Simulation of Fuel Injection Using Euler-Lagrange Approach

Seminararbeit

Jonas Hunkemoller

Introduction

The combustion engine has become the most important tool for mobile energy transformation inthe past century. Today, the high grade of pollution, caused by these engines’ emissions and theincreasing costs for crude oil cause a high demand for alternative gears. However, those alterna-tive gears, e.g. electric motors, are in general still too expensive and their range is too low formost applications. Therefore, combustion engines will remain the most important gear in the nearfuture. Many governments try to reduce the air pollution by introducing legal restrictions for theemissions. Those restrictions increase the demand for a further development of the combustionengine that is focused on the combustion process.The pollutant emissions can be reduced by on optimization of the injection conditions. Therefore,it is necessary to predict the fuel distribution and reaction mechanisms accurately. The atomiza-tion of the injected fuel jet is characterized by the turbulent multiphase flow in the combustionchamber which complicates the simulation and measuring of the combustion relevant quantities.Nevertheless, computational fluid dynamics (CFD) have become an increasingly practical tech-nique to predict reactive turbulent flows in the combustion engines due to the availability ofparallel processing and highly scalable CFD solvers.Direct numerical simulations (DNS) are able to resolve all relevant flow scales of the multiphaseflow completely, but resolving the smallest fluctuations and the interface between both phasesleads to impracticable computational effort. Hence DNS is not practicable to predict the disin-tegration of the jet and the evaporation of the fuel such as the heat transfer between the twophases. Instead, several methods and models are used to reduce the computational costs. Due tothe fact that these models are based on assumptions and simplifications, it is necessary to validatethe accuracy of their application under the conditions that are present during the injection andcombustion process.For this reason, the Engine Combustion Network (ECN) was founded. The objective of the ECNis to provide experimental data that is measured under well-defined conditions. Several condi-tions are defined for different fuels and nozzles. There are measurements under reactive and inertregimes, due to varying pressure and temperature conditions. This enables to validate the modelsand to fit the model parameters for the fuel distribution and for the combustion process separately.In this work experimental data that is measured under inert conditions is compared to computa-tional results obtained by the use of different turbulence models. The RNG k−ε turbulence modelis used to represent RANS simulations while the Dynamic Structure model is used to representLarge Eddy Simulations (LES).The work is structured as follows: At first, an explanation of the methods that are used to predictthe behavior of the two phases is given. Therefore, approaches to describe the liquid and gaseousphase are presented briefly. Afterwards, models which are used to compute the disintegration ofthe fuel jet are discussed in greater detail. In addition, computational results that are obtainedby Senecal et al. and Xue et al. are discussed. Finally, a short conclusion is made.

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Simulation of Fluid Behavior

Modelling of the Gaseous Phase

In order to calculate the penetration of a liquid spray into the gaseous atmosphere of the com-bustion chamber, two phases, the dispersed liquid and the continuous gaseous phase, must beconsidered. The gaseous phase is described using the conservation laws for mass, energy andmomentum in the Eulerian framework. Those declare that in every volume the temporal changeof the conserving quantity is equal to the sum of its transport over the volume boundary and itsproduction inside the volume.One of the most famous methods to solve fluid dynamics problems is the Finite Volume Method(FVM). This method divides the initial volume (in this case the combustion chamber) in non-overlapping finite volumes and applies the conservation laws on each of them. During the appli-cation of the conservation laws every finite volume is linked with its neighboring volumes by theconservation of the flow over the shared boundaries. The spatial derivatives can be approximatedwith the use of a difference scheme between the centers of the finite volumes. This leads to asystem of ordinary differential equations with respect to time.The above described partitioning of the volume and the approximation of the spatial derivativesby a difference scheme is called spatial discretization. The discretization of time and the approxi-mation of those derivatives leads to a system of algebraic equations that can be solved for givenboundary and initial conditions for each time step. Using this method, the relevant flow quantitiescan be calculated for each time step and for each position.Using the Finite Volume Method sketched above is called ‘Direct Numerical Simulation’. One ofthe major issues of this method is that very fine spatial and temporal discretizations are neededto reproduce the fluctuations of turbulent flows. These discretizations are not practicable forlarge technical systems, because they lead to enormous computational effort. To avoid this com-putational effort, different approaches were developed which do not solve for all fluctuations butmodel them instead. One of these approaches is not to solve the classical conservation laws, butthe Reynolds-averaged Navier-Stokes equations (RANS equations). Reynolds [1] decomposed theinstantaneous quantities of the Navier-Stokes equations into its time-averaged and its fluctuatingcomponent. This decomposition leads to new unknowns and additional turbulence models are nec-essary to close the system of equations. In general, those turbulence models consist of additionalpartial differential equations. For instance, the most common turbulence model, the k − ε model,consists of two transport equations. The first equation is used to determine the turbulent kineticenergy k while the second equation is used to determine the dissipation rate of the turbulentkinetic energy ε. Solving these equations increases the computational effort for each finite volumebut in total the computational effort decreases since a coarser discretization is needed to predicta good approximation of the turbulent flows.Another approach to reduce the computational effort is used by Large Eddy Simulations (LES).Using this approach, the flow quantities are decomposed into a filtered and a sub-grid part by theuse of a filter operator. The purpose of this approach is to solve for the filtered quantities using asufficient grid resolution and to describe the sub-grid quantities using models.Between these models there are huge differences in the requirements for mesh resolution in orderto resolve the energy containing length scales. In general Large Eddy Simulations need a signifi-cant higher grid resolution than simulations using the RANS equations. But due to the averagingapproach of the RANS equations, an influence on the results of the simulations is expected aftera refining of the grid, while the influence of the sub-grid models is expected to vanish for LargeEddy Simulations. However, for both, the RANS and LES approach, several turbulence modelsare available. In the simulations that are analyzed below, the Dynamic Structure model [2, 3] isused for LES simulations and the RNG k − ε model [4] for RANS simulations.

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Modelling of the Liquid Phase

In contrast to the continuous gaseous phase, the spray consists of thousands of discrete drops.These drops can be modelled by using the Eulerian framework as well as the gaseous phase. How-ever, this approach is not practicable, because a very fine grid resolution would be necessary toapproximate the surface of the drops moving through the combustion chamber and even morewould be necessary to compute the forces leading to the break-up of the drops accurately. There-fore, another approach, the Lagrangian approach, is used to model the drops of the liquid phase.This approach considers the drop as individual points and assigns properties e.g. diameter, veloc-ity, position and mass to them. The acceleration of the drop is calculated by the equilibrium ofall forces which act on the drop and its velocity and position are obtained by time integration.Both phases are coupled by an exchange of momentum, energy and mass. To obtain a two waycoupling, source terms are implemented in the conservation equations of the gaseous phase. Thosesource terms enable the exchange of each conserving quantity in each cell accordant to the behaviorof the drops passing the cell. However, physical phenomena like drag, evaporation and break-upof the drops need to be modelled.

Break-Up Modeling

Break-Up Regimes of Liquid Drops

Induced by the relative velocity urel between a drop and the surrounding gas, aerodynamic forcesact on the drop’s surface. These forces result in the unstable growth of waves on the surface or inthe whole drop itself. The growing of the waves leads to a break-up or disintegration of the dropand to a formation of smaller drops if the surface tension σ is not high enough to stabilize thedrop. The ratio of aerodynamic and surface tension forces is described by the gas phase Webernumber

Weg =ρgdu

2rel

σ(1)

where d is the drop’s diameter and ρg the density of the gas.Experiments prove that the break-up mode changes with growing Weber number. These modesare displayed in Figure 1 and the corresponding Weber numbers are listed in Table 1.

Figure 1: Schematic illustration of drop break-up regimes [5]

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Break-up regime Weber numberVibrational ≈ 12Bag < 20Bag-streamer < 50Stripping < 100Catastrophic > 100

Table 1: Transition Weber numbers of the different drop break-up regimes [5]

If the ratio of the aerodynamic forces and the surface tension is high, the drops disintegrate intosmaller ones whereas small drops are sheared off from the initial drop in all break-up regimes withthe exception of the vibrational break-up regime. Due to the decrease of the Weber number bythe disintegration of the drop and due to a reduction of the relative velocity, all of these break-upmechanisms occur in engine sprays [6].

Primary Break-Up

The term ‘Primary Breakup’ is used to designate the break-up of the continuous liquid core jet intoseveral discrete drops enforced by the flow condition inside the nozzle holes. Since the continuousjet cannot be represented by the Lagrangian description, which is used to describe the liquidphase, this break-up cannot be simulated directly. In addition a complete CFD simulation of theflow in the injector results in an enormous increase of computational time due to the small spatialdimensions of the nozzle. Therefore, a model for the primary break-up is used. Those modelsdetermine the initial conditions for the drops that leave the injection nozzle. The initial conditionsthat are needed for the simulation are the initial size of the drops, their initial velocity componentsand their temperature. There are several primary break-up models but in the following only theBlob Method which is developed by Reitz and Diwakar [7, 8] is mentioned. This method is basedon the assumption that a detailed description and simulation of the break-up process within theprimary break-up zone of the spray is not required. Therefore, it is sufficient to insert uniformsized drops near the nozzle hole and to calculate the number of drops inserted per unit time fromthe mass flow rate. The diameter of the inserted drops is equal to the size of the injection holeand their velocity can be determined using the conservation of mass. The velocity componentsare defined considering the spray cone angle which needs to be known prior to the simulations.In order to determine the direction of each drop’s velocity a product of the spray cone angle andrandom numbers is used [6].

Secondary Break-Up Models

Kelvin-Helmholtz Break-Up Model

The Kelvin-Helmholtz break-up model (KH model) models the break-up modes that are charac-terised by a separation of small drops from the initial drop. The model assumes that the break-upis caused by so called Kelvin-Helmholtz instabilities. These instabilities occur because of thevelocity difference between the drop and the surrounding gas. This velocity difference leads toaerodynamic forces which act on the interface between the two phases and enable the growth ofoscillations on the drop’s surface. The model assumes that the wave with the highest growth rateω = Ω will be sheared off and form new drops. This process is shown in Figure 2.

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Figure 2: Schematic illustration of the Kelvin-Helmholtz model [6]

Reitz and Bracco [9] succeeded to describe the growth of the oscillations’ amplitude ω, usingthe first order linear stability analysis of the problem. It is shown that there is a single wavelength Λ, for which the wave growth rate curve ω(λ) reaches a maximum and the correspondingsolution is found using curve fittings.The solution for the maximum wave growth Ω is given as

Ω =0.34 + 0.38We1.5

(1 + Z)(1 + 1.4T 0.6)

√σ

ρlr30(2)

where Z =√WelRel

, T = Z√Weg with the liquid and gaseous Reynolds and Weber number. The

corresponding wavelength Λ is given by

Λ

r0= 9.02

(1 + 0.45Z0.5)(1 + 0.4T 0.7)

(1 + 0.865We1.67g )0.6. (3)

The size of the separated drops depends on the wavelength Λ since the new drops are formed bythe oscillations. Reitz [10] suggests a proportional dependence

rnew = B0 · Λ (4)

with constant B0 = 0.61. New drops with the radius rnew are inserted next to the parent drop.To enforce the conservation of mass, the size of the parent drop has to decrease. The rate of thisdecrease is defined by

∂r

∂t= −r − rnew

τbu· Λ with τbu = 3.788 ·B1

r

Λ · Ω(5)

The parameter B1 influences the rate of separation and depends on the nozzle and the spray’sproperties.

Rayleigh-Taylor Break-Up Model

The disintegration of the drops in the catastrophic break-up regime is modelled by the Rayleigh-Taylor Break-Up Model (RT model). The drops are decelerated by aerodynamic forces inducedby the relative velocity between the drops and the surrounding gas. The drag force acts on thefront side of the drop with density ρl and radius r and decelerates it with the deceleration

a =3

8πcD

ρgu2rel

ρlr. (6)

In this equation cD represents the drag coefficient and urel is the relative velocity between thedrop and the surrounding gas.

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Due to the inertia of the liquid, the backside of the drop does not decelerate as fast as the frontsideand a relative velocity between front and backside occurs. Thus, the drop is deformed and thesurface tension acts against this deformation. This process enforces oscillations that are draftedin Figure 3. The drop disintegrates into smaller ones if these oscillations become too large.

Figure 3: Rayleigh-Taylor instability on a liquid drop [6]

Comparable to the Kelvin-Helmholtz Break-Up Model it is assumed that the break-up is ini-tiated by the waves with the fastest growth. The wave length with the fastest growth

ΛRT = 2πC3

√σ

a(ρl − ρg)(7)

can be determined by using the linear stability analysis and neglecting the liquid viscosity [11,12].The corresponding growth is given by

ΩRT =

√2

3√

3σ

[a ((ρl − ρg)]3/2

ρl + ρg. (8)

During the application of the model, the drop will be replaced by smaller drops at the timet = Ω−1RT . According to Su et al. [13], the number of the new drops is determined by the ratio ofthe maximum diameter of the deformed parent drop to ΛRT and the radius of the new drops isdetermined using mass conservation. The break-up can only occur if the drop size is larger thanthe wave length ΛRT .

Combination of Secondary Break-Up Models

As mentioned above, there are different break-up modes and all of them occur during the combus-tion process. A combination of different break-up models is used to increase the accuracy of thebreak-up prediction since there is no single break-up mode to describe all relevant regimes of thebreak-up process available yet. One of the most common used combinations of break-up modelsfor full-cone-sprays is the combination of the Blob Model, as a primary break-up model, with theRayleigh-Taylor and the Kelvin-Helmholtz Break-Up Model, to represent the secondary break-up[6]. It is preferred for the simulation of high-pressure diesel sprays since it has often been validatedwith experimental data [12, 15].Therefore the RT and KH models are implemented in the CFD codes in a competing manner.Using these models, the growing of the unstable waves are computed simultaneously and the KHmodel will produce small child drops and reduce the mass of the parent drop until the drop ispartitioned by the RT model. These models do not consider the behavior of the liquid phase insidethe nozzle. Therefore, two parameters, the parameter B1 from the KH model and the drop sizeparameter C3 from the RT model, are used to regard the impact of the nozzle’s geometry duringthe computations. Due to the fact that these parameters are unknown, they need to be tuned tofit the results of the simulations to the experimental data.To improve the computational results, the RT model is not applied before the drop has passeda certain length - the so called break-up length - since the prediction of the break-up by the RT

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model is too large in the region near the nozzle. Using the above described combination, a fasterdisintegration of big drops and an increased evaporation is obtained. These results match theexperimental data more precisely compared to the results that are obtained by the single use ofthe KH model [6].

Results

Experimental Data and Simulations

In the following, results of simulations, which are based on the above described models, are com-pared to experimental data. This experimental data is obtained from Sandia National Laboratories[16,17] and IFP Energies Nouvelles [18], through the Engine Combustion Network. In the follow-ing only experimental data and simulation results that are optained under ‘Spray A’ conditionsare considered. That means, the simulations and measurements are realized for a constant-volumechamber under inert conditions. Further conditions are listed in Table 2.

Quantity ValueFuel n-dodecaneAmbient composition 0%O2

Ambient Temperature [K] 900Ambient density [kg/m3] 22.8Injection pressure [MPa] 150Fuel temperature [K] 363Nozzle diameter [mm] 0.09Injection duration [ms] 1.5Total mass injected (mg) 3.5

Table 2: Nominal conditions for the vaporizing Spray A experiments at Sandia National Labora-tories [19]

The simulations considered in this work are done within a cooperation of the Argonne NationalLaboratory and the Convergent Science Incorporated. They are performed using the CFD softwareCONVERGE. Simulations using the RNG k − ε and the Dynamic Structure turbulence modelsare realized. The liquid phase is modelled using the Eulerian-Lagrangian approach. The abovedescribed break-up models are used for the simulations. Fuel injection is modelled using the BlobModel while the Kelvin Helmholtz and the Rayleigh-Taylor Break-Up Models are used to predictthe secondary break-up of the drops. The parameter fitting for the spray model parameters isdone using the RNG k − ε turbulence model.The comparisons between the experimental data and the computational results are comparisonsbetween the mean of 20 measurements and a single computational realization if not specifieddifferently. Further explanations of the used models and conditions are listed in the publishedpapers [20, 21, 22, 23].

Grid Convergence and Computational Time

An adapted 3D-grid with a base grid size of 1 mm is used for local mesh refinement. For meshconvergence studies the minimum grid size is varied. Namely computations using a minimum gridsize of 0.5 mm, 0.25 mm, 0.125 mm, 0.0625 mm and 0.03125 mm are realized. For the globalobservation of the injection process two quantities, the liquid and vapor penetration, are defined:The liquid penetration is defined as the axial distance that is encompassed by 90% of the injectedliquid fuel mass. It increases initially with time, before it stabilizes at a quasi-steady value, whichis called the liquid length. The vapor penetration is defined as the maximum distance from theinjector to the location where the fuel mass fraction is 0.1%.

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The curve progression of both quantities during measurements and RANS simulations with fourdifferent mesh resolutions are illustrated in Figure 4.

Figure 4: Liquid (a) and vapor (b) penetrations for Spray A predicted by the RNG k − ε modelwith different minimum grid sizes [20]

Both plots show that a minimum cell size of 0.5 mm is not sufficient to reproduce the liquidand vapor penetration, but with decreasing grid sizes the solution of the simulation converges tothe data of the experimental data. In fact, good results are obtained with a mesh size of 0.25mm and there are only small changes produced by further refinements. Related to the case above,Figure 5 shows the curve shapes of the liquid and vapor penetration predicted by LES simulationswith varying mesh resolutions.

Figure 5: Liquid (a) and vapor (b) penetrations for Spray A predicted by the LES DynamicStructure model with different minimum grid sizes [20]

Similar to the RNG k−ε case, a mesh size of 0.5 mm is too large to reproduce the experimentaldata and again the results of the simulations converge to the experimental data, but a much smallergrid size is needed for a sufficient approximation. However, both turbulence models, RANS andLES predict the vapor penetration very well for a sufficient large mesh resolution, but both methodsfail to predict the liquid penetration before its quasi steady state.Regarding the LES simulation, there is still an offset between the curves of the computed resultsand the measurements for very high mesh resolutions. In addition, the predicted break-up length

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is larger than the measured values. As mentioned before, the break-up model parameters are tunedbased on the RANS model simulations. In order to improve the results of the LES simulations tofit the spray break-up of the experimental data, additional LES simulations were realized with adifferent value for the Kelvin-Helmholtz model constant. As described in the above section, thisconstant influences the reduction of the diameter of the parent drop. Figure 6 shows, that a betteragreement with the experimental data can be obtained by decreasing the spray break-up constantfrom B1 = 7 to B1 = 5. The predicted curves represent an average of 20 realizations for B1 = 7and an average of five realizations for B1 = 5, which is the reason why the curve for the parameterB1 = 7 is much smoother [21].

(a) (b)

Figure 6: Comparasion of measured and predicted liquid (a) and vapor (b) penetration for SprayA conditions [21].

The wall clock time necessary for the computations for both turbulence models on three dif-ferent minimum mesh resolutions is given in Table 3. Note that the computational time is alsoinfluenced by a change of the time step size. This change is neccesary in order to constrain theCourant-Friedrichs-Lewy (CFL) number and to achieve convergence. However, for a minimumgrid size of 0.25 mm and 0.125 mm the computational time of RANS simulations is similar tothose for LES simulations at the same resolutions. Whereas for a minimum grid size of 0.0625mm the computational time needed by the Dynamic Structure turbulence model is significantlylarger than the one needed by the RNG k − ε turbulence model.

Minimum cell size 0.25 mm 0.125 mm 0.0625 mmNumber of CPU cores 24 24 64Tubulence modelDynamic Structure 6 h 10 h 60 hRNG k − ε 5 h 11 h 32 h

Table 3: Computational time using RNG k−ε and Dynamic Structure turbulence model for SprayA simulations [21]

The computational time, which is necessary to achieve mesh convergence, is of higher im-portance. Mesh convergence is reached with a minimum mesh size of 0.25 mm for the RANSsimulations. The corresponding computational time is about 5 h on 24 CPU cores. The LESsimulations show mesh convergence at 0.0625 mm. The computational time needed for those sim-ulations is about 60 h on 64 CPU cores. This means a significant larger computational effort isrequired to predict the break-up of the fuel drops by using Large Eddy Simulations.

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Multiple Cycle Studies

The previous comparisons are based on single computations. To determine cycle-to-cycle varia-tions, several simulations with marginal differences in the initial conditions have to be considered.Therefore, the spray model random number seed is changed in each realization [20, 21, 22, 23].Figure 7 shows a comparison of the liquid and vapor penetration between experimental data andfive predicted realizations for different turbulence models.

Figure 7: Cycle-to-cycle variations of liquid (a) and vapor (b) penetrations for Spray A as predictedby different turbulence models [20]

The thinner lines are predictions of each realization while the thicker line of the same colorrepresent the averaged values of liquid and vapor penetration. The offset between the curves of theexperimental data and the computational results of the LES simulations for the liquid penetrationcan be explained by the choice of the break-up parameter B1 as well.It is shown, that nearly the same values are computed for each variation using the RANS simula-tions and that the cycle-to-cycle variations are not respected very well. This might be explainedby the averaging approach of RANS simulations. Apart from that, variations can be seen in theresults of the LES simulations, for which only the small fluctuations are simplified using a model.This effect can also be found for local quantities like the mixture fraction or the gas-phase velocitywhich is shown in Figure 8.

(a) (b)

Figure 8: Comparison between measured and predicted gas phase axial velocity at 25 mm fromthe nozzle exit at 1.5 ms after start of injection for the RNG k− ε (a) and the Dynamic Structureturbulence model (b) [20].

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Again the differences between the individual realizations computed by the RNG k − ε turbu-lence model are very small while the differences between the individual realizations computed bythe Dynamic Structure turbulence model are significant. Considering that only five different real-izations are regarded, it can be seen, that the mean of the realizations matches the experimentaldata very well for both turbulence models. However, it is important to examine whether the rangeof variation between the individual realizations correspond to the one between the measurements.At this point, one has to take into account that the experimental data used for the comparisonis the mean of 20 measurements which makes it possible to compare statistical quantities such asthe standard deviation which is shown in Figure 9.

Figure 9: Comparison of measured and predicted standard deviation of mixture fraction (20realizations) at 25 mm (a) and 35 mm (b) from the nozzle exit. The predicted results are from1.5 ms after start of injection [21]

The predicted standard deviations are in a good agreement with the measurements. This in-dicates that the differences between the individual computational results are in the same order ofmagnitude as the one of the experimental data.

Conclusions

The models, which are used to predict the fuel distribution inside the combustion chamber, aredescribed within this work. Approaches to model the liquid and gaseous phase are explainedbriefly while the Kelvin-Helmholtz and the Rayleigh-Taylor Break-Up models are discussed ingreater detail. Furthermore, experimental data, which is published through the Engine Com-bustion Network, is compared to computational results considering Spray A conditions. For thecomputation the RNG k − ε and the Dynamic Structure turbulence models are used to compareresults of simulations using the RANS and the LES approach. The numerical data is publishedby the cooperation between the Argonne National Laboratory and the Convergent Science Inc.An adapted 3D-grid with a base grid size of 1 mm is used. It is shown, that a minimum grid size of0.25 mm is necessary for the RNG k− ε turbulence model and a minimum grid size of 0.0625 mmis necessary for the Dynamic Structure turbulence model to achieve grid convergence. Thereforethe computational time increases from 5 hours on 24 CPU cores for the RNG k − ε model to 60hours on 64 CPU cores for the Dynamic Structure turbulence model. However, using a convergentgrid size, both methods succeeded to predict the vapor and liquid penetration fairly well.Although both models need different break-up model parameters to fit the experimental data, theneeded adjustments are marginal in the considered case. An adaption of the Kelvin-Helmholtzmodel parameter from B1 = 7 for the RNG k − ε turbulence model to B1 = 5 for the DynamicStructure turbulence model is sufficient.

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Furthermore, it is shown, that the RNG k − ε model is not suited to predict cycle-to-cycle varia-tions. Instead, reasonable results are achieved by using the Dynamic Structure model. Althougheach case results in a different solution, the curves of the vapor and liquid penetration are verysimilar and it is reasonable to look at these parameters using only a single injection with LES.Therefore, the fitting of model parameters to experimental data is possible using a single real-izations. In contrast to the global quantities, the range of variation of local quantities is relativelarge. It is shown that the mean and the standard deviations of the predictions agree well withthe ones of the experimental data. This indicates, that the Dynamic Structure turbulence modelis suitable to predict cycle-to-cycle variations. Apart from that a single realization of Large EddySimulations is not sufficient to predict the behavior of local quantities. Similar to experimentaldata, several realizations of Large Eddy Simulations need to be considered to obtain comparableresults.

References

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[20] Xue, Q., Som, S., Senecal, P.K., Pomraning, E., Large Eddy Simulation of Fuel-Spray undernon-reaction IC engine conditions, ICLASS Triennial Int. Conf. on Liquid Atomization and SpraySystems, Heidelberg, Germany, 2012.[21] Senecal, P.K., Pomraning, E., Xue, Q., Som, S., Banerjee, S., Hu, B., Liu,K., Deur, J.M.,Large Eddy Simulation of Vaporizing Sprays Considering Multi-injection Averaging and Grid-Convergent Mesh Resolution, ICEF2013, Dearborn, 2013.[22] Som, S., Senecal, P.K., Pomranging, E., Comparison of RANS and LES Turbulence Modelsagainst Constant Volume Diesel Experiments, 24th Annual Conference on Liquid Atomization andSpray Systems, San Antonia, 2012.[23] Som, S., Longman, D.E., Luo, Z., Plomer, M., Lu, T., Three Dimensional Simulations ofDiesel Sprays Using n-Dodecane as a Surrogate, Fall Technical Meeting of the Eastern Stats Sec-tion of the Combustion Institute, Storrs, 2011.

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