculated at the beginning and at the endof the time step. Thus, Equation 11 becomes:

f(ci)

= f(ci1

)−

ci − ci1

τc. (14)

Substituting the expression of τc in Equation 9 thefollowing expression is finally obtained for the sub-gridreaction rate:

ci1 − ci

0

τ=

τc

τc + τmixfm

(ci1

). (15)

The reactive fraction κi becomes equal to:

κi =τc

τc + τmix(16)

Several expressions were proposed for the mixing timeτmix [16, 22]. In this work, it is assumed to be proportionalto a geometric mean of the Taylor and Kolmogorov times:

τmix = Cmix√

τtτk (17)

where Cmix is a tuning constant.

For each chemical species, the following transportequation, containing the turbulence-chemistry interactionhas to be solved:

∂ρYi

∂t+

∂

∂xi

(ρuiYi

)=

∂

∂xi

(ρDt

∂Yi

∂xi

)+ κiωi (18)

i = 1, . . . , Nsp

where ωi is equal to f(ci1

)and represents the reaction

rate of the species according to the used kineticmechanism; Nsp is the number of chemical speciesinvolved.

IN-SITU ADAPTIVE TABULATION (ISAT)

The PaSR concept introduces the complex chemistry inthe specie transport equation. This increases significantlythe computational time, in fact the CFD time-step ismuch larger than the chemical one and for this reasonit is appropriate to employ an operator-splitting approachwhere the change in composition resulting from the CFDtimestep is evaluated separately from the contributions ofadvection and diffusion, and to subcycle the chemistryover the CFD timestep. An ODE stiff solver integrates thearray of the compositions C over the CFD time-step as afunction of their reaction rate S:

C (t0 + ∆t) = C0 (t0) +

∫ t0+∆t

t0

S (C, T, p) dt′. (19)

The reaction mapping R (C0) is thus defined as:

R (C0) = C0 (t0) +

∫ t0+∆t

t0

S (C, T, p) dt′. (20)

The chemical source term in Equation 18 is thendetermined as follows:

ωi =C (t0 + ∆t) −C0 (t0)

∆t. (21)

To correctly calculate ωi, a system of Np stiff and non-linear differential equations should be solved for each cellat each time-step. At present, the existing computational

techniques and computer memory limitations prohibitimplementation of fully detailed description of combustionchemistry into CFD simulation of complex flow patterns.

Several approaches based on tabulation of the reactionrates were proposed in the past to significantly reducethe computational time [18, 23] by using tabulatedreaction-rates. However, the exploration of chemicallook-up tables which take into account more than twoor three coordinates may become prohibitive in termsof computational costs (memory access and multilinearinterpolations). On the other hand, only a very small partof the table is generally used during the simulation sinceonly a small part of the composition space is accessed.To overcome these difficulties, Pope and Young [24, 25]propose to build the chemical table as needed on-the-flyduring the computation (in situ).

Each table entry contains the thermochemicalcomposition (C0, T, p), the reaction mapping R (C0) andthe mapping gradient A (C0) = (∂Ri (C) /∂ci) measuresthe sensitivity of the reaction mapping to changes incomposition and provides the coefficients required forlinear interpolations. The entry is complemented with thesize of the region of accuracy where a reaction mappingmay be estimated from this entry by a linear interpolationwith an error below a tolerance εtol assigned by the user.When the reaction mapping R (Cq) is required for a querycomposition C

q, the closest composition C0 in the table

is first determined trough a binary tree, whose structureis shown in Figure 3.

Leaf (Ci, T, p)

Root

Nodes

Figure 3: Binary Tree used to store the tabulated thermo-chemical states.

Three actions are then possible:

• If Cq lies in the region of accuracy of the existing tableentry C

0, a simple linear interpolation is performed(retrieve).

R (Cq) = R(C

0)

+ A(C

0) (

Cq − C

0)

(22)

• If Cq is outside the region of accuracy of

the table entry C0, R (Cq) is determined by

integration of Equation 19 and is compared tothe linear interpolation of Equation 22, providingthe corresponding error ε. Two cases are thenconsidered:

– If the error ε is lower than the tolerance εtol

prescribed by the user, the size of the regionof accuracy of the table entry C0 is increased(growth).

– If the error ε is larger than εtol, a new table entryis generated (addition).

The ISAT algorithm has been successfully applied tothe simulation of steady combustion systems, where thespeed-up obtained can be of the order of 1000 withrespect to direct integration [26]. Recent application ofISAT for IC engine simulations are reported in [27], wherea speed-up higher than 10 is generally obtained for eachtime-step. This is mainly caused by the drastic changesin temperature, pressure and compositions taking placeduring the combustion process, causing a continuos growof the database. However, the obtained speed-up can beconsidered acceptable.

In the present work, the constant approximation has beenused for the reaction mapping, thus the mapping gradientmatrix is set to zero to reduce the computational time andthe memory overheads. This approach has also beenfollowed in other works applying the ISAT algorithm toengine simulations [27].

PREDICTION OF POLLUTANT EMISSIONS

SOOT EMISSIONS

The processes of soot formation and its subsequentburnout present particular challenges to computationallybased flow-field prediction in a wide range of practicalcombustion systems. Even if the details of thephysical and chemical processes are now understood,severe constraints imposed by the required computationaltime and available memory, limit the complexity ofthe models which can be used. For this reason,simplified phenomenological models are generally used,constructed around a small number of variables which arecharacteristic of the sooting process (for example sootvolume fraction (fv) and number density (Np)). The twodifferent phenomenological models compared in this workwill be now presented.

Hiroyasu Model This is the most commonly used modelfor soot emission prediction in Diesel engines [3, 8, 28]. Itconsiders two competing processes: soot formation andoxidation. The rate of change of the soot mass Ms withina computational cell is determined from the soot formationrate Msf and soot oxidation rate Mso.

dMs

dt=

dMsf

dt−

dMso

dt(23)

The formation rate uses an Ahrrenius expression:

dMsf

dt= Asf MspP

nexp

(−

Esf

RT

)(24)

where Asf is a tuning constant, Msp is the mass of thesoot inception species (C2H2 or fuel), P is the pressureand T is the temperature.

The soot oxidation rate uses the Nagle-StricklandConstable [29] formulation:

dMso

dt=

6MWC

ρsDsMsRtot (25)

Expressions for Rtot can be found in [8].

When detailed chemistry is used, fuel is depleted quicklyto form intermediate hydrocarbon species once reactionsstart [3, 4]. Thus, it is no longer useful to use fuel as theinception species for soot formation. Therefore, basedon the previous literature and available species in thereaction mechanism used in this study, it was decidedto use acetylene C2H2 as the inception species for sootformation, i.e., MC2H2

in Equation 24. This is becauseacetylene is the most relevant specie pertaining to sootformation in hydrocarbon fuels. The pre-exponentialconstant Asf was adjusted accordingly for the presentimplementation and also to account for the fuel effects.

Moss Model The phenomenological model by Moss[30] is based on the simplified representations of theprocesses of nucleation, heterogeneous surface growth,coagulation and oxidation as they apply to the balancebetween transport and production of soot volume fractionfv and particle number density n. The respective sourceterms take the forms:

d

dt(ρsfv) = γn + δ −

(36π

ρs

)1/3

n1/3 (ρsfv)2/3

Rtot (26)

d

dt(n/N0) = α − β (N/n0)

2 (27)

α and β are nucleation and coagulation rates, while γ andδ represent the impact of surface growth and nucleationon the soot volume fraction. The reader is referred to [30,3] for further details about the expressions for the reactionrates.

NOX EMISSIONS

Two different models to predict NOx emissions havebeen evaluated. The first one is integrated into theEddy Dissipation Model and estimates the formationrate of NO according to the simplified reaction rate [8],based on the first reaction of the Zel’dovich mechanismand it evaluates the oxygen concentration from partialequilibrium assumptions [31].

When the PaSR model is used, the chemistry of NOis part of the detailed kinetic scheme. The mechanismconsiders 9 reactions, and the NOx emissions are thesum of NO and NO2 emissions. This approach for NOx

emissions has also been used by Reitz and co-authors in[3, 4].

NUMERICAL CODE

Over the years, great emphasis has been given tothe definition of mathematical models to describe theoccurring phenomena and many fundamental aspectsstill require further studies. In the previous sections, arepresentative range of physical approaches required toachieve Diesel engine modelling have been discussed.Nevertheless the high complexity of the models andthe existing interrelations make the numerical solutionmethodology play a role of equal importance as themathematical modelling.

Discretisation accuracy, solver efficiency, geometry-handling capabilities and computer implementation arethe paramount numerical requirements [2]. In this sectionthe methodology used in OpenFOAM in last two namedwith regard to Diesel engine modelling is discussed.

MESH MANAGEMENT

The OpenFOAM code supports polyhedral cells ofarbitrary shapes and for this reason it can be usedfor the simulation of complex geometries like internalcombustion engines where moving boundaries such aspiston and valves are present. In a recent work [32],the authors implemented into the OpenFOAM code anovel automatic-mesh motion technique with integratedtopological changes, to keep the optimum mesh size andhigh quality during the whole simulation and to avoid thesignificant pre-processing manual work required for meshmotion. Most of Diesel engine CFD simulations considersonly the compression and combustion phases on a sectorof the combustion chamber. In this case mesh motion isaccommodated in two diferent ways:

• Dynamic layering: Far from the TDC, layers of cellsare added or removed close to the piston surfaceto keep the optimum mesh size, this is particularlyuseful in the case of the simulation of pilot injectionshappening 30-50 deg BTDC;

• Mesh deformation: The grid is deformed around theTDC to keep the number of cells at minimum andincrease the mesh resolution when combustion andthe main injection occur.

OBJECT-ORIENTED MODELLING OF DIESEL SPRAYCOMBUSTION

An Eulerian frame model is generally represented as aset of coupled partial differential equations with the termsfalling into several categories (the temporal derivative,convective and diffusive transport and various sourceand sink terms). Its implementation is generally adifficult and challanging subject, since it requires notonly detailed knowledge of the physics and numerics butalso of the software in which the model is implemented.Consequently model implementation may lead to possiblecoding errors, making testing and maintenance extremely

time consuming. Focusing the attention on Dieselengine simulation, code implementation should accountfor several fundamental issues, such as:

• The spray and the pressure field must know all theproperties of the mesh (cells, volumes, boundaries);

• The spray parcels evolve according to the gaspressure and temperature fields, but these two fieldsshould not be modified when the Lagrangian particlesare moved;

• In the implementation of the mass, momentumand energy equations, the spray source terms arerequired;

• New spray sub-models should be introduced withoutmodifying other parts of the code (solvers, mesh,. . . );

An object-oriented framework allows the softwaredesigner to create a more manageable software, withlower maintenance cost, extensive code re-use, fewerbugs and easier extendibility. The leading object-orientedlanguage today is C++ [33, 34]: it provides not only thesupport for object orientation and generic programmingbut also offers near-universal availability and efficiencyneeded for scientific computations. The main features ofthe language are data abstraction, allowing the designerto introduce new data types appropriate for the problem,object orientation, (bundling of data and operations intoclasses, protecting the data from accidental corruptionand the creating class hierarchies), operator overloading,which provides natural syntax for newly defined classesand generic programming, allowing code re-use forequivalent operations on different types.

For what concerns the present work, modelling of Dieselengines involves the following objects in OpenFOAM:

• the engineTime object contains all the controlparameters for the simulation and the enginegeometry data;

• the engineMesh object represents a polyhedral meshwith mesh motion and topological changes;

• the dieselSpray class is the Lagrangian descriptionof the fuel spray. Basically it is a list of points inthe mesh with properites like temperature, diameter,velocity, position, . . . . The spray class includes otherobjects representing the sub-models (breakupModel,atomizationModel, evaporationModel, . . . ). All thespray sub-models are run-time selectable.

• different scalarFields represent the thermo-chemicalstate of the system (pressure, temperature,composition, enthalpy, . . . );

• a vectorField represents the velocity;• a turbulenceModel which can be run-time selectable

(k − ε, RNG k − ε, Low-Re k − ε, . . . ), providing tothe transport equations the turbulent viscosity andthermal diffusivity;

• sootModel : run-time selectable model to predict sootemissions (Moss or Hiroyasu);

• Matrices and their algebra (fvMatrix);• Numerical methods for temporal and spatial

discretizations (ddtScheme, divScheme,laplacianScheme);

The model-to-model interaction is dealt by constant ornon-constant access to protect the object data andfunctions. For example the spray class knows thepressure and velocity field, but cannot modify it. Theinteraction between the liquid and the gas phase is dealtby a series of functions in the spray class, representingthe mass, momentum and energy source terms. In thisway, only the top-level solver becomes a sequence ofoperations performed on each involved object .

Finally, the code is taylored to represent the models. Asan example, the implementation of the Equation 18 in thecode is:

solve

(

fvm::ddt(rho, Yi)

+ fvm::div(phi, Yi)

- fvm::laplacian(turbulence->muEff, Yi)

==

dieselSpray.evaporationSource(i)

+ kappa*chemistry.RR(i)

)

If this is accomplished, the model structure, itsimplementation and inter-equation coupling could beexamined independently from the related numericalissues. Further details about object-orientedprogramming applied to CFD modelling can be alsofound in [7, 35]

EXPERIMENTAL VALIDATION

Experimental data coming from an optically accessiblevessel [36, 37] were used to validate the discussedcombustion and emission models and their codeimplementation. After that, the different models wereapplied to simulate the combustion processes in adirect-injection, turbocharged engine for automotiveapplications.

SANDIA COMBUSTION CHAMBER

The SANDIA vessel is an optically accessible, constant-volume combustion chamber. It has a cubical shape, witha centrally mounted common-rail injector. After burning aspecified premixed mixure before the start of injection, itis possible to reproduce high pressure and temperatureenvironments similar to those found in Diesel engines atthe injection time. Experimental data of vessel pressure,flame lift-off and soot distribution were used to validatethe proposed combustion models. The chosen injectionpressure was 150 MPa with a top-hat profile and the

injected fuel was n-heptane. A wide range of experimentalconditions is available in the database, the ones used forthe present validation are reported in Table 1.

Case 1 2 3 4Ambient density [kg/m3] 14.8 14.8 30 14.8O2 volume fraction [%] 21 15 15 21Ambient temperature [K] 1000 1000 1000 1300

Table 1: Selection of experimental conditions tested for theSANDIA combustion vessel case.

The used computational grid represents a quarter of thereal combustion chamber and has about 22000 cells,with radial and axial resolutions of 2 mm. The walltemperature was adjusted in each case to match theexperimental cool-down pressure-profile [1].

The model constants for the EDM and the PaSR modelare shown in Figure 2.

EDM Cmag = 4; β = 1PaSR Cmix = 0.005

Table 2: Model constants used in the present work for the PaSRand the EDM combustion models.

Figures 4-5 show the flame evolution computed by the twocombustion models for the case 1. The stoichiometric lineis evidenced in black, while the white line evidences the1600 K iso-line. 3 ms after the start of injection, the flamecan be considered fully developed. The two combustionmodels predict a rather different flame structure. In thePaSR model, ignition occurs in a small, lean premixedregion at the side of the vapor jet. Then, the flamepropagates both upstream and downstream along thestoichiometric surface with very different velocities. Thetypical triple flame structure can be recognized whenthe flame is stabilized. The flame structure computedapplying the implemented PaSR model agrees with theresults obtained by Chomiak and Karlsson in [21].

Figure 4: Computed flame evolution predicted by the PaSRmodel (0.5 ms, 1 ms, 2 ms, 3 ms).

Figure 5: Computed flame evolution predicted by the EDMmodel (0.5 ms, 1 ms, 2 ms, 3 ms).

In the EDM model, the fuel ignites along the injector axis,and then the flame propagation is governed by mixingand turbulence, according to Equation 8. This is not inagreement with experimental findings [38] but it is relatedto the chosen correlation for ignition-delay, which is nota function of the equivalence ratio and ignition takesplace where the mixture is rich. As a consequence, thecomputed lift-off is much lower than the one predicted bythe PaSR approach.

A comparison between the experimental and thecomputed pressure rates is displayed in Figure 6 for allthe tested cases. Premixed combustion is evidenced bythe high peak in the pressure rate soon after the ignition,then mixing-controlled combustion takes place with aconstant pressure rate which decreases to zero after theend of the fuel injection. The prediction of the ignitiondelay is strongly influenced by the chosen approach. Inparticular, the Wolfer correlation seems to match very wellthe cases 1-3, where the initial temperature is 1000 K,where complex chemistry overestimates the ignition timedelay. This can be directly connected to the used kineticscheme [39], since the same trend has been obtainedalso considering each cell as a Perfectly Stirred Reactorneglecting the influence of the turbulence, as discussedin [40]. The pressure rise during the mixing-controlledcombustion is correctly predicted by both models, even ifthe PaSR approach slightly underestimates it in the case4. Other investigations are required with different kineticschemes to better understand the PaSR behavior duringthe auto-ignition phase.

Table 3 compares the experimental and predicted flamelift-off. In the calculations, the flame lift-off height wasindentified by a 1600 K temperature iso-line. The lift-offvalues computed by the EDM model are underestimatedin all the cases. This is mainly due to the predictedignition location, which is along the injector axis andvery close to the injector. Considering the axial cell

0 0.0025 0.005 0.0075 0.01

Time [s]

0

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ssur

e R

ate

[MP

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(a) Case 1

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ate

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(b) Case 2

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e R

ate

[MP

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(d) Case 4

Figure 6: Experimental and computed pressure rates.

resolution of 2 mm, the PaSR model results are in goodagreement with the experimental data, except the case 3,where the computed value is strongly influenced by thewrong prediction of the ignition delay. Furthermore, thePaSR correctly reproduces the experimental decrease inflame lift-off when the ambient temperature or the ambientdensity are increased.

Case 1 2 3 4Experimental [mm] 17 23.4 11.9 7.7Computed (EDM) [mm] 8 8 6.7 5Computed (PaSR) [mm] 18 40 10.0 6

Table 3: Experimental and computed flame lift-off values for thefour cases.

Finally, soot luminosity images are qualitatively comparedwith the soot concentrations computed by the twocombustion models. Note that it was observed [36,37] that the spatial locations of soot in PLII imagesclosely coincide with features in the luminosity images,suggesting that the luminosity is due primarily to naturalincandescence from hot soot. In each case shown inFigures 7(a)-(d), the upper image compares the EDMresults with the experimental soot luminosity, while thelower refers to the PaSR results. All fields are shownat 3 ms, a time which is within the quasi-steady period.The computed stoichiometric and 1600 K temperature iso-lines are also reported as well as the experimental lift-offlenghts.

The soot distribution is influenced by the flametemperature and the precursor concentration. The EDMmodel predicts high soot concentrations only very closeto the injector axis, where the mixture is rich and theconsequent fuel concentration is high. The PaSR modelpredictions agrees better than the EDM ones with theexperimental data. However, the peak soot emissionlocation is overestimated by both models in the first andfourth case, where the oxygen concentration is 21%. For

the other two cases with an initial concentration of O2 of15%, the PaSR predictions are in rather well agreementwith experimental data and the model seems to correctlyreproduce experimental variation in the peak soot regionwhen the ambient density is increased [37], even if in thecase 2 the flame lift-off is not correctly predicted.

(a) Case 1

(b) Case 2

(c) Case 3

(d) Case 4

Figure 7: Computed soot fields and experimental soot PLIIdistributions. The experimental lift-off length is also shown inthe pictures for each case.

ENGINE SIMULATIONS

A FIAT 1.2L engine, HSDI, four valve, common rail, multi-jet, turbocharged unit, whose main characteristics arelisted in Table 4, was modelled.

Engine Type HSDI 4-S DieselNumber of cylinder 4 in-lineTotal displacement [cm3] 1248Bore [mm] 69.6Stroke [mm] 82Con. rod lenght [mm] 131.3Compression ratio 17.6:1IVC -147◦ BTDCNumebr of valves per cylinder 4Air Metering VGT turbocharger,

IntercoolerInjection System Common Rail,

Multi-JetMax. Injection Pressure [MPa] 160Injector hole diameter [mm] 0.121Number of injector Holes 6Spray angle 155◦

Table 4: Main specifications of the HSDI turbocharged Dieselengine investigated

An experimental campaign was carried out on this engineat the dynamometer bench, at both full and partial loads[41]. Six engine speeds with different injection strategieswere simulated and they are summarized in Figure 8.These six operating conditions are representative of sixmodes of Diesel combustion with three different injectionstrategies and SOI at full load, and three different EGRconcentrations at partial load. The purpose is to havea significant range of cases, characterized by dominantpremixed combustion or mixing-controlled combustion.

-60 -40 -20 0 20 40Crank Angle [deg]

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[m/s

]

1500 rpm2000 rpm4000 rpm

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-20 -10 0 10 20Crank angle [deg]

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Vel

ocity

[m/s

]

1500 rpm2000 rpm3000 rpm

(b)

Figure 8: Fuel injection strategies [41]. (a) Full load; (b) Partialload.

The computational grid used for the simulations is shownin Figure 9; a 60◦ sector mesh was used in this study,considering that the Diesel injector has six equally-spacednozzle holes. The block-structured mesh is composedof hexahedra and counted about 20000 computationalcells, at bottom dead center (BDC), with 2x1x2.5 mmcell size in the bowl. The mesh was created using theOpenFOAM blockMesh utility, elements are added andremoved, adapting automatically the mesh to the pistonmovement, in order to keep a roughly constant meshresolution. The initial amount of swirl in the incomingair is accounted with a Bessel function profile for the airvelocity within the combustion chamber. For all cases,calculations start at the intake valve closure (IVC). Initialthermodynamic conditions (pressure, temperature and

EGR) were deduced by a 1-D simulation of the wholeengine system [41]. An example of pressure trace

Figure 9: Computational grid at 20 CA BTDC.

comparison between computed values and experimentaldata is shown in Figure 10 (4000 rpm, full load). ThePaSR approach predicts well the peak-pressure, butoverestimates the ignition delay. The Wolfer correlationused in the EDM model provides a better estimation ofthe auto-ignition time.

-150 -120 -90 -60 -30 0 30 60 90Crank Angle [deg]

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Pre

ssur

e [b

ar]

ExperimentalEDMPaSR

Figure 10: In cylinder pressure: full load - 4000 rpm

Figures 11 and 12 compare the computed NOx andsoot concentrations at the exhaust valve opening timingwith the measured values, as a function of the enginespeed at full and partial loads. The PaSR model, whichincludes a detailed description of chemical kinetics, hasthe capability to predict rather well the nitrogen oxidesconcentrations, both in terms of trend and absolutevalues at full load. Discrepancies characterize the partload comparison, even if the absolute values are verylow. Note that the absence of experimental data ofpressure and heat release at partial load did not allowany comparison. The PaSR approach with the Mossmodel and C2H2 as a precursor, captures better the trendof normalized soot than the Hiroyasu model with fuel asa precursor, both at full and partial load. Finally, muchpoorer results were obtained by the EDM approach, dueto the fact that it includes only one global reaction for NOx

and soot.

The flame structure is displayed in Figures 13 and 14

1000 1500 2000 2500 3000 3500 4000 4500Engine speed [rpm]

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NO

x [p

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ExperimentalPaSREDM

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soo

t

PaSR (Moss - C2H2)PaSR (Hiroyasu - fuel)EDMExperimental

Figure 11: Comparison between predicted and measured NOand soot emission as a function of engine speed at full load.

1000 1500 2000 2500 3000 3500Engine speed [rpm]

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ExperimentalEDMPaSR (Moss - C2H2)PaSR (Hiroyasu - fuel)

Figure 12: Comparison between predicted and measured NOand soot emission as a function of engine speed at partial load.

where the cell temperature is plotted at -3◦ and 2◦ ATDCon a horizontal and a vertical plane. In both cases, thereis an inhomogeneous, cleft flame shape as shown bythe high temperature white iso-line. The different ignitionlocations and soot distributions (Figures 15 and 16) canbe appreciated.

Figure 13: Flame structure with the PaSR model at: (a) 2◦

BTDC; (b) 3◦ ATDC (full load, 4000 rpm)

Figure 14: Flame structure with the EDM model at: (a) 2◦ BTDC;(b) 3◦ ATDC (full load, 4000 rpm)

Figure 15: Soot distribution with the PaSR model at: (a) 2◦

BTDC; (b) 3◦ ATDC (full load, 4000 rpm)

Figure 16: Soot distribution with the EDM model at: (a) 2◦

BTDC; (b) 3◦ ATDC (full load, 4000 rpm)

Finally a consideration about the CPU time performancerequired by the different approaches is due. Thesimulations were performed on a AMD 64 3GHzprocessor and the elapsed calculation time are shown

in Table 5. Note that also the comparison between thecalculation time with ISAT versus a direct integration ofthe complex chemistry is shown. A tolerance of 10−4 wasused in the ISAT control parameters and allowed a speed-up factor equal to 6.

Model Elapsed TimeComplex chemistry with DI 170 [h]Complex chemistry with ISAT 30 [h]EDM 3 [h]

Table 5: Computational time required by the differentapproaches.

CONCLUSIONS

In this work, a CFD open-source platform has been furtherdeveloped by the authors to evaluate different modelsfor Diesel combustion. In particular two combustionmodels were implemented: the Eddy Dissipation Model(EDM) and the Partially Stirred Reactor (PaSR) model.The EDM model was modified to account for the effectof the ignition-delay; the PaSR model accounts for theturbulence-chemistry interaction when complex chemistryis used. In this case, to reduce the computational time,the In-Situ Adaptive Tabulation algorithm by Pope [42] wasimplemented by the authors.

Validation was performed with experimental data of acombustion vessel and a direct-injection turbochargerdiesel engine for automotive applications. Bothcombustion models seem to correctly represent thepressure rate trend in the SANDIA combustion vessel andin the Fiat engine. This is rather encouraging for the EDMmodel whose computational time is very low. However,the simplified approach chosen to compute the ignitiondelay influences the predicted flame structure; the effectof tabulated ignition delays approaches, as proposed byDe La Cruz [18], will be evaluated in a future work.The flame predicted by the authors’ implementation ofthe PaSR model resembles the results by Chomiak andKarlsson [21], but further investigations on this model arestill required: experiments and DNS calculations showthat the ignition takes place on the rich side [38, 43].This can also be the cause of an overestimation of theignition delay observed in all the studied cases. The useof complex chemistry can also improve the soot emissioncapabilities by using a semi-empirical model.

The choice of an object-oriented code has also allowedan easy implementation of the combustion and pollutantemission models and offers great possibilities for futuredevelopments of the present work.

ACKNOWLEDGEMENTS

The financial support of Advanced Marine PowerTechnology SEATEK S.P.A. is gratefully acknowledged.The authors are also grateful to Mr. Gilles Hardyand Mr. Mario Mazuran for the interesting suggestions

provided during this work and to the the Msc studentsValentina Contini and Paolo Ferrario for their contributionin the implementation of the Eddy Dissipation Model intoOpenFOAM.

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