g.d’errico ,t.lucchini departmentofenergy

ILASS-Americas 23rd Annual Conference on Liquid Atomization and Spray Systems, Ventura, CA, May 2011

Validation of spray and combustion models for Diesel engines using

constant-volume experiments

G. D’Errico∗, T. Lucchini

Department of Energy

Politecnico di Milano, Milan, Italy, 20156

Abstract

A deep understanding of the dominant physical and chemical phenomena characterizing Diesel spray com-bustion remains the fundamental prerequisite to improve the existing technology towards cleaner and moreefficient engines. To this end, fundamental studies at constant-volume conditions are continuously requiredto evaluate the effects of different fuels, injector configurations and operating conditions on fuel-air mixing,combustion and pollutant formation processes. A relevant contribution to the availability of suitable andaccessible experimental data is represented by the Engine Combustion Network (ECN) database, which isof great interest for model development and validation because of the well-defined boundary conditions andthe wide range of conditions employed. In this paper the authors assess the spray and combustion modelsthey implemented into an open-source CFD code to simulate fuel-air mixing and combustion in Diesel en-gines using detailed chemistry. The spray is modeled with the Eulerian-Lagrangian approach and a modifiedHuh-Gosman model was adopted to describe the primary break-up of the liquid-jet under high injectionpressures. The combustion model is based on direct integration of detailed chemistry in each computationalcell, together with in-situ tabulation and chemical mechanism reduction techniques which are required tominimize the computational time when detailed chemistry is employed. Experimental data of the ECNdatabase were used to validate the proposed approach under both reacting and non-reacting conditions fortwo different fuels (n-heptane and n-dodecane) and injector configurations. The capabilities of the proposedspray model were verified with experimental data of liquid and vapour penetrations and with optical data offuel vapor distributions. Finally, reacting conditions at different initial mixture composition at 1000 K wereconsidered and detailed comparison in terms of auto-ignition time and flame lift-off length is provided.

∗Corresponding Author: [email protected]

1 Introduction

The use of detailed physical and chemical mod-els has become a fundamental pre-requisite for a re-alistic simulation of the combustion process in Dieselengines [1, 2]. Advanced spray models with reducedgrid dependency are required to describe the fuel-airmixing processes, together with detailed chemistryto predict the complex oxidation of multi-componentfuel mixtures under conventional and new combus-tion modes. Computational Fluid Dynamics (CFD)usually integrates the experimental activity carriedout at the test-bench to investigate the combus-tion process and is now part of the industrial de-sign and analysis. The use of detailed chemistryseems absolutely necessary to describe new combus-tion modes, predict the main pollutant emissions [3]and evaluate the effects of multiple injections. Fur-thermore, a fundamental prerequisite for a success-ful CFD simulation is a correct prediction of thefuel-air mixing process because it influences boththe auto-ignition and mixing-controlled combustionphases. The need to keep an acceptable compro-mise in terms of computational time and accuracyjustifies the wide use of the Eulerian-Lagrangian ap-proach, where the spray is composed by a discretenumber of computational parcels, each one formedby an arbitrary number of droplets with the sameproperties. Each parcel evolves in the computationalmesh according to the mass, momentum and energyexchange with the continuous gas phase which istreated in an Eulerian way. Additional phenomeno-logical sub-models are then required to describe thevarious physical processes taking place in the sub-grid length scales: atomization, secondary breakup,drag, evaporation, heat transfer, collision and tur-bulent dispersion [4, 5].

However, detailed CFD models are demandingin terms of computational time. Fine grids are nec-essary to predict the fuel spray evolution and theuse of detailed chemistry involves the operation ofODE stiff solvers to integrate the species and energyequations in each computational cell to obtain thechemical source terms. This aspect limits the ap-plication of detailed kinetics for practical ICE sim-ulations, even when a few species and reactions areinvolved. Within this context, adaptive mesh refine-ment and tabulation of chemical source terms appearto be promising techniques to reduce the compu-tational time and preserve the simulation accuracy[6, 7].

When Adaptive Local Mesh Refinement(ALMR) is used, the overall number of cells remainslow for the whole simulation, but the result accuracyis ensured since the regions where fuel-air mixing

take place are refined depending on the amount offuel in each computational cell. In the proposedapproach, ALMR can be used for engine simulationssince it supports moving meshes with hexahedraltopology. Concerning detailed chemistry, mech-anism reduction and pre-tabulation of reactionrates are extensively applied to single componentfuels and allow to save a significant amount ofcomputational time [8]. However, they have somelimits when applied to simulate multi-componentfuels and advanced combustion modes with multipleinjections, very lean mixtures and high EGR rates.To overcome these limitations, the authors havedeveloped the TDAC method which combines theadvantages of In-situ Adaptive Tabulation andDynamic Adaptive Chemistry techniques. The DACreduces the chemical mechanism at run-time andit is particularly appropriate for simulations wherea wide range of thermo chemical conditions is en-countered. On the other hand, the ISAT algorithmis an example of solution storage and retrievalmethod, achieving good speed-up in the context ofparticle based probability density function methodsand ICE simulations. The proposed techniques toreduce the computational time were embedded bythe authors into the Lib-ICE code, which is a set ofapplications and libraries for IC engine simulationsdeveloped under the OpenFOAM R©technology.Lib-ICE already includes spray and combustionmodels for Diesel engines [9] and supports movingmeshes with topological changes.

In this work, the capabilities of the proposed ap-proach were verified by simulating the air-fuel mix-ture formation process in the SANDIA constant vol-ume combustion chamber [10] under both non re-acting and reacting conditions with n-heptane andn-dodecane used as fuels. The comparison of thesimulation results with available set of experimentaldata allowed to determine the model capabilities todescribe the evolution of the liquid and fuel vapordistribution as well as the ignition delay time andearly stages of the mixing controlled combustion.

2 Computational Models

All the methodologies which will be brieflydescribed here were embedded into Lib-ICE, aset of libraries and applications for internal com-bustion engine simulations developed under theOpenFOAM R©technology. In particular focus willbe given on the spray and combustion models forDiesel and HCCI engines [9, 11].

2.1 Spray model

The spray is modeled using the Lagrangian ap-proach and supports multi-component fuels. Specific

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sub-models are available to describe fuel atomiza-tion, breakup, heat transfer, evaporation, collisionand wall impingement. A modified version of theHuh-Gosman model predicts the liquid jet atomiza-tion [12, 13, 14]. Primary parcels (blobs) are injectedinto the computational mesh with the same nozzlediameter and their velocity is a function of the in-jected mass flow rate profile. Both Kelvin-Helmholtzand turbulence-induced breakup on the jet surfaceare taken into account by the model, describing thediameter reduction of the injected parcels as follows:

dD

dt= −C5

La

τa(1)

where LA and τA are the breakup length and time,while C5 is a model constant. LA is proportionalto the turbulence length scale while τA is a linearcombination of the turbulence time scale (τt) andthe wave growth time scale (τt) due to the Kelvin-Helmoltz instability [15]. The initial value of τt foreach parent parcel depends on the nozzle flow condi-tions [12], then the turbulence decay is described bya simplified version of the k−ε model. For each par-ent parcel, the amount of mass stripped is increasedat each time step by the quantity:

∆mstripped = ρl1

6πNd

(

D3new −D3

old

)

(2)

where Nd is the number of droplets in the par-ent parcel, ρl is the liquid density, Dold and Dnew

are the diameters of the parent parcel before andafter the Equation 1. When a new child parcel iscreated, the amount of stripped mass for the blob isset to zero. The child parcel diameter is taken froma Rosin-Rammler distribution whose mean value isa function of the nozzle flow Reynolds number [14]:

Renoz =ρlUinjDinj

µliq

(3)

where Uinj is the injection velocity, Dinj is the par-cel diameter and µliq is the liquid density. Since par-ent droplets continuously reduce their diameter be-cause of atomization, they will considerably reducetheir Weber number. When the Weber number fallsbelow the threshold of 1000, these parent dropletsare taken in charge by the secondary breakup model[15]. An additional condition was also introduced tocheck if a droplet is suitable to be treated by the at-omization model or not: when the droplet diametersbecome less than the 20% of the injector diameter,the droplets are treated by the secondary breakupmodel.

The drag force acting on the child droplets ismodeled by using the correlation proposed in [16].To correctly describe the mass and energy exchangebetween the liquid and the surrounding gas, thedroplet mass equation requires expressions for theSherwood and Nusselt numbers which are modeledaccording to the approach described in [17]. Theeffects of droplet collision and turbulent dispersionare neglected in this work, to reduce the grid de-pendency and the sensitivity of the results to theturbulence model [18].

Details of the spray sub-models available inOpenFOAM and Lib-ICE are listed in Table 1.

Injection Blob, Huh, Hollow-conepressure-swirl

Atomization Huh-Gosman, WAVE, LISA,Bianchi

Breakup TAB, ETAB, KH,KH-RT, Reitz-Diwakar

Evaporation FrosslingHeat transfer Ranz-MarshallWall-impingement Naber-Rutland, Bai-GosmanCollision Nordin, O’Rourke

Table 1. Spray sub-models available in Lib-ICE

2.2 Reduction of grid dependency

The accuracy of the Eulerian-Lagrangian spraysimulations is related to the various sub-modelsinvolved and to the inadequate spatial resolutionhindering the coupling between the gas and liquidphases [19, 20]. This second aspect is the most im-portant since it often requires an unphysical adjust-ment of the spray sub-models coefficients. Grid de-pendency plays also a very important role in spraysimulation, since coarse meshes are not able to cor-rectly describe the interaction between the liquidand gas phase causing an understimation of thespray penetration, while excessively refined mesheslead to an unphysical fast diffusion of momentumfrom the liquid to the gas phase, resulting in highgas velocities and spray penetration. Hence, the bestmesh size always represents a compromise betweenthe two aforementioned requirements and conver-gence of the computed results cannot be achieved.

Karrholm and Nordin [21] introduced a turbu-lent length scale limiter to reduce the dependencyof spray simulations on the initial ambient diffusiv-ity. Following [22], the turbulent length scale waslimited to the orifice diameter in the cells where thespray parcels are present. A similar approach was

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followed by the authors in this work, in which thelength scale was limited only in the cells where non-atomized droplets exist since, in other parts of thecomputational domain, the relevant length scales aremainly related to the existing in-cylinder flows [11].

The use of adaptive local mesh refinement(ALMR) is also very interesting since it enables ahigh mesh resolution where fuel-air mixing takesplace while the overall grid size is weakly increased[19]. The proposed approach works also with hex-ahedral moving meshes. An initial computationalmesh has to be provided by the user, whose sizeshould be fine enough to correctly reproduce thegeometrical domain to be simulated and the maindetails of the initial flow-field. Following previousapproaches [7, 19], a geometric field is chosen as anerror estimator and when its values lie in a user-specified interval the parent cell is split into eightchild cells by introducing new nodes at the cell cen-troid and at the mesh face centers. An arbitrarylevel of refinements can be chosen by the user as wellas a maximum number of cells to control the meshsize. Grid unrefinement is also possible when thevalues of the error estimator are outside the speci-fied interval. The geometric field used as a refine-ment criterion is represented by the total fuel massfraction (liquid and gas) in each cell:

Yl+g =mf,l + ρYtfVcell

ρVcell, (4)

where mf,l is liquid mass of all the parcels belongingto the cell, Ytf is the fuel mass fraction in the con-tinuous phase, ρ is the gas phase density and Vcellis the cell volume. The lower threshold value liesin the 10−4 ÷ 10−3 range. The consistency of theALMR approach was already verified in a previouspaper [11].

2.3 Tabulation of Dynamic Adaptive Chemistry(TDAC)

In this work the combustion process is describedby means of a Direct Integration of Complex Chem-istry approach, without turbulence/chemistry inter-action. The number of operations required for solv-ing the chemical kinetics in CFD simulations de-pends on the number of cells in the mesh and thesize of the oxidation mechanism. The number ofcells gives the number of time the ODE system willbe integrated. The size of the mechanism defines thelevel of complexity to integrate the system of stiffnonlinear ODE. Reduction of the computational ef-fort for these separated aspects is achieved by theTDAC method, combining the ISAT and DAC tech-niques [6, 24].

The ISAT algorithm intends to reuse computa-tionally demanding results, e.g. the integration oflarge and stiff ODE systems, by storing those resultsand all the necessary data to retrieve them. Duringcomputation, given a query point, ψq, it computes alinear approximation of the mapping:

R(ψq) ≈ Rl(ψq) = R(ψ0) + δRl , (5)

where δRl = A(ψ0)(ψq −ψ0) and A is the mappinggradient matrix defined by

Aij(ψ0) =

∂Ri(ψ0)

∂ψj

. (6)

The linear approximation defined by Equation 5 isvalid in the region of accuracy (ROA) where the fol-lowing condition is respected:

|R(ψq)−Rl(ψq)| = |δR− δRl| ≤ εISAT , (7)

where εISAT is a user-specified tolerance and δR =R(ψq)−R(ψ0). During the calculation, the table isbuilt up according to the received queries. It consistsof a binary tree with leafs and nodes. The leafs storeψ, R(ψ), A(ψ) and the ROA description. The nodescontain the rules that allow to scan the binary treeto retrieve the appropriate point [6].

The DAC method computes reduced mecha-nisms that are valid for the local thermo chemi-cal conditions.The DAC has been extended to fullCFD meshes with wall heat transfer. The reduc-tion algorithm is executed before every call to thestiff solver according to the directed relation graph(DRG) method, which identifies the relevant speciesand reactions according to the thermodynamic con-ditions in each cell [24].

When ISAT receives a query ψq that needs tointegrate the ODE set, it provides ψq to the DACalgorithm which then finds the reduced mechanismfor the local thermo chemical conditions and pro-vides the reduced set of active species ψq

a to the ODEsolver. This solver computes the reaction mappingfor the reduced set R(ψq

a) that is used by ISAT tobuild the reaction mapping R(ψq) in the full com-position space. Using simplification methods at dis-tinct levels combines their effects and allows a sig-nificant reduction of the computational cost. Theefficiency of ISAT depends on the level of inhomo-geneity and the range of thermo chemical conditions.Further details about the TDAC method and its im-plementation by the authors can be found in [25].

3 Results and discussion

The proposed approaches were validated withdifferent sets of experimental data at non-reacting

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and reacting conditions, which were selected withinthe Engine Combustion Network database. Amongthe wide range of available experiments, the twoconditions which received significant attention fromthe CFD community correspond to experiments con-ducted in an optical, constant-volume vessel us-ing as fuel C7H16 (baseline n-heptane) and C12H26

(Spray A). The vessel has a cubical-shaped combus-tion chamber, whose characteristic dimension is 108mm. The fuel injector is located in one side portusing a metal insert that forms the right wall of thecombustion chamber. Optical access is provided byfour sapphire windows with clear apertures of 102mm located in the other four ports [26]. This com-bustion vessel has been operational at Sandia since1997 and is currently in use [26, 27].

3.1 Baseline n-heptane

The so-called baseline n-heptane is not currentlyactive experimentally, but it has been the focus ofseveral previous studies. A common-rail fuel injectorwith a single, non-hydroground, axial hole is used.The orifice has a 0.1 mm diameter, a discharge coef-ficient Cd equal to 0.8, a area-contraction coefficientCa equal to 0.91 at 72 MPa and 0.86 at 138 MPa.The length-to-diameter ratio, L/d, is equal to 4.0.In the non-reacting conditions the oxygen concen-tration is equal to 0 and the ambient temperatureand density are respectively equal to 1000 k and 14.8kg/m3.

In previous studies the authors have already pro-posed a computational analysis of this sets of exper-iments, using a computational domain reproducinga quarter of the combustion chamber (50.46 x 50.46x 108 mm). In this work, instead, no symmetryplane was used, therefore the entire domain was con-sidered, in order to better assess the quality of theadopted numerical schemes.

Liquid fuel was provided according to the exper-imental mean injection profile. Initially the domainwas divided in 14x14x14 cells, which correspond toa cell size about 7.7 mm. Simulations were run withdifferent refinement levels (1-4), such that a mini-mum cell size of 0.48 mm was considered.

In the shown test cases, all the simulations endat 2.5 ms after SOI. If the vapor penetration is cor-rectly predicted for such a long time, the combus-tion model will probably succeed for most of theoperating conditions which can be encountered inDiesel engines [10]. First-order numerical schemeswere used for these simulations to preserve the re-sults stability and to be consistent with the typicalcase setup which is used for the simulations of Dieselengines. Table 2 illustrates the minimum size and

the overall cell number with a ALMR at 2.5 ms andwith a fixed uniform mesh.

Refinement Min. size ALMR Fixed meshlevels [mm] cell size cell size1 3.85 3962 21.952E32 1.93 9975 17.561E33 0.96 47320 14.049E44 0.48 306516 11.234E6

Table 2. Cell size of ALMR and fixed meshes.

The use of ALMR drastically reduces the num-ber of required cells, and, as a consequence, also a re-duction of the computational time can be achieved.However the reader must also consider that in Dieselengine simulations, multiple-hole injectors are com-monly used and the ratio between the volume occu-pied by the spray and the total volume is typicallymuch higher than in this constant volume experi-ment.

The consistency of the Adaptive Local Mesh Re-finement technique was firstly verified. For each levelof refinement, the computed liquid and vapor pen-etrations were compared with the ones obtained bya simulation performed on a fixed mesh with thesame minimum size where the fuel-air mixing pro-cess takes place. An example of such a consistency isgiven in Figure 1 where the vapor spray penetrationswith 3 and 1 levels of refinement, computed with theALMR technique and fixed meshes, are plotted.

0 0.5 1 1.5 2 2.5Time ASOI [ms]

0

20

40

60

80

100

120

Vap

or P

enet

ratio

n [m

m]

Fixed mesh, 3 lev.ALMR, 3 lev.Fixed mesh, 1 lev.ALMR, 1 lev.

Figure 1. Computed spray vapor penetrations withALMR and equivalent fixed meshes with 3 and 1levels of refinement.

The effect on the CPU time reduction, which isachieved by the use of the ALMR technique, can be

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appreciated in Figure 2, where CPU data were nor-malized with respect to the maximum time requiredby the reference fixed mesh to reach 2.5 ms of simu-lated time in the case of 3 levels of refinements. Theachieved speed-up factor varies between 35 and 10,with its value progressively decreasing as the num-ber of cells using ALMR grows. These results can beconsidered satisfactory, especially because the higherinterest for Diesel engine application is in the lowertime intervals after start of injection.

0 0.5 1 1.5 2 2.5Time ASOI [ms]

0

0.2

0.4

0.6

0.8

1

Nor

mal

ized

CP

U ti

me

ALMR, 3 lev.Fixed mesh, 3 lev.

0

5

10

15

20

25

30

35

40

Spe

ed-u

p fa

ctor

Speed-up

Figure 2. Comparison between ALMR and the ref-erence fixed mesh in the case of 3 levels of refinement.

The effects of the grid size on the computed liq-uid and vapor spray penetration are shown in Fig-ure 3 and in Figure 4 together with the correspond-ing experimental data. The computed liquid pene-trations seem not stabilize initially for the coarsermeshes, but this is simply due to the penetration ofthe first liquid droplets in the initial mesh. Then allsolutions converge to a steady penetration, showinga moderate increase of this steady value as the num-ber of mesh refinements increases. For what con-cerns the vapor penetration, only the coarsest meshis not able to reproduce the measured trend, whileall the other results can be considered in a satisfac-tory agreement with the measured data.

All the results shown so far were obtained us-ing the Realizable k-ε turbulence model and a timestep equal to 5.0e-7 s. Figure 5 shows the depen-dency of the results on the chosen computation timestep, evidencing a rather good convergence. Aboutthe turbulence model, motivations beyond such achoice were given by the analysis of the comparisonof the results obtained by the different turbulencemodels in term of vapor penetration and mixturefraction distribution. The first of this two analysis

0 0.5 1 1.5 2 2.5Time ASOI [ms]

0

5

10

15

20

Liq

uid

Pene

trat

ion

[mm

]

ExperimentalALMR, 4 lev.ALMR, 3 lev.ALMR, 2 lev.ALMR, 1 lev.

Figure 3. Baseline case: computed liquid spraypenetrations with different ALMR levels, using theRealizable k-ε turbulence model.

0 0.5 1 1.5 2 2.5Time ASOI [ms]

0

20

40

60

80

100

120V

apor

Pen

etra

tion

[mm

]ExperimentalALMR, 4 lev.ALMR, 3 lev.ALMR, 2 lev.ALMR, 1 lev.

Figure 4. Baseline case: computed vapor spraypenetrations with different ALMR levels, using theRealizable k-ε turbulence model.

is performed in Figure 6, outlining a definite over-estimation by the RNG k− ε turbulence model anda similar level of accuracy achieved by the standardand the Realizable k−ε models, with a minor higherprecision achieved by the first of these two. The au-thors would like to point out that no calibration ofthe involved constants was performed on any model,but the literature data were directly used [18]. Ofcourse results might possibly be improved by a tun-ing of the constants, but this was out of the scopesof the current investigation.

To assess the model capability to correctly re-produce both the auto-ignition and the mixing con-

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0 0.5 1 1.5 2 2.5Time ASOI [ms]

0

20

40

60

80

100

120V

apor

Pen

etra

tion

[mm

]Experimentaldt = 5.0e-6dt = 1.0e-6dt = 5.0e-7dt = 1.0e-7

Figure 5. Baseline case: computed vapor spraypenetrations with different time steps, using the Re-alizable ε turbulence model and 3 ALMR levels.

0 0.5 1 1.5 2 2.5Time ASOI [ms]

0

20

40

60

80

100

120

Vap

or P

enet

ratio

n [m

m]

ExperimentalStandard k - ε Realizable k - ε RNG k - ε

Figure 6. Baseline case: computed vapor spraypenetrations different turbulence models and 3ALMR levels.

trolled combustion phases, not only the spray andvapor tip penetrations must be considered, sincethese data are not completely representative of thefuel-air mixing process, but, when possible, radialdistributions of the mixture fraction at different dis-tances from the injector must be compared [10].

Figure 7 shows the comparison at steady condi-tions at 20 mm, 30 mm, 40 mm and 50 mm distancesfrom the injector for the standard and the Realizablek−ε models, using 4 levels of refinements, which areneeded to have an adequate resolution. For bothmodels, the overall results are considered satisfac-tory since the mixture fraction distribution

-9 -6 -3 0 3 6 9Distance from the injector axis [mm]

0

0.05

0.1

0.15

0.2

Mix

ture

fra

ctio

n

ExperimentStandard k - ε Realizable k- ε

(a) x = 20 mm


0

0.05

0.1

0.15

0.2

Mix

ture

fra

ctio

n


(b) x = 30 mm


0

0.05

0.1

0.15

0.2

Mix

ture

fra

ctio

n


(c) x = 40 mm


0

0.05

0.1

0.15

0.2

Mix

ture

fra

ctio

n


(d) x = 50 mm

Figure 7. Baseline case: comparison between ex-perimental and computed mixture fraction distribu-tions at different distance from the injector at steadystate conditions: (a) 20 mm; (b) 30 mm; (c) 40 mm;(d)50 mm

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0 10 20 30 40 50 60 70 80 90Distance from the injector [mm]

-10

-5

0

5

10

Dis

tanc

e fr

om th

e in

ject

or [

mm

]

ExperimentComputed

(a) Time = 0.5 ms ASOI


-10

-5

0

5

10

Dis

tanc

e fr

om th

e in

ject

or [

mm

]

ExperimentComputed

(b) Time = 1.0 ms ASOI


-10

-5

0

5

10

Dis

tanc

e fr

om th

e in

ject

or [

mm

]

ExperimentComputed



-10

-5

0

5

10

Dis

tanc

e fr

om th

e in

ject

or [

mm

]

ExperimentComputed



-10

-5

0

5

10

Dis

tanc

e fr

om th

e in

ject

or [

mm

]

ExperimentComputed

(e) Time = 2.5 ms ASOI

Figure 8. Baseline case: comparison between experimental (black line) and computed fuel vapor distribution(blue squares) at different times after SOI:(a) 0.5 ms; (b) 1.0 ms; (c) 1.5 ms; (d) 2.0 ms; (e) 2.5 ms.

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is well reproduced for all locations. However the ac-curacy achieved by using the Realizable k−ε turbu-lence model is considered higher, so this model hasbeen selected as definite choice in this investigation.The model provides the best description of the fuel-air mixture formation process, both at the peripheryof the vapor region, where auto-ignition takes place,and close to the injector, where soot emissions areformed.

Since auto-ignition takes place at different timesdepending on the operating conditions, it is of rele-vant interest to verify if the model is able to describethe evolution of the fuel vapor distribution duringthe whole simulation. For this reason, Figure 14compares the experimental boundary of vapor pen-etration with the computed fuel vapor distribution.Experimental data were extracted from a single in-jection event while the computed data represent thepositions of the cell centroids having mixture frac-tion values higher than 10−4. The comparison wasperformed for five different times after SOI rang-ing from 0.5 m to 2.5 ms with a step equal to 0.5.For all the tested cases, the model correctly repro-duces the entire evolution of the fuel vapor regionin terms of vapor boundary, presence of fuel closeto the injector and vapor tip penetration. The maindifferences are considered to be associated with theinstantaneous experimentally observed non unifor-mities, which cannot be described by the used CFDapproach and are partially related to the slight over-estimation of the vapor penetration by the model.

Finally, some reacting conditions were takeninto consideration to give the reader a clearer pictureof the following simulation activity, which can be es-tensively carried out only the fuel vapor distributionis well described by the proposed CFD approach.The thermodynamic conditions are the same as inthe non reacting case, while the composition of theinitial mixture had an oxygen concentration rangingform 21% to 10%. In this way, the combustion modelcapabilities to account for the effect of different EGRfraction are assessed. As explained in the introduc-tion, the prediction of such conditions requires theuse of complex chemistry schemes to describe in de-tails the governing reactions. In this work the re-duced mechanism for n-heptane with 52 species de-veloped by Lu et al. [28] was used. This mecha-nism was derived from a detailed mechanism with561 species and validated for ignition and extinctionapplications over the parameter range of equivalenceratio between 0.5 and 1.5, pressure between 10 and50 atm, and initial temperature between 700 and1600 K for ignition.

Figure 9 compares the measured and computed

0 0.5 1 1.5 2 2.5Time ASOI [ms]

0

0.01

0.02

0.03

0.04

0.05

Pres

sure

ris

e [M

Pa]

Exp. O2 =21%Comp. O2=21%Exp. O2=15%Comp. O2= 15%Exp. O2 = 10%Comp. O2 =10%

Figure 9. Baseline case: computed and measuredpressure rise at 1000 K and different initial compo-sition

0 0.5 1 1.5 2 2.5 3Time ASOI [ms]

0

10

20

30

40

50

60

70

80

90

100L

ift o

ff [

MPa

]Exp. O2 =21%Comp. O2=21%Exp. O2=15%Comp. O2= 15%Exp. O2 = 10%Comp. O2 =10%

Figure 10. Baseline case: computed transient andmeasured steady lift off at 1000 K and different ini-tial composition

pressure for the three different initial oxygen con-centration: 21%, 15%. 10%. The model seems tooverestimate the ignition delay in all cases, howeverthis difference does not vary significantly with thedecreasing oxygen concentration, as very often it isexpericed in such simulations. Then, the early stageof the mixing controlled combustion is rather wellpredicted in all cases: the description of the vapordistribution and its mixing with the ambient mis-ture plays a dominant role. Another important para-menter which must be evaluated is the flame lift-off.In Figure 10 the lift-off lenghts were identified by the1600 K iso-surface and plotted versus the measured

9

steady value for all the cases. To better understandthe computed flame structure, Figure 11 shows a cutplane of the computed temperature field for steadyconditions and O2 = 15%. The black line evidencesthe 1600 K iso-surface which was used to determinethe flame lift-off. This figure also evidences very wellthe grid refinement along the fuel spray.

Figure 11. Baseline case: temperature distributionand isoline (black) at 1600 K with O2 equal to 15%in steady conditions

3.2 Spray A

The second test case which will be consideredin this study is the so-called spray A [26]. Thecombustion chamber is the same as in the previoustest case. A common-rail system with fuel at 1500bar prior to the start of injection is used. The in-jector nozzle is a Bosch CRIP 2.2 injector with aKS1.5/86 orifice and diameter equal to 0.090 mm.Fuel is pure n-dodecane at 90 ◦C tip temperature.In the non-reacting conditions the oxygen concen-tration was equal to 0 and the ambient temperatureand density were respectively equal to 900 K and22.8 kg/m3.

In Figure 12 and Figure 13, the computed va-por and liquid spray penetrations are plotted versusthe experimental data, considering the three turbu-lence models described earlier. The setting of allspray models were unchanged with no tuning andconstants taken from literature [18]. The best re-sults in terms of vapor penetration were achievedby the use of the realizable k − ε turbulence model,while the liquid penetration is well predicted by allmodels. Once the injection terminates, computed

results and measured data seem to have a divergenttrend. This difference is only due to the fact that thecomputed liquid penetration is defined as the pen-etration of 99% of the liquid mass in the chamber.When injection terminates a very reduced amount offuel which did not evaporate might still be presentin the chamber and continue to penetrate.

0 0.5 1 1.5 2 2.5Time ASOI [ms]

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Figure 12. Spray A case: computed vaporspray penetrations different turbulence models and3 ALMR levels.

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uid

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[mm

]


Figure 13. Spray A case: computed liquidspray penetrations different turbulence models and3 ALMR levels.

Hence, as it was done for the n-heptane testcase, the evolution of experimental boundary ofvapor penetration as function of time was comparedwith the computed fuel vapor distribution with theRealizable k − ε turbulence model.

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Figure 14. Spray A case: comparison between experimental (black line) and computed fuel vapor distri-bution (blue squares) at different times after SOI:(a) 0.5 ms; (b) 1.0 ms; (c) 1.5 ms; (d) 2.0 ms; (e) 2.5ms.

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Experimental data were extracted from a singleinjection event while the computed data representthe positions of the cell centroids having mixturefraction values higher than 10−4. The comparisonwas performed for five different times after SOI rang-ing from 0.5 m to 2.5 ms with a step equal to 0.5, asbefore. The model correctly reproduces the entireevolution of the fuel vapor region in terms of vaporboundary. The last two time steps show some dif-ferences as tip penetration, however, since this valuewas already verified, as shown in Figure 12, thesedifferences are considered to be due only to the in-stantaneous behavior of the spray.

4 Conclusions

A comprehensive methodology to describe theliquid and vapor evolution of the fuel spray forDiesel applications was assessed in this work by sim-ulating evaporating spray of pure n-heptane and n-dodecane in a constant volume chamber . Attentionwas mainly given on the evaluation of the modelsto predict the vapor penetrations and distributionsin steady and transient conditions for non-reactingspray. This aspect is considered to be a fundamentalprerequisite for any future investigation of the foll-wing combustion processes. Neverthless some initialresults considering reacting sprays were already pre-sented to give the reader a clearer picture of theachieved potentialities.

The detailed description of the vapor spray dis-tributions and the interest in low temperature com-bustion modes, and hence in the description of thecombustion by direct integratin of complex chem-istry schemes, motivated the definition of efficiencttechniques to reduce the required CPU time. Com-nclusions arising from the presented analyisis showthe great benefits achieved by the use the Adap-tive Local Mesh Refinement (ALMR) on the sprayevolution: it represents a very powerful tool for thesimulation of high-pressure diesel sprays, it drasti-cally reduces the computational time and, once aninitial coarse mesh is generated, the result accuracycan be easily controlled by changing the level of meshrefinements. The proposed approach works with un-structured hexahedral meshes, hence it can be usedto simulate real Diesel engine combustion chambers.

For the reacting conditions, the TDAC methodwas applied to reduce the computational time whendetailed chemistry is used, by combining ISAT(In-Situ Adaptive Tabulation) and DAC (DynamicAdaptive Chemistry). The model capabilities to pre-dict the auto-ignition and the early stage of the mix-ing combustion process with different compositionsof the initial mixture were assesed. As aforemen-

tioned, the exploitation of the such capabilities wasnot the focus of the present work but it was its driv-ing motivation, to be able, in the near future, to relyon a validated spray description methodology.

5 Acknowledgements

The authors gratefully acknowledge the EngineCombustion Network for the high quality and widequantity of the experimental data which were madepublicly available and for creating a collaborative en-viroment for the assessment of CFD spray and com-bustion models.

References

[1] Singh, S., Reitz, R. D., Musculus, M. P. B.,2006. Comparison of the Characteristic Time(CTC), Representative Interactive Flamelet(RIF), and Direct Integration with DetailedChemistry Combustion Models against OpticalDiagnostic Data for Multi-Mode Combustionin a Heavy-Duty DI Diesel Engine. SAE Paper2006-01-0055.

[2] D’Errico, G., Ettorre D., Lucchini T., 2009.Simplified and Detailed Chemistry Modelingof Constant-Volume Diesel Combustion Exper-iments. SAE Int. Jou. of Fuel and Lubricants 1,452-465.

[3] Kong, S.C., Sun, Y., Reitz, R. D., 2007.Modeling Diesel Spray Flame Liftoff, SootingTendency, and NOx Emissions Using DetailedChemistry With Phenomenological Soot Model.Journal of Engineering for Gas Turbines andPower 129, 245-251.

[4] Kolaitis, D. I., Founti M. A., 2006. A compar-ative study of numerical models for Eulerian-Lagrangian simulations of turbulent evaporat-ing sprays. International Journal of Heat andFluid Flows 27, 424-435.

[5] Beck, J. C., Watkins, A. P., 2002. The dropletnumber moments approach to spray modelling:The development of heat and mass transfer sub-models. International Journal of Heat and FluidFlows 24, 242-259.

[6] Pope, S. B., 1997. Computationally efficientimplementation of combustion chemistry usingin situ adaptive tabulation. Combust. Theor.Model, 1, 41-63.

[7] P. K. Senecal et al., 2007. Development and Val-idation of a Primary Breakup Model for DieselEngine Applications. SAE Paper 2007-01-0159.

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[8] A. Pires De La Cruz, Comb. Scie. Techn. 176(2004) 867-887.

[9] T. Lucchini et al., 2009. Numerical Investi-gation of Non-Reacting and Reacting DieselSprays in Constant-Volume Vessels, SAE Int.Jou. of Fuel and Lubricants 2, 966-975.

[10] Idicheria, C. A., Pickett, L. M., 2007. Effectsof EGR on Diesel Premixed-Burn EquivalenceRatio. Proceedings of the Combustion Institute31, 2931-2938.

[11] Lucchini, T., D’Errico, G., Ettorre, D., 2011.Numerical investigation of the spray-mesh-turbulence interactions for high-pressure, evap-orating sprays at engine conditions. Interna-tional Journal of Heat and Fluid Flow, 32(1),pp. 285-297.

[12] Huh, K. Y., Gosman, A. D., 1991. A Phe-nomenological Model of Diesel Spray Atomiza-tion. In:Proceedings of the International Con-ference on Multiphase Flows.

[13] Bianchi, G. M., Pelloni, P., 1999. Modeling theDiesel Fuel Spray Breakup by Using a HybridModel. SAE Paper 1999-01-0226.

[14] Bianchi, G. M., Pelloni, P., Corcione, F. E., Al-locca, L., Luppino, F., 2001. Modeling Atom-ization of High-Pressure Diesel Spray. Journalof Engineering for Gas Turbines and Power 123,419-427.

[15] Reitz, R. D., 1987. Modeling Atomization Pro-cesss in High-Pressure Vaporizing Sprays. At-omization and Spray Technology 3,309-337.

[16] Kralj, C., 1995. Numerical Simulation of DieselSpray Processes. Phd thesis, Imperial Collegeof Science, Tecnology and Medicine.

[17] Crowe, C., Sommerfeld M., Tsuji Y., 1998. Mul-tiphase Flows with Droplets and Particles. CRCPress LLC.

[18] Stiesch G., 2003. Modeling Engine Spray andCombustion Processes, Springer, ISBN: 978-3-540-00682-4.

[19] Lippert, A. M., Chang, S., Are S., Schmidt, D.,2005. Mesh Indipendence and Adaptive MeshRefinement For Advanced Engine Spray Simu-lations. SAE Paper 2005-01-0207.

[20] Aneja, R., Abraham J., 1998. How far does theliquid penetrate in a diesel engine: computed

results vs. measurements. Combustion Scienceand Technology 138, 233-255.

[21] Karrholm, F., Nordin, N., 2005. Numerical In-vestigation of Mesh/Turbulence/Spray Interac-tion for Diesel Applications. SAE Paper 2005-01-2115.

[22] Abraham J., 1997. What is Adequate Resolu-tion in the Numerical Computations of Tran-sient Jets? SAE Paper 970051.

[23] Tonini S., Gavaises M., Theodorakakos A.,2008. Modeling of High-Pressure Dense DieselSprays with Adaptive Local Grid Refinement.International Journal of Heat and Fluid Flow29, 427-448.

[24] L. Liang et al., 2009. Proc. Combust. Inst.32(2009) 527-534.

[25] Contino, F., Jeanmart, H., Lucchini, T.,D’Errico, 2010. Coupling of in-situ adaptivetabulation and dynamic adaptive chimistry: anaffective method for solving combustion in en-gine simulations. Proc. of the Combustion In-stitute.

[26] 2011, http://www.sandia.gov/ecn/index.php

[27] Siebers, D. L., Higgins, B. S., 2002. Effectsof Injector Conditions on the Flame Lift-OffLength of DI Diesel Sprays. Proceedings of theTHIESEL 2002, Conference on Thermo- andFluid-dynamic Processes in Diesel Engines.

[28] Lu, T. F., Law, C.K., Yoo, C.S., Chen, J.H.,2009. Dynamic Stiffness Removal for Direct Nu-merical Simulations. Combustion and Flame,Vol. 156 No. 8 pp.1542-1551.

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g.d’errico ,t.lucchini departmentofenergy

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