Simulation of spray–turbulence–flame interactions in a lean direct injection combustor

Combustion and Flame 153 (2008) 228–257www.elsevier.com/locate/combustflame

Simulation of spray–turbulence–flame interactions in a leandirect injection combustor

Nayan Patel, Suresh Menon ∗

School of Aerospace Engineering, Georgia Institute of Technology, 270 Ferst Drive, Atlanta, GA 30332-0150, USA

Received 2 May 2007; received in revised form 25 August 2007; accepted 25 September 2007

Available online 11 December 2007

Abstract

Large-eddy simulation (LES) of a liquid-fueled lean-direct injection (LDI) combustor is carried out by resolv-ing the entire inlet flow path through the swirl vanes and the combustor. A localized dynamic subgrid closure iscombined with a subgrid mixing and combustion model so that no adjustable parameters are required. The in-flow spray is specified by a Kelvin–Helmholtz (or aerodynamic) breakup model and compared with LES withoutbreakup, where the incoming spray is approximated using measured data just downstream of the injector. Overall,both time-averaged gas and droplet velocity predictions compare well with the measured data. The major impactof breakup is on fuel evaporation in the vicinity of the injector. Further downstream, a broad spectrum of drop sizesare recovered by the breakup simulation and produces spray quality, as in the no-breakup case. It is shown that thevortex breakdown bubble (VBB) is smaller with more intense reverse flow when there is heat release. The swirlingshear layer plays a major role in spray dispersion and the VBB provides an efficient flame-holding mechanism tostabilize the flame. Unsteady features such as the efficient dispersion of the spray by the precessing vortex core(PVC) are well captured. Flame structure analysis using the Takeno flame index shows the presence of a diffusionflame in the central portion, whereas premixed burning mode is observed farther away. Instantaneous thermo-chemical states of fuel–air mixing and oxidation indicate significant departure from the gaseous diffusion limits,consistent with earlier observations. Additionally, particle–particle and particle–gas correlations are analyzed anddiscussed.© 2007 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: LES; Spray; Combustion; PVC; Atomization

1. Introduction

Improved combustion efficiency and low emis-sion to meet future environmental regulations are nowthe primary driving factors in the design of next-generation gas turbine combustors. Both land-based

* Corresponding author. Fax: +1 (404) 894 2760.E-mail address: [email protected]

(S. Menon).

0010-2180/$ – see front matter © 2007 The Combustion Institute.doi:10.1016/j.combustflame.2007.09.011

(which are primarily gas-fueled) and flight-qualified(which are liquid-fueled) combustors are being revis-ited in the industry with these constraints in mind. Forliquid-fueled systems, several approaches have beenproposed to achieve high efficiency and low emis-sions. One particular concept, called lean direct in-jection (LDI), has been of active interest due to itspotential for low emissions under operational (high-temperature, high-pressure) conditions [1–3]. In theLDI concept, the liquid fuel is injected from a ven-

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N. Patel, S. Menon / Combustion and Flame 153 (2008) 228–257 229

turi directly into the incoming swirling airstream, andthe swirling airflow is used both for atomizing theinjected liquid and for fuel–air mixing. Autoignitionand/or flashback are minimized since the fuel is nei-ther premixed nor prevaporized [4], and low CO andNOx emissions with no combustion instability havebeen reported in experimental studies [1,3].

These experimental observations have not fullyexplained the dynamics of the mixing and combus-tion processes that resulted in the measured low emis-sion and stable performance. Measurements are rathercrude and (in the past) have been limited to observa-tion of the exhaust emissions. Focused experimentaland numerical studies are currently underway, and theresults reported here are part of an effort to explainsome of the underlying unsteady physics of the LDIcombustor. Computational study using an advancedlarge-eddy simulation (LES) approach [5,6] is em-ployed here to further investigate and understand theunsteady dynamics, and also to compare with newlyavailable data.

In order to achieve a physical insight, the simu-lation needs to resolve not only the fluid dynamicprocesses created by the swirl vanes but also cap-ture the combustion process occurring in the smallscales. Fluid dynamics of the inlet shear flow can be(perhaps) addressed with reasonable accuracy by in-cluding the entire inlet swirl assembly (as done here)and with proper resolution of the swirling shear layer.However, scalar mixing and combustion offer newchallenges since these processes occur at the smallscales that are not typically resolved in a conventionalLES.

Spray combustion modeling introduces additionalchallenges, since phase change and interaction of theliquid phase with the gas phase needs to be properlyaccounted. The traditional approach is to track dis-crete droplets (that are much smaller than the localgrid resolution) using a Lagrangian formulation [7].The flow field inside and around the particles are notresolved but its effects are considered in the formof analytical and empirical correlations [7], and in-terphase exchange terms [8] account for interactionsbetween the two phases. Past studies have shown thatthis approach is reasonable as long as the droplets areof the order of the Kolmogorov scale η. However, theapplication of this approach in a LES requires newconsiderations since the typical grid resolution willbe much larger than η, and coupling between the twophases will require some sort of averaging or filteringwithin the control volume. This issue remains an ac-tive research area and is only indirectly addressed inthis paper.

Additional complexity occurs when one considersthe actual spray injection process. Typical sprays havean initial dense regime where the liquid jet breaks

up and significant particle–particle interactions oc-curs [9,10]. Further downstream the droplets dispersesufficiently to reduce the local volumetric occupancyand a dilute regime forms. From a combustion pointof view one would prefer to create a dilute regime sothat the vaporized fuel can mix efficiently with the airstream. However, it is nearly impossible to avoid thedense regime and the associated jet breakup process.In addition, very little information in the dense regimeis currently available from experiments, and compu-tational models are also limited since a full resolutionof the liquid jet breakup regime imposes severe reso-lution requirement [11,12].

Thus, there are many unresolved issues regard-ing the breakup process and how to incorporate thisprocess within computational models. Nevertheless,many studies in the past have implemented breakupmodels [11,13–15] in steady-state (RANS) simula-tions. Two models have been particularly popular. Thebreakup of the liquid jet due to growth of Kelvin–Helmholtz (KH) instability [16] at the liquid–gas in-terface has been used extensively, since this approachprovides a means of predicting the droplet size distri-bution. Another model, based on the Taylor-analogybreakup (TAB) [17] approach, uses a modeled equa-tion to predict the growth of distortion between theinterface. A major limitation of the TAB model is thatthe droplet size distribution needs to be prescribed apriori, and this may not be appropriate for many appli-cations. More recent models have relied on stochasticapproaches [18,19] to model the breakup process, buttheir application in simulations has not yet been re-ported.

In this paper, we report on the LES of spraycombustion in an axial-swirler type LDI combustor[20]. In an earlier study [6], a dilute spray modelwas implemented in which the inflow spray char-acteristics were approximated using available (time-averaged) measured data. Gas phase velocity mea-surements were predicted reasonably with this ap-proach. Here, this approach is revisited using the KHbreakup model so that the actual spray distributionis predicted downstream of the injector. Also, newdata on the droplet size and velocity field that werenot available earlier have been used to evaluate thesensitivity of predictions on the liquid phase modelemployed for the simulation. The present focus is onevaluation of an existing breakup model in a LES ofa complex combustor flow field. For all these studies,the full LDI combustor (including the swirl vanes) issimulated, and this approach eliminates a major ambi-guity regarding the inflow conditions for the air flow.

This paper is organized as follows. In the nextsection, a description of the LES formulation for two-phase flow and the sub-grid closure models with andwithout breakup are presented. In Section 3, we sum-

230 N. Patel, S. Menon / Combustion and Flame 153 (2008) 228–257

marize the experimental setup and computational ap-proach employed. This is followed by results and dis-cussion in Section 4 and conclusions in Section 5.

2. Mathematical formulation

The conservation equations for compressible re-acting flow are solved using the LES methodology ina generalized coordinate system. To simulate multi-phase (spray) combustion, Lagrangian spray modelis concurrently solved with the Eulerian gas phase.This section will briefly describe two-phase formula-tion and the two-way coupling employed here.

2.1. Gas-phase LES equations

Applying a low-pass box filter (appropriate for thefinite-volume approach employed here), to the instan-taneous Navier–Stokes equations, the following fil-tered LES equations are obtained,

∂ρ

∂t= ˜ρs − ∂ρuj

∂xj,

∂ρui

∂t= ˜Fs,i − ∂

∂xj

[ρui uj + pδij − τij + τ

sgsij

],

(1)

∂ρE

∂t= ˜Qs − ∂

∂xi

[(ρE + p)ui + qi

− uj τj i + Hsgsi

+ σsgsi

],

where ρ is filtered mass density, ui is the resolvedvelocity vector, p is the filtered pressure determinedfrom filtered equation of state, E is resolved total en-ergy per unit mass, τij is filtered viscous stress, andqi is the heat flux vector. The subgrid terms resultingfrom the filtering operation, denoted with superscriptsgs, represent the small-scale effects on the resolvedscales in the form of additional stresses and fluxes.Subscripts s denote source terms from the dispersedphase. Filtered equations for the kth species massfraction Yk are not shown here, since they are solvedusing a subgrid approach, as described later.

The filtered viscous stress tensor and the heat fluxvector are approximated as

¯τij = μ

(∂ui

∂xj+ ∂uj

∂xi

)− 2

3μ

(∂uk

∂xk

)δij ,

qi = −κ∂T

∂xi+ ρ

Ns∑k=1

hkYkVi,k +Ns∑k=1

qsgsi,k

,

where the diffusion velocities are approximated us-ing Fick’s law as Vi,k = (−�Dk/Yk)(∂Yk/∂xi). Here,molecular viscosity (μ) is approximated by the Suther-land’s law based on resolved temperature (T ), andthe thermal conductivity (κ) is approximated as κ =

μCp/Pr, where Cp is the specific heat at constantpressure for a gaseous mixture and Pr is the Prandtlnumber. Also, �Dk is the kth species diffusion coeffi-cient and the index k for species varies from 1 to Ns ,where Ns is the total number of species present in thesystem.

The SGS terms that require closure are the sub-grid stress tensor, the subgrid enthalpy flux, and thesubgrid viscous work, respectively,

τsgsij

= ρ(uiuj − ui uj

),

Hsgsi

= ρ(Eui − Eui

) + (pui − pui

),

(2)σsgsi

= uj τij − uj τ ij .

The closure of these terms and the source terms forthe dispersed phase in Eq. (1) are described below.

2.1.1. Momentum transport closureThe subgrid stress tensor τ

sgsij

is modeled using aneddy viscosity concept as

(3)τsgsij

= −2ρνt

(Sij − 1

3Skkδij

)+ 2

3ρksgsδij ,

where the resolved strain rate is given as Sij =(1/2)

[ ∂ui∂xj

+ ∂uj

∂xi

]. The subgrid eddy viscosity is

modeled as νt = Cν(√

ksgs), where =(xyz)1/3 is based on local grid size (x,y,

z). The subgrid kinetic energy (ksgs is defined as

ksgs = 12 [u2

k− u2

k]) and is determined by solving a

transport model [21–23],

∂ρksgs

∂t+ ∂

∂xi

(ρuik

sgs)(4)= P sgs − Dsgs + ∂

∂xi

(ρ

νt

σk

∂ksgs

∂xi

)+ Fd ,

where σk is a model constant assumed to be unity.Here, P sgs = −τ

sgsij

(∂ui/∂xj ) and Dsgs = Cε ×ρ(ksgs)3/2/ are, respectively, the production andthe dissipation of ksgs. In the above equation, Fd =˜ui Fs,i − ui

˜Fs,i is the source term due to the parti-cle phase (this term can be closed exactly, as shownearlier [7,24]).

The two coefficients in this model, Cν and Cε ,are obtained dynamically as a part of the solution us-ing a localized dynamic technique (LDKM) [22,23,25]. The dynamic evaluation of the coefficients us-ing the LDKM is stable locally (both in space andtime) without requiring any smoothing. The LDKMapproach also satisfies all of the realizability [26]conditions at majority of grid points even in com-plex reacting flows. Seven realizability conditionsneed to be satisfied [27] for a subgrid scale stresstensor to guarantee a realizable solution. Those con-ditions are (1–3) τii � 0, where i = 1,2,3; (4–6)


|τij | � √τiiτjj , where i �= j ; and (7) det(τij ) � 0.

For the current simulations, all seven conditions weresatisfied simultaneously at over 96% of the grid pointsfor the nonreacting case and over 90% for the reactingcase. Both cases indicated over 95% realizability fornormal stress components (conditions 1–3). The lastcondition imposed the most stringent requirement forrealizability, but is nevertheless satisfied at over 90%of the grid points.

Past studies by other independent researchers[28,29] and recent evaluation in several commer-cial codes (CFD-ACE v2004, Fluent v6.2.16, andCFX v5.7.1) [30] has demonstrated the ability of theLDKM closure. Additional key details are given else-where [5,25,31,32] and are avoided here for brevity.

2.1.2. Energy transport closureThe subgrid total enthalpy flux, H

sgsi

, is also mod-eled using the eddy viscosity and a gradient assump-tion as

(5)Hsgsi

= −ρνt

Prt

∂H

∂xi.

Here, H is the filtered total enthalpy and Prt is aturbulent Prandtl number that can also be computedusing a dynamic procedure but is currently assumedto be unity. The total enthalpy term H is evaluatedas the sum of specific enthalpy of the mixture, spe-cific kinetic energy, and specific subgrid scale energy,

H = h+ ui ui2 + ksgs, where h = ∑Ns

k=1 hkYk . The re-

maining unclosed term (σ sgsi

) is often neglected [33],as is the case here.

2.1.3. Subgrid scalar closureIn the current approach [34,35] to reaction–dif-

fusion modeling in LES, the gas-phase species trans-port equations are not spatially filtered. Rather, mole-cular diffusion, small- and large-scale turbulent con-vection, and chemical reaction are all modeled sepa-rately, but concurrently, at their respective time scalesusing a two-scale approach. The subgrid scalar mix-ing modeling is based on the linear-eddy mixing(LEM) model [34,35], which is integrated with a LESapproach. This combined technique is called LEM-LES hereafter.

To describe this model mathematically, we splitthe velocity field as ui = ui + (u′

i)R + (u′

i)S . Here, ui

is the LES-resolved velocity field, (u′i)R is the LES-

resolved subgrid fluctuation (obtained from ksgs) and(u′

i)S is the unresolved subgrid fluctuation. Then con-

sider the exact species equation (i.e., without any ex-plicit LES filtering) for the kth scalar Yk , written in aslightly different form as

ρ∂Yk = −ρ

[ui + (

u′i

)R + (u′i

)S]∂Yk

∂t ∂xi

(6)− ∂

∂xi(ρYkVi,k) + wk + Ss,k.

In LEMLES, the above equation is rewritten as

(7)Y ∗k

− Ynk

tLES= −[

ui + (u′i

)R]∂Ynk

∂xi,

(8)

Yn+1k

− Y ∗k =

t+tLES∫t

− 1

ρ

[ρ(u′i

)S ∂Ynk

∂xi

+ ∂

∂xi(ρYkVi,k)

n − wnk − Sn

s,k

]dt ′.

Here, tLES is the LES time-step. Equation (7) de-scribes the large-scale 3D LES-resolved convectionof the scalar field, and is implemented by a La-grangian transfer of mass across the finite-volume cellsurfaces [36,37]. Equation (8) describes the subgridLEM model, as viewed at the LES space and timescales. The integrand includes four processes that oc-cur within each LES grid, and represent, respectively,(i) subgrid stirring, (ii) subgrid molecular diffusion,(iii) reaction kinetics, and (iv) phase change of theliquid fuel. These processes are modeled on a 1Ddomain embedded inside each LES grid where the in-tegrand is rewritten in terms of the subgrid time andspace scales.

We first describe the subgrid processes in Eq. (8)and then the 3D advection process in Eq. (7).

2.1.4. Subgrid reaction–diffusion processesWithin each LES cell, the following 1D reaction–

diffusion model is solved:

(9)ρ∂Ym

k

∂ts= Fm

k − ∂

∂s

(ρYm

k V ms,k

) + wk + Sms,k,

(10)

ρCmp,mix

∂T m

∂ts= Fm

T −Ns∑k=1

[ρCp,kY

mk V m

s,k

∂T m

∂s

]

+ ∂

∂s

(κ

∂T m

∂s

)−

Ns∑k=1

[hkωk].

Here, ts indicates a local LEM time scale and thesuperscript m indicates that the subgrid field withineach LES cell is discretized by NLEM subgrid cellsalong the local subgrid coordinate s, such that theLES-resolved quantity Yk is obtained by a Favre av-erage of the subgrid field. Thus, Yk = 1∑NLEM

m=1 ρm×∑NLEM

m=1 (ρYk)m. Fm

kand Fm

Trepresent subgrid stir-

ring of species and temperature, respectively, withineach of the subgrid domains. Mixture specific heat is

evaluated as Cmp,mix = ∑Ns

k=1 Cp,kYmk

. The reactionrate (ωk ) for the kth species is determined directlyfrom the chemical kinetics.


The LEM domain s is aligned in the direction ofthe maximum scalar gradient [34] and its length isequal to the local LES filter width, . The numberof LEM cells, NLEM, is chosen so that all the relevantscales are resolved. Typically, the smallest eddy (e.g.,the Kolmogorov scale, η) is resolved using six LEM

cells, and η is estimated from the relation η ≈ Re3/4

.

Here, Re

= u′/ν is the local subgrid Reynoldsnumber and u′ = √

2ksgs/3 is the subgrid turbulenceintensity.

In practical applications, the optimal NLEM varieslocally in space since the subgrid turbulence variesover a range. Computational implementation of thislocal variation requires significant programming fordynamic load balancing in a parallel simulation model(employed here). Therefore, in the present study,NLEM is chosen based on the resolution requirementin the primary region of interest (typically, regions ofhigh shear flow where scalar mixing and combustionare occurring). Then, this LEM resolution is used inall LES cells.

Equation (9) is solved using a standard finite-difference scheme along the 1D domain s. The timestep for this integration, tLEM is determined as theminimum of the local diffusion tdiff or the chemicaltchem time scale.

Inflow and outflow conditions to Eq. (9) are pre-scribed by the mass transport in the Lagrangian step,Eq. (7). The inflow is prescribed at one end of theLEM domain and the outflow at the other end. Boththese conditions are implemented by the splicingprocess described below and enforce strict mass con-servation at every LES time-step.

Detailed multicomponent kinetics can be includedwithin this model using either direct integration orin situ adaptive tabulation (ISAT) [38]. Since all theturbulent scales below the grid are resolved in thisapproach, both molecular diffusion and chemical ki-netics are closed in an exact manner at the subgriddomain. As a result, unclosed terms typically seenin conventional LES approaches, such as ρ[uiYk −ui Yk], ρ[ ˜Vi,kYk − Vi,kYk], and ¯wk , do not arise, andneed no closure.

The phase change of the liquid fuel into its gaseousform results in the source term in Eq. (9). This sourceterm is determined from the Lagrangian solver, as de-scribed later.

2.1.5. Subgrid stirringIn the LEM domain, the effect of eddies smaller

than the grid scale is physically accounted forby subgrid stirring. This effect is symbolically rep-resented as Fm

kin Eq. (9), and represents the term

− ∫(u′ )S ∂Yn

k dt ′ in Eq. (8). Similarly, the term Fm
i ∂xi T
in Eq. (10) represents − ∫(u′

i)S ∂T n

∂xidt ′. In the one-

dimensional LEM domain, this 3D term is approx-imated assuming locally isotropic conditions and isimplemented using stochastic re-arrangement eventscalled triplet maps. Each triplet map [34] representsan instantaneous action of a 3D (but isotropic) tur-bulent eddy on the subgrid scalar field. The mappingprocess is designed such that it compresses and in-creases the scalar gradient so that the local scalar fieldreflects the aforementioned orientation of the 1D do-main in the direction of the scalar gradient.

Since all scalar processes are resolved in the 1DLEM domain, it is implicitly assumed that the turbu-lent scales involved in the stirring of the scalar fieldswithin this domain are isotropic. This assumption isquite reasonable since it is consistent with LES ap-proach.

To implement this subgrid stirring, three parame-ters have to be prescribed: the local eddy size, thefrequency of stirring, and the location of the stirringevent within the LEM 1D line. The eddy size l ispicked randomly from an eddy size distribution f (l)

in the range to η (Kolmogorov scale), and stirringevents occur at a specified frequency, λ and the lo-cation of this stirring event is chosen from a uniformdistribution. Both f (l) and λ are obtained using 3Dinertial-range scaling laws (for isotropic scales) de-rived from Kolmogorov’s hypothesis as

(11)λ = 54

5

ν Re

Cλ3

[(/η)5/3 − 1][1 − (η/)4/3] .

Cλ is a constant determined to be 0.067 [39]. Theeddy size (l) is chosen from the PDF

(12)f (l) = (5/3)l−8/3

η−5/3 − −5/3,

where η = NηRe−3/4

. The empirical constant Nη

reduces the effective range of scale between the inte-gral length scale and η but does not change the tur-bulent diffusivity. Past studies have investigated thesensitivity of predictions to Nη , and we use Nη = 11based on past studies [40].

It has been demonstrated that the turbulent scalinglaws predict correctly the growth of the flame sur-face area under the influence of turbulent strain. Notethat this model does not require any change when theflame type (premixed, nonpremixed or spray) or thecombustion regime (flamelet, TRZ or BRZ regimes)changes. This ability has been demonstrated in thepast [41–43], and it is this ability that we believe iscrucial to deal with combustion and flame dynamicsas the system approaches LBO. All parameters in thismodel are fixed based on scaling rules and are not ad-justed for simulation [5].


2.1.6. Subgrid scalar transportThe transport of the subgrid scalar field, Eq. (7) is

carried out across the LES cell faces in a Lagrangianmanner reminiscent of the turbulent transport used inthe PDF method [44]. However, unlike in PDF meth-ods where the transport is random, in LEMLES thistransport is deterministic and is achieved by a proce-dure that “cuts and pastes” the subgrid scalar fieldsfrom adjacent LES cells based on mass conservation.The mass-flux on each of the six control surfaces (fora hexahedral control volume) is determined based onthe LES resolved mass flux and then sorted in an as-cending order following the sign convention of posi-tive influx and negative efflux. The number of LEMcells is then determined based on the amount of massflux that needs to be transported across each LES cellface (at many locations, fractional LEM cells have tobe transported to maintain mass conservation). Masstransported out of the LEM domain is taken out fromone end of the 1D domain and the incoming mass isadded to the other end of the 1D domain in a deter-ministic manner. Thus, in LEMLES the subgrid scalarstructure is transported and recovered across LEScells. Further details are given elsewhere [35–37].

2.1.7. Volumetric expansionCombustion at the subgrid level increases the tem-

perature and decreases the local density (since pres-sure is assumed to be constant in the subgrid betweenLES time step). This effect results in a volumetric ex-pansion and is included explicitly by expanding theLEM domain by an amount equal to

(13)V ∗LEM,i = ρn

i

ρ∗i

,

where VLEM,i is the change in volume of LEMcell i. ρn

iand ρ∗

iare, respectively, the density of the

ith cell at the previous and the current time integrationlevels in the LEM simulation (not at the fluid-dynamictime-step (tLES) at LES level).

Chemical reaction at the LEM level determinesheat release and thermal expansion at the LEM level,which at the LES level generates flow motion that, inturns, transports the species field at the LEM level.Full coupling is maintained in the LEMLES to ensurelocal mass conservation.

2.2. Liquid-phase equations

The discrete droplet model (DDM), which repre-sents the spray in the form of discrete particles usinga Lagrangian formulation [7], is employed here. Thisapproach eliminates errors due to numerical diffusion[9] and better represents the physical aspects of spray.Additionally, complex processes such as drop/dropcollisions, drop/wall interaction, and drop breakup

can be considered within the DDM. Also, to maintaincomputational expediency, following Dukowicz [45],characteristic groups of droplets, all having identicalsize, location, velocity, and temperature, are repre-sented as computational parcels, and are then tracked.However, the number of particles per group dependson the diameter/volume of the particle to avoid unre-alistic averaging [19] of drop properties.

The classical picture of atomization involve pri-mary breakup of a liquid core into ligaments or largedrops, followed by secondary breakup into smallerdrops with negligible effects of collisions [10]. In thedense regime [9], effect of discrete interdrop spac-ing on transport rates, drop/drop collisions, turbu-lence modulation due to volume occupied by liquidphase, etc., become significant. The dilute regime in-volves no particle/particle interactions and the effectof liquid phase volume on transport becomes negligi-ble [7,10]. Therefore, the single-drop transport ratescan be employed directly. In general, in the near fieldof the injector, both regimes can coexist, but furtherdownstream, the dense regime is very rare.

The filtered values of turbulent velocity and othergas phase variables are obtained from the LES equa-tions for these variables. Additionally, the effect ofsmall-scale (or subgrid) turbulence upon drop disper-sion is incorporated using ksgs. Thus, the presence ofparticles in the gas phase is incorporated both via di-rect source terms in the filtered LES variables (mass,momentum, energy, scalar concentration) and indi-rectly by modification of the subgrid kinetic energy(ksgs). This ensures two-way coupling among thephases within the LES context. An additional effectis included in the force term in the droplet momentumequations by including an effect of subgrid turbulencein the gas-phase velocity. This approach is an exten-sion of the stochastic separated flow (SSF) approach[7] to LES and is briefly summarized below. More de-tails of these equations and the coupling issues aregiven elsewhere [5].

2.2.1. Secondary breakup modelThe primary breakup is not addressed in this study

and only the secondary breakup of the initially in-jected liquid drops is considered. As discussed in theintroduction, both the Taylor analogy breakup (TAB)and the Kelvin–Helmholtz (KH) models have beenparticularly popular and applied widely for practicalareas such as automotive engines. Their usage in thefield of gas turbine combustors within a LES frame-work is new and an emerging research arena. A briefdescription of these breakup models is given next;however, interested readers are referred back to theoriginal papers for additional details.

The TAB model [17] implements the breakupbased on an analogy, suggested by Taylor, between


an oscillating and distorting droplet and a spring–mass system (forced damped harmonic oscillator).The spring force (restoring) is related to the surfacetension forces; the external force (driver) is relatedto the carrier (gas) aerodynamic force; and dampingforces are related to the liquid viscosity. The maincontribution of the model is its ability to predict thestate of oscillation and distortion (shape), which mayaffect the exchange rate between the gas and thedroplets. The TAB model keeps track of one oscilla-tion mode (fundamental mode), which is the longest-lived, but for large Weber numbers other modes arepossible and contribute to the breakup. The Tayloranalogy equations do not give drop size informationand thereby, in this model, the product drop sizesare estimated based on an energy conservation (be-fore and after breakup) argument. A major observa-tion with this model is that the product drop sizesare underpredicted and the changeover from parent toproduct drop is rather abrupt.

The KH (or wave) model [16] is entirely basedon stability analysis of Kelvin–Helmholtz waves andconsiders the stability of a cylindrical liquid surfaceto perturbations using a first-order linear theory. Thewaves arises due to aerodynamic or shear effects be-tween the liquid and the carrier gas across the liquidinterface. The analysis leads to a dispersion equationwhich relates the growth rate (ω) of an initial per-turbation to its wavelength (λ) or wavenumber (k =2π/λ). Numerical solutions for the dispersion relationindicate a single maximum [46] in the wave growthrate curve (ω(k)). Subsequent curve-fits for the max-imum growth rate (ω = Ω) and the correspondingwavelength (λ = Λ) gives their (Ω,Λ) variation interms of the Ohnesorge parameter and carrier We-ber number. The size of the product drop is basedon wavelength of unstable waves on the surface ofblobs rather than experimental correlations. A majorcontribution of this approach is its ability to predicta core (intact) region (consisting of large drops nearthe nozzle exit traveling at nozzle discharge velocityuntil they break up), as seen in several experimentalstudies [47,48].

Although two models, the TAB [17] and the KHaerodynamic breakup [16] models, have been imple-mented and validated (see Appendix A), only the KHmodel is used for the LDI simulations. The primaryreason is that the TAB model does not give drop sizeinformation, whereas the KH model provides this in-formation, and is also capable of predicting the intactcore length and the various breakup regimes.

Blob-injection method [16] is employed in thebreakup simulations, in which the liquid jet is approx-imated as a large droplet or “blob” with a character-istic size equal to the injector nozzle diameter. Thenumber of blobs injected in unit time is a function of

liquid mass flow rate. During the injection, new blobsor particles introduced into the domain are pure drops(one particle per parcel). These drops evolve down-stream and undergo breakup producing new particles,which are then tracked as parcels. The blob injectionvelocity is dependent on the net injection pressure andthe nozzle discharge coefficient [16].

In the current LES implementation for the KHmodel, once a parent blob (with radius, a0 and oneparticle per group, N0) is injected into the compu-tational domain, a rate expression is used to reduceits size. The rate expression [49] describes the rateof change of drop radius in a parent parcel as da

dt=

−(a(t) − a0)/τ , where a(t = t0) = a0 is the initialdrop size and τ (= 3.726B1a/ΛΩ) is the breakuptime with constant B1 = 10 [16]. While awaitingfor sufficient product drops to accumulate, the par-ent number of particles per group (N ) is adjusted sothat Na3 = N0a3

0 . This accounts for the mass con-servation. After this, the Lagrangian droplet evolutionoccurs and if certain criteria [16,17] are exceeded, abreakup event is executed creating new product parcel(of radius r), which takes both the temperature andphysical location as the parent. Typically, the strip-ping criterion for creating product droplets in the KHmodel is based on accumulation of 3% of initial par-ent drop mass, whereas the breakup criterion for theTAB model is based on distortion amplitude equalinghalf drop radius. For the combustor simulation, thebreakup time constant and the mass stripping crite-rion of 2.0 and 0.5% were chosen, respectively. Prod-uct droplets inherit the parent droplet velocity plus anormal velocity in the cross-plane accounting for rimexpansion. The parent number of particles per groupis then restored to N0 following the creation of thenew product parcel. Then both the parent and productparcels are tracked by the Lagrangian solver and areequally likely to undergo further breakup dependingon the local stability criterion.

2.2.2. Lagrangian equation-of-motionUnder the assumption that the particle density is

much greater than that of the carrier fluid (ρp/ρg ≈103), particle/particle interactions are negligible, andthe Kolmogorov scale is of the same order of or largerthan the largest droplet, the Lagrangian equations ofmotion for a droplet can be expressed as [7,8,50]

dxi,p

dt= ui,p,

(14)dui,p

dt= f

τV

[(ui + u′′

i

) − ui,p

] + gi,

where ui,p is the ith component of the parcel ve-locity, xi,p is the ith component of parcel position,f is the drag factor (ratio of the drag coefficient tothe Stokes drag), τV is the particle velocity response


time, and gi is the ith gravity component. Subscript p

represents liquid phase quantities and quantities with-out subscripts correspond to the gas phase (except asnoted). Here, the sum ui + u′′

irepresents instanta-

neous (ui ) gas-phase velocity components, consistingof both the LES resolved velocity ui and a stochasticterm u′′

i(obtained using ksgs at intervals coincident

with the local characteristic eddy lifetime). The inter-action of a droplet with an eddy is assumed to occurfor a time that is smaller that either the eddy lifetimeor the transit time required to traverse the eddy. Thedrag factor and particle velocity response time are

(15)f = CD Red

24,

(16)τV = ρpd2p

18μg,

where ρp is the liquid density, dp is the parcel di-ameter (= 2rp , where rp is the parcel radius), μg isthe gas-phase dynamic viscosity, νg is the gas-phasekinematic viscosity (μg/ρg ), CD is the drag coeffi-cient, and Red is the relative particle Reynolds num-ber expressed as Red = (dp/νg)|ui − ui,p|.

The drag coefficient accounts for the dynamicinfluence of pressure and viscous forces acting ondroplet surfaces. Following Crowe et al. [50], thedrag coefficient (assuming drops retain the sphericalshape) is given by

(17)CD ={

24Red

(1 + 1

6 Re2/3d

), Red � 1000,

0.4392, Red > 1000.

The effect of droplet distortion on the drag coeffi-cient can be accounted by a breakup model [51,52].This relies on tracking droplet distortion and its ori-entation in relation to the carrier phase. Alternatively,existing empirical drag correlations incorporate thiseffect implicitly by treating the drop as an equivalentsphere [9]. Current correlations ignore [53] blowingeffects at the drop surface due to evaporation.

The droplet mass transfer is governed by thedroplet continuity equation

(18)dmp

dt= −mp,

where mp is the mass of the particle given by43ρpπr3

p , and mp (> 0) is the net mass transfer rate(or vaporization rate) for a droplet in a convectiveflow field, expressed [8] as

(19)mp

mp,Red=0

= 1 + 0.278√

Red Sc(1/3)[1 + 1.232

Red Sc(4/3)

](1/2),

where Red=0 is the Reynolds number for particle atrest. Under quiescent conditions, the mass transfer

rate reduces to

(20)mp,Red=0 = 2πρsDsmdp ln(1 + BM),

where ρs and Dsm are respectively the gas mixturedensity and the mixture diffusion coefficient at thedroplet surface. Also, BM is the Spalding mass trans-fer number [9] given by

BM ≡ b∞ − bs = (YF,s − YF,∞)

(1 − YF,s),

where b ≡ YF

YF,s − 1.

In the above relations, Sc (≡ νg,s/Dsm, ratio of mo-mentum to mass transport) is the Schmidt number.Subscript s represents quantities at the droplet sur-face and ∞ indicates the far field. Also, YF is the fuelspecies (that is evaporating) mass fraction. Surfacefuel mass fraction is obtained from Raoult’s Law [54],which assumes that the mole fraction at the dropletsurface is equal to the ratio of the partial pressureof fuel vapor (pvap) to the total pressure of the gasphase (p). Various correlations exist [55] to evaluatethe partial pressure of fuel vapor. Note that the gas-phase variables (e.g., T and YF ) correspond to thefar-field conditions [53] for the droplets and must beinterpolated from the Eulerian numerical grid to thedroplet location during the simulations.

Droplet heat transfer is governed by the droplet en-ergy equation, which consists of the external and theinternal energy, as well as the energy associated withsurface tension. The equation governing the internaltemperature distribution based on this uniform tem-perature model [8,9] is

mpCldTp

dt= Qconv − mpLv

(21)= hpπd2p(T − Tp) − mpLv,

where Qconv is the convective thermal energy transferrate, mp is the particle mass, Cl is liquid heat capac-ity, hp is the heat transfer coefficient, and Lv is thelatent heat of vaporization. Additional details of thismodel, including the heat transfer coefficient and thelatent heat of vaporization, are given elsewhere [8,9,53].

Equations (14), (18), (21) are integrated using afourth-order Runge–Kutta scheme [8]. The integra-tion is carried out based on the smallest of the timescales [8,56] (i.e., the smallest of the particle veloc-ity relaxation time, the droplet lifetime, the turbulenteddy interaction time, the droplet surface temperatureconstraint time, and the LES gas-phase time) govern-ing the particle evolution. Initial conditions for theLagrangian system involve the specification of initialparcel positions, velocities, masses, and temperaturesand the number of droplets represented by each par-cel.


2.3. Eulerian–Lagrangian coupling

Eulerian–Lagrangian coupling is through the in-terphase exchange terms [8] (not presented here, forbrevity). If np number of particles are present per par-cel/group, then the volume-averaged source terms forall the droplet parcel/group trajectories that cross acomputational cell (of volume V ) are computed bysumming the contribution from every parcel/group as⎛⎜⎜⎜⎜⎝

˜ρs˜Fs,i˜Qs˜Ss,k

⎞⎟⎟⎟⎟⎠ = 1

V

×

⎛⎜⎜⎜⎜⎜⎝

∑m np[mp]∑

m np

[mpui,p − 4π

3 ρpr3p

dui,p

dt

]∑m np

[mphv,s − hpπd2

p(T − Tp)

− ui,pmpdui,p

dt+ mp( 1

2u2i,p

)]∑

m np[mp]

⎞⎟⎟⎟⎟⎟⎠ ,

where the summation index m is over all the dropletparcels/groups crossing a computational cell (of vol-ume V ). Also, note that the species source term

(˜Ss,k) for all species (k) is zero, except for the speciesthat is present in liquid form and evaporating.

2.4. Combustion modeling

In this study, we consider liquid fuel (C12H23) toapproximate the experimental Jet-A fuel and employa three-step, seven-species global reduced mechanism

[57,58] of the form

C12H23 + (35/2)O2 → 12CO + (23/2)H2O,

2CO + O2 → 2CO2 and N2 + O2 → 2NO.

For the first step, the rate expression (Ae(−Ea/RuT ) ×[C12H23]m[O2]n) [57] has pre-exponential factor (A)and activation energy (Ea , kcal/g mol) of 4.7 × 1011

and 30, respectively. Empirical coefficients (m,n) arechosen to be 0.25 and 1.5, respectively. The CO oxi-dation step involves both forward (1014.6e(−40/RuT )

× [CO][H2O]0.5[O2]0.25) and reverse (5 × 108 ×e(−40/RuT )[CO2]) rates. The NO global mechanismaccounts for both thermal and nonthermal path-ways [58].

3. Experimental and numerical set-up

The LDI combustor [20] consists of a 60◦, sixhelical swirl-vaned inlet that leads to a venturi, fol-lowed by a short divergent diffuser section that endsat the dump plane of a square combustion chamber.The converging–diverging venturi is designed [20]to reduce the possibility of the return of the spraydroplet from downstream and to prevent the flash-back of the flame and autoignition inside the swirler.The swirler has an outer diameter of 22.5 mm withan inner diameter of 8.8 mm. The calculated swirlnumber is 1.0 [20]. Both converging and divergingangles are set at 45◦. Figs. 1a and 1b show respec-tively the computational dimensions and the grid inthe swirl vane region. Air at stagnation temperature

(a) Schematic diagram (b) Grid through swirler vanes

Fig. 1. LDI combustor schematic in the center plane (a) and computational grid through the swirler vanes (b). The dump planemarks the position x = 0 for streamwise locations. Probe locations (P1–P4, D1–D5) used for collecting unsteady signal andstatistics are also shown.


(a) Energy spectra (b) W spectra

Fig. 2. Turbulent kinetic energy (TKE) and the azimuthal velocity (W ) spectra for nonreacting and reacting cases at specifiedprobe locations. Probe signals are shifted upward nominally by 5 m/s in (b) for clarity.

To = 294 K and 1 atmosphere enters with a bulk ve-locity of Uo = 20.14 m/s [20]. The combustor squarecross-sectional area is 4Ro × 4Ro (Ro = 12.6 mm).For the nominal conditions noted above, the Reynoldsnumber (based on inlet diameter Do = 2Ro and Uo),ReDo

, is 30,759. The fuel is injected at 0.415 g/s,which in combination with an air mass flow rate of8.16 g/s gives equivalence ratio of 0.75 for the react-ing case.

Experimental data [20] have been acquired for ve-locity (mean and fluctuation) at six streamwise loca-tions for nonreacting (gas velocity) and reacting (gasand drop velocity) cases. No temperature or speciesdata have been reported so far.

Characteristic inflow and outflow conditions [59]are used along with no-slip, adiabatic, and noncat-alytic walls. The inflow conditions for the spray isparticularly critical for accurate predictions. Withoutbreakup, a lognormal profile with a Sauter mean ra-dius (R32) of 18 µm and a droplet cutoff radius of1 µm is used with a spray inner cone angle of 90◦based on experimental data [20]. With breakup in-cluded, no initial distribution is specified. Rather, amonomodal radius distribution of 100 µm “blob” isinjected every 7.68 µs (to satisfy the fuel mass flowrate). Particles are injected along the centerline justbehind the centerbody approximately 1 mm down-stream of the injector tip. Typically, around 30,000and 10,000 droplet parcels are present in the combus-tor in an average sense in the no-breakup and breakupcases, respectively. Larger number of parcels are ob-served in the no-breakup simulation due to relativelysmaller drop sizes and fewer particles per group.

The numerical scheme is an explicit finite-volumescheme that is second-order accurate in space andtime [5]. A butterfly two-domain grid of 253×84×97for the cylindrical and 253 × 25 × 25 for the in-ner Cartesian grid is used in the streamwise, radial,

and azimuthal directions, respectively. Clustering isemployed near the walls and regions of high shear.Within the swirler assembly the minimum spacingis y+ ≈ 6 along the walls and approximately 8–12cells are in the shear layer near the dump plane. Gridstretching is limited everywhere to be below 2% inthe near field of the injector.

The maximum subgrid Reynolds number, Re

(based on ksgs and LES filter width, ), is about 56in regions of high turbulence, which suggests that theKolmogorov scale (η) is around 18 µm. Twelve LEMcells are used in each LES volume, which implies thatthe minimum subgrid resolution is (2–3)η in the high-shear region. In other regions, Re is lower and theLEM resolution becomes closer to η. Even thoughgrid independence study has not been performed forthis particular rig, past experience with LEMLES forgas turbine combustors [5,41,60,61] suggests that thisresolution is reasonable.

For a single characteristic time τ , around 170 and1800 single-processor hours are needed on a Linux(2.66 GHz Xeon) cluster for nonreacting and react-ing cases, respectively. Here, τ is defined as the timefor one revolution of the precessing vortex core (seediscussion later). After the initial transient, approxi-mately 25τ and 21τ of data are statistically averagedfor nonreacting and reacting cases, respectively. Al-though LEMLES is expensive, due to the high par-allel scalability of the solver the turnaround time isreduced by using a larger number of processors.

Fig. 2 shows the typical spectra of the resolved tur-bulent kinetic energy for both reacting and nonreact-ing simulations in the region of high shear. For bothcases, a reasonable inertial range spectrum (−5/3law) is recovered, suggesting that the current resolu-tion is acceptable to resolve momentum transport inthe shear layer regions.


(a) Centerline variation (b) Close-up

Fig. 3. Centerline mean streamwise velocity comparisons with measurements are shown for both nonreacting and reactingsimulations. Axial distance is nondimensionalized by the diffuser diameter. Close-up near the injector and the dump planeregion is shown in (b).

4. Results and discussion

We first consider steady state results and compari-son with available data. Then we focus on unsteadyfeatures to explain the nature of spray–turbulence–flame interactions observed in this combustor.

4.1. Stationary state analysis

Comparisons with measurements [20] for gas anddroplet velocity field are reported for both breakupand no-breakup cases. Earlier comparison of gasphase velocity predictions without breakup [6] areincluded here only to compare with the new resultswith breakup. However, all comparisons of predic-tions (with and without breakup) of droplet velocity,size distribution and SMD with data are new results.The analysis, therefore, will focus substantially on thedroplet statistics and the impact of the breakup model(if any).

4.1.1. Gas phase velocity fieldCenterline mean streamwise velocity along the

length of the combustor is shown in Fig. 3. A promi-nent central recirculation zone (CRZ) along the axisis observed for nonreacting [6] (not shown) and react-ing cases. This CRZ is created by the swirling inflow[62,63] due to a radial pressure gradient caused bythe centrifugal effect, which in turn gives rise to anaxial (and adverse) pressure gradient. For high swirlnumbers (amount of rotation imparted to axial flow>0.6), a strong coupling between axial and tangen-tial velocity occurs, and the adverse pressure gradientis strong enough to overcome the axial motion of the

fluid. This establishes a recirculation zone, a form ofvortex breakdown [62] in the central region, and thisregion is the primary aerodynamic flame holding andstabilizing mechanism in gas turbine combustors.

The streamwise extent of the CRZ for the non-reacting case is approximately twice that for the re-acting case. However, the CRZ has a significantlystronger reverse flow region in the reacting simula-tions due to heat-release effects. Flow accelerationfrom 0.9 m/s (nonreacting) to 15.0 m/s for react-ing cases is observed further downstream. The start-ing location along the axial centerline for the CRZ(where the axial velocity is zero) is sufficiently up-stream of the dump plane (x/Do = 0). This location(x/Do ≈ −0.2) is coincident for nonreacting and re-acting cases, as observed in close-up view in Fig. 3b.High streamwise velocity is seen for all cases aroundx/Do = −0.35 and it is related to the precessingvortex core (PVC) (discussed later). PVC is a flowphenomenon of displacement of vortex core and (asa consequence) reverse flow region from the centralaxis of symmetry to a new precessional center [64].

The effect of breakup is seen primarily close tothe dump plane around x/Do = 0.4, as expected. Inthe breakup case, the reverse flow region is slightlyweaker (by ≈5 m/s), which is attributed to the changein flame location since the fuel evaporation rate is dif-ferent due to the relatively larger initial particles. Inthe far field, there is not much noticeable differences,suggesting that once the droplets have vaporized andburned, the far field evolution is no longer dependenton the features near the fuel injectors.

Flow visualization and comparison of the gasphase velocity profiles were reported to some ex-


tent earlier [6] and therefore are not repeated herefor brevity. Nevertheless, some comments are neces-sary here so that these earlier results can be contrastedwith the cases discussed in much detail here. As notedearlier, the vortex breakdown bubble (VBB) or CRZfor the nonreacting case is shallower but longer inextent when compared to the reacting cases. It is ob-served to be a single contiguous region with meanflow swirling into and around the VBB. The senseof rotation is counterclockwise (CCW) when viewedfrom the outflow boundary. Presence of corner recir-culation zone just past the dump plane near the outercombustor walls is also observed [6]. High level ofturbulence is concentrated between the VBB and theincoming flow, especially in the shear layer regionthat is around the VBB. As discussed later, for the re-acting case, it is in these regions where fuel/air mixingoccurs.

Radial profiles of the time-averaged streamwiseand tangential mean and fluctuating (or RMS) veloc-ity at various locations for the nonreacting case werecompared with data earlier [6] and very good quanti-tative agreement was obtained at all locations exceptthe first location at x = 5 mm. At the x = 5 mm lo-cation, both measurements and LES indicate the pres-ence of peak mean axial velocity away from the cen-terline and a reverse flow region in the central zone.However, the LES data exhibits symmetry in the pro-files in contrast to the experiments. The discrepancyat this location may be due to a variety of reasons. Inaddition to the obvious computational reasons suchas grid resolution, there was also some experimentaldifficulty in obtaining data at this location (for bothnonreacting and reacting cases), as discussed earlierin [6,65]. Nevertheless, the overall agreement withmeasurements for the nonreacting case offered con-fidence in the LDKM-based LES approach and in thestrategy of simulating the entire swirler assembly toeliminate any ambiguity in the inflow conditions.

The presence of heat release alters the flow-field significantly, especially making the flow motionstronger and more compact in the VBB (Fig. 3).A three-dimensional flow visualization of meanstreamlines and the reaction rate isosurface for thetwo reacting cases is presented in Fig. 4. For bothcases, the VBB is observed to be a contiguous regionwith mean flow swirling into and around it. Stream-lines undergoing CCW rotation are observed to movedownstream relatively quickly at a smaller radial an-gle, in part due to a smaller VBB (when compared tothe nonreacting case). The mean flame, representedas fuel oxidation rate (in the background), is observedto be lifted off and positioned in the high-shear re-gion between the VBB and the incoming reactants.The time-averaged flame region appears here spreadover a wide area, primarily due to the unsteady move-

ment of the thin flame surface (discussed later). Thetime-averaged flow fields with and without breakupshow very similar global features. However, a closerexamination shows that the effect of larger particlesupstream of the dump plane in the breakup case isto position the flame slightly downstream to compen-sate for an overall slower evaporation rate. This shiftis more noticeable in the centerline mean axial veloc-ity profile, as discussed above.

The time-averaged radial profiles for mean stream-wise axial velocity are compared to measurements[20] at various axial locations in Fig. 5. At the firstmeasurement station, LES data predict a strong recir-culation in the central portion with almost symmetricpeaks on either sides. However, the measurement dataare devoid of any reverse flow and the velocity mag-nitude is relatively higher. In the experimental study[20], the authors acknowledged difficulty in sortingseeder particles from high-momentum spray particlesat this location, and this may be the reason for the pos-itive axial velocity measured in spite of a recirculationzone.

Further downstream, the comparison between theLES and the measurements are reasonable, althoughthere are still some discrepancies. The profiles be-come uniform further downstream indicating rapid3D mixing. The velocity magnitudes are significantlyhigher relative to the nonreacting case, especially forthe wall-jet (closer to the outer combustor walls). Theeffect of breakup is more dominant again, only in thenear field of the injector (e.g., x = 5 mm); unfor-tunately, this is also the same location where mea-surements are uncertain. The breakup case predictsslightly different radial variation with a weaker re-verse flow peak velocity.

Streamwise RMS profiles for both reacting casesare compared in Fig. 6. Profiles are observed to be-come progressively uniform going downstream, withreasonable comparisons for intensity. The highest in-tensity is observed at the first location, with clearpeaks on either sides of the VBB. The measurementdata are erroneous in this position, as noted before.Although the magnitude and overall trend of the radialvelocity are similar to data at all axial locations, thecomputational results show more fluctuations whencompared to data. This may be attributed to a com-bination of the limited time signal used for statis-tics (typically, the RMS takes much longer to con-verge than the mean) and the relatively coarser gridused in the downstream locations. Within the con-straint of the computational resource and time effortfor these simulations, the overall agreement is con-sidered reasonable. Similar comments are relevant forthe azimuthal components (both mean and RMS). Forbrevity, these comparisons are not shown here, al-


(a) VBB (b) Flame surface

(c) VBB (d) Flame surface

Fig. 4. Streamlines along with zero mean streamwise velocity isosurface and solid contours for fuel reaction rate are shown inleft column, visualizing 3D flow field and the associated VBB. Also, fuel reaction rate isosurface at 8 × 10−6 along with meanaxial velocity contours is shown in the right column. The top row is for simulation without breakup and the bottom row is withbreakup.

Fig. 5. Radial profiles of the time-averaged streamwise velocity at various axial locations for the reacting simulations. Solid linesrepresent simulation with breakup, whereas the dashed lines are for simulation without breakup.


Fig. 6. Radial profiles of the time-averaged streamwise fluctuating velocity at various axial locations for the reacting simulations.Solid lines represent simulation with breakup, whereas the dashed lines are for simulation without breakup.

(a) Sauter mean (D32) (b) Arithmetic mean (D10)

Fig. 7. Radial profiles of time-averaged Sauter mean (SMD) and arithmetic mean (D10) diameter at various axial locations.Closed symbols represent measurement data, whereas solid and dashed lines indicate simulation with and without breakup,respectively.

though some of these results for both nonreacting andwithout breakup cases were discussed earlier [6].

4.1.2. Droplet velocity fields and statisticsThe droplet statistics offer more insight into the

flow just downstream of the injector and around theVBB. It is also these regions where the breakup modelshould have some impact on the flow features.

Radial profiles of the time-averaged Sauter-mean-diameter (SMD or D32) and the arithmetic mean di-ameter (D10) at various axial locations are shown inFig. 7. Closer to the dump plane at x = 5 mm, themeasurements indicate an increase (from 22 to 90 µm)in SMD as the centerline is approached. LES datafor both cases also indicate similar increase (from 22

to 45 µm); however, this increase is not as strong asseen for measurements. Again, this discrepancy maybe due to the reasons discussed earlier for the veloc-ity field. In addition, the underprediction in D32 but areasonable prediction of D10 may be a consequenceof the meager presence of smaller diameter particles.This effect is more pronounced in LES due to the par-cel approach, which assigns more particles per parcelfor smaller diameters. This creates a situation whereevaporation of one parcel with smaller diameter takesaway several particles (associated with that parcel),and thereby artificially reducing the total count. Thiserror can be removed easily by tracking more parti-cles, but at an added expense.


Fig. 8. Radial profiles of the time-averaged droplet streamwise velocity at various axial locations for the 16–30 µm (left),31–45 µm (middle), and 46–60 µm (right) bin sizes. Symbols represent measurement data whereas the solid and dashed linesindicate simulations with and without breakup, respectively.

Fig. 9. Radial profiles of the time-averaged droplet radial velocity at various axial locations for the 16–30 µm (left), 31–45 µm(middle), and 46–60 µm (right) bin sizes. Symbols represent measurement data whereas the solid and dashed lines indicatesimulations with and without breakup, respectively.

Further downstream, both D32 and D10 pro-files becomes more uniform and approach approxi-mately 80 and 55 µm, respectively. Simulation with-out breakup under predict D32 although the D10predictions are more reasonable. Some oscillationsare noted in the LES data especially at downstreamlocations. This is again due to low particle count inthis region. In the simulation with breakup more par-ticles are seen closer to the centerline. This is likelydue to the penetration of initially larger particles intothe VBB and their subsequent evaporation.

Measurements [20] for drop velocity componentswere obtained for five groups/bins based on their ra-dius. Fig. 8 shows the radial variation of the time-averaged streamwise velocity for the bin sizes 16–30 µm, 31–45 µm, and 46–60 µm. Closer to thedump plane, smaller particles move more swiftly thanlarger particles. Also, smaller particles are more likelyto be entrained and achieve momentum equilibriumwith carrier gas due to their lower inertia. Furtherdownstream, sudden expansion at the dump plane andadverse pressure gradient due to the swirling mo-

tion slow down the gas-phase; however, particles donot respond to these changes as swiftly, due to theirhigher inertia.

As the spray evolves past the dump plane, effectsof drag decelerate its motion, which appears in theform of lower velocity for all bin sizes. Radial varia-tion observed closer to the dump plane in the form ofdistinct (broad) peaks disappears further downstreamand oblique line profile emerge with high velocity re-gions away from the centerline.

Particle radial velocity profiles for the same threebin sizes are compared with measurement data inFig. 9. Closer to the dump plane the radial motionof the spray is reflected in these profiles with the ve-locity increasing with radial distance. However, themagnitude of the peak decreases with axial distancepossibly due to 3D effect. Velocity lag between thelarge and small particles is again observed with peaksfor bin size 16–30 µm approaching 32 m/s, whereasfor bin size 46–60 µm they are closer to 22 m/s. Thiseffect is more prominent for smaller particles, due toreduced inertia effect. Both simulations show similar


Fig. 10. Particle size histograms at six locations as indicated in the schematic are shown both with and without breakup simula-tions. Spatial variation of discrete locations includes preflame as well as postflame regions.

behavior for all three bin sizes, with slightly moreradial extent toward the centerline for the breakupcase.

In summary, the time-averaged particle velocityprofiles for the droplets show reasonable agreementwith data, except at the first location at x = 5 mm. Thereason for this initial disagreement has been discussedearlier. Both cases, with and without breakup, showvery similar results, especially in the far field, indicat-ing that once the spray is formed, rapid evaporation,fuel/air mixing, and combustion, all of which are gasphase processes, dominate. Closer observation showsone feature consistently in the breakup simulations:the particle field shows droplets closer to the center-line in the far field (especially for the smaller parti-cles). This is consistent with the measurements andsuggests that one contribution of the breakup model isto provide a broad spectrum of drop sizes (especiallylarge) and therefore increase the dispersion into theregion closer to the centerline, where there is substan-tial recirculation. However, overall, this effect doesnot seem to dominate the flame-holding characteris-tics in this combustor.

As noted earlier, the case without breakup em-ployed an inflow droplet distribution extracted frommeasurements, and therefore, reasonable agreementis expected if the LES is conducted properly (as isthe case here). However, the reasonable prediction ofdroplet statistics (both magnitude and radial extent forvarious bin sizes) for the breakup case demonstratesthat the breakup model in conjunction with the La-grangian tracking approach is able to achieve correctmomentum for a spectrum of drop sizes.

Another way to demonstrate the effect of breakupis to examine the predicted particle distribution atvarious locations. Particle size histograms at six lo-cations (as indicated in the schematic) are shown inFig. 10. For each set, the time-averaged data in termsof number of particles per bin size for a particularcontrol volume is used. Number density for each binis obtained as the ratio of the number of particles inthat bin to the sum of particles across all bins for thatcontrol volume. The number of particles and its sumacross all bins varies in space, and it is also differentfor with- and without-breakup cases. Therefore, sim-ilarly to SMD or D10 at a particular location, the size


(a) Without breakup (b) With breakup

(c) Without breakup (d) With breakup

Fig. 11. Spatial distribution of fuel mass fraction (top row) is shown along with an isosurface for zero mean axial velocity.Bottom row indicates spatial variation of D10 (solid contours) in relation to mean fuel reaction rate (line contours).

histogram is dependent on characteristics of particlespresent in the control volume of interest.

Locations for the histogram are positioned so thatthe spray quality can be assessed (i) just after injec-tion (P2, 3 mm after injection), (ii) just downstreamof the dump plane (P3, 7 mm after injection), and(iii) in the VBB (P4). All these locations are along thecenterline. An additional two locations diagonally (at45◦; D2, D3) and an off-center location (D5) withinthe VBB are also analyzed. These histograms clearlyshow the effect of breakup. At P2, without breakup,the size distribution is similar to a spray with D10 of18 µm. However, with breakup, since a monomodaldistribution of 200-µm-diameter drops is injected, thesubsequent breakup results in a broader distribution(with D10 of 31 µm) of particle sizes.

Further downstream at P3, both cases show similardistribution among bin sizes; however, the proportionfor midsize bins (16–45) with breakup is relatively

higher. Within the VBB region (location P4), predom-inantly large particles are noted for both cases. A sim-ilar observation can be made at D5. The conspicuousabsence of small particles (0–15) is also noted. Boththese locations within the VBB have high tempera-tures, making the existence of small particles rare.Diagonal locations (D2, D3) show not only the radialdispersion of droplets due to PVC but also the effectof evaporation. This is especially true in the breakupcase.

Time-averaged gaseous fuel mass fraction in thevicinity of the VBB for the two cases is comparedin Figs. 11a and 11b in the X–Z center plane. Dif-ference in injection size distribution is observed justdownstream of the nozzle exit in the form of a signifi-cant region of gaseous fuel for no-breakup simulation.This is because its initial distribution already containssmall droplets, which, due to higher surface area pervolume, evaporate faster right after injection. Further


(a) Nonreacting (b) Reacting

Fig. 12. Instantaneous visualization of PVC (gray), precessing VBB (yellow), and flame surface (green) at some arbitrary timeinstant for both nonreacting (a) and reacting (b) simulations. VBB and flame portions past r > Ro are not shown to increaseclarity of visualization.

downstream, the two cases achieve similar gaseousfuel profiles, with maximum gaseous fuel located inor around the VBB. Complete oxidation of fuel is ob-served by x/Do ≈ 1.0, with most of the fuel locatedupstream of x/Do ≈ 0.5. A visualization of D10 vari-ation (solid contours) along the X–Z center planesuperimposed with fuel reaction rate line contours isshown in Figs. 11c and 11d. Within the reaction front,for both cases, a larger particle size is observed. How-ever, no particles exist past the downstream end of theflame brush.

4.2. Transient analysis

Spray interaction with the turbulent shear layerand the subsequent mixing of the vaporized fuel withair and combustion are all unsteady events. In addi-tion to the steady data discussed above, analysis of thetime-evolving features in the combustor is expected toshed further insight into these interactions as well asany effect of breakup in the near field. Therefore, acloser examination of the flow in and near the vicinityof the VBB and the swirling shear layer is carried outto determine the performance of the breakup modeland its relevance for this type of combustor simula-tions.

4.2.1. Spray–vortex–flame interactionsUnlike the steady state picture of VBB (discussed

earlier), which showed a single contiguous (and sym-metric) region, the instantaneous picture is quite dif-ferent, with significant local asymmetry that is highlyunsteady. Figs. 12a and 12b show, for nonreacting

and reacting cases, respectively, precession of the re-verse flow region and flame surface (reacting case)by the PVC rotation. The presence of swirling mo-tion creates hydrodynamic instability in the form ofa spiral around the reverse flow region, just past thestagnation point, where axial vortex breakdown oc-curs. PVC is visualized using a pressure isosurface(at 93.5 kPa) and is observed to be a helical (or spi-ral) filament with counterclockwise (looking from theinflow boundary) winding in space and clockwise ro-tation in time. The turnover (or one rotation) time isestimated at τ = 0.4 ms, corresponding to a frequencyof about 2.3 kHz (this frequency shows up in the span-wise spectra, Fig. 2b).

Velocity vectors (not shown) around the PVCshowed clockwise rotation all along the filament.Also, the leading (or outer) edge was observed to havepositive axial velocity, whereas the inner regions hada reverse flow. Both reacting and nonreacting casesshow a reverse flow region positioned along the innerconfines of the PVC and forming a similar spatiallywinding helical shape. However, since it is located onthe trailing side of the temporal rotation, it lags be-hind the PVC. When averaged over time it gives asimple, geometrically centered VBB as noted in pre-vious discussion.

Precessing motion of the carrier gas entrains theparticles (except for large-Stokes-number drops) andthus, the PVC plays an effective role in their disper-sion (shown later). The flame is also confined by thePVC and the reverse flow region created by the VBB,as shown in Fig. 12b. Transient analysis (not shown)of the flow field indicated that the most upstream (in


(a) Without breakup, t = 0.25τ (b) Without breakup, t = 0.75τ

(c) With breakup, t = 0.25τ (d) With breakup, t = 0.75τ

Fig. 13. Instantaneous droplets, the fuel reaction rate (dark-colored), and the PVC (light-colored isosurface and inset) at twoinstants for simulation with and without breakup. Also shown are the time-averaged streamwise velocity contours.

streamwise direction) point of the flame surface neverprotrudes into the diffuser section. However, it is po-sitioned closest to the dump plane, based on the PVCrotation (described below).

Fig. 13 shows two snapshots of transient motionof particles, flame surface, and the PVC for with- andwithout-breakup cases. The rotation of the PVC dis-perses the liquid fuel particles around and into theVBB region (its boundary is identified by a zero-axial-velocity line contour). The particles are dis-persed radially right to the venturi walls, just halfwayto the dump plane. Preferential accumulation of smalldroplets around the PVC, while the heavier dropletsmove downstream relatively unaffected by the localflow structures is clearly observed. The instantaneousflame structure (visualized in form of fuel oxidationrate) is relatively thin in the central portion, while itis somewhat thicker near the outer combustor. Thesefeatures are just representative as the flame motionis highly transient. Analysis shows that the flamethickness is approximately 0.5–0.7 mm in the cen-ter (resolved with 2–4 LES cells and hence 24–48

LEM cells). Thicker flame regions could be explainedby both the (coarse) grid resolution and the multipleflame-regime behavior (discussed next).

Instantaneous flame structure is analyzed using theTakeno flame index, FI = ∇YFUEL · ∇YO2 [66]. Todetermine the flame regime, an indexed reaction rateis defined based on the flame index as ω∗

F= |ωF | FI

|FI| ,and is shown in Fig. 14. The stoichiometric equiva-lence ratio is shown as a thin line in the same figure.The flame is premixed when the FI (and consequentlyω∗

F) is positive and diffusion when the FI is negative.

In the central region, presence of fuel vapor in prox-imity of recirculating hot gases devoid of oxidizergenerates diffusion flame, as seen by a light-colored“V”-shaped flame surface. This is confirmed by thecoincidence between the flame and the stoichiomet-ric line. Further outward in the radial direction, sig-nificant dark-colored contours are seen, indicating apremixed flame. Along the outer edges there is suffi-cient time for fuel–air mixing to be completed beforeignition. It is also noted that nonpremixed and pre-mixed flames occur adjacently near the top half of the


Fig. 14. Flame index at some time instant is shown for the re-acting simulation. Instantaneous fuel oxidation rate is repre-sented by solid gray-scale contours. Also, the stoichiometricequivalence ratio is indicated as a thin line.

combustor, making the overall flame surface appearthick, as seen in Fig. 13b. Several light-colored re-gions are seen in the postflame region. There regionsindicate diffusion burning fuel vapor evaporated from

the particles that have gone through the primary flamewithout completely losing their identity.

These results confirm earlier observations [5] thatin complex swirling spray combustion systems theflame structure can be very complex and locally rangefrom nonpremixed to premixed burning. The currentLEMLES approach does not make any a priori as-sumptions regarding the nature of the flame and there-fore, is able to capture the multifaceted flame struc-ture in these combustors.

4.2.2. Effect of breakup on near-field spray evolutionInstantaneous spray visualization at some arbi-

trary time is shown in Figs. 15a and 15b, for without-and with-breakup cases, respectively. All droplets arecolored and sized by their respective particle radius.Progressive sequence of breakup events is seen inFig. 15b with a 200-µm-diameter particle/blob in-jected into the swirling airstream. Effect of PVC isseen by the change in trajectory of streamwise particleevolution. Within the first 1 mm of injection loca-tion, initial breakup appears to be completed with theformation of several (approximately 70–150 groups)


(c) X = (0,4) mm slice (d) X = (6,9) mm slice

Fig. 15. Instantaneous visualization of droplets both with and without breakup simulations. All droplets are colored and sizedby their particle radius. Also, droplet diameter histogram over specified volume for respective simulations is presented andcompared.


product particles. Furthermore, shear stripping of theparent blob continues, forming more product parcelsdownstream and depending on local conditions andWeber number, both product and parent particles un-dergo further breakup. It appears that in the presenttest case, all breakup events are completed within thefirst 4 mm of injection and a finer particle distributionemerges downstream.

Quantitative metrics in form of particle size his-tograms are presented in Figs. 15c and 15d. A 15-µm-diameter bin is chosen for both histograms. Qualityof spray is accessed by considering histogram of par-ticles in certain regions. Fig. 15c is taken over a spaceencompassing all particles from injection location to4-mm-downstream. Large-sized particles are seen forthe breakup simulation, as expected. For the inter-mediate size range, both simulations produce similardistributions. Further downstream, around the dumpplane region in the high-shear mixing region, Fig. 15dindicates that the breakup simulation achieve distri-bution similar to the without breakup case. Analy-sis shows that the droplet distribution created in thebreakup simulation is equivalent to the prespecifieddistribution in the no-breakup case.

Since the breakup process occurs within a narrow4-mm region just downstream of the injector, the ma-jor impact of breakup is on the fuel evaporation inthis region. This was shown before in the form ofsteady state gaseous fuel mass fraction in the cen-ter plane. The other processes in the injector vicin-ity such as the PVC is not affected by the breakupsince it is driven by the incoming swirling gas flowfrom the swirler vane assembly. Since the spray dis-tribution downstream of the initial breakup region issimilar to the no-breakup case (where the spray wasadjusted to match experimental data), the gaseous fuelconcentration and its eventual mixing with incomingswirling air produces similar flame response, as seenin Fig. 13.

4.2.3. Local flame structure and its thermochemicalstate

The thermochemical states of fuel/air mixing andoxidation provide information on flame structure inthe mixture-fraction space. Spray flame responsein the mixture-fraction (f ) space was studied byReveillon and Vervisch [67]. They showed that sprayflame behavior differs significantly from the classicalgaseous diffusion flames [68]. The two-phase (2PH)oxidation limits were noted to be lower and departfrom the single-phase (SPH) limits. Both no-breakupand breakup cases show similar results (as seen next)and therefore, only characteristic results for the no-breakup case are discussed.

Instantaneous scatterplots for temperature ver-sus mixture fraction at various streamwise locations

(from the fuel injector exit) are shown in Fig. 16for both with- and without-breakup cases. Lines areshown for both the mixing and the reacting equi-librium limits. The stoichiometric mixture fraction(fSTOIC) based on assumed C12H23 chemistry is ap-proximately 0.064 and the corresponding adiabaticflame temperature (TADIA) is about 2320 K. Theglobal mixture fraction (fglob) based on global equiv-alence ratio (of 0.75) is 0.049.

The scatter in the mixture-fraction space variesfrom f = 0 (pure air) to f ≈ 0.4 (equivalence ra-tio φ = 9.7), with the majority of the samples withinf < 0.1. This is indicative of fast mixing of the fuel,air, and postflame gases. Samples closer to the mix-ing line (T ≈ 300) are noted only for the 3-mm lo-cation, suggesting some (f < 0.03) mixing. Furtherdownstream at 6 mm, samples are in the interme-diate temperature (400–1000) range, indicating bothpreheating of the vaporized fuel and the presenceof postflame species. The presence of flame (in theform of high-temperature samples) is observed onlydownstream of the dump plane. For example, at the12-mm location, two distinct branches are observed:one along the SPH equilibrium line on the left (f <

fSTOIC) and the other along the 2PH equilibrium(f > fSTOIC) on the right. The equilibrium limit onthe left is followed well; however, the aforementioneddeparture from the SPH equilibrium is observed onthe right. Peak temperature is observed around thefSTOIC.

Further downstream (past 16 mm), the thermo-chemical state reaches an equilibrium with most sam-ples lying around the designated limits. Peak temper-atures predicted by the LES are close to analyticallycomputed TADIA. Scatter in both mixture fraction andtemperature decreases beyond 60 mm, with almost allsamples falling along the left equilibrium line. This isindicative of a completely reacted mixture undergo-ing bulk advection with no further reaction.

The radial distribution of thermochemical states12 mm downstream of the injector exit is shown inFig. 17. This location lies about 5 mm downstreamof the dump plane. Instantaneous temperature, fuel,water vapor, and oxygen mass fractions, and fuel oxi-dation rates are plotted in the mixture-fraction space.Analyzing the scatter data as a function of the ra-dial location bins helps identifying local states in theregions of interest. Five radial bins are selected toseparate regions of VBB, high-shear, and corner re-circulation zone. Temperature scatter shows distinctregions of highest temperatures around the VBB (allred, some green and blue) region. These sampleslie very close to the adiabatic equilibrium line, in-dicating a completely reacted mixture. Intermediatesamples (400–1000 K) are also noted (mostly blueand magenta, some green) in the scatter, indicating



Fig. 16. Instantaneous scatterplot for temperature versus mixture fraction at various streamwise locations for simulations withand without breakup. The analytical stoichiometric mixture fraction is noted to be around 0.064.

(a) Temperature (b) Gaseous fuel

(c) Oxidizer (d) Fuel-oxidizer

(e) Temp-H2O (f) Fuel oxidation rate

Fig. 17. Instantaneous scatterplot for various quantities such as temperature, gaseous fuel, oxidizer, water vapor, and fuel reactionrate 12 mm downstream of the injector. The data are dissected into five radial bins from the combustor centerline. The fuelreaction rate is normalized by ωo = 10−4.


mixed states of fluid: the presence of preheated vapor-ized fuel and partially reacted gas. This state stemsfrom a high-shear region between the venturi wallsand the VBB. Additionally, high turbulence activitywithin this region forms a wide range of gas compo-sitions (reactant/product mixture) and temperatures.Such mixtures undergoing reaction are subject [69] toignition delay, giving rise to the observed partially re-acted mixtures. Samples beyond r > 15 mm (cyan)show lower values for f and temperature with scat-ter around f ≈ 0.01–0.06, T ≈ 500–1900 K, indicat-ing both completely reacted samples (those along theequilibrium line) and partially reacted (intermediatetemperature) mixtures. This region is part of cornerrecirculation zone, which provides longer residencetime for complete reactions but also entrains freshreactants at the same time forming samples with in-termediate temperatures.

A scatterplot for species mass fractions at 12 mmis also shown in Fig. 17, which to a large extent isin agreement with the above explanation for the tem-perature field. Samples from the VBB (r < 8 mm) arenoted to lie along the equilibrium line seen in Fig. 17band contains negligible oxidizer, as seen in Fig. 17c.Very few samples in either plot are noted along themixing line, indicating a diffusion burning mode atthis location. Fuel mass content seen in Figs. 17band 17d for the VBB region is due to penetrationof large fuel particles undergoing evaporation. Thehighest product species is observed for the VBB re-gion, as seen in Fig. 17e, consistent with the presenceof a high-temperature region in the VBB. Reactionrates (normalized) shown in Fig. 17f in this regionare found to be relatively low due both to equilibriumlimits reached for certain samples, and to negligiblecontent of oxidizer available for the gaseous fuel toburn. Samples for the corner recirculation zone areobserved to contain significant amounts of oxidizercompared to the fuel content, as seen in Fig. 17d, in-dicating a recirculation zone allowing complete fuelburning. The entire range of product species is ob-served in this region, as seen in Fig. 17e. Scatter forthe reaction rate is observed to have a peak around thestoichiometric mixture fraction. This is in agreementwith observations of Reveillon and Vervisch [67].

4.2.4. Particle–particle and particle–gascorrelations

Scatterplots at two axial locations of parcel tem-perature, and streamwise and azimuthal velocity ver-sus parcel diameter are shown in Fig. 18. Both with-and without-breakup results are shown side by side tounderstand the effect of breakup modeling. To furthervisualize the spatial dependence of these correlations,the data are separated into radial bins. Some overallcomments valid for both with- and without-breakup

cases can be made, based on the analysis of these re-sults. In the current case, the liquid parcel is at 380 Kwhen injected, while the gas temperature is initially300 K. Thus, when the droplets evaporate, their tem-perature drops. Also, the thermal response time [50]is proportional to the square of drop diameter and isrelatively smaller for smaller droplets. As shown inFig. 18a, the smaller droplets respond more quicklyto the local changes. The presence of a heat source(VBB) further downstream (beyond the dump plane)is observed in the form of higher drop temperatures inthe range 400–650 (Fig. 18b). Again, smaller parcelsoverwhelmingly show both the higher and lower tem-perature peaks.

The effect of breakup is clearly noticeable in thesefigures. Closer to the injector location (radial loca-tion r < 5 mm), particles are observed to have largerdiameters and temperatures close to the injection tem-perature. Only after breakup, for radial locations r >

5 mm, are smaller particles observed with significantthermal response. Further downstream, past the dumpplane, both cases show similar the diameter rangesand thermal response, with most scatter in the diam-eter range of 20–40 µm for the breakup case. Thepresence of smaller particles at this location in the no-breakup case is from the specified inflow distribution.This is evident from their thermal response and theirradial position in the shear layer (r ≈ 5–12 mm) re-gion.

Parcel velocity correlations with its size are shownin Figs. 18c, 18d and Figs. 18e, 18f for axial andtangential components, respectively. A dashed lineshown in these figures indicate initial velocity im-parted to parcels during injection. The velocity re-sponse time for particles is also proportional to thesquare of drop diameter. Thus, particles with lowerinertia are able to follow gas-phase more closely andthis is seen in form of peaks (min, max) for smallersizes. At 3 mm downstream, however, parcels in theouter regions (green, blue) have significantly differ-ing velocities. This is in part due to the presence ofthe PVC, which entrains the droplets into its vorticalflow. Further downstream (at 12 mm), parcels in therange 5 < r < 15 mm move quickly, whereas those inthe outer regions (r > 15 mm) have slowed down toaround 10 m/s. Tangential correlation shows mostlycounterrotating motion of particles closer to the in-jection location, however, further downstream, a neg-ative tangential component is dominant (same as forthe gas phase). Parcels within r < 2.5 mm show a lowpositive component in part due to the flow field pro-vided by the off-center PVC switches directions in thecentral region close to the injector based on its move-ments. Flow past the dump plane is rotating counter-clockwise and analogous attributes are observed forthe liquid phase, as seen in Fig. 18f.


(a) x = 3 mm (b) x = 12 mm

(c) x = 3 mm (d) x = 12 mm

(e) x = 3 mm (f) x = 12 mm

Fig. 18. Drop/drop correlations at two axial locations for droplet temperature (top row), axial (middle row), and azimuthal(bottom row) velocity versus drop diameter. The scatter data are dissected into three to five radial bins.

Overall, the breakup case yields larger particlescloser to the injector, and thereby exhibits delayedresponse. Also, the PVC rotation is observed to af-fect the breakup somewhat by entraining the parentdroplet, as seen in Fig. 15b. This entrainment impartsvelocity components different from those of the injec-tion condition to the parent droplets. After breakup,the new droplets inherit these velocities. Also, sincethe velocity of a particle is based on its temporalevolution, the history of its trajectory and diameterchanges plays a major role on its velocity as well. This

is clearly seen in the breakup case for both velocitycorrelations.

Correlation of gas/particle characteristics is shownin Fig. 19 for 1 mm downstream of the dump plane inthe form of temperature and all three velocity com-ponents. Each scatter datum is separated into fourparticle radius bins (in micrometers) to show the ef-fect of particle inertia. Fig. 19a shows scatter for gasand drop parcel temperature for with- and without-breakup simulations. The carrier flow field has a sig-nificant temperature range, 300–1500 K, whereas the


(a) Temperature (b) Axial velocity

(c) Radial velocity (d) Azimuthal velocity

Fig. 19. Drop/gas correlations 8 mm downstream of injector for temperature and all three components of velocity are shown.The scatter data are dissected into four bins of droplet radius (in micrometers).

liquid phase varies about 300–650 K. The upper limitfor the liquid phase is set by the critical tempera-ture limit, beyond which distinct phases cease to ex-ist. Most of the scatter lies within 500 K, which isthe boiling point limit. The thin line at 45◦ indicatesperfect correlation among the phases. Smaller parti-cles are observed to follow this line well. Thermalresponse for large particles (black, red) is noted tofollow an almost horizontal line, implying negligiblecorrelation with the gas phase. Momentum couplingamong the phases is observed in the form of scatterfor three components of velocity shown in Figs. 19b–19d. Two dashed lines indicating positive and neg-ative correlations are shown for reference. All threecomponents exhibit a positive correlation, especiallyfor smaller particles (green). With increase in parti-cle size, the correlation deviates from the 45◦ lineand gets flatter (or horizontal). This is to be expectedbased on the higher velocity response time for suchparticles and is more prominent in the breakup case.

4.2.5. PVC and spray correlationThe spatial structure of the PVC, as well as its

entrainment effect on particles, can be seen in theform of spatial correlation between the drop parceland PVC position. No substantial differences are ob-served between the two simulations. Two character-istic time instants for the no-breakup simulation areshown in Fig. 20. The PVC position is characterized

in the form of the lowest-pressure position (shownas a big solid circle) at a particular streamwise Y–Z

plane. The parcel positions coincident in this planeare shown in form of small (open) squares. Combi-nation of colors (black, red) and (blue, green) showdistinct time sequence half-wavelength (τ/2) apart.At 1.5 mm downstream of the injection location, theparcels are noted to be clustered close to the PVC.Progressing further downstream, the particles moveradially outward as well as rotate with the PVC. ThePVC has a counterclockwise twist in space and the di-ameter of the path traced out by the temporal rotationof the PVC increases further downstream. The parti-cle movement is observed to follow the PVC motionwith some particles lagging behind. Radial disper-sion of particles enabled by the PVC is observed tobe effective. For example, the particles are dispersedapproximately 12 mm radially outward by 7.5 mmdownstream of the injector. This is close to a 120◦ in-ner cone angle for the dispersion. The cross-sectionalspray structure is neither solid- nor hollow-cone.

Preferential entrainment of particles into the PVCstructure can be observed by parsing the spatial cor-relation among the droplet parcels and the PVC intobins of parcel radius. This is performed 6.5 mmdownstream of the injector at two time instants shownin Fig. 21. As seen previously, the big solid circle in-dicates the PVC position, whereas small open squareslocate the parcels. Transient spatial structure in terms


Fig. 20. Spatial correlation between droplet parcel and PVC position at two time-instants for without-breakup simulations. Bigsolid circles indicate PVC positions whereas small open squares represent droplets. Black and red colors indicate positions att = 0.25τ whereas blue and green are at t = 0.75τ . (For interpretation of the references to color in this figure legend, the readeris referred to the web version of this article.)

Fig. 21. Spatial correlation between droplet parcel and PVC position at two time instants 6.5 mm downstream of the injector.Big solid circle indicates PVC position whereas small squares represent droplets. The data are dissected into four bins of dropletradius (in micrometers).

of particle positions relative to the PVC is observed.The scatter is made up of three regions: the lead-ing edge (LE), the trailing edge (TE), and the tailregion. The leading edge region contains small parti-cles (green color), whereas the large particles (black,red) are mainly concentrated at the trailing edges.The primary reason for this is the faster responseof the smaller particles to movement of PVC via anoutwardly oriented (from the PVC position) velocityfield. There is also a tail region, which is consideredto be a lag effect from the previous PVC rotation.

5. Conclusions

Large eddy simulation of an experimental liquid-fueled LDI combustor is performed using a sub-grid mixing and combustion model. A liquid breakupmodel is employed to eliminate the need to specifya liquid-phase size–velocity inflow condition. Stand-alone validation on a solid-cone spray jet is performedfor two breakup models and overall reasonable agree-ment for transient spray tip progression and spreadingangle is obtained. The Kelvin–Helmholtz (or aero-


dynamic) breakup model is adopted for the combus-tor simulation. Two simulations (with and withoutbreakup) are performed and compared with measure-ments. Time-averaged velocity prediction compari-son for both gas and liquid phase with available datashows reasonable agreement. The major impact ofbreakup is on the fuel evaporation in the vicinity ofthe injector. Further downstream, a wide range ofdrop sizes are recovered by the breakup simulationand produce a spray quality similar to that in the no-breakup case.

Unsteady features such as the efficient dispersionof the spray by the rotating PVC structure and theflame stabilization by the VBB are captured in thesimulations, thereby providing an opportunity to in-vestigate the coupling between these features in thecombustor. Flame structure in the form of the Takenoflame index shows the presence of a diffusion flamein the central portion, whereas the premixed burn-ing mode is seen farther away. Analysis of the in-stantaneous thermochemical states of fuel/air mixingand oxidation indicates significant departure from thegaseous diffusion limits and is consistent with thetwo-phase studies of Reveillon and Vervisch [67].Particle/particle correlations showed effects of parti-cle response time for both thermal and velocity inertiain the form of swift response of smaller droplets. Par-ticle/gas scatter indicated overall positive correlationsamong their temperature and all three velocity com-ponents. This is especially true for smaller particles.Spatial structure of the PVC and resulting entrainmentof particles indicated highly temporal- and spatial-dependent particle behavior.

Acknowledgments

This research is supported by NASA/GRC. Com-putational resources provided by NASA AdvancedSupercomputing (NAS) are greatly appreciated.

Appendix A. Validation of breakup model

A standard test case of nonevaporating, solid-cone, high-speed liquid atomization in a cylindricalchamber by Hiroyasu and Kadota [70] is used to vali-date the implementation of breakup models discussedpreviously. Measurements [70] of solid-cone dieselspray were conducted in an enclosed cylindrical ap-paratus with inside gas as nitrogen under isothermal(293 K) and quiescent conditions for varying (0.1 to5.0 MPa) chamber pressures. The injector is a single-hole nozzle with orifice diameter of 300 µm and9.9 MPa nozzle-opening pressure. Table 1 presentsthe test conditions for the three cases used here for

Table 1Test conditions for the measurements of solid-cone spray byHiroyasu and Kadota [70]

Case 1 Case 2 Case 3

Pgas (MPa) 1.1 3.0 5.0ρgas (kg/m3) 12.6 34.4 57.7Vinj (m/s) 102.0 90.3 86.4

Note. Orifice diameter do = 300 µm; liquid density840 kg/m3; liquid surface tension 29.5 × 10−3 N/m; liq-uid kinematic viscosity μl = 2.1 × 10−3 Pa s.

validation. Since liquid injection velocity was notmeasured, it is estimated [17,45,49] based on the pres-sure drop (P ) across the nozzle as CQ

√2P/ρp ,

where CQ is the nozzle discharge coefficient (0.705).The droplet size distribution were measured using acollection system located about 65 mm (or 217 noz-zle diameters) downstream of the injector.

The computational domain is a closed cylinder150 mm in length and 200 mm in diameter dis-cretized by a two-domain butterfly grid approach.Wall boundary conditions are applied on the top (in-jector end) and the side walls, whereas the charac-teristic outflow is employed at the bottom boundary.The domain is composed of (axial, radial, azimuthal)≡ (50 × 50 × 80) for the outer cylindrical portionand (50 × 21 × 21) for the inner Cartesian domain.Nonuniform grid spacing is employed in the axial andradial directions so that the minimum resolution of(axial, radial) ≡ (1,0.6) × 10−3 m near the injector(located at the center axis) and gradually stretchingoutward. A uniform grid is used in the azimuthal di-rection.

Figs. 22a and 22b show, respectively, transientspray tip penetration (left) and time-averaged sprayangle (right) for three back pressures compared withexperimental data [70]. Overall, reasonable agree-ment for transient spray penetration depth has beenobtained for both models. Due to there being no pre-cise definition of spray tip position either in measure-ments or computations, the tip penetration is the loca-tion of the leading spray drop parcel or alternatively isthe location where 99% of the liquid mass is included.The spray angle is determined by drawing a tangent tothe radial spread of the spray, starting from the end ofthe jet breakup and ensuring 99% of injected liquidmass. Increase in back pressure is observed to de-crease the penetration depth and increase the sprayangle. This is due to efficient momentum exchangebetween the denser gas phase (at higher pressures)and liquid droplets. Overall, the TAB model [17] isobserved to overestimate the spray cone angle, in partdue to rapid breakup of injected blobs causing smallerparticles to be entrained in the gas vorticity.


(a) Penetration (b) Spray angle

Fig. 22. Transient spray tip penetration (a) for different back pressures and time-averaged spray angle (b) comparisons withmeasurements [70].

(a) Sauter mean radius (b) KH model visualization

Fig. 23. Cross-sectional averaged Sauter mean radius (SMR) variation with axial distance for different back pressures. Closedsymbols represent measurement data. Transient spray visualization of the KH model [16] for the 1.1-MPa case is shown in (b).Particle spheres shown in (b) are proportional to drop diameter.

The cross-section averaged Sauter mean radius(SMR) variation with axial distance is shown inFig. 23a. Closer to the injector, for both the mod-els, the SMR is around 150 µm, corresponding tothe size of the injected droplets. It decreases rapidlyover a small distance from the injector exit, indi-cating breakup/atomization of parent (or injected)drops. Further downstream, it remains more or lessconstant. In this study, we have neglected agglomer-ation/coalescence of droplets, and therefore under-prediction of SMR at the measurement location isexpected. Both models give similar size distributionsin the far field. However, there are differences in thenear field, with the TAB model predicting an instan-taneous breakup of the parent droplet from 150 µmto the final size. In contrast, in the KH model, theparent drop size decreases gradually according to therate equation (which is based on measured mass loss).As is observed by other researchers [13,19], both themodels, especially the TAB model, predict exces-

sive breakup, leading to very small drop sizes andthus small SMR (not accounting for coalescence).The presence of a liquid core (in form of large par-ticles) is seen in the wave model and its length hasbeen observed (not shown here) to decrease with in-crease in gas pressure. No such features are evident inthe TAB model, due to its steplike breakup of parentdrops.

Fig. 23b shows an instantaneous snapshot of thetransient spray field for the 1.1-MPa case using theKH model. The size of the spheres scales with thediameter of the droplets, as represented by the compu-tational parcels. Two inset boxes indicate the presenceof a broad spectrum of drop sizes with simultaneousexistence of large and small droplets. The strippingbreakup of the liquid core is also seen in the topleft inset picture. As the spray evolves downstream,the drop size decreases and radial spreading formsa cone-shaped structure with its apex at the injectorexit.


In summary, both breakup models perform ade-quately even though there are still some well-knowndeficiencies in both models. The present focus is noton developing a new breakup model, but rather on theevaluation of existing models in a LES of a complexcombustor flow field. Since overall the KH model issuperior in terms of tip penetration, spray angle, andpresence of liquid core, it is used for the simulationsdiscussed in this paper.

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Simulation of spray–turbulence–flame interactions in a lean direct injection combustor

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