predictions of transient fuel spray phenomena in the...

July 26, 2002 10:43

2002-02-FFL-80

PREDICTIONS OF TRANSIENT FUEL SPRAY PHENOMENAIN THE INTAKE PORT OF A SI-ENGINE

M. Burger, R. Schmehl1, P. Gorse, K. Dullenkopf, O. Schafer, R. Koch, S. WittigInstitut fur Thermische Str¨omungsmaschinen, Universtit¨at Karlsruhe

1 presently at the European Space & Technology Centre ESA-ESTEC, The Netherlands

Copyright 2002 Society of Automotive Engineers, Inc.

ABSTRACT

The present study addresses the numerical prediction of thetwo-phase flow in the intake port of a SI-engine. Particular em-phasis is put on transient phenomena, as well as secondary ef-fects, such as droplet breakup and droplet wall interaction. Thesephenomena have a significant influence on the fuel air mixturecharacteristics and cannot be neglected in the numerical predic-tion.The numerical methodology, presented in this paper, is based ona 3D body-fitted Finite Volume discretization of the gas flow fieldand a Lagrangian particle tracking algorithm of the disperse fuelphase. The Unsteady Reynolds Averaged Navier-Stokes equa-tions (URANS) are solved by a time-implicit three level scheme.In the Lagrangian particle tracking algorithm, the spray is mod-eled by superposition of a large number of droplet trajectories.Two advanced numerically effective models are presented for theprediction of droplet breakup and droplet wall interaction. Spe-cial emphasis is put on the correct reproduction of the dropletstatistics.In the present study the fuel injection and spray preparation pro-cess within the intake port of a SI-engine is investigated. Spraypreparation is dominated by atomization processes like dropletbreakup and wall interaction which predominantly take place atthe valve seat. In order to find the principal characteristics offuel preparation in a SI-engine, a parametric study has been car-ried out focusing on the influence of the gap sizes of the intakevalve which strongly affects the complete fuel preparation pro-cess. The study is concluded by an analysis of qualitative andquantitative results of the predicted flow field.

NOMENCLATURE

Symbolsc f m convection correction fac.c f h convection correction fac.cp specific heat capacityCD aerodyn. drag coefficientd deposite mass flux rateD droplet diameterD0�x D at x% of tot. liqu. vol.D10 length mean diameterD32 Sauter mean diameterh enthalpyk turbulent kinetic energym mass fluxLa Laplace numberL integral length scalen droplet number densityOn Ohnesorge numberp pressurePr Prandtl numberRe Reynolds numbers source termS splashing parameterSc Schmidt numbert charact. time scale, timeT temperatureTu degree of turbulenceU velocity componentWe Weber numberY vapor mass fractionz gap size

Greek Symbolsα heat transfer coefficientβ spray cone angleε dissipation rate ofkη deposition rateΓ diffusion coefficientλ thermal conductivityµ dynamic viscosityµ mean valueν kinematic viscosityφ generic transport variableρ densityσ variance, surface tensionτ shear stress

Subscripts0 initial stateb boilc crossinge turbulent eddieen�ex entry, exitg�d gas, dropletk class indicatorL Leidenfrostrel relatives surfacen normalt turbulentout outletvap vapor

1

INTRODUCTION

The stringent emissions standards for automotive spark igni-tion engines require a comprehensive and detailed study of fuelpreparation, combustion and emission formation. Particular em-phasis has to be put on fuel mixture quality which directly affectsthe emission of the SI-engine.The present paper addresses the fundamentals of fuel prepara-tion process for open valve injection inside the intake port of aSI-engine. Spray propagation as well as secondary spray effectswhich occur principally at the valve seat are studied in detail.Droplet breakup and droplet wall interaction are important sec-ondary effects and have been included as well. Both may dependon the gas velocity and therefore mixture quality and fuel deposi-tion will be strongly affected by the gap size of the intake valve.In order to achieve a better understanding of fundamental fuelpreparation processes, a parameter study has been carried out forvarying gap sizes.Experimental investigations of fuel preparation inside the intakeport have been reported previously [14] [9]. However, spray ef-fects at the valve seat within the intake port are difficult to ana-lyze by measurement techniques. In order to asses and optimizefuel-air mixture preparation, a comprehensive numerical investi-gation is presented herein.The present study introduces an efficient approach for the pre-diction of the complex two-phase flow field in the intake port ofa SI-engine. The accurate discretization of the duct geometryrequires a body fitted mesh. A three-dimensional compressiblein-house CFD code, based on the Finite Volume method (FVM)is used to calculate the gas flow field. Since fuel injection causestransient flow interaction phenomena, the Unsteady ReynoldsAveraged Navier-Stokes equations (URANS) are solved in con-junction with a time-implicit three level scheme. An additionalLagrangian in-house code for the prediction of the fuel sprayis is used in conjunction to the CFD code. The spray is mod-eled by superposition of a large number of droplet trajectories.Spray dispersion by the turbulent gas flow is taken into accountby stochastic variations of the velocity field along the individualdroplet trajectories. Spray evaporation is also considered by thewell known Uniform Temperature Model [22] [1].Two advanced models have been developed to account for theproper description of droplet breakup and droplet wall interac-tion. Special emphasis was put on the correct reproduction of thedroplet statistics. Both models are based on empirical correla-tions, which have been derived from experimental data [20] [21].The models are formulated in terms of non-dimensional parame-ters such as Reynolds, Weber and Laplace number.The two-phase flow to be considered is characterized by intenserates of interphase mass, momentum and energy transfer. Typ-ically, a major part of the interaction between droplets and gasphase occurs in the flow region near the nozzle. In order toconsider unsteady mutual influences of continuous (gas) and dis-

perse (liquid) phases, the CFD code is coupled with the Lagrangecode by interfacial source terms.The present studies are based on experimental investigationswhich have been carried out for part loaded operation. As thesurface temperature of the inlet valve is exceeding 100ÆC (373K) for these operating conditions [14], hot surfaces with wallfilms are approximated as dry walls in the present study assum-ing rapid evaporation of the deposited liquid fuel.The accuracy of the numerical codes in terms of gas/droplet ve-locity, droplet number density and fuel vapor concentration hasbeen investigated previously [2] [19].

GAS PHASE

The computation of the gas flow field is carried out by meansof the in-house code METIS. The numerical description is basedon the Unsteady Reynolds Averaged Navier-Stokes equations(URANS), represented by the following system of equations,

∂∂t

ρ�∂

∂xiρui � sρ�d (1)

∂∂t

ρu j�∂

∂xiρuiu j � � ∂p

∂x j�

∂τi j

∂xi� su j �d (2)

∂∂t

ρh�∂

∂xiρuih � �

∂∂xi

�µ

Pr�

µt

Prt

�∂h∂xi

�∂p∂t

�ui∂p∂xi

� τi j∂ui

∂x j� sh�d (3)

∂∂t

ρY �∂

∂xiρuiY � �

∂∂xi

�µSc

�µt

Sct

�∂Y∂xi

� sρ�d (4)

The stress tensorτi j for Newtonian fluids is given by

τi j � �µ�µt�

�∂ui

∂x j�

∂u j

∂xi� 2 ∂uk

3 ∂xkδi j

�� (5)

assuming the validity of the Boussinesq approximation. In orderto determine the turbulent viscosityµt , the standardk-ε turbu-lence model is included [7]. The turbulent Prandl and Schmidtnumber are set to the constant values ofPrt=0.9 andSct= 1.0.The unsteady terms in Eq. (1)-(4) are discretized by a time-implicit three level scheme [5]

∂φ∂t

��t�∆t

�3φt�∆t � 4φt � φt�∆t

2 ∆t� (6)

In contrast to explicit schemes, implicit methods have no restric-tion regarding the Courant number. Hence, implicit methodsexhibit better numerical stability. However, in order to resolve

2

the transient processes, the Courant number was adjusted to thepresent flow conditions.The system of transport equations is formulated in a body-fitted 3D Cartesian system and discretized by means of a finite-volume method. The coupled velocity-pressure field is deter-mined by using the SIMPLEC pressure-correction algorithm onnon-staggered grids [25]. In order to reduce numerical diffusion,a second order bounded Monotonized Linear Upwind scheme[11] is used in the present study for the discretization of convec-tive fluxes. The finite-volume balance equations for structuredgrids are arranged in a sept-diagonal matrix , which is solvedby an iterative solution procedure based on a conjugate gradientmethod [12].

LIQUID PHASE

The liquid fuel spray is predicted by the in-house codeLADROP. The program is based on the Lagrangian approach ofdispersed two phase flow in terms of tracking a statistically sig-nificant number of droplet parcels in the gas flow. Each parcelis represented by an individual droplet and is determined by dis-cretization of the continuous spectra of droplet initial conditionsin the near field of the atomizer.

EQUATION OF MOTION

The droplet tracking algorithm is based on the integration ofthe droplets equation of motion

d�ud

dt��3

4ρg

ρd

CD

D��ud � �ug� ��ud � �ug� � (7)

As the aerodynamic drag coefficientCD is a function of theReynolds number, it varies along the trajectory integration. Theaerodynamic drag force on the droplet is also strongly affectedby the deformation of the droplet. As droplet deformation byaerodynamic forces is a complex phenomena, the following cor-relation [27] is used to approximate the influence of deforma-tion, governed by internal flow patterns and the flow around thedroplet

CD � 0�28�21

Red�

6�Red

� We�0�2319� 0�1579logRed � 0�0471�logRed�

2

� 0�0042�logRed�3�� Red � 2000� (8)

SPRAY DISPERSION

In order to account for the effect of turbulent spray disper-sion, the gas flow field equations are superposed by stochasticfluctuations along the droplet trajectories [6] [8]. In this concept,the local turbulence is characterized by the length scalel e anddissipation time scalete of eddies representing the coherent flowstructures

le �C12µ

k32

ε� te �

le��u�g�

� (9)

In addition to the life timete, a crossing timetc is calculated from

�� tc

t0��ug � �ud�dt

�� le� (10)

taking into account the droplet dynamics. The minimum of bothtime scales determines the instance of a droplet leaving the tur-bulent eddy. Consequently, a new velocity fluctuation�u �

g is pro-duced by a random generator from a Gaussian distribution whichis determined by the probability density function

f �u�g� �1

σ�

2πexp

��1

2

�u�g�µ

σ

�2

� µ� 0 � σ�

23

k� (11)

This velocity fluctuation remains constant for the period ofdroplet-eddy interaction and is added to the local value of thegas flow velocity.

SPRAY EVAPORATION

Droplet evaporation is simulated by means of the UniformTemperature Model [4] [22] [1]. This computationally effectivemodel is based on the assumption of a homogeneous tempera-ture distribution within the droplet and phase equilibrium condi-tions at the liquid/gas interface. Compared to the droplet interior,diffusion time scales in the gas phase are smaller by orders ofmagnitude giving rise to a quasi-stationary description of the dif-fusive transport processes. Using reference values for the fluidproperties (1�3-rule from [23]), the integration of the transportequations inside the droplet for mass and enthalpy yields ana-lytical expressions for the diffusive transport fluxes. Convectivetransport is considered by empirical correction factorsc f m andc f h (Eq. 14) resulting in differential equations for droplet mass(Eq. 12) and temperature (Eq. 13).

dmd

dt��c f m 2πD ρg�re f Γim�re f ln

1�Yvap�g

1�Yvap�s(12)

3

dTd

dt� � 1

md cp�d

dmd

dt

�c f hc f m

cp�vap�re f �Tg�Td�

��1�Yvap�g

1�Yvap�s

� 1Le

�1

�1

�hv

�� (13)

c f m � 1 � 0�276Re12 Sc

13 �

c f h � 1 � 0�276Re12 Pr

13 (14)

SECONDARY DROPLET BREAKUP

The details and the validation of the present breakup modelhave been presented previously [19] [20]. At low relative ve-locities, the spherical shape of the droplets is preserved by thedominating effects of surface tension and internal viscous forces.With increasing velocities, the destabilizing aerodynamic forceson the droplet surface result in deformation, oscillations and dis-integration of the droplet.

Figure 1. Droplet deformation and bag breakup [17]

Correlations for classifying secondary droplet atomization pro-cesses typically are based on two characteristic non-dimensionalparameters,

We �ρg u2

rel D

σd� On �

µd�ρd D σd

� (15)

The Weber number is the ratio of the strength of aerodynamicforces relative to surface tension forces, whereas the Ohnesorgenumber represents the damping effect of viscous friction in thedroplet compared to surface tension. In the Weber number rangefrom We � 1 up to a critical valueWe � Wec, non-destructivedroplet deformation and oscillation is observed. Three differentmechanisms govern the breakup of droplets within the regime ofWeber numbers typical of flows in combustion engines.Exceeding the critical Weber number ofWec = 12, the first mech-anism observed isbag breakup (Fig. 1). This process is charac-terized by the formation of a thin hollow bag of droplet fluid be-ing extracted from a toroidal rim. With increasing aerodynamicforces, thebag-plume breakup regime(Fig. 2) is observed ,starting atWe = 18 . Flow interaction is forming an additionalfluid filament in the center of the bag structures which is aligned

Figure 2. Droplet deformation and bag-plume breakup [17]

with the relative flow velocity.shear breakup (Fig. 3) occursat Weber numbers exceeding the value of 40. This mechanismis fundamentally different to the preceding mechanisms and ischaracterized by a rapidly disintegrating film being continuouslystripped off the rim of the disc-shaped droplet by shear forces.

Figure 3. Droplet deformation and shear breakup [17]

For the present predictions, a stochastic technique is applied toaccount for secondary droplet breakup. It is based on correla-tions, derived from experimental data [17]. In order to take intoaccount for viscosity effects for On� 0.1, a corrected Webernumber is introduced [20]

Wecorr �We

1�1�077On1�6 � (16)

The Sauter mean diameterD32 of the resulting secondarydroplets is determined from a universal non-dimensional corre-lation

D32

D0� 1�5On0�2We�0�25

corr � (17)

In contrast to theD32, the size distribution of the secondarydroplets depend on the breakup mechanism. The fragments ofbag and bag-plume breakup (Fig. 1, 2) are described by a uni-versal root normal distribution (Eq. 18), with a fixed ratio ofD0�5�D32� 1�2

f �x� �1

2σ�

2πxexp

��1

2

��x�µσ

�2

� (18)

x �D

D0�5� µ � 1�0 � σ� 0�238�

Due to the nature of shear breakup mechanism (Fig. 3) , thesecondary droplet spectrum is characterized by a bimodal sizedistribution. It consists of a fraction of small droplets, strippedof the parent droplet and a single much larger core droplet. Inthe computational model, the maximum stable diameterD c ofthe core droplet is evaluated from the local value of the critical

4

Weber numberWec. The fraction of the small droplets is dis-tributed according to Eq. (18), based on a reduced Sauter meandiameter

D32�red �45

D32 Dc

Dc�D32� (19)

The time scales of the initial deformation and the subsequentbreakup mechanisms are determined by correlations which havebeen derived from extensive experimental data. Normalized bythe characteristic time scale

t� �

ρd

ρD0

vrel� (20)

the temporal evolution of bag, bag-plume and shear (incl. plume-shear) breakup is summarized in Fig. 4. The temporal stages ofeach breakup process are implemented in the numerical modelsin terms of time dependant droplet deformation and generationof secondary droplets. A detailed derivation of the numericalapproach is available [18].

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8

We

t/t*

bag

small bags

breakup

breakup

breakup

ring

breakupplume

detachment at rim of disk

plume/core-droplet complex

larger fragments

plumebag

plume

distortion & flattening

bump ligaments at rim of disk

bag bag-plume plume-shear shear breakup

Figure 4. Temporal stages of droplet breakup (On � 0�1) [18]

WALL INTERACTION

The wall interaction can be discriminated into the regimesof cold wall (T � 1�05 Tb), hot wall (1�05 Tb � T � TL) andvery hot wall (T � TL) [16]. Since wall temperatures are wellbelow 1�05Tb in the present study, cold wall interactions are con-sistently used throughout the computation.In this temperature regime, the two basic mechanisms are eithersplashingor complete depositionof the droplet. In the case ofsplashing, a fraction of the droplet mass is deposited on the wall

whereas the remainder is decomposed into secondary dropletsand rejected back into the gas flow. A possible approach to dis-tinguish between splashing and complete deposition involves theimpact Reynolds number and the Laplace number,

Re �un D ρd

µd� La �

D σd ρd

µ2d

(21)

The impact Reynolds number is based on a corrected droplet ve-locity normal to the wallun � ud sinα0�63. An analysis of numer-ous droplet impact experiments indicates that splashing is sepa-rated from complete deposition by the limiting function

Re � 24La0�419� (22)

In order to quantify the splashing process, it is necessary to es-tablish a relation for the deposition rateη characterizing thefraction of the deposited droplet mass. Up to now, experimen-tal studies reveal only little information about the details of thesplashing process and the deposition rate. However, it is evidentfrom several studies [26] [24] [10], that the distance from thesplashing/deposition (Eq. 22) separation line in the logarithmicRe-La plane has a dominating influence on the deposition rate inthe splashing domain. Analytically, the distance from the splash-

Figure 5. Droplet impact and splashing on wall [15]

ing/deposition separation line can be described by the splashingparameterS, expressed by the relation

Re � S 24La0�419� (23)

whereS� 1 represents zero distance. Because the splashing pro-cess is insufficiently understood, a practical approach is chosenin this study for the deposition rate

ηdrywall � S�0�6 � (24)

which is based on an extrapolation of experiments on the inter-action of droplets with thin wavy films [16].The determination of initial conditions of the secondary dropletsis a second important part in modeling the splashing process.Secondary droplets have much smaller diameters compared totheir parent droplet. The logarithmic diameter distribution of thedroplet cloud produced by splashing can be described by a Log-Normal distribution

5

f �x� �1

xσ�

2πexp

��1

2

�lnx�µ

σ

�2

� (25)

x �D

Dm� µ � 0 � σ� 0�45 �

including the empirical characteristic diameterDm :

lnDm

D0� �2� D0

Dre f�0�05S � Dre f � 4066µm (26)

In this relation,D0 denotes the droplet diameter just before im-pact. The correlations are in good agreement in comparison toexperimental data [15] [24]. Ejection angles of the secondarydroplets are typically in the range ofα � 10Æ to α � 15Æ relativeto the wall whereas initial velocities are about 60% of the impactvalue. In the present study, secondary droplets from splashingare very tiny and instantly follow the gas flow in the near wallregion. Therefore, a detailed modeling of initial velocity and po-sition is not necessary for the secondary droplets generated bysplashing.Wall films have a strong impact on the deposition rate, but theydo not affect spray statistics of secondary droplets. As only verythin wall films are expected for the operating conditions con-sidered in the present study, the effect of wall films can be ne-glected.

COUPLED SOLUTION OF THE TWO PHASE FLOW

The gas and the liquid phase interact by means of mass, mo-mentum and energy transfer. Hence the influence of the spray tothe gas phase has to be considered by interfacial droplet sourceterms.As transient phenomena can be initiated due to the presence ofspray, the discretization of the unsteady droplet source terms isimportant in the numerical approach. In the following, a timeimplicit procedure is presented for the prediction of an unsteadytwo phase flow field:In a first step, the gas phase is solved by the CFD programMETIS. Based on the results of the gas code, the dispersion andevaporation of the spray for the next time step is computed byLADROP. Secondary spray effects as droplet breakup and spraywall interaction are included. The overall time step is limited bythe gas and the spray solver. Whereas the implicit gas solver canhandle CFL numbers� 1, the time step of the explicit Runge-Kutta solver in the spray code has to be adjusted to a CFL num-ber� 1. Another limiting factor is of course the numerical errorsintroduced by the discretization scheme. As a result, LADROPreturns droplet source terms (Eqs. 27-29) which describe thelocal rates of mass, momentum and energy transfer across theliquid-gas interface [3]. Subsequently the gas phase is solved for

this next time step, adding source terms of the liquid phase to thematrix of the discretized Eqs. (1)-(4). Based on the result of theactual time step, the solution for the following time step has tobe solved in the same way. By this method the whole period ofliquid fuel injection is predicted, considering unsteady couplingeffects.

�V

sρ�ddV �N

∑k�1

nk�mend �mex

d �k� (27)

�V

sUi �ddV �N

∑k�1

nk�mend Uen

d�i�mexd Uex

d�i�k (28)

�V

sh�ddV �N

∑k�1

nk�mend hen

d �mexd hex

d �k� (29)

NUMERICAL INVESTIGATION

Figure 6. Fuel injection within the intake port [t= 4 ms]

The numerical investigation to be presented subsequently isbased on preceding experimental studies of the fuel preparationat part loaded operation of the engine [13] [14]. The base engineis a four-cylinder four-valve production type. Fuel is injectedvia a sequential multi-point injection system. To study the fuelpreparation at various operating conditions, optical access to theinterior has been realized by cutting off the cylinder head of theouter cylinder. Based on original CAD data, the inner contour ofthe missing part was then machined from acrylic glass and fittedto the cylinder head. A detailed description of the test rig and themeasurement techniques has been published [14]. In the experi-ment, a steady air flow through the intake port was generated bya vacuum pump. Fuel atomization was realized by a productiontwo jet pintle type injector using an injection pressure of 0.46MPa. The experimental setup is illustrated in Fig. 6, showing avisualization of the spray 4 ms after starting fuel injection. The

6

inlet boundary conditions have been adapted to operating con-ditions of the base engine at a revolution of 1500 RPM and anIMEP of 0.4 MPa. In comparison to the operating engine, the in-let boundary conditions are constant over time in the experiment(Table 1).

gas flow (air) fuel (n-octane)

mg 58�4 gs m f uel 3�3 g

s

Tg 299K Tf uel 293K

pg 0�1 MPa Uf uel 24 ms

Ug 33�3 ms β 10Æ

Table 1. Inlet boundary conditions

The focus in the present numerical study is put on fuel-air mix-ture generation, which is dominantly affected by droplet breakupand droplet wall interaction [9]. As these atomization processesare strongly influenced by the valve gap, a parametrical studyhas been carried out: A completely opened, a halfway openedand a nearly closed intake valve. As specified in Table 1, theinlet boundary conditions are identical for all three cases. Dueto the restricted cross section the gas velocities increase dramati-cally at the valve gap in particular for the case with a minimizinggap size. Hence, different mechanisms of droplet breakup areobserved as well as varying splashing events. For a completelyopened intake valve (z = 8 mm) the predicted results are illus-trated in Fig. 7. The velocity field of the gas phase is shownas a vector plot on the symmetry plane, whereas the fuel sprayis represented by a limited number of droplet trajectories. Thegeneration of secondary droplets, caused by splashing events onthe valve surface is also obvious in Fig. 7.By deposition of fuel on the valve surface a liquid wall film isgenerated [28], in particular for cold starting conditions. For thestudied operating conditions, the surface temperature of the valveincreases and is even exceeding 100ÆC (373 K) [14]. Under theseconditions the evaporation rate of the liquid film significantly ex-ceeds the deposition rate. Very thin wall films are the conse-quence. Because of this effect hot surfaces with wall films areapproximated as dry walls in the present study assuming rapidevaporation of the deposited liquid fuel.The computational domain is illustrated in Fig. 7. Due to thesymmetric design of the intake port only one half is computed.The turbulent inlet boundary conditions are approximated bypipe flow conditions. In order to achieve a fine discretizationat the valve gap, the mesh resolution is less than 1 mm at the portexit.

Figure 7. Computational domain for a valve gap of z = 8 mm

DROPLET STARTING CONDITIONS

The position of the spray is indicated by representative tra-jectories originating from the injection nozzle. Since primaryatomization of the fuel is completed within a short distance of 1mm, the initial conditions of the spray can be specified close tothe nozzle orifice. Each representative droplet parcel is describedby a specific combination of droplet diameter, velocity and po-sition. One of the major advantages of the Lagrangian methodis the possibility to specify a large number of different dropletinitial conditions to achieve a detailed resolution of the primaryatomization process [20] [19]. Droplet initial conditions are gen-erated stochastically according to the distribution recorded byPDA during bench experiments. The normalized number densityand the Sauter mean diameter are illustrated for the fuel spray inFig. 8 recorded 2 ms after injection start. A detailed descriptionof droplet initial conditions which have been used in the presentstudy is available [2].

Figure 8. Bench PDA measurements of the injected fuel spray

7

TRANSIENT SPRAY EFFECTS

The injection of a fuel spray is characterized by transientphenomena. For example, unsteady acceleration of the gas phaseis induced by aerodynamic interaction with the fuel spray. Asmomentum source terms are strongly dependent on the relativevelocity, transient forces on the gas flow are predominant closelybehind the nozzle. The resulting phenomena have to be consid-ered by an unsteady approach of the two-phase flow field for anaccurate prediction of the fuel propagation.Due to constant inlet conditions over time, transient effectswithin the gas phase can only be caused by the fuel spray. Thesimulation is started at the begin of fuel injection (t = 0 ms). Theoverall time stepping is limited to a maximum of 0.1 ms through-out the complete simulation. Additionally, the time step has to beadjusted to account for a CFL number� 1 of the explicit Runge-Kutta solver for the droplet phase. Subsequently, two results arepresented fort = 1 ms(left) and t = 5 ms (right) along the cen-terline of the spray cone, as shown in Fig. 9. The gas velocity is

Figure 9. Side view along the centerline of the spray cone

illustrated by streamlines and the spray is shown as a contour plotof the normalized number density. A vortex is observed betweenthe spray cone and the upper wall of the domain. It is causedby flow separation at the flange of the cylinder head. A simi-lar vortex has been observed by two phase PIV measurements[14]. As gas velocities are low in the shear flow of the vortex, thespray causes an acceleration of the rotating gas phase increasingthe size of the vortex. Due to the inertia of the vortex, its sizeincreases to a maximum which is observed 5 ms after begin ofinjection. Since tiny droplets of the fuel spray are captured bythe vortex, fuel propagation is directly affected.Spray penetration is also influenced by the unsteady accelera-tion of the gas phase. Subsequently, the penetration of two rep-resentative droplets is studied. The first droplet is injected attin j � 0 ms representing the spray tip, the second att in j � 5 ms.

The predicted results (Fig. 10) are compared to data from laserlight sheet measurements and are found in good agreement.Analyzing the gradientsds

dt in Fig. 10, two inflection points are

Figure 10. Spray penetration

found. It is obvious that droplets are retarded after the injec-tion and accelerated subsequently to a constant velocity. Sincespray interactions are stronger for the first droplet (t in j � 0 ms),the penetration time is larger, compared to the second droplet(tin j � 5 ms).

GAS PHASE RESULTS

Predictions of the gas phase are presented for the three cases:a completely opened (z = 8 mm), a halfway opened (z = 4 mm)and a nearly closed (z = 2 mm) intake valve. As the inlet con-ditions are constant over time for all cases, the gas velocities arein principal different at the valve seat. In general, the gas flowis accelerated and directed towards the port exit. A significantrecirculation zone is found behind the valve stem. A typical re-sults of the gas flow field in the longitudinal section is illustratedin Fig. 11. The quantitative numbers of flow at the port exit ofthe intake port have been evaluated and are summarized in Table2. It is obvious, that if the gap size is minimized, gas velocitieswill increase dramatically at the valve seat. For Mach numbersgreater than 0.1, compressibility effects become important in par-ticular at the valve gap. As a consequence, the gas temperaturesat small gap sizes are significantly reduced. Gas velocities arealso affected by the compressibility effects. Thus, mean gas ve-locities are not linear to the reciprocal gap size at the port exit,as it would be the case for an incompressible fluid. In particu-lar, compressible effects are strong forz = 2 mm, where a Machnumber of 0.54 is observed at the valve gap.

8

Y

X

Z

100 m/s

Figure 11. Gas velocity vector in a longitudinal section for z = 8 mm

z 8 mm 4 mm 2 mm

Ug�max 66�2 ms 110 m

s 181 ms

Ug 28�9 ms 60�0 m

s 126 ms

Tg 297K 293K 279K

pg 0�0979MPa 0�0925MPa 0�0842MPa

Table 2. Gas flow quantities at the port exit

DROPLET PHASE RESULTS

As mentioned previously, fuel preparation in the intake portis strongly affected by droplet breakup and droplet wall interac-tion, like splashing [9]. Since droplet breakup is a function ofthe Weber and Ohnesorge number and splashing of the Reynoldsand Laplace number, these mechanisms are depending on the ve-locity field of the gas phase. If gas velocities are increasing witha smaller valve gap, secondary spray effects will dramaticallychange. Fuel propagation has been investigated for three cases:The intake valve is completely opened (z = 8 mm), halfwayopened (z = 4 mm) and nearly closed (z = 2 mm). The predictedresults at the valve seat in terms of representative trajectories ofthe fuel spray, deposit mass flux rate of the liquid fuel and pat-terns of dominating spray mechanisms are depicted in Fig. 12 (z= 8 mm), Fig. 13 (z = 4 mm) and Fig. 14 (z = 2 mm). Dropletstatistics have been evaluated at the port exit of the intake portand are summarized in Table 3.Analyzing the predicted results of the fuel spray for acompletelyopenedintake valve (Fig. 12), it is obvious, that the major partof the fuel spray is impinging on the valve surface 15. The dom-inating area of impingement is indicated by an intensive rate of

4.85

4.44

4.04

3.64

3.23

2.83

2.42

2.02

1.62

1.21

0.81

0.40

0.00

d [kg/(m2s)]

Figure 12. Results at the valve seat for z = 8 mm: Droplet trajectories

[top left], deposit mass flux rate [top right], spray mechanisms [bottom]

deposited liquid fuel. Less droplets hit the wall of the intake port.In particular, tiny primary droplets are deflected by the gas flowand are then deposited on the wall above the port exit or carriedto the valve exit, as indicated in Fig. 12 and Fig. 7. Study-ing the secondary spray effects, the dominating mechanisms aresplashing and deposition. Only big droplets are atomized by bagbreakup at the valve seat.

4.85

4.44

4.04

3.64

3.23

2.83

2.42

2.02

1.62

1.21

0.81

0.40

0.00

d [kg/(m2s)]



9

At a halfway opened intake valve (Fig. 13), different mech-anisms become dominant due to greater gas velocities. Bigdroplets are atomized by bag breakup close to the valve surfacebefore they splash. The generated secondary droplets are de-posited or carried to the port exit. Bag breakup and bag-plumebreakup are observed in the proximity of the valve gap. Only lessdroplets are directly carried to the port exit without being atom-ized (Fig. 15). Comparing the deposition to the previous case (z= 8 mm), the major area of impingement has moved towards thefront side of the valve stem (from the viewers perspective). Thisvariation is caused by the modified position of the intake valvewith respect to the spray.

4.85

4.44

4.04

3.64

3.23

2.83

2.42

2.02

1.62

1.21

0.81

0.40

0.00

d [kg/(m2s)]



Complex sequences of secondary events are observed for anearly closedintake valve (Fig. 14). As gas velocities are veryhigh, secondary droplets leave the intake port for the most part(Fig. 15). Tiny primary droplets are deflected and deposited atthe wall above the port exit, bigger droplets are destroyed byaerodynamic forces or hit the surface of the intake valve. Twodominating splashing sequences are detected at the valve sur-face, shown in Fig. 14. Droplets generated by splashing areeither deposited, being broken up or carried to the port exit. Asmajor difference compared to previous cases (z = 4 mm, 2 mm),secondary droplets from splashing are atomized in a quick suc-cession. Only tiny droplets are carried to the port exit or willbe deposited at the edge of the intake valve. In addition, the

droplet size decreases close to the valve gap due to bag breakupand bag-plume breakup. As result of these processes, very finedroplet sizes are observed at the port exit. The fuel deposition onthe intake valve is indicated by two distinct and separated areas(Fig. 14). The first area is generated by direct impingement ofthe fuel spray. The second area is caused by the deposition ofsecondary droplets.A spray statistic has been compiled for droplet sizes at the exitof the intake port (Table 3). Comparing these to the droplet start-ing conditions (Fig. 8), droplet sizes are significantly reduced,in particular, for small valve gaps. This way, fuel preparation issignificantly improved by secondary atomization processes, sim-ilar to air-blast atomizers [20]. As mentioned, rapid evaporationis assumed for the deposited liquid fuel. Thus, generation ofdroplets by detachment and breakup of a wall film is excludedfor the part loaded operation conditions studied.

z 8 mm 4 mm 2 mm

D10 10�8 µm 4�47µm 3�11µm

D32 25�0 µm 14�2 µm 9�47µm

D0�1 13�2 µm 7�80µm 4�86µm

D0�5 27�3 µm 16�2 µm 11�4 µm

D0�9 86�7 µm 72�4 µm 62�2 µm

Table 3. Spray statistics at the port exit

Fuel evaporation is nearly identical for all three cases (Fig. 15).The evaporation rate of the spray is identical being approx. 2 %of the injected fuel mass. Thus, droplet evaporation is an inferiorcontribution to the fuel preparation process. The evaporation ofdeposited fuel on hot surfaces is the dominant process. The de-position of the fuel spray shows an identical rate of approx. 61%.Though the splashing parameter (Eq. 23) for impinging primarydroplets is nearly identical for the three cases, the deposition pro-cess of secondary droplets is completely different. This unex-pected identity of the global deposition rate can be explained byconsidering two limiting cases. Secondary droplets are depositedor reaching the port exit in the case of a completely openedintake valve. These droplets are mostly destroyed by aerody-namic forces in the case of a nearly closed intake valve with theconsequence of a distinct fuel deposition of atomized droplets.Thus, more droplets are eventually deposited in the second case,whereas bigger droplets are deposited in the first case. Despitethese rather different mechanisms the deposition rate is nearlythe same for both cases. Droplet sizes, however, are significantlyinfluenced by the valve gap.

10

Figure 15. Mass fraction of global spray quantities

Conclusions

Transient phenomena, as well as fuel preparation processesinside an intake port have been studied by numerical predictions.The numerical scheme is based on the Unsteady Reynolds Av-eraged Navier-Stokes equations (URANS) which is solved by atime-implicit three level scheme. Secondary spray effects havebeen accounted for by two advanced models for droplet breakupand droplet wall interaction. Both models have been developedunder the objective to reproduce the statistics of the secondarydroplet products correctly.Transient spray effects are generally present closely behind theinjector nozzle. In the present study, two transient spray effectshave been observed. First, the vortex located behind the flangeof the cylinder head is increased. This vortex directly affects thefuel propagation in the intake port because tiny droplets are cap-tured by the vortex. Secondly, the penetration time for a coredroplet is shorter compared to a droplet at the tip of the spray.The fuel preparation process is dominantly influenced by sec-ondary spray effects, in particular droplet breakup and dropletwall interaction. As these processes are influenced by the valvegap, the fuel mixture generation has been studied for three dif-ferent valve positions: completely opened, halfway opened anda nearly closed. The study revealed that droplet sizes are signif-icantly influenced by the valve gap. In contrast, the fuel deposi-tion has been found to by nearly identical for all three cases.Mixture quality of the liquid fuel is significantly improved bysmall valve gaps. The initial droplet diameters, generated by thefuel injection have a minor influence on the overall droplet sizesat the port outlet. Big droplet sizes are decreased by secondaryspray effects at the valve seat. In order to achieve an optimal at-omization process, the spray cone has to be justified to the valvesurface. As fuel deposition is rather high for all studied cases,a procreation of droplets by detachment and breakup of a shear-driven wall film is most problematic for cold starting conditions.

ACKNOWLEDGMENT

The authors would like to thank Mr. G. Rottenkolber andMr. I. Kakuta for their valuable contributions to this project.

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