Herrmann10a

1

iecobRrjsceslTjctocccWdcsbes

l

J

Downloa

Marcus HerrmannDepartment of Mechanical and Aerospace

Engineering,Arizona State University,

Tempe, AZ 85287e-mail: [email protected]

Detailed Numerical Simulationsof the Primary Atomization of aTurbulent Liquid Jet in CrossflowThis paper presents numerical simulation results of the primary atomization of a turbu-lent liquid jet injected into a gaseous crossflow. Simulations are performed using thebalanced force refined level set grid method. The phase interface during the initialbreakup phase is tracked by a level set method on a separate refined grid. A balancedforce finite volume algorithm together with an interface projected curvature evaluation isused to ensure the stable and accurate treatment of surface tension forces even on smallscales. Broken off, small scale nearly spherical drops are transferred into a Lagrangianpoint particle description allowing for full two-way coupling and continued secondaryatomization. The numerical method is applied to the simulation of the primary atomiza-tion region of a turbulent liquid jet �q�6.6, We�330, Re�14,000� injected into agaseous crossflow �Re�570,000�, analyzed experimentally by Brown and McDonell(2006, “Near Field Behavior of a Liquid Jet in a Crossflow,” ILASS Americas, 19thAnnual Conference on Liquid Atomization and Spray Systems). The simulations take theactual geometry of the injector into account. Grid converged simulation results of the jetpenetration agree well with experimentally obtained correlations. Both column/bagbreakup and shear/ligament breakup modes can be observed on the liquid jet. A gridrefinement study shows that on the finest employed grids (flow solver 64 points perinjector diameter, level set solver 128 points per injector diameter), grid converged dropsizes are achieved for drops as small as one-hundredth the size of the injector diameter.�DOI: 10.1115/1.4000148�

Introduction

The atomization of turbulent liquid jets injected into fast mov-ng subsonic gaseous crossflows is an important application forxample in gas turbines, ramjets, and augmentors. It is a highlyomplex process that has been extensively studied experimentallyver the past decades. Early studies of the atomization of nontur-ulent liquid jets in crossflows have recently been reviewed inef. �1�, whereas newer studies of this case include the work

eported in Refs. �1–8�. Most experimental work has focused onet penetration, including both the column trajectory and the re-ulting spray penetration. Some recent jet penetration correlationsan be found in Refs. �4,8�. Unlike turbulent liquid jets atomizedither by injection into still air or by a coflowing fast moving gastream, experimental access to the primary atomization region ofiquid jets injected into crossflows is relatively straightforward.his is due to the fact that at least the windward side of the liquid

et is typically not surrounded by many drops that could otherwiseonceal the jet phase interface geometry. This is not, however,ypically the case for the leeward side. Still, experimental studiesf nonturbulent liquid jets injected into subsonic crossflows haveoncluded that depending on the momentum flux ratio and therossflow Weber number, essentially two different breakup modesan be observed �8�. For low momentum flux ratios and crossfloweber numbers, the liquid jet breaks up as a whole some distance

ownstream of the injector. For high momentum flux ratios androssflow Weber numbers, on the other hand, surface breakup ortripping at the sides of the liquid jets is observed prior to columnreakup �8�. Unlike nonturbulent jets, turbulent liquid jets do notxhibit this clear separation of breakup modes �9�. Stripping at theides of the liquid column occurs even at low Weber numbers,

Manuscript received May 5, 2009; final manuscript received May 6, 2009; pub-
ished online March 30, 2010. Review conducted by Dilip R. Ballal.
ournal of Engineering for Gas Turbines and PowerCopyright © 20

ded 30 Mar 2010 to 129.219.24.167. Redistribution subject to ASM

where nonturbulent jets exhibit only the column-breakup mode.Turbulence initiates the generation of ligaments that then break updue to the Raleigh mechanism �9�.

Even though at least some level of consensus exists concerningthe dominant breakup modes, modeling attempts of the atomiza-tion process have had mixed results. While correlations for jetpenetration derived from experimental data give good agreementfor parameter ranges and configurations for which they were de-veloped, numerical simulations predicting the jet penetration, dropsizes, and liquid volume fluxes have had mixed success �1,10,11�.This is in part due to the fact that under most operating conditions,turbulence interaction is strong and several different atomizationmechanisms occur on the jet’s surface at the same time. Detailednumerical simulations can help study these simultaneously occur-ring mechanisms, even in regions of the liquid jet where tradi-tional experimental methods cannot observe the phase interfacedynamics.

Although detailed simulations solve the Navier–Stokes equa-tions directly, it is incumbent on any numerical simulation to dem-onstrate that spatial and temporal discretization errors are not un-duly impacting the obtained results. It is this required gridindependence of the numerical results that has yet to be demon-strated in numerical simulations of the primary atomization ofhigh speed liquid jets �12–16�. Besides the enormous resolutionrequirement, detailed numerical simulations are challenging be-cause one not only has to track the position of the liquid/gasinterface and handle a large number of topology changes, but onealso has to account for the fact that the phase interface is a dis-continuity and the surface tension force represents a singular force�17�. Treating the surface tension force numerically in a stable andaccurate manner is of crucial importance, since breakup by defi-nition involves small scales where capillary forces are dominant.

The outline of this paper is as follows: after summarizing thegoverning equations, the numerical methods employed to solve
them are briefly outlined. Finally detailed simulation results of the
JUNE 2010, Vol. 132 / 061506-110 by ASME

E license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

p==a

2

pe

wdnmsx

aD

Av

wH

wvt

Ue

w

gr

0

Downloa

rimary atomization of a turbulent liquid jet �q=6.6, We330, Re=14,000� injected into a gaseous crossflow �Re570,000� analyzed experimentally in Ref. �2� will be presentednd discussed.

Governing EquationsThe equations governing the motion of an unsteady incom-

ressible immiscible two-fluid system are the Navier–Stokesquations

�u

�t+ u · �u = −

1

�� p +

1

�� · ��u + �Tu�� +

1

�T� �1�

here u is the velocity, � is the density, p is the pressure, � is theynamic viscosity, and T� is the surface tension force, which isonzero only at the location of the phase interface xf. Further-ore, the continuity equation results in a divergence-free con-

traint on the velocity field, � ·u=0. The phase interface locationf between the two fluids is described by a level set scalar G, with

G�xf,t� = 0 �2�

t the interface, G�x , t��0 in fluid 1, and G�x , t��0 in fluid 2.ifferentiating Eq. �2� with respect to time yields

�G

�t+ u · �G = 0 �3�

ssuming � and � are constant within each fluid, density andiscosity at any point x can be calculated from

��x� = H�G��1 + �1 − H�G��2 �4�

��x� = H�G��1 + �1 − H�G��2 �5�here indices 1 and 2 denote values in fluid 1, respectively, 2, andis the Heaviside function. From Eq. �2� it follows that

��x − xf� = ��G��G� �6�

ith � the Dirac delta function. Furthermore, the interface normalector n and the interface curvature � can be expressed in terms ofhe level set scalar as

n =�G

��G�, � = � · n �7�

sing Eqs. �6� and �7�, the surface tension force T� can thus bexpressed as

T��x� = ��x − xf�n = ��G��G�n �8�

active super-grid block

Fig. 1 RLSG

ith � the surface tension coefficient.

61506-2 / Vol. 132, JUNE 2010


3 Numerical MethodsIn this section, we first briefly summarize the refined level set

grid �RLSG� method used to track the phase interface during pri-mary atomization. Then, the level set-based balanced force algo-rithm is reviewed that allows for the accurate and stable treatmentof surface tension forces. Finally the coupling procedure of theRLSG tracked phase interface to the Lagrangian point particlemethod is described.

4 Refined Level Set Grid MethodIn the RLSG method, all level set-related equations are evalu-

ated on a separate equidistant Cartesian grid using a dual-narrowband methodology for efficiency. This so-called G-grid is overlaidonto the flow solver grid on which the Navier–Stokes equationsare solved and can be independently refined, providing high res-olution of the tracked phase interface geometry, see Fig. 1. Detailsof the method, i.e., narrow band generation, level set transport,re-initialization, curvature evaluation, and its performance com-pared with other interface tracking methods in generic advectiontest cases, can be found in Ref. �18�.

In the current simulations, refinement of the G-grid is limited toa factor two in each spatial direction as compared with the flowsolver grid. While higher refinements are feasible from an effi-ciency standpoint, they would require the use of a subflow solvergrid model to correctly capture the otherwise nonresolved phaseinterface dynamics on the G-grid scale �19�. Instead, here, therefined G-grid simply serves to increase the accuracy of the levelset-based phase interface tracking scheme.

5 Balanced Force AlgorithmIn the Navier–Stokes equations, the position of the phase inter-

face influences two different terms. The first term is due to Eqs.�4� and �5�, since H�G� is a function of the position of the phaseinterface. For finite volume formulations, the volume fraction cvof a control volume is defined as

cv = 1/Vcv�Vcv

H�G�dV �9�

with Vcv the volume of the control volume cv. In the RLSGmethod, the above integral is evaluated using the high-resolutionG-grid, see Refs. �18,20� for a detailed description. Then bothcontrol volume density and viscosity are simply

�cv = cv�1 + �1 − cv��2 �10�

activeG-grid cells

ghost cells boundary cells

hG

id structure

�cv = cv�1 + �1 − cv��2 �11�

Transactions of the ASME


tbbop�

w

w

Tio�Rni

6

sicsdaLsgsa

a

wsefccpbsFm

psvifnsu

7

i

J

Downloa

The second term that is a function of the interface position ishe surface tension force term, Eq. �8�. Here it is critical for sta-ility and accuracy that the surface tension force can be balancedy the pressure gradient �jump� across the phase interface exactlyn the discrete level. This is ensured by the balanced force ap-roach �18,21� based on the continuum surface force �CSF� model22�. Then the surface tension force at the control volume face f is

T�f= �� f�� f �12�

ith the phase interface curvature at the control volume face

� f =cv�cv + nbr�nbr

cv + nbr�13�

here nbr is the control volume sharing the face with cv, and

cv = �1 : 0 � cv � 1

0 : otherwise� �14�

he control volume curvature �cv is calculated from the phasenterface geometry on the high-resolution G-grid using a second-rder accurate interface projected curvature calculation method18�. A detailed description of the balanced force algorithm for theLSG level set method and its performance compared with alter-ative numerical methods in a range of test cases involving cap-llary forces can be found in Ref. �18�.

Coupling to Lagrangian Spray ModelAtomization typically produces a vast number of both large and

mall scale drops. Resolving the geometry by tracking the phasenterface associated with each of the resulting drops quickly be-omes prohibitively expensive, such that a different numerical de-cription has to be employed. An alternative approach is to intro-uce simplifying assumptions concerning the drop shape and treatll drops smaller than a cut-off length scale in a point particle,agrangian frame. One of the typical prerequisite of such standardpray models is that the drop size be smaller that the flow solverrid size. Note that the RLSG approach can resolve and trackubflow solver sized liquid structures. Drop transfer is initiated ifseparated liquid structure has a liquid volume

VD � Vtrans �15�nd its shape is nearly spherical

rmax � 3

4�VD1/3

�16�

ith typically =2 and rmax the maximum distance of the liquidtructure’s surface to its center of mass. This second criterionnsures that small scale detached ligament structures that wouldulfill the first criterion are not transferred and replaced by spheri-al drops, since these ligaments often continue to break up byapillary instabilities producing a range of small scale drops. Notrematurely transferring stretched out structures thus allows thisreakup process to be simulated directly instead of relying onecondary atomization models for the Lagrangian description.urther details concerning the application of the Lagrangian sprayodel coupling procedure can be found in Refs. �23,24�.In the Lagrangian description, full two-way momentum cou-

ling between the drop and continuous phase is used including atochastic secondary atomization model �25�. However, the cellolume occupied by the Lagrangian drops is not explicitly takennto account and neither drop/drop nor drop/tracked phase inter-ace collisions are modeled. But as long as liquid structures haveot been transferred into the Lagrangian description, i.e., they aretill tracked by the level set scalar, secondary breakup, cell vol-me effects, and all collisions are fully captured.

Employed SolversIn this work we use the flow solver CDP/CHARLES that solves the

ncompressible two-phase Navier–Stokes equations on unstruc-

ournal of Engineering for Gas Turbines and Power


tured grids using the finite volume balanced force algorithm �18�.In the single phase regions, the employed scheme conserves thekinetic energy discretely. Turbulence in the single phase regionsof the flow is modeled using a dynamic Smagorinsky large eddysimulations �LES� model, however, none of the terms arising fromfiltering the phase interface are modeled. The approach insteadrelies on resolving all relevant scales at the phase interface, thus,ideally reverting to a direct numerical simulation �DNS� at thephase interface. As such, the current simulation approach is acombination of LES in the single phase regions and ideally DNSat the phase interface. A Lagrangian particle/parcel technique isemployed to model the small scale liquid drops of the atomizingliquid spray �26�.

The liquid/gas phase interface during primary atomization istracked by the interface tracking software LIT, using the RLSGmethod �18�. The solver uses a fifth-order WENO scheme �27� inconjunction with a third order TVD Runge–Kutta time discretiza-tion �28�. The phase interface’s curvature on the level set grid isevaluated using a second-order accurate interface projectionmethod �18�.

The flow solver CDP/CHARLES and the interface tracking soft-ware LIT are coupled using the parallel multicode coupling libraryCHIMPS �18,29�. In order to couple the level set equation to theNavier–Stokes equation, u in Eq. �3� is calculated from the flowsolver velocity by trilinear interpolation. To achieve overallsecond-order accuracy in time, the level set equation is solvedstaggered in time with respect to the Navier–Stokes equations.

8 Computational Domain and Operating ConditionsThe case analyzed in this paper is one studied experimentally

by Brown and McDonell �2�. Table 1 summarizes the operatingconditions and resulting characteristic numbers. Note that al-though the density ratio is artificially reduced from the experimen-tal values, all relevant characteristic numbers, i.e., momentum fluxratio q, crossflow Weber number Wec, jet Weber number Wej,crossflow Reynolds number Rec, and jet Reynolds number Rej,are the same as in the experiment.

Figure 2 depicts the computational domain and the used bound-ary conditions, as well as a zoom into the near-injector region toshow the mesh detail used in the simulations. The chosen compu-tational domain �−25D . . .50D 0. . .25D −10D . . .10D� issmaller than the channel used in the experiment �−77D . . .127D 0. . .54D −27D . . .27D�. However, simulations using the fullexperimental channel geometry were conducted to verify that thereduced computational domain does not impact the reported re-sults.

The injector geometry used in the experiments consists of along initial pipe section of diameter 7.49 mm, followed by a 138deg angled taper section, followed by a short pipe section of di-

Table 1 Operating conditions and characteristic numbers

Experiment Simulation

Jet exit diameter D �mm� 1.3 1.3Crossflow density �c �kg /m3� 1.225 1.225Jet density � j �kg /m3� 1000 12.25Crossflow velocity uc �m/s� 120.4 120.4Jet velocity uj �m/s� 10.83 97.84Crossflow viscosity �c �kg/ms� 1.82 10−5 1.82 10−5

Jet viscosity � j �kg/ms� 1.0 10−3 1.11 10−4

Surface tension coeff. � �N/m� 0.07 0.07Momentum flux ratio q 6.6 6.6Crossflow Weber number Wec 330 330Jet Weber number Wej 2178 2178Crossflow Reynolds number Rec 5.7 105 5.7 105

Jet Reynolds number Rej 14,079 14,079

ameter D with L /D=4, whose exit is mounted flush with the

JUNE 2010, Vol. 132 / 061506-3


lgtrcrspcdiifRpsjsa

Ft

0

Downloa

ower channel wall. The experiments conducted for this injectoreometry suggest that the specifics of the liquid velocity distribu-ion in the injector exit plane can have a large impact on theesulting atomization process of the liquid jet �2,3�. Both the dis-harge coefficient of the nozzle and the geometry of the taperegion are critical. To account for their effect in the atomizationimulations, detailed single phase large eddy simulations of theretaper pipe, the taper, the post-taper pipe, and the crossflowhannel in the vicinity of the injector exit were performed using aynamic Smagorinsky model. The channel section was includedn these simulations to capture the effect of the crossflow on thenjector exit plane velocity distribution. The simulations were per-ormed using the correct experimental momentum flux ratio andeynolds number, see Table 1. Inflow boundary conditions for theretaper pipe were taken from a precomputed LES pipe flowimulation database at the appropriate Reynolds number. The in-ector exit plane velocity distributions were then stored as a timeequence in a database to be used in the subsequent two-phasetomization simulations.

ig. 3 Zoom of the instantaneous axial velocity distribution inhe injector midplane

Fig. 4 Instantaneous injector exit plane velocity distributio

x

y

z

x-: channelinflow

injector

y-: wall

y+: slip wallz-: slip wall

z+: slip wall x+: channoutflow

Fig. 2 Computational domain and boundainjector „right…

transverse direction.

61506-4 / Vol. 132, JUNE 2010


Figure 3 shows part of the injector simulation depicting theaxial velocity distribution in the post-taper pipe section of theinjector. All velocities are made dimensionless with the corre-sponding bulk jet velocity uj. The effect of the sharp corners at theend of the taper are clearly visible, generating both recirculationregions in the pipe immediately following the corners and signifi-cant velocity fluctuations further downstream.

Figure 4 shows an example of the velocity distributions in theinjector exit plane that are stored in the database for use as inflowboundary conditions in the crossflow atomization simulations. Theeffect of the channel crossflow is clearly visible in the shift of theaxial velocity distribution in the downstream channel direction.

The two-phase atomization simulations were performed usingthree different grids of increasing resolution in order to addressthe important question of how much the employed grid resolutionimpacts the atomization results. Table 2 summarizes the meshesemployed in the three cases c01, c12, and c23. The flow solvergrid consists of hexahedra of edge length D /4, which are isotro-pically refined in layers near the injector and lower channel walls,such that the spatial region where the phase interface is tracked iscompletely filled with equidistant grid cells of the minimum cellsize �x reported in Table 2, see also Fig. 2. Note that in each case,the G-grid is a factor 2 finer than the flow solver grid in order toenhance numerical accuracy of the interface tracking scheme.Separate simulations were conducted to ensure that this does notnegatively impact the resulting drop size distributions, i.e., using aflow solver minimum grid size equal to the respective G-grid sizeyielded virtually identical drop size distributions.

At t=0, the liquid jet is initialized in the computational domainby a small cylindrical section of length D capped by a half-sphereprotruding into the crossflow channel.

9 Results and DiscussionFigure 5 shows the temporal evolution of the level set tracked

liquid mass for the three different grid resolutions. All cases showan initial linear increase. This is due to the fact that at this earlystage, almost no small scale drops are generated that would betransferred out of the tracked and into the Lagrangian representa-

From left to right: crossflow direction, axial direction, and

conditions „left… and mesh detail near the

ns.

el

ry



ttstbttocbushmabiwsac

epun

d�

dRagsa

C

FRFR

J

Downloa

ion. Then at around t=5, significant numbers of small scale dropshat fulfill the transfer criterion start to be generated resulting in alower increase in the tracked mass until at around t=20 a statis-ically steady state is reached. From this point on, a balance existsetween the injected liquid mass and the atomized liquid masshat is transferred into the Lagrangian description. It is interestingo note that the coarse grid simulation c01 tends to a larger valuef the tracked liquid mass, whereas the two higher resolutionases result in slightly smaller but similar values. This appears toe due to the fact that for the coarse grid simulations, small scalenresolved turbulent eddies cannot initiate atomization, thus, re-ulting in a smaller transfer rate per phase interface area. Theigher resolution cases, on the other hand, do resolve significantlyore small scale turbulent eddies that can corrugate the interface

nd thus initiate atomization quicker. This conjecture is supportedy analyzing the instantaneous phase interface geometries shownn Figs. 7–9 that show significantly more small scale structuresith increasing grid resolution. Since Fig. 5 indicates that a steady

tate is reached for t�20, all statistics presented in the followingre evaluated only for t�20 for a total of 43 time units for case01, 35 time units for case c12, and 8.1 time units for case c23.

Figure 6 shows averaged side views of the atomizing liquid jetsvaluated for t�20. The jet penetration is compared with theredictions of two common correlations for the penetration of thepper edge of the liquid jet derived by fitting experimental data,amely

y

D= 1.37q

x

D1/2

�17�

ue to work of Wu et al. �8� valid in the near-injector region onlyshown in upper curve� and

y

D= 2.63q0.442 x

D0.39

We−0.088 �l

�H2O−0.027

�18�

ue to the work of Stenzler et al. �4� �shown in lower curve�.ecent experimental observations reported in Ref. �2� show bettergreement with the latter correlation even in the near-injector re-ion. This is the case in the simulation results as well. Figure 6hows better agreement with the correlation of Stenzler et al. �4�nd thus also to the experimental results �2�. Note that there is

Table 2 Grid resolution and mesh sizes

ase c01 c12 c23

low solver min �x D /16 D /32 D /64LSG �xG D /32 D /64 D /128low solver mesh size �1 106� 8.7 21 110LSG max active cells �1 106� 3.5 13 66

0

10

20

30

40

50

0 10 20 30 40 50 60time

0

10

20

30

40

50

0 10 20

Fig. 5 Temporal evolution of tracked liquid mass for different g



virtually no difference between the three different resolutioncases, indicating that even for coarse grids, good jet penetrationresults can be obtained.

Figures 7–9 show snapshots of the atomizing liquid jets at dif-ferent times and different grid resolutions viewed from the side,the front, and the top. Two main simultaneous atomization mecha-nisms can be observed. All cases show instability waves beinggenerated, predominantly visible on the windward side. These in-stabilities generate role-ups and continue to grow along the jetaxis until they form bag like structures that rupture resulting in abroad range of drop sizes, not unlike the column-breakup mode. Itis speculated that this instability mode is due to a Kelvin–Helmholtz instability, however, this conjecture is still to be veri-fied using the generated simulation data. The larger scale instabil-ity mode is most clearly visible in the lowest resolution case c01.It is equally present in the higher resolution cases, but there it isoverlaid by significant turbulence induced surface corrugationsand thus not as visibly pronounced.

In addition to the conjectured column-breakup mode, ligamentsare formed at the sides of the liquid jets near the injector exit thatstretch out and then break up forming a range of drop sizes. At thecurrent stage, the above description of the breakup mechanism isspeculative and still requires a detailed, yet to be performed, quan-titative study of the generated time dependent simulation data.

Note that due to the turbulent �chaotic� nature of the flow, itcannot be expected that the instantaneous phase interface geom-etry shown in Figs. 7–9 converges under grid refinement. Onlystatistical quantities, such as the mean jet penetration or the dropsize distribution, should converge. However, it can be seen thatmany of the larger scale structures on the liquid jet appear to besimilar for all three grid resolutions, indicating that the large scaleinstability mode generated on the upstream pointing side of theliquid jet might be deterministic and sufficiently resolved even onthe coarser grids. However, the higher resolution cases show sig-nificantly more fine scale structure on the liquid jet and maintainthe thin liquid sheets associated with the bag breakup mode in theupper half of the jet slightly longer. This is due to the fact thatunlike on the coarse grid, the artificial grid induced topology

0 40 50 60e

0

10

20

30

40

50

0 10 20 30 40 50 60time

Fig. 6 Impact of grid resolution on averaged side view of theliquid jet; case c01 „left…, c12 „center…, and c23 „right…. Jet pen-etration is compared with correlations due to Wu et al. †8‡ „up-per curve… and Stenzler et al. †4‡ „lower curve….

3tim

rid resolutions: case c01 „left…, c12 „center…, and c23 „right…

JUNE 2010, Vol. 132 / 061506-5


cbMs

0

Downloa

hange event is slightly delayed because the level set inherentreakup length scale �being equal to the grid size� is reduced.oreover, the higher resolution cases generate significantly more

Fig. 7 Side view snapshots of jet in crossflow atomibottom…; case c01 „left…, c12 „center…, and c23 „right…

mall scale drops.

61506-6 / Vol. 132, JUNE 2010


Besides mean jet penetration and observed breakup modes, thekey quantity to ascertain the quality of a numerical simulation isthe grid dependency/independency of the resulting atomized drop

ion at t=5, 10, 15, 20, 25, and 28.1 time units „top to
zat
size distribution. Figure 10 depicts the calculated drop size distri-



btoii

J

Downloa

utions obtained from the primary atomization at t�20 for thehree different grid resolutions analyzed in this study. Shown arenly those drops that are generated directly from the liquid jet,.e., drops that are transferred from the level set tracked phase

Fig. 8 Front view snapshots of jet in crossflow atombottom…; case c01 „left…, c12 „center…, and c23 „right…

nterface representation to the Lagrangian point particle descrip-



tion. Note that these drops can continue to atomize via secondaryatomization mechanisms further downstream; however, within thecomputational domain, only a limited number of these secondaryatomization events occur.

tion at t=5, 10, 15, 20, 25, and 28.1 time units „top to
iza
The drop size distributions in Fig. 10 were generated by bin-

JUNE 2010, Vol. 132 / 061506-7


naba

0

Downloa

ing the data into 20 bins of equal size in terms of log�D�. Thepproximate total number of drops used to calculate each distri-ution was 40,000 �c01�, 176,000 �c12�, and 193,000 �c23�. To be

Fig. 9 Top view snapshots of jet in crossflow atomizbottom…; case c01 „left…, c12 „center…, and c23 „right…

ble to compare the three probability density functions �pdfs�, the

61506-8 / Vol. 132, JUNE 2010


coarser grid pdfs were normalized using a single bin of the finestgrid pdf. Also shown in Fig. 10 is a log-normal fit to the largerdrop sizes of the finest grid results. All three cases show a similar

on at t=5, 10, 15, 20, 25, and 28.1 time units „top to
ati
behavior. Larger drop sizes collapse well to the log-normal fit,



hfitvtkscrdslssfawdbpiero1dtp

1

bobnt

dttgtolsa

Fgcl

J

Downloa

owever, for each grid there is a distinct departure point from thet from which point on smaller drop sizes do not collapse and fail

o match the log-normal fit. This departure point dp decreases inalue proportional to the employed grid size, with dp=1.6�xG forhe coarse and medium grids and dp=1.3�xG for the fine grid. Theey result of Fig. 10 is the fact that larger drops, i.e., those re-olved by at least 1.6 G-grid cells, collapse to a single pdf, in thisase a log-normal distribution independent of the employed gridesolution. These drop sizes can thus be considered grid indepen-ent. Drops smaller than about d=1.6�xG, however, show atrong grid dependency. The reason for this behavior is the fol-owing: fixed grid methods used to track interfaces, like the levelet method used here, have an inherent topology change lengthcale that is proportional to the local grid size. As soon as tworont segments enter the same grid cell, a topology change event isutomatically triggered. The exact moment of breakup is thus al-ays a function of the employed grid size. However, for largerrops, the error introduced by missing the exact moment ofreakup due to the inherent grid size dependency is small com-ared with the generated drop size. Thus larger drop sizes are gridndependent, as demonstrated in Fig. 10. For smaller drops, thexact moment of breakup is however the dominant source of er-or; thus, smaller drops are dominated by the employed grid res-lution. The cut-off appears to occur at drops resolved by about.6 G-grid cells. This number is surprisingly low and appears toecrease with increasing grid resolution. This seems to indicatehat the numerically induced topology change starts to mimic thehysical breakup mechanism on small scales.

0 ConclusionDetailed simulation results of the primary atomization of a tur-

ulent liquid jet injected into a subsonic gaseous crossflow previ-usly analyzed experimentally by Brown and McDonell �2� haveeen presented. The simulations match all key nondimensionalumbers, except for the density ratio, which is artificially reducedo study its impact on jet penetration and atomization.

A preliminary qualitative analysis of the simulation results in-icates that breakup of the liquid jet occurs via two main simul-aneous atomization mechanisms. In the first, instability waves onhe liquid column, predominantly visible on the windward side,enerate role-ups and continue to grow along the jet axis untilhey form baglike structures that rupture resulting in a broad rangef drop sizes, not unlike the column-breakup mode. It is specu-ated that this instability mode is due to a Kelvin–Helmholtz in-tability. In the second mode, corrugations on the liquid jet surface

c23

c12

c01

d

d

ig. 10 Grid convergence study of pfd of drop diameters denerated directly by primary atomization: case c01 „openircles…, c12 „open triangles…, and c23 „solid squares…. Solidine is log-normal fit to large drop sizes on finest grid.

re stretched out into ligaments at the sides of the liquid jet near



the injector exit. The stretched out ligaments then break up andform a range of drop sizes. At the current stage, the above descrip-tion of the breakup mechanisms is speculative and still requires adetailed, yet to be performed, quantitative study of the generatedtime dependent simulation data.

Grid independent predictions of the jet penetration in agreementwith experimental observations can be achieved on relativelycoarse grids �D /�x=16�. Moreover, the large scale instabilitymode conjectured to be responsible for the first atomizationmechanism is sufficiently resolved even on these coarse grids.Analysis of the temporal evolution of the pre-atomization trackedmass indicates that it is important to resolve turbulent eddies atleast up to the maximum flow solver resolution considered�D /�x=64�, since these turbulent eddies can generate significantsurface corrugations to initiate the second atomization mecha-nism. The grid independent prediction of atomized drop sizes re-quires significant computational resources. Grid independent dropsizes on the finest grids have been achieved for drops as small as13 �m, or one-hundredth of the injector exit diameter.

While the reduced density ratio analyzed in this paper appearsto have no significant impact on the jet penetration determinedfrom averaged side views of the jet geometry, it is conceivablethat the atomization mechanism and resulting drop sizes are afunction of the chosen density ratio. Currently ongoing simula-tions employing higher density ratios will focus on this question.

AcknowledgmentThis work was supported in part by CASCADE Technologies

Inc. under the NavAir SBIR Project No. N07-046. The authorwould like to thank S. Hajiloo and Y. Khalighi for valuable help ingenerating the fluid solver meshes, and F. Ham for many valuablediscussions concerning the flow solver CDP/CHARLES.

Nomenclatured � drop diameter

dp � minimum grid independent drop diameterD � injector diameterG � level set scalarH � Heaviside functionn � phase interface normal vectorp � pressureq � momentum flux ratior � radius

Re � Reynolds numberu � velocityt � time

T� � surface tension forceV � volume

VD � drop volumeWe � Weber number

xf � location of phase interfacex � crossflow direction

�x � flow solver grid size�xG � level set grid size

y � jet direction

Greek Symbols� � Dirac delta function� � phase interface curvature� � dynamic viscosity� � volume fraction� � density� � surface tension coefficient

Subscripts1 � fluid 1, i.e., liquid2 � fluid 2, i.e., gas
c � crossflow
JUNE 2010, Vol. 132 / 061506-9


R

0

Downloa

cv � control volumef � control volume facej � jet

eferences�1� Aalburg, C., van Leer, B., Faeth, G. M., and Sallam, K. A., 2005, “Properties

of Nonturbulent Round Liquid Jets in Uniform Gaseous Cross Flows,” Atomi-zation Sprays, 15�3�, pp. 271–294.

�2� Brown, C. T., and McDonell, V. G., 2006, “Near Field Behavior of a Liquid Jetin a Crossflow,” ILASS Americas 19th Annual Conference on Liquid Atomi-zation and Spray Systems.

�3� Brown, C. T., Mondragon, U. M., and McDonell, V. G., 2007, “Investigationof the Effect of Injector Discharge Coefficient on Penetration of a Plain LiquidJet Into a Subsonic Crossflow,” ILASS Americas 20th Annual Conference onLiquid Atomization and Spray Systems, ILASS Americas, Chicago, IL.

�4� Stenzler, J. N., Lee, J. G., Santavicca, D. A., and Lee, W., 2006, “Penetrationof Liquid Jets in a Cross-Flow,” Atomization Sprays, 16, pp. 887–906.

�5� Mazallon, J., Dai, Z., and Faeth, G. M., 1999, “Primary Breakup of Nontur-bulent Round Liquid Jets in Gas Crossflows,” Atomization Sprays, 9�3�, pp.291–312.

�6� Sallam, K. A., Aalburg, C., and Faeth, G. M., 2004, “Breakup of RoundNonturbulent Liquid Jets in Gaseous Crossflow,” AIAA J., 42�12�, pp. 2529–2540.

�7� Fuller, R. P., Wu, P.-K., Kirkendall, K. A., and Nejad, A. S., 2000, “Effects ofInjection Angle on Atomization of Liquid Jets in Transverse Ai,” AIAA J.,38�1�, pp. 64–72.

�8� Wu, P. K., Kirkendall, K. A., Fuller, R. P., and Nejad, A. S., 1997, “BreakupProcesses of Liquid Jets in Subsonic Crossflows,” J. Propul. Power, 13�1�, pp.64–73.

�9� Lee, K., Aalburg, C., Diez, F. J., Faeth, G. M., and Sallam, K. A., 2007,“Primary Breakup of Turbulent Round Liquid Jets in Uniform Crossflows,”AIAA J., 45�8�, pp. 1907–1916.

�10� Madabhushi, R. K., 2003, “A Model for Numerical Simulation of Breakup ofa Liquid Jet in Crossflow,” Atomization Sprays, 13�4�, pp. 413–424.

�11� Arienti, M., Madabhusi, R. K., Slooten, P. R. V., and Soteriou, M. C., 2005,“Numerical Simulation of Liquid Jet Characteristics in a Gaseous Crossflow,”ILASS Americas 18th Annual Conference on Liquid Atomization and SpraySystems.

�12� de Villiers, E., Gosman, A. D., and Weller, H. G., 2004, “Large Eddy Simu-lation of Primary Diesel Spray Atomization,” SAE Technical Report No. 2004-01-0100.

�13� Menard, T., Beau, P. A., Tanguy, S., Demoulin, F. X., and Berlemont, A.,2006, “Primary Break Up Modeling, Part A: Dns, a Tool to Explore PrimaryBreak Up,” ICLASS-2006, pp. 1–7, Paper No. ICLASS06-034.

�14� Menard, T., Tanguy, S., and Berlemont, A., 2007, “Coupling Level Set/Vof/

61506-10 / Vol. 132, JUNE 2010


Ghost Fluid Methods: Validation and Application to 3d Simulation of the Pri-mary Break-Up of a Liquid Jet,” Int. J. Multiph. Flow, 33�5�, pp. 510–524.

�15� Bianchi, G. M., Pelloni, P., Toninel, S., Scardovelli, R., Leboissetier, A., andZaleski, S., 2007, “3d Large Scale Simulation of the High-Speed Liquid JetAtomization,” SAE Technical Paper No. 2007-01-0244.

�16� Desjardins, O., Moureau, V., and Pitsch, H., 2008, “An Accurate ConservativeLevel Set/Ghost Fluid Method for Simulating Turbulent Atomization,” J. Com-put. Phys., 227�18�, pp. 8395–8416.

�17� Gorokhovski, M., and Herrmann, M., 2008, “Modeling Primary Atomization,”Annu. Rev. Fluid Mech., 40�1�, pp. 343–366.

�18� Herrmann, M., 2008, “A Balanced Force Refined Level Set Grid Method forTwo-Phase Flows on Unstructured Flow Solver Grids,” J. Comput. Phys.,227�4�, pp. 2674–2706.

�19� Herrmann, M., and Gorokhovski, M., 2008, “An Outline of a LES SubgridModel for Liquid/Gas Phase Interface Dynamics,” Proceedings of the 2008CTR Summer Program, Center for Turbulence Research, Stanford University,pp. 171–181.

�20� Herrmann, M., 2007, “On Simulating Primary Atomization Using the RefinedLevel Set Grid Method,” ILASS Americas 20th Annual Conference on LiquidAtomization and Spray Systems, ILASS Americas, Chicago, IL.

�21� Francois, M. M., Cummins, S. J., Dendy, E. D., Kothe, D. B., Sicilian, J. M.,and Williams, M. W., 2006, “A Balanced-Force Algorithm for Continuous andSharp Interfacial Surface Tension Models Within a Volume Tracking Frame-work,” J. Comput. Phys., 213, pp. 141–173.

�22� Brackbill, J. U., Kothe, D. B., and Zemach, C., 1992, “A Continuum Methodfor Modeling Surface Tension,” J. Comput. Phys., 100, pp. 335–354.

�23� Herrmann, M., 2006, “Simulating Two-Phase Flows Using the Refined LevelSet Grid Method,” ILASS Americas 19th Annual Conference on Liquid Atomi-zation and Spray Systems, ILASS Americas, Toronto, Canada.

�24� Kim, D., Desjardins, O., Herrmann, M., and Moin, P., 2007, “The PrimaryBreakup of a Round Liquid Jet by a Coaxial Flow of Gas,” ILASS Americas20th Annual Conference on Liquid Atomization and Spray Systems.

�25� Apte, S. V., Gorokhovski, M., and Moin, P., 2003, “Les of Atomizing SprayWith Stochastic Modeling of Secondary Breakup,” Int. J. Multiphase Flow,29�9�, pp. 1503–1522.

�26� Moin, P., and Apte, S. V., 2006, “Large-Eddy Simulation of Realistic GasTurbine Combustors,” AIAA J., 44�4�, pp. 698–708.

�27� Jiang, G.-S., and Peng, D., 2000, “Weighted ENO Schemes for Hamilton-Jacobi Equations,” SIAM J. Sci. Comput. �USA�, 21�6�, pp. 2126–2143.

�28� Shu, C. W., 1988, “Total-Variation-Diminishing Time Discretization,” SIAM�Soc. Ind. Appl. Math.� J. Sci. Stat. Comput., 9�6�, pp. 1073–1084.

�29� Alonso, J. J., Hahn, S., Ham, F., Herrmann, M., Iaccarino, G., Kalitzin, G.,LeGresley, P., Mattsson, K., Medic, G., Moin, P., Pitsch, H., Schluter, J.,Svard, M., der Weide, E. V., You, D., and Wu, X., 2006, “CHIMPS: A High-Performance Scalable Module for Multi-Physics Simulation,” 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA Paper No.2006-5274.



Herrmann10a

Documents

Transcript of Herrmann10a