Correction: Sub-grid Scale Modeling of Turbulent Spray Flame using Regularized Deconvolution Method Author(s) Name: Qing Wang(1); Xinyu Zhao(2); Matthias Ihme(1) Author(s) Affiliations: 1. Stanford University, Stanford, CA, United States. 2. University of Connecticut, Storrs, Storrs, CT, United States.

Correction DOI: 10.2514/6.2018-2082.c1

Correction Notice The x and y labels in Fig. 14 should be swapped. The x label should be Da and y label should be Da v.

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Copyright © 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

AIAA SciTech Forum

Sub-grid Scale Modeling of Turbulent Spray Flame usingRegularized Deconvolution Method

Qing Wang� and Matthias Ihme†

Stanford University, Stanford, CA, 94305, United States

Xinyu Zhao‡

University of Connecticut, Storrs, CT, 06269, United States

A new model based on regularized deconvolution methods (RDM) is developed for the clo-sure of sub-grid scale (SGS) terms in turbulent spray combustion. Previous a priori numericalstudies of these flames have identified sensitivities to the turbulence-droplet and turbulence-flame interactions. The objective of this work is to examine e�ects of the SGS closures thoughlarge-eddy simulations (LES) of an acetone spray flame. A series of experiments of turbulentspray flames were conducted at the University of Sydney to establish a benchmark databaseto support model developments, including the measurements of the target acetone spray flame.Three LES cases using di�erent modeling combinations for the SGS turbulence-droplet andturbulence-flame interactions are conducted to assess the performance of the new model. Sys-tematic model evaluations show that the consideration of SGS turbulence-droplet interactionsusing RDM improves the prediction of gas-phase combustion downstream where the mesh iscoarse. Further improvement in temperature prediction is observed in the case where RDM isalso used as the closure for turbulence-flame interaction.

I. Introduction

T������� spray combustion, as seen in internal and aeronautical combustion engines, is critical for power generationin the aerospace industry. To improve the e�ciency of such engines, numerical studies have been conducted

extensively using large-eddy simulation (LES) for these configurations. Due to their multiphase and multiphysicsnature, LES simulations of spray combustion are sensitive to the discrete-phase models, the gas-phase models and thetwo-phase interaction models. In the present study, the sub-grid turbulence-droplets and turbulence-flame interactionsare investigated. For this, a new sub-grid model based on regularized deconvolution method (RDM) is developed for theclosure of these sub-grid scale (SGS) e�ects.

For the discrete phase, the RDM based turbulence-droplet interactions model accounts for the fluctuation of both thegas-phase velocity and temperature fields, which provides corrections for the droplet momentum and energy equations.In particular, the fluctuation of temperature can significantly change the distribution of the sub-grid temperature undercertain conditions [1, 2]. However, the reconstruction of the gas-phase temperature has rarely been considered inliterature [3]. The velocity and temperature fields that are reconstructed using independent Wiener processes are oftendecorrelated. Therefore, the primary objective of the present study is to provide a comprehensive and consistent SGSclosure model for both e�ects.

For the gas-phase, the RDM based turbulence-flame interactions model is proposed to reconstruct the SGS turbulentflame structure. Sub-grid fluctuations of the reaction source term are represented explicitly on a high-resolution grid inthis approach. It is therefore of interest to assess the capability of RDM as a turbulence-flame interaction model forgas-phase combustion, as a secondary objective.

To achieve these goals, the turbulent spray flame experiments conducted by Gounder et al. [4] are employed astest cases. The well-quantified boundary conditions in these experiments make them desirable for the development ofmodeling capabilities to predict turbulent mixing, reaction chemistry, and multiphase transport. This series of flames

�Graduate student, Department of Mechanical Engineering, Stanford University, 488 Escondido Mall, Stanford, CA 94305, United States, AIAAstudent member.

†Associate Professor, Department of Mechanical Engineering, Stanford University, 488 Escondido Mall, Stanford, CA 94305, United States,AIAA member.

‡Assistant Professor, Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road Unit 3139, Storrs, CT 06269,United States, AIAA member

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2018 AIAA Aerospace Sciences Meeting 8–12 January 2018, Kissimmee, Florida

10.2514/6.2018-2082

Copyright © 2018 by authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

AIAA SciTech Forum

have been studied by various groups, considering di�erent modeling approaches for droplet transport and gas-phasecombustion [5–8]. While the majority of the existing research focuses on the e�ects of di�erent turbulent combustionmodels, the evaporation models [9], the influence of inlet velocity profiles [10], and the e�ects of sub-grid fluctuation onthe droplet velocity are also studied [11]. The ethanol-based experiments are more investigated than the acetone-basedexperiments due to the increasing interest in bio-fuel. However, the acetone/air flame is shown to behave closer to apremixed flame than the ethanol/air flame due to faster evaporation [6]. From a model assessment point of view, theacetone/air flame is more challenging to models, hence is chosen as the test flame in the present study.

The rest of the paper first introduces the modeling approaches, highlighting a new RDM based turbulence-dropletand turbulence-flame interactions model. The experimental and numerical setup is introduced next, with quantifiedboundary and initial conditions. Finally, results obtained from di�erent models are compared, and the reasons that leadto the observed di�erences are discussed.

II. Governing Equations and ModelingIn the present study, we analyzed the performance of LES in simulating a spray jet flame. Di�erent SGS closure

models are considered, and their performance is evaluated. Detailed formulations for both carrier phase and dispersedphase are described in the following subsections. Configurations on the SGS modeling approaches are discussed.

A. Governing Equations and Physical ModelsIn the present work, flamelet progress variable (FPV) is used to model the chemical reactions in LES. The governing

equations describing conservation of mass, momentum, and scalars in the gas-phase take the following form:

@

@t⇢ +

@

@xi(⇢eui) = 0, (1a)

@

@t�⇢eu j

�+@

@xi

�⇢euieu j

�= � @p

@xi+@⌧i j@xj+ �u j � (md

dud,i

dt+ ud,i

dmd

dt), (1b)

@

@t

⇣⇢eZ⌘ + @

@xi

⇣⇢euieZ⌘ =

@

@xi

✓⇢DZ

@Z@xi

◆+ �Z � 1

Vdmd

dt, (1c)

@

@t

⇣⇢eC⌘+@

@xi

⇣⇢eui eC⌘

=@

@xi

✓⇢DC

@C@xi

◆+ �C + ⇢ €!C, (1d)

where Z is the mixture fraction and C = YCO2 + YCO + YH2O + YH2 is the progress variable [12].The sub-grid stress term is described by �� = @(⇢euie�)/@xi � @(⇢ui�)/@xi for � = ui, Z,C. The dispersed phase is

modeled by a Lagrangian approach where the following equations are solved with the LES equations [13]:

dmd

dt= �

Shgmd

3Scg⌧dlog(1 + Bm), (2)

dud

dt=

f1⌧d

us, (3)

dTd

dt=

f2⌧d

NugCp,m

3PrgClTs +

Lv

mdCl

dmd

dt. (4)

Here ⌧d = ⇢lD2/(18µg) is the droplet relaxation time constant, Cp,m = (1 �Yv)Cp,g +YvCp,v is the heat capacity of thegas mixture , Bm = (Ys � Yv)/(1 � Ys) is the Spalding number, and f1 and f2 are the correction factors [13]. us and Ts

are the unclosed slip velocity and temperature di�erence, respectively. In Eqs. 2 to 4, subscript g, d and v denote thegas-phase, dispersed phase and vapor phase respectively.

The FPV chemistry table is constructed from one-dimensional counterflow di�usion flame simulations. In thisFPV-model, liquid fuel is assumed to be pre-vaporized. In this approach, the temperature of the fuel stream is reducedby an amount that corresponds to the latent heat of evaporation in the one-dimensional flamelet computations. Thisapproach is valid for flows with small Stokes numbers [14, 15], which is defined as the ratio of the relaxation time scale⌧d = ⇢dd2

p/(18µ) to the convective time scale. Note that the Stokes number for the configuration considered in thisstudy is St = 10, showing that the pre-vaporization assumption is valid for the current configuration.

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B. Modeling approaches in LESThe sub-grid turbulence-droplet and turbulence-chemistry interactions are identified to be two major SGS e�ects in

multiphase reacting LES. In literature, the sub-grid turbulence-droplet interactions are often neglected in LES [11].Filtered velocities and temperature from the carrier phase equations are interpolated at the droplet locations and areused to compute the unclosed terms in Eqs. 3 and 4, as

us = eu(xd) � ud, (5)

Ts = eT(xd) � Td . (6)

The e�ects of sub-grid fluctuation in velocity and temperature can be significant in multiphase reacting flow simulations,especially for sprays with relatively small Stokes numbers [2]. Ignoring the e�ect of sub-grid fluctuations canoverestimate the slip velocity and temperature di�erences. The incorrect characterization of interactions between thedispersed and carrier phase can lead to mis-predictions in flame topology hence heat release.

The impact of sub-grid fluctuations on velocity (i.e., sub-grid dispersion) has been investigated by a few studies.However, the sub-grid scalar dispersion is rarely studied or modeled in the literature [3]. To consider both e�ects,a regularized deconvolution method (RDM) [16] is proposed in this study. This method reconstructs the sub-gridfluctuations of the flow field, hence can capture the interactions between droplets and flow structures that are smallerthan the mesh grid. In practice, for a filtered variable, e�, RDM is formulated as:

¯�? = arg min

=C

¯�?= e�,

��¯�?�+

k⇣=P e� �

=G

¯�?k2 + ↵k =D¯

�?k2

⌘, (7)

where �? is the deconvolved solution, P is the interpolation matrix that projects the LES solution from the computationalgrid to a refined grid, G is the filter kernel which is assumed to take a top-hat profile, D is a finite di�erence secondorder derivative matrix, C is the mean preserving constraint matrix, and ↵ is the regularization factor which is estimatedas ↵ = tr(eGT eG)/tr(I) [17]. The solution of Eq. (7) takes the following form:

"¯�?

¯⌫?

#=

"=GT

=G + ↵

=DT

=D

=CT

=C

=0

#�1 "=GT

=P

=I

#e�, (8)

where ⌫? is the Lagrange multiplier that is discarded in the model formulation. The inequality constraints are enforcedby rescaling the deconvolved solution obtained from Eq. (8). The scaling factors are computed as:

S+ = min©≠≠´�+ � e�i

maxj

⇣¯�?j � e�i⌘ , 1

™Æƨ, (9)

S� = min©≠≠´

e�i � ��max

j

⇣ e�i �¯�?j

⌘ , 1™Æƨ. (10)

By rescaling the deconvolved solution around the LES solution using the minimum scaling factor obtained from Eqs. (9)and (10), the deconvolved solution is updated as:

¯�?j,new = min(S+, S�)(

¯�?j � e�) + e�. (11)

With this, the turbulence-droplet interaction terms are modeled as:

us = u?(xd) � ud, (12)Ts = T?(xd) � Td . (13)

Additionally, for reacting flow LES, a turbulence closure for chemical reaction term is required. The classicalapproach to this for FPV is to apply the presumed PDF model [18]. In this model, the filtered chemical source term forC is computed as:

g€!C =π π

€!C (Z,C)P(C |Z)eP(Z)dZdC. (14)

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Table 1 Modeling terms for LES cases considered in the present study.

SGS modeling term LES-1 LES-2 LES-3Turbulence-droplet interaction None RDM RDMTurbulence-flame interaction �-PDF �-PDF RDM

In Eq. 14, P(C |Z) is the probability density function (PDF) of progress variable conditioned on the mixture fraction,and is modeled as a �-PDF. eP(Z) is the PDF of the mixture fraction, which is modeling using a �-PDF.

An alternative approach for the closure of turbulence-flame interaction is to apply RDM. In this approach, thereaction source term is first computed using the reconstructed scalar field and then filtered explicitly. Applying thistechnique, the sub-grid structures are represented explicitly; therefore the interactions between the flame and the sub-grideddies are considered per se. The source term is then filtered explicitly using a top-hat filter and projected back onto theLES grid, which is: g€!C = ü€!C(Z?,C?) (15)

Based on di�erent modeling approaches, three sets of LES are conducted, as shown in Table 1.

III. Experimental and Computational SetupNumerical simulations are performed for the spray flame that was experimentally investigated at the University of

Sydney [4]. In this configuration, fuel is provided by a central turbulent jet. Liquid fuel is atomized by a nebulizerlocated 215 mm upstream of the exit plane and injected through the central jet. The diameter of the jet is 10.5 mm andsurrounded by a 25-mm-diameter premixed stoichiometric pilot that is generated from a mixture of C2H2, H2, and air.The burner is accommodated in a wind tunnel of diameter 104 mm with ambient air flow at 4.5 m/s. The temperaturewas measured using thermal couples, and larger uncertainty is expected with the temperature measurement near thecenterline [5].

Fig. 1 Experimental configuration for the spray jet flame [4].

In the present study, LES calculations of the operating condition AcF3 are performed, corresponding to a carrier gasvelocity of u j = 24 m/s and exit equivalence ratio of � = 1.8. The Reynolds number for this flow is 20, 700. The carriermass flow rate is 150 g/min, and the liquid fuel injection rate is 45 g/min.

The LES calculations are conducted in a cylindrical coordinate system on a structured mesh with Nx ⇥ Nr ⇥ N =392 ⇥ 130 ⇥ 64 cells in a domain of size 40dj ⇥ 15dj ⇥ 2⇡. The spray jet inflow is generated from a separate simulation

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of the injection tube, and inflow profiles are collected at the location where the gas-phase fuel mass flux and equivalenceratio match the inlet conditions reported in the experiment. The droplet distribution at the inlet is prescribed from aRosin-Rammler distribution with the scale factor a = 1 and the shape factor b = 1.8, as shown in Fig. 2. Parametersof the PDF are fitted from the droplet diameter distribution obtained from the experiment. Reacting flow LES withmodeling specifications listed in Sec. II are conducted and compared against experiments. Results of the simulations areshown in the subsequent sessions.

d [µm]0 20 40 60 80 100

PDF

0

0.01

0.02

0.03

0.04

Exp.Rosin-Rammler

Fig. 2 Droplet diameter distribution at the inlet.

IV. Results and Discussions

A. Instantaneous flow-field resultsQualitative comparisons of the LES results with experimental flow field results for OH and CH3COCH3 are provided

in Fig. 3. The size of each window in Fig. 3 is 1dj ⇥ 1dj . Each window is positioned such that one of its vertical edgescoincides with the centerline and the x-location of its center is given by the specified coordinate. The left columnof each sub-figure shows the PLIF results from the experiment, and the right column shows the instantaneous FRCsolution. The top row is OH and the bottom row is CH3COCH3. Qualitative agreement in the flame location, reactionzone thickness, and flame-turbulence coupling between LES and experiments is observed at all locations. The flowtopology is well captured by the LES.

Figures 4 to 6 show instantaneous iso-contours of the gas-phase flow field of the axial velocity, temperature andreaction source term for the three modeling approaches. The location of the flame front in the center of the jet is di�erentfor the three cases, which are at x/dj = 20, x/dj = 25, and x/dj = 28 for LES-1, LES-2, and LES-3, respectively.Consequently, the temperature in the jet core is higher for LES-1 compared to LES-2 and LES-3.

B. Analysis of dispersed-phase resultsFigures 7 to 10 show the mean and root mean square (RMS) velocity of droplets in the axial and radial directions

respectively. Good agreement in RMS velocities is observed for all cases with experiment, showing that the sub-griddispersion model is insensitive in representing these quantities. The mean radial velocity from all LES cases matcheswith experimental results at x/dj = 20 and 30, but shows and underprediction at x/dj = 10. This is due to themisrepresentation of droplet velocity distribution at the inlet. As the droplets move downstream, the e�ect of boundarycondition diminishes.

At x/dj = 10 and 20, the mean axial velocity of the droplets in all LES cases show good agreement with theexperiment. At x/dj = 30 where the grid is relatively coarse compared to upstream, the mean axial velocity isover-predicted in LES-1. The overprediction of mean velocity is compensated in LES-2 and LES-3 by the application ofsub-grid dispersion model, where good agreements with the experiment are observed. As has been shown in [2], theslip velocity of droplets is over-predicted without considering the e�ect of sub-grid turbulence-droplet interactions inthe a posteriori simulations. As shown in Figs. 4 to 6, the velocity of the carrier phase decays at x/dj � 30. Dropletswith large inertia supersede the mean flow of the carrier phase and experience a drag force. This causes dissipationof the kinetic energy of the droplets, which leads to decay of droplet velocity. In LES-1 where only large-scale flowstructures are considered when computing the slip velocity, the energy dissipation for droplet moment is underestimated.This leads to an over-prediction of the axial droplet velocity. By considering the sub-grid fluctuation of the carrier flow

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x/d = 5 x/d = 10 x/d = 15

x/d = 20 x/d = 25 x/d = 30

OH

OH

Experiment LES

CH3COCH3

CH3COCH3

Fig. 3 Qualitative comparison of OH and CH3COCH3 between experiment PLIF results and LES results withFRC.

u

T

��C

Fig. 4 Temperature, streamwise velocity field, and reaction source term for LES-1 from x/dj = 0 to 40.

with RDM, as in case LES-2 and LES-3, the prediction of dispersed phase energy dissipation is improved. Hence theaxial component of the mean velocity reduces and agrees with the experiment for LES-2 and LES-3.

Figure 11 shows the radial profile of mean droplet Sauter mean diameter (D32) at x/dj = 10, 20, and 30. In all threecases, D32 is under-estimated across the shear layer between the jet and pilot, especially for flow at x/dj = 10. Based onresults shown in Fig. 8, an underestimation of droplets radial velocity is observed. This suggests that only small dropletscan penetrate through the shear layer between the jet and the pilot stream in the simulations. The misrepresentation ofinlet droplet velocity distribution directly influences the spreading of the liquid jet at upstream locations.

C. Analysis of gas-phase resultsThe net influence of the sub-grid turbulence-droplet and turbulence-flame interactions models to the heat release

of the spray flame is assessed in Fig. 12, where the temperature profiles of the carrier phase from the simulations

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u

T

��C

Fig. 5 Temperature, streamwise velocity field, and reaction source term for LES-2 from x/dj = 0 to 40.

u

T

��C

Fig. 6 Temperature, streamwise velocity field, and reaction source term for LES-3 from x/dj = 0 to 40.

r/dj

0 0.2 0.4 0.6 0.8 1

⟨u⟩[m

/s]

20

25

30

35

40Exp.LES-1LES-2LES-3

r/dj

0 0.2 0.4 0.6 0.8 1

r/dj

0 0.2 0.4 0.6 0.8 1

Fig. 7 Mean axial velocity profiles from x/dj = 5 to 30.

are compared with those obtained from the experiment. At x/dj = 10 and 20, all cases show good agreement withexperimental results. This suggests that the gas-phase flow field is insensitive to the SGS closures in these regions. Onthe one hand, as we show in Section B, sub-grid dispersion is insignificant in these regions for the dispersed phase.

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r/dj

0 0.2 0.4 0.6 0.8 1

⟨v⟩[m

/s]

0

1

2

3

4Exp.LES-1LES-2LES-3

r/dj

0 0.2 0.4 0.6 0.8 1

r/dj

0 0.2 0.4 0.6 0.8 1

Fig. 8 Mean radial velocity profiles at x/dj = 10, 20, and 30.

r/dj

0 0.2 0.4 0.6 0.8 1

urm

s[m

/s]

0

2

4

6

8Exp.LES-1LES-2LES-3

r/dj

0 0.2 0.4 0.6 0.8 1

r/dj

0 0.2 0.4 0.6 0.8 1

Fig. 9 RMS axial velocity profiles at x/dj = 10, 20, and 30.

r/dj

0 0.2 0.4 0.6 0.8 1

v rms[m

/s]

0

0.5

1

1.5

2Exp.LES-1LES-2LES-3

r/dj

0 0.2 0.4 0.6 0.8 1

r/dj

0 0.2 0.4 0.6 0.8 1

Fig. 10 RMS radial velocity profiles at x/dj = 10, 20, and 30.

r/dj

0 0.2 0.4 0.6 0.8 1

D32

[µm]

0

20

40

60

80

100Exp.LES-1LES-2LES-3

r/dj

0 0.2 0.4 0.6 0.8 1

r/dj

0 0.2 0.4 0.6 0.8 1

Fig. 11 Mean Sauter mean diameter profiles at x/dj = 10, 20, and 30.

Feedbacks from the dispersed-phase to the gas-phase is comparable in all cases. On the other hand, it is observed thatthe peak of temperature is correlated with the hot reaction product in the pilot stream. The increment of temperature inthe centerline of the jet is a result of heat penetration from the pilot stream to the jet. The influence of reaction heatrelease is secondary in these regions, therefore the di�erence in turbulence closure of chemical source term does nota�ect the results.

At x/dj = 30, we see a clear distinction in temperature profiles for the three cases, especially near the centerline ofthe jet. In LES-1, the centerline temperature is significantly overpredicted. The prediction improves in LES-2, afterthe consideration of droplet dynamics with the sub-grid closures. Further improvement is observed in LES-3, where

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RDM is used as the turbulence closure for the chemical reaction term. In this region, the increment in temperaturenear the centerline of the jet is dominated by heat release from combustion. The presumed-PDF model underestimatesthe turbulent fluctuation of the scalar field, which leads to over-estimated chemical reaction terms. The RDM modelenhances the SGS turbulent fluctuation, which leads to a reduction in reaction source term and improved agreementwith the experiment.

r/dj

0 1 2 3

T−T0[K

]

0

500

1000

1500

2000

Exp.LES-1LES-2LES-3

r/dj

0 1 2 3r/dj

0 1 2 3

Fig. 12 Mean temperature, progress variable and mixture fraction profiles at x/dj = 10, 20, and 30.

To further understand the reasons leading to the observed di�erence at x/dj = 30, the mean profiles of the progressvariable and the mixture fraction are examined, as shown in Fig. 13. The scatter plot of temperature in the mixturefraction space is provided to understand the e�ects of the model on the distribution of the temperature. With increasingcomplexity of models, a non-monotonic behavior is observed in the mean temperature, mixture fraction, and progressvariable profiles, indicating coupled evaporation-turbulence-reaction e�ects. In LES-2, the production of mixturefraction due to evaporation is enhanced slightly near the centerline; this can be a combined e�ect of enhanced evaporationby using RDM and the over-estimation of temperature by using the �-PDF assumptions. Interestingly, LES-3 showscloser mixture fraction profiles to LES-1, which again can be a combinational e�ect of the reduced temperature due toturbulence-flame interactions and suppressed evaporation due to reduced temperature. The scatter plot obtained fromLES-3 shows no data points after Z = 0.2 and more scattered data points between 0.15 and 0.2. LES-3 recovers thenon-premixed flame feature on the lean side of the flame (i.e., corresponding to the coflow side in the physical space;�st = 0.09), and it displays more premixed flame features on the rich side of the flame, as evident by the scatter of thetemperature data. The scatter plots provided by LES-3 are more consistent with previous studies where similar flamesare simulated [19].

r/dj

0 1 2 3

! Z

0

0.05

0.1

0.15

0.2

r/dj

0 0.5 1 1.5 2 2.5 3

! C

0

0.1

0.2

0.3

0.4

!Z

0 0.1 0.2 0.3

! T

500

1000

1500

2000

2500

Fig. 13 Mean mixture fraction and progress variable profiles, and temperature scatter conditioned on mixturefraction at x/dj = 30.

The competition between the evaporation, turbulence, and chemical reactions determines the dynamics of theobserved phenomena in Fig. 13, and such competition can be quantified through the time scale analysis. By takingthe ratio of turbulence and reaction time scales, a Damköhler number (Da) can be defined. Da is used as an indicatorof the extent to which turbulence-flame interactions are expected to be important. Similarly, the ratio (Dav) of aturbulence time scale to an evaporation time scale can serve as an indicator of the degree of turbulence-evaporationinteractions [20, 21]. Dav is defined as Dav = ⌧turb/⌧evap, where ⌧ed = (D2L)1/3/u0 is the turbulence timescale,⌧evap = �m/vr is the evaporation timescale, �m = dd/(Shg � 2) is the di�usion film thickness, and vr = €md/4⇡r2

d isthe equivalence velocity of evaporation. Below the critical value of unity, the turbulence energy is able to increasethe mass transfer. For a higher value of Dav , an inverse behavior is even observed [21]. The Damköhler number Davdirectly analyzes the e�ect of the evaporation source terms €md , hence provides a direct measure of the e�ects of the SGSmodels. Because the same definition is used for the turbulence timescale in Da and Dav , the ratio of the two Damköhler

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numbers provides a measure of the relative rates of evaporation and chemical reactions. The relations between the threetimescales are plotted in Fig. 14. The values of Dav and Da are plotted for each grid points at x/d = 30. Dav obtainedfrom LES-2 and LES-3 in the slow chemistry limit (close to Da = 0 and inert flows) extend to a larger range than theones obtained from LES-1, indicating enhanced evaporation rates by using LES-2 and LES-3. However, Dav from allthree models are larger than unity, suggesting that evaporation is faster than the turbulence eddy turnover time in thetarget flame. This is the major reason why minor di�erences are observed in mean profiles, even though the SGS modelsdirectly lead to di�erent distributions of the timescales. Moreover, more points from LES-2 and LES-3 fall into the highDa and high Dav zones near the diagonal, showing that the reaction time scales and the evaporation timescales arereduced, compared to those produced by LES-1. In particular, the accumulation of the data points obtained from LES-3near Da ⇠ 0 further demonstrates the di�erence created by the use of a more realistic turbulence-flame interactionmodel.

Dav

0 5 10 15 20

Da

0

5

10

15

20

LES-1

LES-2

LES-3

Fig. 14 Comparison of turbulence, reaction, and evaporation times scales for droplets at x/dj = 30.

The discrepancy between LES-3 and the experiment is approximately 30% near the centerline. Based on the timescale analysis, combustion models that consider the finite-rate chemical reactions should be considered to improvethe predictability of the simulation [22, 23]. It should also be pointed out that experimental uncertainty is anothercontributing factor, especially near the centerline when thermal couples are used.

V. ConclusionIn the present study, a new model based on regularized deconvolution method (RDM) for the closure of sub-grid

turbulence-droplet and turbulence-chemistry interactions in a Eulerian-Lagrangian framework is proposed. To study thee�ect of these modeling approaches, three LES cases with di�erent model combinations are conducted for a turbulentspray jet flame that is studied experimentally at the University of Sydney. Based on our results, we conclude thefollowing:

• Sub-grid dispersion can be important in both droplet dynamics and reaction heat release, and RDM model ise�cient in representing this e�ect

• For FPV, RDM improves the sub-grid scale turbulence modeling which leads to better agreement to the experimentcompared to the presumed-PDF model

• Modeling of droplet dispersion by the mean flow in the radial direction needs to be improved to capture thedynamics of the dispersed phase correctly

• Inflow droplet velocity distribution is important in representing the liquid jet spreading upstreamAdditionally, it is observed that evaporation is faster than the turbulence eddy turnover time in the target flame; thereforethe reconstruction of the SGS fluctuation might not a�ect the evaporation rates significantly. However, the distributionsof the temperature, as well as the timescales, can be significantly impacted, and such changes can potentially beimportant for the prediction of pollutants emission.

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AcknowledgmentsResources supporting this work were provided by the NASA High-End Computing (HEC) Program through the

NASA Advanced Supercomputing (NAS) Division at Ames Research Center. Financial support through NASA award#NNX15AV04A is acknowledged.

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