2012 - Development of OpenFOAM application for internal combustion engine simulation.pdf

8/10/2019 2012 - Development of OpenFOAM application for internal combustion engine simulation.pdf

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Development of OpenFOAM application for

internal combustion engine simulation

G. DErrico, T. Lucchini, G. Montenegro, M. Zanardi

Dipartimento di Energetica, Politecnico di Milano, Italy

Summary

This work illustrates the current research activities carried out by the authors by de-

veloping OpenFOAM applications in the field of I.C. engine simulation: steady flow

analysis, gas exchange modeling, diesel combustion, 1D-3D simulations to model theunsteady gas motion in complex intake and exhaust systems. A first use of the codewhich has a significant interest in the I.C. engines industrial applications is the evalua-tion of the flow coefficients of intake and exhaust ports or other complex geometry de-

vices. Examples of this applications, which make use of standard steady-state solvers,

are given. The next step is the simulation of the gas exchange phase. A fundamen-tal requirement for this task is a reliable and efficient moving mesh strategy. This is

achieved by using an automatic mesh motion solver based on the Laplace equation ofmotion and including the possibility to change the mesh topology to keep a high mesh

quality during the whole simulation. Concerning Diesel combustion modeling, the au-

thors are currently evaluating two different models: the first one is based on the EddyDissipation Model with reduced chemistry, while the second accounts for complex ki-

netics. To reduce the computational time required by the latter, the ISAT algorithm hasbeen implemented by the authors. A last application regards the coupling of Open-

FOAM with a 1D fluid-dynamic code, Gasdyn, developed by the authors to simulate

the whole engine cycle. The proposed approach, based on the solution of the Rie-mann problems at each boundary cell, allows the simulation of the unsteady flows in

complex systems such as intake plenums, multi-pipe junctions and silencers.

1 Introduction

The development and assessment of a CFD methodology and its implementation intoa numerical simulation toolkit specifically tailored for engine simulation represents avery challenging task. In fact it requires to describe into details many simultaneous

interacting thermofluids and chemical processes, which take place in a domain with

a complex geometry and moving boundaries. On the modeling front, the task is to

assemble a complete and accurate description of the involved physical process, whileon the numerical point of view the challenge is the development of flexible and effi-cient algorithms with respect to the implementation of the model equations and to the

description of the engine geometry [1]. The objective to aim at is the definition of a


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reliable CFD code which can be used as a predictive tool from a qualitative viewpoint

in a design stage and as a diagnostic tool to achieve a deeper understanding of theoccurring physical phenomena. To these ends, the authors have contributed over thelast years to the development OpenFOAM applications for internal combustion engine

simulation, considering its prerequisites to be fully open-source and written in an highlyefficient object-oriented programming, which allow an easy implementation and testing

of new models.This paper provides an overview of the ongoing research activities carried out by theauthors in this field:

OpenFOAM coupling to a 1D fluid-dynamic code for the simulation of the entireengine system to model the unsteady gas motion in complex devices, including

acoustic analysis;

steady-state flow bench simulations;

development of moving mesh algorithms to cope with in-cylinder simulations;

simplified and detailed chemistry modeling of diesel combustion, applied to constant-volume experiments with optical access.

2 Coupling approach

x

left state right state

star region

SS

SL

R

*

t

L x

Rx O

W W* *

L R

1D DOMAIN

Figure 1: Structure of the Riemann problem at the inter-cell region and its adoption at

the interface between the 1D and the 3D domain.

The issue of coupling 1D models to complex CFD codes is not something new in thefield of internal combustion engine simulation. Several works concerning this topichave been published during the last few years, among which three common strategies

can be identified. The most simple approach consist in the adoption of CFD models todetermine flow coefficient of valves, orifices and abrupt area changes, which are then

adopted in the fully 1D simulations.Another approach is the one way coupling, in which the 1D tool is exploited to cal-

culate at a fixed position the pressure and velocity traces, which are subsequently


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Figure 2: The 5 into 1 junction modeled in 3D and the 1D schematic of the Lamborghini

V10 engine.

imposed as boundary conditions in the multidimensional tool. With this method no

information are passed back from the multidimensional code to the one-dimensional,allowing to study only the flow details in complex geometries under unsteady flow con-

dition. To take into account the effects of eventual variation of the multidimensional

domain on the 1D side, the so called strict coupling was proposed. In this procedurethe two codes are passing forth and back information at each time step in such a way

that one domain is affected by what happens in the other one. Some authors attainedthis purpose relying on the exchange of boundary conditions at the interface betweenthe two domains, however this strategy does have some constraints on the position of

the domain interface. In particular, to avoid the generation of instabilities, the interfacebetween the two domains has to be placed in regions where the flow can be reason-

ably considered one-dimensional.

A more stable procedure has been developed, to overcome the cited problem, in orderto truncate the 3D domain in regions that are close to highly 3D shapes. This approach

involves the solution of the Riemann problem for every cell which owns the face con-stituting the boundary surface. In particular, at the beginning of each time step (asshown in Figure 1), the average of the conserved variables in the centroids of the cells

is assigned to the last node of the 1D domain, while the conserved variables in the

n-1 node are assigned to the left state of local Riemann problems. Therefore, eachface constituting the 1D/multiD boundary identify a Riemann problem, which is solvedadopting the HLLC solver or its extension to the second order accuracy.

2.1 Engine application

It has been already demonstrated that the integrated 1D-3D approach can give results

comparable to 1D calculation if applied to simple geometries [2], justifying the adop-

tion of well experienced corrective lengths to tune the model, since the computationalburden brought by an eventual 3D domain would not add any detail at all to the final


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Figure 3: Pressure versus crank angle: measured, calculated by means of 1D-3Dcoupling and fully 1D calculation. The engine operating condition are at full load a) 2

000rpm, b) 2500 rpm, c) 3000 rpm, d) 6500 rpm, e) 7000 rpm and f) 7500 rpm.

results. Conversely, this approach can be very useful in the case of complex geome-try systems, to capture the multi dimensional wave effects. The integration of the twomodels has been applied to simulate a V10 high performance engine in which the 5into 1 junction has been simulated by means of a 3D approach. This application is

particularly critical, since the interfaces between the two domain are characterized bybeing crossed by contact surfaces, compression and rarefaction waves and the velocity

field is rarely uniform over the cross section. In particular, only the left bank junction

has been modeled by means of a 3D domain, while the remaining parts of the en-gine duct system have been discretized as 1D, as shown in Fig. 2. The experimental

campaign, carried out in Lamborghini laboratories, focused on the measurements of


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Figure 4: Pressure and velocity field inside the 5 into 1 junction at 270 crank angle

degrees, 7500 rpm full load.

pressure pulses upstream of the junction and of volumetric efficiency. Several oper-ating conditions were considered; in particular, the range from 2000 rpm to 7500 rpm

was covered at full load with a step of 500 rpm. A fully 1D investigation of this enginehas been recently published, in which a detailed description of the 1D approach for themulti-pipe junction and of the combustion model can be found [3]. The 3D mesh ofthe junction is composed by up to 18000 computational cells whose average spacing

is half centimeter. No refinement of the mesh was done, to avoid the increase of the

computational time. The simulation of 5 thermodynamic cycles, needed by the method

to converge to a solution, involved an average time of 20 hours on a single proces-sor 2GHz PC. The comparisons between the measured pressure pulses downstreamof the cylinder and the calculations carried out adopting the two models, namely the

1D-3D integrated code and the fully 1D code, are shown in Fig. 3. It can be noticedthat the hybrid model is remarkably more predictive than the fully 1D approach, exhibit-

ing a good agreement with the measured data both in the absolute value and phaseof the wave motion. The pressure and velocity field shown in Fig. 4 point out the un-

steadiness of the flow field inside the junction and how the Riemann approach tolerates

strong flow non uniformities at the interface between the two domains.

D

L

LL21 Conf. A Conf. B

51 51D 107 113

L 253 280L1 45 54L2 116 100

Figure 5: Layout and specification of the muffler configurations.


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Figure 6: Transmission loss (TL) of mufflerConf. A: measured, 1D-multiD calculation,

fully 1D calculation.

Figure 7: Transmission loss (TL) of mufflerConf. B: measured, 1D-multiD calculation,

fully 1D calculation.

2.2 Acoustic simulationsFor the transmission loss calculation the coupled approach was adopted mainly to

exploit the flexibility of the 1D boundary conditions. Two different configurations (Fig.5) with a similar layout and different dimensions have been simulated. In particular, theimposed boundary conditions were an inlet with a withe noise pressure signal imposed

and a anechoic termination at the outlet. The instantaneous pressure trends at inletand outlet were decomposed by the FFT algorithm and the transmission loss evaluatedaccording to correlation of linear acoustics, evaluating the incident and transmitted

acoustic power [4]. To remain within the validity range of linear codes, the white noiseperturbation was imposed with an oscillation amplitude of 50 Pa. In Fig. 6 and 7 the

comparisons of the calculated TL with the measured one, taken from the literature [5],are shown. Simulations were also carried out with a fully 1D approach and the resultsincluded in the plots.

The comparison shows that the fully 1D approach, being also very fast, is able to

predict with fairly good accuracy the global trend of the TL. However in certain pointssome attenuation peaks are not well captured as well as transparency frequencies,

whereas the coupled approach predicts a transmission loss which globally agrees fairlywell with the measured one. This improvement can be due to the capability of the

multiD approach to capture the non planar wave effects present in correspondence ofthe pipe extensions.

3 Steady-state flow bench simulations

The intake port design has a significant impact on Diesel engines performance and

efficiency: they have to provide a high amount of air to the cylinder, but in the same

time they must create swirl motion to enhance air/fuel mixing and combustion velocity.Computational fluid-dynamics could be useful to improve these components, providing

an insight into the cylinder air motion together with an estimation of the flow coefficientfor new intake port configurations.


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3.1 Engine Geometry and Case setup

In this work, OpenFOAM has been applied to simulate the air flow in the intake portsof a high performance Diesel engine for marine applications. In Figure 8 the simulated

geometry is shown: the two ports have different lengths and curvature to ensure bothhigh air mass flows and swirl number. The main engine data are summarized in Table1.

Engine type Seatek 850 Plus

Valve seat diameter 35.5 mm

Maximum valve lift 12 mm

Inlet pressure 1 bar

p 0.025 barInlet temperature 300 K

Table 1: Engine geometry and experimen-

tal setup.

Solver rhoSimpleFoam

Convection schemes upwind

Laplacian schemes linear limited 0.5

Relative Tolerance 0.1 (0.01 for p)

Absolute tolerance 105 (106 for p)

Table 2: Control parameters of the simula-

tion.

TherhoSimpleFoamsolver was used to perform steady-flow calculations and the Table2 displays the main control parameters of the simulation. The Algebraic Multigrid Solver

(AMG) was used to compute the pressure field.An automatic, Cartesian mesh-generator has been used in this work. The user pro-

vides the STL geometry to the program and specifies the internal and boundary cellsizes. Initially, a first attempt grid is created which is then improved and smoothed tocorrectly account for the original geometry of the boundary. The polyhedral cell support

of the code allows grid refinement close to the boundaries [6, 7]. In this way the timeneeded for grid generation is drastically reduced, furthermore the grid quality is rather

high for most of the computational cells.The total number of cells is 900000 with a mean cell size about 3 mm. The grid isrefined close to the port and valve walls to a size about 1 mm. The details of the original

geometry are correctly captured: in Figure 9 the surface mesh of both the intake portsis displayed. Concerning the boundary conditions, total pressure was imposed at the

Figure 8: Seatek enginecylinder head Figure 9: Details of the computational grid

inlet and static pressure at the outlet to correctly account for the experimental pressuredrop. The standardk model was used for turbulence. Inlet temperature was set to300 K.


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0 2 4 6 8 10 12 14

Valve Lift [mm]

0

0.2

0.4

0.6

0.8

Flo

w

Coefficient

Calculated

Experimental

Figure 11: Comparison between experimental and calculated flow coefficients.

4 Moving Mesh Algorithms with Topological Changes

Internal combustion engine simulation represents a very challenging task for CFD mod-eling: reliable computational tools are required to handle the multiple interacting ther-

mophysical process and geometrical constraints imposed by the engine design. Gen-

erally unstructured grids are used to account for complex shapes like piston bowls,

cylinder head and valves. The presence of moving boundaries (piston and valves)requires to move efficiently the grid points, to keep the mesh quality high and avoidnon-orthogonality and skewness errors. Changing the grid topology can be also useful

to keep an optimum cell size during the whole simulation.In this context, the authors have developed moving mesh algorithms dedicated to en-

gine simulation, where both the points motion and topology changes are performed,significantly reducing the manual work required for the case setup. Two approachesare possible:

The MUMMI(multiple mesh motion and mesh to mesh interpolation) approachrequires a series of meshes to cover the whole simulation. Each mesh is valid fora certain crank angle interval during which its points are moved and the flow is

solved. Then the solution is mapped from the actual source mesh to the following

target mesh.

The FAMA(fully automatic mesh adaptation) approach allows to perform the

whole simulation with only one mesh. To do this, the grid point motion is cou-pled with topology changes to the mesh such as dynamic cell layering and sliding

interfaces [9].

4.1 MUMMI approach

This approach is widely used [10, 11] for its reliability and simplicity but requires aseries of different meshes to perform the whole simulation. Each mesh is moved for a

certain crank angle interval and the flow is solved on it, then all the computed fields aremapped on the new mesh. The grid points motion should be correctly specified from


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motion boundary conditions, and a robust algorithm should be used to avoid that the

moving mesh quickly becomes tangled and invalid. For these reasons, the polyhedralvertex-based motion solver developed in [12, 13] has been adopted by this approach.

4.1.1 Polyhedral vertex-based motion solver

The grid points velocity is computed by solving the Laplace equation of motion withprescribed boundary conditions:

(u) = 0 (1)

where the diffusion fieldcan be constant or variable. The point velocity fielduis thenused to modify point positions:

xnew =xold+ ut, (2)

wherexoldand xneware the point positions before and after mesh motion and tthetime step. Solving for motion velocity is preferred over solving for point position: the so-

lution is less polluted by round errors and a better initial guess is available. To preservethe mesh validity, Equation 1 is solved on a tetrahedral Finite Element (FE) decompo-sition of the polyhedral meshes [12, 13]: a polyhedral cell is split into tetrahedra on the

fly by dividing its faces into triangles and introducing a point in cell centroid as shownin Figure 12.

The Algebraic Multigrid (AMG) solver [14] is used to solve the Equation 1. Despite thenumber of equations in the discretized mesh motion equation is considerably larger

than the number of cells, the form of the operator and the regularity of tetrahedral

decomposition result in a robust motion algorithm.

Figure 12: Cell-and-face decomposition of a polyhedral cell into tetrahedra.

4.2 FAMA approach

Advantages of this approach are represented by the very limited amount of time re-quired for mesh generation, since only one mesh has to be provided, decomposed into

a series of different regions depending on their geometry or mode of motion. Within

each region, the grid motion is accommodated in different ways and after the meshmotion regions are re-connected. To keep an optimum mesh size and avoid grid distor-

tions close to the valves, a combination of different topological changes is used to addor remove cell layers, to deal with sliding mesh interfaces and the valve closure event.


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A multiple-region decomposition for a typical two-stroke engine mesh is illustrated in

Figure 14. Three regions can be identified: cylinder, scavenging and exhaust ports.Piston motion is handled by mesh deformation and layering, with port section remainingfixed for the entire simulation. When overlap exists, cylinder and port meshes are

connected using a sliding interface. The presence of moving valves increases the

Figure 13: Geometry decomposition

for a four-stroke engine mesh: portscells (red), valve region cells (cyan

and yellow), remainder of the cylinder(blue).

Figure 14: Geometry decomposi-tion for a two-stroke engine mesh:

scavenging ports (red), exhaust port

(green), cylinder (blue).

number of regions used to describe mesh motion in four-stroke engines. A minimumof five different regions can be identified in this case:

Intake and exhaust ports;

Cells above and below the intake and exhaust valve poppets, from valve seat tothe piston surface;

Other cells within the cylinder.

A series of sliding interfaces connects the valve regions with the remainder of the

cylinder. Piston and valve motion is handled by dynamic layering or deformation. Thereader is referred to [9] for a detailed description about the mesh topological change

algorithms implemented in the OpenFOAM code.

4.3 Application: intake stroke computation in a GDI engine

This study has been performed on the Mitsubishi-GDI engine: it has 4 valves per cylin-der, a pent-roof combustion chamber and the fuel is directly injected in the combustion

chamber. The piston bowl shape is used to enhance the tumble motion and to createa stratified charge close to the spark at the ignition time. The main geometry data aresummarized in Table 4.3. This engine has been object of several studies in the past

[15, 16].


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Inlet p (total) 1.01 bar

Inlet T 320 KInlet k 4 m2/s2

Inlet 450 m2/s3

Table 6: Inlet boundary conditions.

In-cylinder p 1.01 barIn-cylinder T 373 K

In-cylinder k 4 m2/s2

In-cylinder 450 m2/s3

Table 7: Initial conditions.

4.3.3 Preliminary results

The Figure 16 shows the computed flow field for four different crank angles. It is possi-ble to see the tumble motion generated by the incoming air jet, enhanced by the piston

shape.

(a) 40 CA (b) 80 CA (c) 120 CA

Figure 16: Computed velocity field during the intake stroke for the Mitsubishi GDI en-

gine.

The computed turbulent kinetic energy distribution is displayed in Figure 17. As ex-

pected, high flow velocities generate turbulence across the valve lift as well as the flowdeflection close to the liner surface.

(a) 40 CA (b) 80 CA (c) 120 CA

Figure 17: Computed turbulent kinetic energy field during the intake stroke for the

Mitsubishi GDI engine.

Finally, the computed temperature field in Figure 18 represents the EGR distributionwithin the cylinder.


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(a) 40 CA (b) 80 CA (c) 120 CA

Figure 18: Computed temperature field during the intake stroke for the Mitsubishi GDI

engine.

It is very important that the total domain mass is conserved after each remapping

phase. Mass differences around 0.5% are reported, which are rather negligible and donot influence the computed results.This work is currently under-development: a real operating condition is being simulated

with unsteady pressure and temperature boundary conditions at the inlet. Then thecompression and combustion phases will be simulated, accounting for the liquid fuel

spray injection using the models implemented in [19].

4.4 FAMA application: scavenging in a two-stroke engine

The scavenging modeling has been extensively investigated in the past [2022], andit has always been emphasized the importance of a good moving mesh algorithm to

correctly account for the piston motion relative to the scavenging ports. The data of the

simulated engine for motorcycle applications are taken from [23] and summarized inTable 8. The engine has one exhaust port and five scavenging ports, with symmetrical

design. The ports geometry has been established according to [24].

Bore 66.5 mm

Stroke 57 mm

Compression Ratio 10.8

Displacement 198 cm3

Exhaust Timing 160 o CA

Scavenge Timing 126 o

CASpeed 2500 rpm

Boost pressure 1.05 bar

Table 8: Geometry, operating conditions and computational mesh for the simulated

two-stroke engine.

Total pressure and fixed temperature are imposed at the intake ports, fixed pressure atthe exhaust port. No-slip conditions and fixed temperature was imposed at the walls.


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The standard k turbulence model has been used in this case, considering its reli-ability and robustness for high-Reynolds number flows in complex internal geometries[25, 26].

Results The proposed approach used for mesh motion in two-stroke engines presentsa sliding interface to account for the dynamic connectivity between the cylinder and the

ports. Furthermore, layers of cells are added and removed close to the piston surface.The sliding interface should ensure a correct prediction of the incoming fresh air flowwithin the cylinder and exhaust gas discharge.

The scavenging process is summarized in Figures 19(a)-(d) where the residual gas

distribution is illustrated at four different crank angles. Early in the scavenging process,the fresh air jet penetrates into the burned gas and moves firstly toward the cylinder

head and then toward the exhaust port [24]. Later short-circuiting starts to occur andthe outflowing gas contains an increasing amount of fresh air.

(a) 115 CA (b) 145 CA (c) 165 CA (d) 185 CA

Figure 19: Residual gas distribution during the scavenging process. Computed range:0-1.

The reader is referred to [9] for a more detailed analysis of this case where also thecomputed in-cylinder flow-field and turbulence intensity are compared successfully with

literature experimental data.

5 Diesel combustion modeling

The high complexity of the interplaying physical and chemical phenomena occurring inDiesel combustion has brought an increasing interest versus experimental and com-

putational fundamental studies. In this study the authors implemented in OpenFOAMtwo different combustion models of different complexity and applied them to simulate

a selection of significant test cases from the SANDIA Engine Combustion Network

database [27]. Global heat release rate and flame lift-off lengths are compared withthe available experimental data.

OpenFOAM contains a robust particle tracking algorithm and has been recently usedfor Lagrangian spray modeling. The code already includes most of the widely used sub-models for spray breakup, fuel injection, droplet collisions, evaporation and turbulent

dispersion. Further details about the spray implementation and validation can be foundin [19,2831].


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5.1 Combustion models

5.1.1 Modified Eddy Dissipation Model (EDM+ID)

In Diesel combustion, the fuel is injected into hot, compressed air and auto-ignition

plays an important role in the combustion and flame stabilization processes. Afterignition, combustion is generally mixing-controlled [32]. For these reasons, the fuel

reaction rate can be expressed as:

F = (1 ) F,HT+F,mix (3)

whereis used to switch from the auto-ignition ( = 0) to the mixing-controlled com-bustion mode ( = 1). Expressions of the two terms F,HTand F,mix are thus re-quired. The approach of Pires De La Cruz [33] is used to estimate high-temperature

auto-ignition: a transport equation is solved for an integral function YHIwhose sourceterm depends on the amount of fuel tracer in the computational cell and on the lo-cal self-ignition delayHT, which depends on the fresh gas thermodynamic conditions.The ignition delay is computed by a linear interpolation in a tabulated database whose

values are the result of complex chemistry calculations, performed by the authors, withan extensively validated detailed kinetic scheme for n-heptane [34].

The mixing-controlled fuel burning rate F,mixdepends on the fuel (YF), oxidizer (YO),product mean mass fractions (YP) and on the turbulent mixing time, estimated fromintegral length scales ast=k/:

F,mix =Cmag

kmin

YF, YOs ,

YP(1 +s)

(4)

whereCmagand are two model constants. In Equation 4, the reaction rate is limited

by the deficient mean specie. In the present workCmagis set to 4, whileis 1, follow-ing [32]. When the Eddy Dissipation Model is coupled with an ignition treatment it ispossible to predict both ignition and flame stabilization since fuel and oxidizer do not

immediately ignite as soon as they meet [32].

5.1.2 Perfectly Stirred Reactor (PSR)

In this model the mixture is assumed to be homogeneous within each computationalcell, hence any sub-grid scale turbulence-chemistry interaction is neglected. This

model has recently been applied in [3537] for both combustion bomb and diesel en-

gine simulations. The reactive mixture in each computational cell is treated as a closedsystem. When the chemical time scale is much lower than the fluid-dynamic time-scale,

an operator-splitting [32, 38] technique is used: at the beginning of the each computa-tional time an ODE stiff solver takes the thermodynamic conditions (T, p, YI) in eachcell and integrates the chemical problem within the time-step, solving the specie and

the energy equations. Then it updates the specie mass fractions as:

Yi (t+ t) =Yi(t) +

t+tt

iWidt (5)


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where is the density, iis the reaction rate and Wiis the molecular weight of thespecies i. The chemistry solver adopted in this work is based on a multi-step, Semi-Implicit Bulirsch-Stoer method,SIBS[39]. Finally, the reaction rate Yiis estimated as:

Yi=Yi

(t+ t) Yi(t)

t (6)

The chemical mechanism can be provided to the OpenFOAM code in the CHEMKIN

format [40], then suitable functions and libraries compute the reaction rates. A skele-tal mechanism with 32 species and 70 reactions was used to simulate the n-heptanechemistry [41].

The operation-splitting technique increases significantly the computational time, mak-ing use of detailed chemistry. For this reason the authors have implemented in theOpenFOAM code the ISAT (in situ adaptive tabulation) algorithm [42, 43], where the

chemical reaction rates are tabulated on-the-fly during the computation (in situ) andused to approximate the reaction rates of the cells with a composition close to the

tabulated ones.

5.2 Validation

Experiments conducted in the SANDIA combustion chamber were used to evaluate the

proposed models. It is an optically accessible, cubical vessel where spray-combustion

experiments are performed under ambient similar conditions to those occurring in a

diesel engine at the time of injection. The fuel is injected by a common-rail injectormounted on one side of the chamber with a Mexican-hat injection profile. A piezoelec-tric pressure transducer measures the vessel pressure during the experiments. The

experimental apparatus is accurately described in [44, 45].

amb[kg/m3] T [K] [O2]

Case 1 14.8 1000 21%Case 2 14.8 1000 15%

Case 3 14.8 1000 10%

Case 4 14.8 1300 21%

Table 9: Operating conditions simulated: initial ambient temperatures, densities andoxygen concentrations.

Different operating conditions were simulated, as summarized in Table 9. N-heptanewas used as fuel and the injected mass for each case was taken from [27]. The models

were validated in terms of

heat release rate;

flame lift-off location;

In this study, a constant spray angle is used in the simulations, while the initial droplet

diameter was derived by the injector diameter and its area contraction coefficient [28].

Both the Kelvin-Helhmoltz and Rayleigh-Taylor mechanisms are accounted for to modelthe spray breakup [46]. The Ranz-Marshall correlation [47] is used to model the droplet

evaporation. Droplet to droplet interactions and turbulence dispersion effects are ne-glected.


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5.2.1 Geometry

The computational mesh adopted for the calculations is displayed in Figure 20. Con-sidering the axial-symmetric geometry, only a quarter of the combustion chamber was

modeled. After a mesh size investigation [41], a cell size of 1 mm close to the sprayaxis was chosen: in this way the mesh is very fine where combustion takes place anda coarse grid is used elsewhere, reducing the required computational time. The total

number of cells is 90000. A time step of 1e-3 ms has been used to better describethe spray evolution at the beginning of the injection phase and correctly reproduce theair/fuel ratio distribution at the ignition time [41,48].

Figure 20: Computational mesh representing the SANDIA combustion vessel [27].

5.2.2 Vessel pressure history

The proposed case setup was then used to simulate the combustion process. The wall

temperature was adjusted to reproduce the experimental temperature cool down before

the injection starts [27]. To correctly predict the engine performance, a model for dieselcombustion should estimate the premixed and mixing-controlled combustion phases.Measured data of vessel pressure and its rise versus time will be used to evaluate

the proposed approaches for the Cases 1-4. Figure 21 compares the experimentalpressure rise and its derivative with the computed ones for all the tested cases.Both the combustion models correctly captures the experimental pressure rise during

both premixed and mixing-controlled combustion phases for the Cases 1 and 2 asshown in Figures 21(a)-(b), representing no EGR and medium EGR (28%) operating

conditions. It is interesting to see that this happens also for the PSR model: the gridsize is fine enough that the sub-grid turbulence-chemistry interaction can be neglected.Results for the Case 3 are affected by an overestimation of the ignition delay for high

EGR conditions (52%), as shown in Figure 21(a). However, the PSR model correctlycaptures the mixing-controlled combustion phase. The results are not satisfactory forthe EDM+ID model, probably because the ignition delay table is too coarse around the

flammability limit for high EGR.The Case 4 represents operating conditions similar to those found after a pilot-injection

and is characterized by a very short ignition-delay. In Figure 21(b), the ignition delay

time is correctly estimated by both models. The pressure rise is rather well predictedby the EDM+ID model during the mixing controlled combustion phase, while it is over-

estimated by the PSR model, probably because the turbulence-chemistry interaction isneglected.


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0 0.0025 0.005 0.0075 0.01

Time [s]

0

50

100

150

200

250

300

Pressu

rerise[KPa]

ExpPSREDM+ID

Tamb

= 1000 K, O2= 21%,

amb= 14.8 kg/m

3

0

30

60

90

120

dp/dt[MPa/s]

(a)

0 0.0025 0.005 0.0075 0.01

Time [s]

0

50

100

150

200

250

300

Pressu

rerise[KPa]

ExpPSREDM+ID

Tamb

= 1000 K, O2= 15%,

amb= 14.8 kg/m

3

0

30

60

90

120

dp/dt[MPa/s]

(b)

0 0.0025 0.005 0.0075 0.01

Time [s]

0

50

100

150

200

250

300

Pressurerise[KPa]

ExpPSREDM+ID

Tamb

= 1000 K, O2= 10%,

amb= 14.8 kg/m

3

0

30

60

90

dp/dt[M

Pa/s]

(c)

0 0.0025 0.005 0.0075

Time [s]

0

50

100

150

200

250

300

Pressurerise[KPa]

ExpPSREDM+ID

Tamb

= 1300 K, O2= 21%,

amb= 14.8 kg/m

3

0

30

60

90

120

dp/dt[M

Pa/s]

(d)

Figure 21: Comparison between experimental and computed pressure rise and itsderivative versus time for the Cases 1-4.

5.2.3 Prediction of the Flame Lift Off

A deep understanding of the mechanism of lift-off stabilization is required as well as ofthe interrelation with the following soot formation [49]. The computed and experimental

lift-off lengths are compared in Figure 22. The computed value was identified by a2200K iso-line according to [50]. Both models predict correctly the lift-off dependency

on EGR and mixture temperature [49]. However, the EDM tends to overpredict the

lift-off length, showing significant errors for Case 3 and Case 6, where it fails in theprediction of the ignition delay since it does not account for cool-flame effects.

6 Conclusions

The paper provided an overview of the research activity carried out by the authors bydeveloping OpenFOAM applications for internal combustion engines. The aim was to

propose OpenFOAM either as a CFD platform for fundamental studies either as indus-trial toolkit. This second field of applications motivated the development of a novel 1D-

3D coupling approach, which was implemented into the code to perform multiple cycle

simulations of the entire engine system or to evaluate the transmission loss of complexmufflers. Another requirement which is strongly demanded by the industrial engine re-


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Figure 22: Computed and experimental averaged lift-off length for the Cases 1-4.

search is the assessment of efficient moving mesh algorithms as well as the possibilityof performing steady-state tests for flow coefficient evaluation. The authors contribu-tions and experience in these field were extensively reported in the paper. Finally the

object-oriented and open-source structure of OpenFOAM makes it very attractive to

perform collaborative fundamental studies. To these ends, the authors illustrated theimplementation of Diesel combustion models and its application to simulate the SAN-

DIA constant-volume test cases, whose data are available to the research communityfor model assessment.

7 Contacts

Dr. Gianluca DErrico, Politecnico di Milano

e-mail: [email protected]: http://www.engines.polimi.it/CFD.html

8 Acknowledgments

This research has been financed by Advanced Marine Propulsion Technology SEATEK

S.P.A., Lamborghini Automobili S.P.A., MV Agusta S.P.A., Fondo Giovani Ricercatori ofDipartimento di Energetica, CNR Istituto Motori.

The authors are grateful to Institut Francais du Petrole (IFP) for providing the CADgeometry of the Mitsubishi GDI engine used in this study.The contribution of Daniele Ettorre to the Diesel combustion modeling section is grate-

fully acknowledged.

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