ILASS-Americas 30th Annual Conference on Liquid Atomization and Spray Systems, Tempe, AZ, May 2019

High-Fidelity Modeling and Simulation of Primary Breakup fo a GasolineSurrogate Jet

B. Zhang and Y. Ling∗

Department of Mechanical EngineeringBaylor University

Waco, TX 76798 USA

AbstractIn the present work, we model and simulate the injection and atomization of a gasoline surrogate jet bydetailed numerical simulation. The surrogate fuel has a low volatility and thus no phase change occurs inthe process. The nozzle geometry and operation conditions are similar to the Engine Combustion Network(ECN) “Spray G”. We focus the present study on the near field where inter-jet interaction is of secondaryimportance. Therefore, we have considered only one of the eight jets in the original Spray G injectors. Theliquid is injected from the inlet into a chamber with stagnant gas. A tangential component of velocity isintroduced at the inlet to mimic the complex internal flow in the original spray G injector, which leads to thejet deflection. A parametric study on the inlet tangential velocity is carried out to identify the proper valueto be used. Simulations are performed with the multiphase flow solver, Basilisk, on an adaptive mesh. Thegas-liquid interface is captured by the volume-of-fluid method. The numerical results are compared to theX-ray experimental data for the jet deflection angle and the temporal variation of penetration length. Thevortex dynamics in the near field are also presented by the assistance of the vortex-identification criterion.

∗Corresponding Author: stanley ling@baylor.edu

Introduction

Application of direct injection techniques ingasoline engines has been shown to be a promisingapproach to improve fuel efficiency and to reducepollutant emission. Accurate fuel delivery, such asreducing cycle-to-cycle variation, is critical to gaso-line direct injection (GDI) systems, since the fuelsprays formation has a direct impact on subsequentfuel/air mixing, spark ignition, and flame propa-gation [1]. Formation of gasoline sprays throughfuel atomizers is a process of enormous complexity,involving liquid breakups, cavitation, evaporation,and turbulent dispersion of droplets. Recent studieshave also shown that the spray formation process issensitive to the geometry details of the injector noz-zle [1]. Experiment has been the major approachto understand spray formation in GDI in the past[2]. Since the sprays in the near field are dense,the capability of the optical approach in obtainingaccurate details is limited. In recent years, X-raydiagnostics have been applied to studies of gasolineinjection. Duke et al. [3] investigated the internalflow and near-nozzle sprays generated by the En-gine Combustion Network (ECN) “Spray G” gaso-line injector, using X-ray tomography, phase dopplerinterferometry, and laser induced fluorescence. TheX-ray measurements were also compared to data ob-tained from other approaches.

Even with advanced diagnostics techniques, it isstill difficult to obtain the details of the interfacialdynamics inside the nozzle and the liquid breakupsoccur in the near field. Therefore, numerical simu-lation is an important alternative to understand thephysical process involved. Mitroglou et al. [4] exper-imentally studied the performance of the multi-holeinjectors by measuring the spatial and temporal dis-tributions of the droplet velocity and diameter atdistinct locations and have also used CFD (Compu-tational Fluid Dynamics) simulation with k-epsilonturbulence model to assist the interpretation of theexperimental observations. In recent years, high-fidelity simulations with the liquid-gas interface ac-curately captured become viable. Befrui et al. [5]performed a numerical study of the ECN “SprayG” seat flow and the near-field primary atomizationwith the volume-of-fluid method and large-eddy sim-ulation (VOF-LES). More recently, Mohan et al. [6]has performed simulation with VOF and RNG k-εmodel to investigate the effect of transient needlemotion on the effects of cavitation and flash boilingin ECN “Spray G” multi-hole injector.

In spite of remarkable progress in both exper-iments and simulations of gasoline direct injection,high-fidelity numerical simulation of the atomization

of a gasoline jet with both turbulence and interfa-cial dynamics accurately resolved is still lacking inthe literature. Such a detailed simulation will of-fer high-level details of the multiphase flows insidethe nozzle and the near field, which are essential tounderstanding spray formation in GDI systems.

The goal of the present paper is to perform ahigh-fidelity simulation of the primary breakup ofa gasoline surrogate jet injected under an opera-tion condition that is similar to the ECN “SprayG”. Since the computational cost for resolving thegas-liquid interface in atomization is very high, onlyone of the eight jets in the original “Spray G” injec-tors is taken into account. This simplification is ac-ceptable since we limit our interest only on the nearfield where the inter-jet interaction is less important.Furthermore, since we consider a low-volatility gaso-line surrogate, the fuel evaporation can be ignored.The adaptive multiphase flow solver, Basilisk, is ap-plied and the volume of fluid (VOF) method is usedto resolve the interface. A tangential component ofthe injection velocity is added in the inlet to mimicthe effect that the velocity of the fuel entering thenozzle is not exactly perpendicular to the nozzlecross section. This tangential velocity componentwill not influence the mass flow rate but will createa plume deflection that is seen in experiments [3].

Numerical Modeling and Simulation Setup

Governing Equations

The one-fluid approach is employed to resolvethe two-phase flow, where the phases correspondingto the fuel and the ambient air are treated as onefluid with material properties that change abruptlyacross the interface. The incompressible, variable-density, Navier-Stokes equations with surface ten-sion can be written as

ρ(∂tu + u · ∇u) = −∇p+∇ · (2µD) + σκδsn , (1)

∇ · u = 0 , (2)

where ρ, µ, u, and p represent density and viscos-ity, velocity and pressure, respectively. The defor-mation tensor is denoted by D with componentsDij = (∂iuj + ∂jui)/2. The third term on the righthand side of Eq. (1) is a singular term, with a Diracdistribution function δs localized on the interface,and it represents the surface tension force. The sur-face tension coefficient is σ, and κ and n are the localcurvature and unit normal of the interface.

The volume fraction C is introduced to distin-guish the different phases, in particular C = 1 inthe computational cells with only the ambient air(respectively C = 0 in the fuel), and its time evolu-

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tion satisfies the advection equation

∂tC + u · ∇C = 0 . (3)

The fluid density and viscosity are then defined by

ρ = Cρa + (1− C)ρl , (4)

µ = Cµa + (1− C)µl . (5)

where the subscripts a and w represent the ambientair and the fuel respectively.

Numerical Methods

The Navier-Stokes equations (Eqs. (1) and (2))are solved by a novel adaptive multiphase solverBasilisk [7]. In Basilisk, the interface between thedifferent fluids are tracked using a Volume-of-Fluid(VOF) method [8, 9]. A quad/octree spatial discreti-sation is used, which gives a very important flex-ibility allowing dynamic grid refinement into user-defined regions. Finally the height-function (HF)method is utilized to calculate the local interfacecurvature, and a balanced-force surface tension dis-cretization is used [10, 11].

Modeling and Simulation Setup

A schematic of the cross section of the Spray“G” injector is shown in Fig. 1. In the present studywe focus on the near field dynamics and thus onlyone of the original eight jets is considered. The re-gion simulated is indicated by the green rectangle.The computational domain for the atomizing jet isshown in Fig. 2. The fuel is injected into a cubic

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domain filled with stagnant nitrogen gas along thex direction from the left boundary. To mimic theeffect that the fuel velocity at the nozzle inlet is notperpendicular to the cross section, a tangential com-ponent of the injection velocity is introduced in thesimulation. Two different ways include the tangen-tial inlet velocity were tested. In setup 1, the tan-gential velocity is added along the y axis; while insetup 2, the tangential velocity is added along 45 de-grees from the y axis. A large simulation domain isused for this study owing to the octree discretizationof Basilisk such that the effects of boundaries to theatomizing jet are negligible.

The outflow boundary condition is invoked atthe right boundary. All the rest boundaries of thedomain are then taken as symmetric boundaries.The edge length of the domain is 64 Rinj , whereRinj is the inner nozzle radius. The minimum cellsize of the adaptive mesh used is indicated by ∆min,

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Fuel

Density ρl 838 kg/m3

Viscosity µl 9.64× 10−4 Pa sSurface tension σ 0.0278 N/mJet radius Rinj 8.65× 10−5 m

Normal injectionvelocity Uinj 89 m/s

Tangential injectionvelocity Vinj 0, 17.8, 35.6 m/s

Ambient gas N2

Density ρg 3.6 kg/m3

Viscosity µg 1.77× 10−5 Pa s

Table 1. Fuel properties and injection parameters.

Reg Rel Wel r η

2RinjUinj

νg

2RinjUinj

νl

ρl2RinjU2inj

σρlρg

Vinj

Uinj

3130 13400 41300 233 0 to 0.4

Table 2. Key dimensionless parameters.

which is equal to 5.4 µm. A snapshot of the atom-izing jet and the corresponding adaptive mesh areshown in Fig. 2. It is easily seen that high meshresolution is used to resolve the liquid-gas interfacewhile the mesh away from the jet is coarsen to de-crease computational costs. The total number ofcells increases in time as more liquid is injected intothe domain. The mesh shown in Fig. 2 consists ofabout 16 million cells.

Key parameters

The fluids properties and the injection condi-tions are chosen based on the Argonne X-ray ex-periments by Duke et al. [3]. The liquid is a low-volatility gasoline surrogate with a cerium contrastagent. Due to the low vapor pressure in the chamberand the use of low-volatility liquid, fuel evaporationis ignored. The gas in the chamber is nitrogen, witha pressure and temperature of 3.15 bar and 298 K,respectively. The density and viscosity of the gas are3.6 kg/m3 and 1.77× 10−5 Pa s, respectively.

If the gas density ρg, the jet radius Rinj , andthe injection velocity Uinj are chosen to be refer-ence scales, the key dimensionless parameters canbe calculated, see Table 2. The Reynolds and We-

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ber numbers of the liquid jet are defined as Rel =ρl(2Rinj)Uinj/µl and Wel = ρl(2Rinj)U

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spectively, which characterize the inertial effect com-pared to the viscous and surface tension forces.When Rel and Wel are large, the viscous and sur-face tension forces are insufficient to hold the in-jected fuel as a bulk liquid, resulting in atomizationof the liquid jet into smaller droplets. As the gasmotion is induced by the injected liquid in the cham-ber, the Reynolds number in terms of gas properties,Reg = ρg(2Rinj)Uinj/µg, is utilized to characterizethe gas flow around the liquid jet. When Reg isbig enough the gas flow can become turbulent. Theliquid-to-gas density ratio is represented by r withr = ρl/ρg. The ratio between the tangential andnormal components of the injection velocity is de-noted as η = Vinj/Uinj and three different values ofη are considered. Other dimensionless parameterscan be computed based on these four parameters,for example, the liquid-to-gas viscosity ratio can becomputed as µl/µg = rReg/Rel.

Results

Evolution of the atomizing jet

The general behavior of the atomization of theliquid jet for η = 0.2 evolution and atomization arepresented. The normal of the view plane shown

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here is perpendicular to the tangential velocity atthe inlet (pointing upward). The gasoline surrogateis injected into the stagnant nitrogen gas from theleft. When the head of the jet interacts with the sta-tionary gas, liquids are pushed radially outward andform a liquid sheet rolling up. This mushroom-likeshape of the jet head (see Fig. 3 (a)) has also beenobserved in former studies [12]. Due to the non-zerotangential velocity component introduced at the in-let, the azimuthal symmetry breaks down and thejet head tilts upward, in the same direction of thetangential inlet velocity. With the jet progressing,the mushroom head grows in size and the top of thejet head moves faster than the bottom. As a result,the head is stretched along the streamwise directionand the streamwise width of the jet head increasesover time. This observation is important to the mea-surement of the penetration length of the jet. Inthe present study the penetration length is definedbased on the transverse integrated mass (TIM) ofthe spray, following the experiment [3]. The stretch-ing of the jet head will introduce a more gradualvariation in TIM near the head and the thresholdof TIM for penetration length calculation requiresadditional caution.

It is also observed that the breakup of the jethead generates a large number of droplets. TheKelvin-Helmholtz instability develops at the inter-face of the liquid jet core, forming circumferentialwaves around the jet. These waves will grow spa-tially and eventually break and form droplets as well.The addition of tangential inlet velocity changes thetransverse distribution of velocity within the jet,e.g., at the same streamwise location the top of thejet moves faster than the side and the bottom, asa result, the Kelvin-Helmholtz instability which isdriven by the shear and the velocity difference be-tween gas and liquid will also be different. As thejet advects further a large number of droplets aregenerated.

Effect of tangential component of injection velocity

A parametric study is performed by varying thetangential inlet velocity. The temporal evolutions ofthe jet penetration length and the jet deflection an-gle for different ratios between tangential to normalcomponents of the injection velocity, η = Vinj/Uinjare shown in Fig. 4. The penetration length ismeasured through streamwise distribution of TIM,following the experiment [3]. Different thresholdshave been tested and it is shown that as long as0.05<TIM/TIMinlet < 0.2, the penetration lengthis not sensitive to the specific value of the threshold.The simulation results for different η is compared to

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Figure 4. Temporal evolution of (a) the liquid jetpenetration and (b) the plume angle deviation fromthe drill angle for different η. The simulation resultsare compared with the experimental data [3].

the experiment data in Fig. 4(a). The penetrationspeed increases with η and the numerical result forη = 0.2 is shown to agree well with the experiment.

The tangential inlet velocity also influences thedeflection of the jet. The deflection angle in theoriginal spray G is defined as the difference betweenthe plume and drill angles. For the present case,it can be calculated based on the center of liquidmass at a cross section. The results shown in Fig.4(b) is measured at about x/Rinj = 24, which isconsistent with one of the measurement location inexperiment [3]. Therefore, the data for deflectionangle do not appear until the jet head reaches themeasurement location. The initial large-amplitudevariation is purely due to the passage of the head.After that, the deflection angle is more or less a con-

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stant in time. The fluctuations in the deflection an-gle is simply due to the interfacial instability on thejet surface. For η = 0, the deflection angle is closeto zero, namely the jet is along the nozzle axis andthere is no deflection. The deflection angle increaseswith the tangential inlet velocity. The deflection an-gle measured in experiments has a quite large errorbar, which is indicated in Fig. 4(b). The simulationresults for both η = 0.2 and 0.4 agree well with theexperimental data [3].

Effect of simulation setup

We have also investigated the effect of simula-tion method on the results. Three different tests areperformed here. For tests 1 and 2, a conventionalvolume-of-fluid method is used and there is no spe-cial treatment for momentum flux calculation nearthe interface. For test 3, we employed a momentum-conserving VOF method (details of which can befound in [13]). Furthermore, the tangential inlet ve-locity is along the y axis for test 1 and along 45degrees from y and z axes for tests 2 and 3.

The temporal evolutions of the penetrationlength and the deflection angle for different tests forη = 0.2 are shown in Fig. 5. It is shown that all threetests yield reasonable agreement with experiment.The test 3 results seem to agree with the experi-mental result of the jet penetration length slightlybetter.

In spite of the fact that the three different testsyield similar macro-scale behavior, the micro-scalefeatures are quite different. The interface morphol-ogy of the atomizing jet, viewed from different an-gles, for the different cases are shown in Fig. 6. Forthe side, top, and bottom views, the tangential inletvelocity points upward, outward normal to the pa-per, and inward normal to the paper, respectively.Since a Cartesian mesh is used for a cylindrical jet,it is well known that the numerical error due to meshalignment in the Cartesian grid will influence the in-terfacial instability. For test 1, since the tangentialvelocity is added along the mesh, the interfacial in-stability is contaminated by the numerical error anda “fin” is formed on the top of the jet, which is laterconfirmed as a pure numerical artifact. When werotate the direction of the tangential velocity to 45degrees, then the “fin” vanishes as shown in Fig. 6for tests 2 and 3.

Comparing the results of tests 2 and 3,namely results from the conventional VOF and themomentum-conserving VOF methods, it is foundthat the macro-scale features are similar but moresmall-scale liquid structures, like thin sheets and lig-aments, were captured in test 3. Due to the large

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Figure 5. Temporal evolution of (a) the liquid jetpenetration and (b) the plume angle deviation fromthe drill angle for different tests for η = 0.2. Thesimulation results are compared with the experimen-tal data [3].

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liquid-to-gas density ratio r, the numerical errorfor not conserving momentum will introduce fakebreakup of liquid structures [14]. As time elapsesand after the jet head moves downstream, the liquidcore in the near-field seems to reach a statisticallysteady state, see Fig. 6.

It can also be observed that the morphology ofthe jet is different along the azimuthal direction,since the symmetry of the cylindrical jet broke downdue to the tangential inlet velocity. From the resultsof test 3, it can be observed that the interface onthe top of the jet exhibits a larger number of small-scale interfacial waves, while the bottom of the jet ispretty much flat and no wave is observed. A carefulobservation will also reveal that the wavelength atthe top of the jet is actually smaller than those onthe side.

Vortex dynamics in the near field

The λ2 vortex-identification criterion is used toillustrate the vortex dynamics and turbulence devel-opment in the near field [15]. The scalar, λ2, is thesecond invariant of the velocity gradient tensor. Theλ2 iso-surfaces colored by the streamwise velocity forη = 0.2 and test 3 are shown in Fig. 7. Due to thehigh Reynolds and Weber numbers, the liquid jetand the surrounding gas flow are unstable and willtransit to turbulence.

As shown in Fig. 7 (a), a vortex tube near thenozzle exist still exhibits an axisymmetric shape, butthe symmetry will eventually break down at latertime or further downstream. The shapes of vortextubes near the jet surface exhibit similar pattern asthe interfacial waves on the jet surfaces shown inFig. 6. Vortices are formed also inside the inner noz-zle, which indicates that the gas entrained into thenozzle (note that cavitation is not considered here).The entrainment of ambient gas into the nozzle isprobably due to the lower pressure created insidethe counterbore, which is induced by the fast flow-ing liquid. The gas entrainment explains why theliquid surface detaches from the wall of the innernozzle, as shown in Fig. 6. The in-nozzle vorticeswill perturb the interface and may enhance the de-velopment of Kelvin-Helmholtz interfacial waves andthe primary breakup of the jet further downstream.The azimuthal asymmetry created by the tangentialinlet velocity caused different entrainment dynamicsin the azimuthal direction. As a result, the liquid jetcross section is compressed along the direction of thetangential inlet velocity and exhibit an oval shape.From Fig. 7(b), it can be observed that the gas flowbecomes fairly turbulent downstream (about 5 jetdiameters).

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Summary

The atomization of a gasoline surrogate jet is in-vestigated in the present study through high-fidelitysimulation. The overarching goal is to understandthe near-field liquid breakup dynamics under opera-tion condition similar to the ECN spray G. In orderto focus computational resources on resolving thegas-liquid interface, only one of the eight jets is sim-ulated. A tangential inlet velocity is introduced tomimic the fuel flows entering the nozzle. A para-metric study is performed for the ratio between thetangential and normal inlet velocity components, η.The temporal evolutions of the penetration lengthand deflection angles are presented and comparedto the experimental measurement through X-ray di-agnostics. Both the penetration speed and the jetdeflection angle increase with the tangential inletvelocity. When the ratio η = 0.2, the simulationresults match well with experimental data for bothpenetration length and deflection angle. Further-more, different tests have been conducted to inves-tigate the effect of simulation methods on the keyfindings obtained. The momentum-conserving VOFmethod along with adding tangential velocity notaligned with the Cartesian grid seems to produce thebest results, capturing both small-scale liquid struc-tures formed in breakup and also avoiding the nu-merical artifact in interfacial instability. Due to thehigh-fidelity simulation obtained, the λ2 vortex iden-tification criterion can be calculated to illustrate thetemporal evolution of vortical dynamics. The detailsfor vortex deformation and breakups and the turbu-lent transition of the gas flow are clearly shown.

Acknowledgements

The authors acknowledge the support of Na-tional Science Foundation (NSF #1853193). Thesimulations presented in this paper were performedon the machine Stampede2 at the Texas AdvancedComputing Center cluster (TACC) and also on theBaylor cluster Kodiak.

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