mbu

ch098

Available online 1 April 2014

Keywords:Spray combustionSoot

erico-

ondary streams, on ame structure, soot formation and radiative heat transfer in the combustor ring

l spray

found that LES [1] and DNS [2] based models can provide valuableinsight of ow in the combustors. However, the latter models arevery expensive particularly in three dimensional geometries. Inthe RANS based models, the turbulence quantities are usuallysolved using two equation models with eddy viscosity concept.Different forms of the ke models, like standard, RNG andrealizable ke models are commonly employed in the literature

ray is consideredhose trajectorieserning equetween th

phases are computed as source terms and accounted in tphase governing equations.

Soot formation in combustion is important in liquid fueames. Soot particles present in the ames result in a highly lumi-nous radiation and thereby inuence the heat transfer phenome-non from the ame. As a consequence, soot in ame augmentsthe wall and burner heating considerably. It is therefore importantto precisely model the soot formation process in spray ames andstudy its inuence on radiative heat transfer from the ame.Kerosene (or jet fuel) is widely used as fuel in aero gas turbine

Corresponding author. Tel.: +91 33 23355813; fax: +91 33 23357254.E-mail address: amdatta_ju@yahoo.com (A. Datta).

International Journal of Heat and Mass Transfer 74 (2014) 143155

Contents lists availab

H

.eof the component models, which have been employed in the wholescheme. Some of the models are quite well established in the liter-ature. For example, the uid ow is commonly solved with RANSbased models for their computational economy, though it has been

11]. In the discrete droplet model, the liquid spto consist of a nite number of droplet classes, win the gas phase are tracked using suitable govThe mass, momentum and energy exchanges bhttp://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.03.0010017-9310/ 2014 Elsevier Ltd. All rights reserved.ations.e twohe gas

l sprayused as a predictive tool for the performance analysis of gas tur-bine combustors and liquid fuel furnaces. Spray combustion is acomplex phenomenon consisting of various physical and chemicalprocesses, like atomization of liquid jet and movement of dropletsin a gaseous eld, vaporization of droplets, turbulent transport andmixing, chemical reaction, thermal radiation and pollutant forma-tion. The prediction of the entire process depends on the accuracy

Karim et al. [8] showed that standard ke model is over-diffusivein highly swirling ows in comparison with realizable ke model.In spray combustion calculation, a suitable model is also requiredto predict the initial spray characteristics following breakup ofthe liquid fuel jet. Thereafter, the interactions between the contin-uous and dispersed phases are often captured using the discretedroplet model (DDM) in the EulerianLagrangian formulation [9RadiationDiscrete droplet modelAir ow distribution

1. Introduction

Numerical modeling of liquid fuekerosene as fuel. Turbulence is modeled using realizable ke model and radiation is modeled using dis-crete ordinate method with weighted sum of gray gases model. The combustion is modeled using equi-librium presumed probability density model. The results show that an increase in the proportion ofprimary air ow, from 30% to 50% of the total air, results in a more compact ame with lower soot pro-duction and a better pattern factor at the combustor exit. However, the corresponding reduction in sec-ondary air ow rate increases the combustor wall temperature. The decrease in soot in ame at higherprimary air fraction reduces the incident radiative heat ux on the injector body while, the injector sur-face temperature remains almost unaffected due to increased convective heat transfer rate from the gas.

2014 Elsevier Ltd. All rights reserved.

combustion is widely

[35]. Hsiao and Mongia [6] and Joung and Huh [7] used standardand realizable ke models to predict swirling ows in connedgeometries and found reasonable prediction of ow parameters.Received in revised form 6 February 2014Accepted 2 March 2014

tion and radiative heat transfer and has been validated with experiments conducted on a combustor ofidentical geometry. The paper investigates the effect of air ow distribution, between primary and sec-Effect of air ow distribution on soot fortransfer in a model liquid fuel spray com

Prakash Ghose a, Jitendra Patra a, Amitava Datta a,, AaDepartment of Power Engineering, Jadavpur University, Salt Lake Campus, Kolkata 700bDepartment of Mechanical Engineering, Jadavpur University, Kolkata 700 032, India

a r t i c l e i n f o

Article history:Received 12 July 2013

a b s t r a c t

In the present paper, a numcombustor admitting air as

International Journal of

journal homepage: wwwation and radiative heatstor ring kerosene

intya Mukhopadhyay b

, India

cal model has been developed for spray combustion in a model gas turbineaxial primary and secondary streams. The model incorporates soot forma-

le at ScienceDirect

eat and Mass Transfer

l sevier .com/locate / i jhmt

eatNomenclature

A surface area, m2

ak weighting factorCd coefcient of dischargeCdrag drag coefcientCf vapor concentration in the continuous phaseCfs vapor concentration at the droplet surfaceCL ligament constantCp specic heat, J/kg KCl a variable, function of mean strain rateD diameter of the combustor, md diameter, mdL ligament diameter, mdo mean droplet diameter, mdpsoot mean diameter of soot particle, mDHv latent heat of vaporization, J/kgh convective heat transfer coefcienthD mass transfer coefcientI radiation intensity, W/m2 sr

2 2

144 P. Ghose et al. / International Journal of Hcombustors, where a high overall airfuel ratio is maintained in or-der to keep the exit gas temperature within the allowable limit forthe turbine blade material. The total air is distributed in differentzones, so that a stable ame can be established on the burner.The air ow distribution inuences the stoichiometry in the amezone and affects the soot formation there. The cooling of the com-bustor wall and the temperature uniformity of the exit gas also de-pend on the air ow distribution in the combustor.

Soot formation in hydrocarbon combustion is a very complexprocess, which initiates with the formation of precursor moleculesand completes through the growth of poly aromatic hydrocarbons[12,13]. Detailed formulations using elementary reactions for thegas phase and soot [14,15] are often found to be unfeasible inthe real combustor congurations (e.g. in gas turbine combustor)because of their complexities. Therefore, different semi-empiricalmodels had been proposed by Kennedy et al. [16], Leung et al.[17], Moss et al. [18], and Brookes and Moss [19] for the predictionof soot in hydrocarbon ames, like methane or ethylene. The mod-els compute the soot nucleation and surface growth rates based onthe concentration of precursor species, which is commonly consid-ered as acetylene in these works. Oxidation models, proposed byLee et al. [20], Nagle and Strickland-Constable [21], and Fennimoreand Jones [22] were also adopted in the soot models. Wen et al.

k turbulent kinetic energy, m /skw wave numberM soot mass concentration, kg/m3

m mass, kg_m mass ow rate, kg/sN particle number density, 1/m3

NA Avogadro number 6.022045e+26 kmol/lOh Ohnesorge numberP pressure, N/m2

P(n) probability density functionDP pressure differential, N/m2

p total partial pressure, N/m2

Q ratio between gas and liquid densityq radiative heat ux, W/m2

R universal gas constantRe Reynolds numberS sourceT temperature, Kt liquid sheet thickness, mU resultant (total) velocity of fuel jet, m/su velocity, m/sWe Weber numberwi quadrature weightX mole fractionz path length

Greek symbolsC diffusivityq density/ scalar variablel dynamic viscositylt dynamic eddy viscosityr Prandtl/Schmidt numberrs surface tension of the liquide rate of dissipation of turbulent K.E.h spray cone half angleq densityxr growth rate of sinuous wavem kinematic viscosity

and Mass Transfer 74 (2014) 143155[23] modeled soot formation in a turbulent jet diffusion ame ofkerosene vapor and air. They considered two different nucleationmodels of soot, viz. (i) acetylene nucleation model consideringacetylene as the precursor and (ii) PAH nucleation mode takingtwo and three ring aromatics as precursor. However, surfacegrowth is modeled using acetylene concentration and the numberof active sites on the soot particles. It was found that the PAHnucleation model contributes signicant improvement in the mod-el prediction in comparison to the experimental data. On the otherhand, Moss and Aksit [24] applied the soot model, proposed byBrookes and Moss (for a methane non-premixed ame), in the lam-inar non-premixed ame of a surrogate kerosene fuel. They foundthat adjustments in the model parameters, from the values inmethaneair ame, are necessary to satisfactorily reproduce theexperimental measurements of soot under the change of fuel.Accordingly, they proposed two alternate models. In one of them,acetylene is considered as the precursor in nucleation and surfacegrowth and the model parameters are changed to match the exper-imental results. In the other case, acetylene is considered as theprecursor of soot nucleation only, while the precursor for surfacegrowth is taken as acetylene and benzene. New model constantsare evaluated for this case as well. Both the models are found topredict the soot concentration nearly equally, though the latter

n mixture fractionj absorption coefcientjk gray gas absorption coefcient

Subscriptb black bodycrit criticald dropleteff effectivef liquidf fuelg gasi ith coordinate directioninj injectionj jth coordinate directionk kth coordinate directionl liquidor oricep particlerad radiation/ scalar variable

one comes closer to the measurement at some locations. Theseworks show that uncertainties still exist in considering the sootmodel with kerosene fuels.

Soot particles in combustion signicantly contribute to radia-tion heat transfer due to their high emissivity [25,26]. Byun andBaek [27] investigated numerically the combustion of liquid kero-sene in a rocket engine considering soot formation and radiation.The radiation model considered the contributions of non-graygases using weighted sum of gray gas model and gray soot parti-cles. They reported that radiation from the ame makes the hightemperature zone smaller and affects the wall temperature consid-erably. Tesse et al. [28] reported that in a sooty turbulent non-pre-mixed ame, in addition to soot particles, gaseous species such asCO2 and H2O play important role in global radiative heat loss.

In the present work, we have presented numerical results on

considered at 40 mm upstream to the swirler plane, both in theprimary and secondary air streams. The Favre-averaged governingequations in the gas phase are solved and the turbulence parame-ters are computed using realizable kemodel [30]. Favre averaginghelps to avoid extra terms in the governing equations due to theuctuating and variable density in the ow. The injected spraywith a particular cone angle from the pressure swirl atomizer isconsidered to break up following the linearized instability sheetatomization model (LISA) of Schmidt et al. [31]. This model as-sumes little knowledge of the atomizer hydrodynamics and helpsto nd out an average droplet size following break up using theavailable observations of external spray and atomizer characteris-tics. The LISA model is simple, requires less computational cost andreduces the empirical constants and geometrical data required forpredicting lm formation and sheet break up following spray from

The gas phase conservation equations are solved in the Eulerian

P. Ghose et al. / International Journal of Heat and Mass Transfer 74 (2014) 143155 145kerosene (C12H23) spray combustion in a model combustion cham-ber (Fig. 1) and predict the soot formation and radiation heat trans-fer from the ame. The combustion chamber has two co-axial airentries, considered as primary and secondary air streams. The pri-mary air is admitted through a constant vane angle swirler, at thecenter of which a pressure swirl atomizer is tted to inject the fuel.Therefore, the primary air ow regulates the stoichiometry of fueland oxidizer in the ame zone while, the secondary air contributesin cooling the combustor wall and diluting the product gas mix-ture. The two-equation soot formation model following Brookesand Moss [19] has been adopted along with the soot oxidationmodel due to Fennimore and Jones [22]. The model parametershave been suitably chosen by matching the predicted soot resultswith the experimental data for kerosene ame. Radiation heattransfer has been modeled using the discrete ordinate (DO) model[29]. Experiments have been conducted to nd out the initial sprayconditions, like spray cone angle and injection pressure differen-tial, which are required as input to the model. Further experimentshave also been conducted in a combustor of the same geometry toget results for model validation. Finally, soot distribution in thecombustor and distributions of incident radiation heat ux andthe temperature on the combustor wall and fuel injector are com-pared for different primary to secondary air ow splits usingnumerical predictions.

2. Model

A numerical model of the spray combustion process in the com-bustion chamber is developed in three dimensions taking into ac-count the geometry of the swirler. The combustion chamber is0.1 m in diameter (D) and 0.5 m in length from the plane of theswirler (Fig. 1). The inlet plane to the computation domain isFig. 1. Physical geometry of thframe of reference taking into consideration the source terms forthe inter-phase transport from the liquid phase. The general formof the Favre-averaged conservation equation for variables (~/) inthe gas phase can be written as.

@

@tq~/ @

@xjq~uj~/ @

@xjC/;eff

@~/@xj

! Sg Sl 1

The terms on the left hand side of the above equation representthe temporal variation and advective transport of the variables,respectively, while the terms on the right hand side are the diffu-sive transport, gas phase source (Sg) and inter-phase source (Sl).The variables ~/ for the different gas phase conservation equationsalong with the respective gas phase and inter-phase source termsa pressure swirl atomizer. This model has been subsequently usedby various researchers for computing dispersion and combustionof spray from swirl type atomizers [32,33]. The motion of the evap-orating droplets in the continuous gas phase is tracked stochasti-cally using an EulerianLagrangian approach and the inter-phasetransport terms are suitably accounted for use in the gas phaseconservation equations. The gas phase combustion reactions areassumed to be innitely fast in comparison to the transport pro-cesses so that local chemical equilibrium among the species isreached. An assumed b-pdf is considered to statistically correlatethe average concentrations of the species with the mean mixturefraction computed from the model. The entire computation hasbeen conducted using the Ansys Fluent commercial software(version 13.0).

2.1. Gas phase ow modelse combustor under study.

S0

SG

C

0

C

eatare listed in Table 1. The term C/;eff leff =r/;eff in Eq. (1) charac-terizes the effective diffusivity for the variable ~/ in turbulent ow.The effective dynamic viscosity (leff = l + lt) accounts the molecu-lar diffusivity (l) and the eddy diffusivity (lt), where the latterterm is given by lt Clq ~k

2

~e . The term r/,eff represents the effectivePrandtl/Schmidt number for the uid.

In the present model, the turbulent ow variables (~k; ~e) aresolved using realizable ke model [30]. In this model, a variableCl is considered in the expression of eddy viscosity to ensure real-izability even at large mean strain rate avoiding negative normalstress and satisfying Schwarzs inquality for shear stresses. More-over, the source terms of the dissipation (~e) equation are differentin realizable ke model, compared to the standard model, in orderto make the equationmore robust. The energy equation is solved tond out the average enthalpy at each grid point. Radiative heat ex-change occurs as the gas phase source term (Srad) in the energyequation.

2.2. Spray atomization model

The liquid fuel is injected into the combustor through a pres-sure swirl atomizer tted at the center of the swirler. The massow rate of the liquid ( _mf ), injector orice diameter (dor), injectionpressure differential (Dpinj) and spray cone angle (2h) have been gi-ven as input to the model. These quantities are obtained from sep-arate experiments performed in a test rig for spray with a pressureswirl atomizer. The transition from the internal hydrodynamicswithin the atomizer to the fully developed spray occurs in threesteps: sheet formation at the atomizer exit, sheet breakup andatomization. These steps have been modeled using the linearizedinstability sheet atomization (LISA) model [31], considering pri-mary atomization following breakup to form the spray. Secondaryatomization, coalescence and collision of the droplets in the sprayhave been neglected.

In the model, the injection velocity of the liquid at the atomizer

Table 1Gas and liquid phase source terms for the gas phase governing equations.

Conservation of ~/

Mass 1

Momentum ~ui

Energy ~hTurbulent kinetic energy ~kDissipation rate of turbulent kinetic energy ~e

Mixture fraction ~nMixture fraction variance ~n002

146 P. Ghose et al. / International Journal of Hexit is calculated using the injection pressure differential and thecoefcient of discharge (Cd) of the nozzle in use as,

Uinj Cd2Dpinjqf

s2

A mass balance of the liquid fuel at the atomizer exit evaluatesthe thickness of the liquid sheet (t) emanating from the nozzle as,

_mf pqf Uinj cos htdor t 3From the knowledge of the liquid sheet thickness and sheet veloc-ity, the breakup of the liquid sheet leading to the formation of drop-lets is modeled. The liquid sheet rst breaks up into ligaments as aresult of growth of the instabilities developing on the liquid surface.The ligaments, in turn, further break up into drops. The linear stabil-ity analysis of Senecal et al. [34] is used for investigating the insta-bility of the liquid sheet. Since the liquid sheet thickness is muchsmaller than the mean radius of the sheet, for the purpose of stabil-ity analysis, the curvature of the liquid sheet is neglected and theresults for planar liquid sheet moving with a prescribed velocity Uinjin a stationary gas phase is used. The sinuous mode of instabilitydominates over the varicose mode at low velocities and low gas-to-liquid density ratios while the two modes become indistinguish-able at large velocities. Hence instability of only sinuous mode isused for the instability analysis. Following Senecal et al. [34], thedispersion relation is given by

xr 2mlk

2w tanh kw

t2

tanh kw t2

Q

4m2l k

4wtanh

2 kw t2 Q2U2k2w tanh kw t2 Q QU2k2wrk3w=qlq

tanh kw t2 Q

4

In deriving the above equation, second order terms in viscosity havebeen neglected as they are very small in value. For Weber numberWeg > 2716, a condition satised by most modern pressure-swirlatomizers, the most unstable waves are short waves. For shortwaves, the ligament diameter is assumed to be proportional tothe most unstable wavelength that breaks up the sheet. Thus theligament diameter is given by

dL 2pCLkwcrit5

In the above equation, kwcrit is the most unstable wavenumber givingthe highest growth rate as obtained from the dispersion relation. CLis a ligament constant, considered as 0.5. The breakup of the liga-ment into drops is obtained fromWebers analysis for capillary jets.The resulting drop size is given by

do 1:88dL1 3Oh1=6 6In the above equation, Oh is the Ohnesorge number dened as

1/2

g Sl

_S@@xi

p 23 q~k 23leff@~uj@xj

@

@xjleff

@~ui@xj

@~uj@xi

h i_SM ~ui _S

_rad

_SE ~h _Sk q~e ~k _S1 qS~e C2 q ~e2~k m~ep , where S = 2SijSijp and Sij = 1

2@~ui@xj

@~uj

@xi

~e _S~n _S

g1lt@~n002@xj

2 Cg2 ~e~k q~n002 ~n002 _S

and Mass Transfer 74 (2014) 143155Oh = ll/(qlrsdL) .The initial size distribution of the droplets in the spray follow-

ing atomization is considered using the RosinRammler distribu-tion function. The droplet diameter following breakup (do) isconsidered as the size parameter of the distribution function, whilethe dispersion parameter is taken as 3.5 [35].

2.3. Liquid phase ow model

In order to compute the inter-phase source terms over the lifetime of the droplets, the spray is considered to comprise of a nitenumber of droplet classes distributed over an initial dispersion an-gle. The velocity, mass and temperature histories of each of thedroplet classes are obtained along their trajectories using therespective conservation equations in a Lagrangian frame.

The trajectory of a droplet of the kth class is computed by eval-uating the velocity and position along its motion. The velocity of

The instantaneous production rate of soot mass per unit volume

Heatthe droplet is found out from the conservation of momentumequation considering only inertia and drag forces to be signicant.The equation can then be written as,

mdkdupi kdt

p8

qdk2jui upi kjui upi kCdrag 7

where, Cdrag is the drag coefcient on the droplet, which is evalu-ated following the spherical drag law [36]. The effect of gas phaseturbulence on the droplet dispersion is simulated using a stochasticapproach. Instantaneous gas phase velocity (ui) around the dropletis obtained in the above equation by computing the uctuatingvelocity following a discrete random walk model. The position ofthe droplet is obtained by integrating the velocity over short timerange. If any droplet, in course of its motion, strikes the combustorwall, it is assumed to reect from the wall following elasticcollision.

Evaporation of the liquid from the surface of the droplets takesplace considering the vapor pressure on the droplet surface to beequal to the saturation pressure at the droplet temperature. Apiecewise linear variation of the saturation pressure for the liquidfuel with temperature is considered for evaluation. The mass trans-fer coefcient (hD) is calculated from the Sherwood number corre-lation of Ranz and Marshall [37]. The change in droplet mass cantherefore be accounted as,

dmpdt

pd2phDCfs Cf 8

where, Cfs and Cf are the mass fractions of the fuel vapor on thedroplet surface and in the surrounding gas.

In order to nd out the variation of temperature of the dropletan energy balance across the droplet surface is considered as,

mpcppdTpdt

hApT Tp dmpdt DHv 9

The heat transfer coefcient (h) is found out from the Nusselt num-ber correlation of Ranz and Marshall [37] and the radiation ex-change with the gas phase is neglected.

The liquid phase conservation equations are solved for each ofthe droplet classes along their trajectory till the class gets evapo-rated. The inter-phase source terms for mass, momentum and en-ergy are accordingly computed at different grid points dependingupon the positions of the droplets and are used in the gas phaseequations.

2.4. Equilibrium presumed probability density function model

The equilibrium presumed probability density function modelis used to obtain the mean values of species concentration, temper-ature and density in the gas phase from the mixture fraction values[38]. Mixture fraction is dened as the elemental mass fractionoriginated from the fuel, which enters the gas phase within thecomputational domain due to evaporation of the liquid droplets.The combustion reactions take place in the gas phase and thekinetics of reactions are assumed to be fast enough to reach equi-librium provided the local fuel air ratio remains within a rich am-mability limit (Equivalence ratio at RFL = 1.5). Beyond this limit,the mixing of species in the gas phase is only considered withoutany chemical reaction. The instantaneous species concentration,temperature and density in the gas phase have been computedas functions of mixture fraction considering chemical equilibriumand heat transfer from the system. Sixteen chemical species (O2,N2, C12H23, CO2, CO, H2O, H2, OH, H, O, HO2, H2O2, HCO, CHO,HONO, HCOOH) have been considered in the equilibrium product

P. Ghose et al. / International Journal ofmixture following chemical reaction.The Favre averaged mixture fraction and its variance are ob-

tained within the combustor by solving their respective equations(M) is expressed as,

dMdt

CaMp XC2H2PRT

exp TaT

Cc XC2H2PRT

exp TcT

pN1=3 6M

qsoot

2=3" #n

CoxidCxgcollXOHPRT

T

ppN1=3 6M

qsoot

2=313

The model constants Ca and Cc for nucleation and surfacegrowth have been given in the work of Brookes and Moss as54 s1 and 11700 kg m kmol1 s1, respectively, for methaneame. The model constants Ca and Cc are modied, consideringthe fact that these two kinetic dominated processes will have dif-ferent rates in a kerosene ame from the rates in a methane ame.with source terms listed in Table 1. The density-weighted averagevalues of species concentration, temperature and density are ob-tained assuming local beta-probability density function ePn inturbulent reacting ow as,

~/ Z 10

/nePndn 10Local beta pdfs, ~Pn, are constructed in terms of mean mixture frac-tion and its variance as,

ePn na11 nb1R 10 n

a11 nb1dn11

where, a ~n ~n1~n~n002 1h i

and b 1 ~n a~n

2.5. Soot model

Soot formation chemistry in hydrocarbon ame is much slowercompared to the combustion reactions and is separately modeled.We have adopted the BrookesMoss model [19] of soot formationin a turbulent ame. The model solves two soot quantities, sootnumber density (N) and soot mass concentration (M) within thecombustion chamber. These two quantities are evaluated consider-ing separate model expressions for nucleation, coagulation, surfacegrowth and oxidation. While the nucleation and coagulation inu-ence the number density of the soot particles, the soot mass con-centration depends on nucleation, surface growth and oxidation.Acetylene is considered as the precursor species both for nucle-ation and surface growth. The equilibrium chemistry modeladopted in the gas phase does not solve acetylene as a product spe-cies. Moss and Aksit [24] presented a variation of acetylene con-centration against mixture fraction as a amelet relation forkerosene surrogate fuel. We have used these data to form a corre-lation which computes the acetylene concentration from the mix-ture fraction value in a kerosene ame. A mixture fraction basedprobability density function approach is adopted to compute thesoot formation accounting the turbulence-chemistry interaction.

The soot model of Brookes and Moss calculates the instanta-neous production rate of soot particles number density (N) as,

dNdt

CaNA XC2H2PRT

exp TaT

Cb 24RTqsootNA

1=2d1=2psootN

2 12

and Mass Transfer 74 (2014) 143155 147The modied constants are xed by comparing the predicted re-sults with the experiments conducted in a turbulent non-premixedame of kerosene vapor and air [23].

sidered as opaque and diffuse with an internal emissivity denedfor stainless steel [39]. A mixed heat transfer boundary condition,

eat2.6. Radiation model

The radiation calculation within the combustor has been per-formed assuming the medium to consist of participating gasesand soot in which scattering is neglected (considering the particlesto be extremely ne and dispersed). The solution for radiative ex-change has been done using discrete ordinate model [26,39,40] andthe non-gray behavior of the gases has been accounted byweighted sum gray gas model (wsggm) [39].

In the discrete ordinate method, a discrete representation of thedirectional variation of the radiative intensity is considered. Theradiative transfer equation is solved for a set of n discrete direc-tions s^i; i 1;2;3 . . . n spanning over the total range of solid an-gle 4p. The equation for a particular direction is given as,

s^i:rIi jIb Ii 14where, Ii is the radiation intensity in the ith direction, j is theabsorption coefcient and Ib is the blackbody radiation intensity.The absorption coefcient has both gas phase and particle (soot)phase contributions expressed as,

j jgas jsoot 15The gas phase contribution of the absorption coefcient (jgas)

has been modeled using weighted sum of gray gas model (wsggm)with the constant gray gas absorption coefcients (jk) for the par-ticipating gases (k = 1K) along with suitable weighting factors (ak)as,

jgas ln 1PKk0ak1 ejkpzh i

z16

where, p is the total partial pressure of all the absorbing gases and zis the path length, which is considered as the mean beam lengthcorresponding to the combustor geometry [39]. The model consid-ers the contributions of carbon dioxide and water vapor in the gasphase for the absorption coefcient. The weighting factors are takenas temperature dependent polynomial functions [41] as,

ak X

bk;jTj 17

The absorption coefcient contributed by soot (jsoot) is foundfrom the equation,

jsoot 1232:4qsootb1 4:8 104T 2000c 18The radiative source term (Srad) in the energy equation is com-

puted as the divergence of the radiative heat ux vector as,

Srad r:qrad j 4rT4 XNi1

wiIi

!19

where, wi is the quadrature weight associated with the direction i inthe discrete ordinate method [39].

3. Numerical model, operating parameters and boundaryconditions

The governing equations have been solved using the pressurebased, steady solver in Ansys Fluent 13.0. The pressure velocitycoupling in the gas phase has been accounted with the SIMPLEalgorithm. The terms in the governing equations have been discret-ized by the power law scheme while, the radiation model equationis discretized using second order upwinding scheme. The Eulerianand Lagrangian phase calculations have been performed in an iter-ative way with 200 continuous phase iterations per particulate

148 P. Ghose et al. / International Journal of Hphase iteration. Twenty discrete classes of droplets have been in-jected initially within a dispersion angle of 6. The discrete ordi-nate model of radiative transfer considers 5 divisions in the polarconsidering both radiation and convection from the surface, is ap-plied on the outer peripheral wall of the combustor. The wall bodyis of stainless steel with 5 mm thickness. The emissivity of the out-er wall surface is taken as equal to the inner surface and a convec-tive heat transfer coefcient is assumed, which results in a balanceof energy owing out from the combustor. However, the injectorand the other solid walls are considered as adiabatic.

4. Experimental

Sample experiments have been performed in test rigs to gener-ate the spray data required for the model and also for the valida-tion of combustion model predictions. The spray data areobtained by conducting experiments in a spray test rig. The detailsof the spray test rig are given in a separate publication [42]. In thetest rig, kerosene is injected through the pressure swirl atomizerunder consideration to generate sprays in open atmosphere. Theinjection pressure is measured by tting a calibrated pressuregauge just before the nozzle and the corresponding volume owrate is measured by collecting the liquid in a measuring ask overdenite time. The coefcient of discharge of the nozzle is found outfrom the measured values of volume ow rate and injection pres-sure differential. The spray cone angles are measured by obtainingthe spray images using a light sheet and a camera.

In another experiment conducted in the model combustor, hav-ing the same geometry and shape as used in the computation, akerosene spray ame is established with the same pressure swirlatomizer as used in the spray test rig. The primary and secondaryair ow supplies to the combustor and the ow rates are measuredby orice meters. The fuel ow rate is measured using a calibratedrotameter. In order to measure the combustor wall temperature,eight thermocouples (K-type) are tted with silicon heat sink com-pound close to the inner wall surface at an interval of 50 mm in theaxial direction. A traversing thermocouple near the exit plane mea-direction and 5 divisions in the azimuthal direction of every octantaround the control volume for radiation computation. Thus a totalof 200 angular directions over the solid angle 4p have been takenin the model.

The total mass ow rate of air _mair into the combustor is set at0.04 kg/s, which is entering the combustor at 300 K. The Reynoldsnumber (Re 4 _mair=pDl) based on the air ow inlet conditionsand combustor diameter is 26,300. The air ow is split betweenthe primary and secondary streams at the entry to the combustor.Three different air ow splits, with primary:secondary as 30:70,40:60 and 50:50, have been considered in the analysis. A constantangle (60) vane swirler is tted at the entry of the primary streamto the combustor (Fig. 1). However, the inlet plane of computationis considered at 40 mm upstream to the swirler plane. The fuel, at300 K temperature, is injected through a 0.25 mm diameter oriceof the pressure swirl atomizer at a rate of 0.00036 kg/s in all thecases. The spray cone angle and the injection pressure differentialcorresponding to the liquid ow rate through the atomizer areexperimentally obtained to feed to the model.

The plug ow velocity boundary condition is considered at theinlet planes of both primary and secondary streams, depending ontheir respective ow rates. A 4% turbulent kinetic energy and a tur-bulent length scale of 0.007 m are set at the inlet boundaries.Atmospheric pressure boundary condition is considered at the out-let plane of the combustor.

The inner surface of the peripheral wall of the combustor is con-

and Mass Transfer 74 (2014) 143155sures the variation in exit gas temperature from the centerline tothe wall. Radiation correction has been done for these thermocou-ples to get the measured gas temperatures at different radial loca-

tions. The temperature variations along the wall and in the exit gasare used for the validation of the model predictions.

5. Results and discussion

5.1. Validation of soot model

It has been pointed out in the introduction that most of the sootmodels have been formulated for predictions in gaseous hydrocar-bon ames, like methane and ethylene ames. The works of Mossand Aksit [24] and Wen et al. [23] showed that it is possible to usethe existing soot models, developed for gaseous fuels, in keroseneames by suitably adjusting the empirical model parameters.Accordingly, we have used the soot model proposed by Brookesand Moss [19] for the kerosene spray ame along with the soot oxi-dation model of Fennimore and Jones [22]. The model parametersare adjusted to match the experimental data of kerosene non-pre-mixed ame. In order to x the model parameters we have simu-lated the turbulent, non-premixed ame of Wen et al. [23], withkerosene vapor as fuel in a co-axial burner. However, the othermodels like the realizable ke model, discrete ordinate radiationmodel and the equilibrium presumed probability density functionmodel, as described earlier have all been incorporated in thecomputation.

Fig. 2(a) shows the predicted centerline distribution of soot vol-ume fraction above the burner for the experimental conditionsconsidered by Wen et al. The experimental data points have alsobeen plotted in the gure. It is shown in the gure that too little

soot is predicted in the combustion zone with the values of modelconstants proposed by Brookes and Moss for methane ame. In or-der to predict the soot according to the experiment, we have variedthe model constants Ca and Cc and compared the results with theexperiments. With a Ca = 324 s1 and Cc = 70200 kg m kmol1 s1

the predicted results agree reasonably well with the experiments,particularly in the upstream region, closer to the burner. We have,therefore, considered the Brookes and Moss soot model with acet-ylene as precursor species and modied empirical constants in theprediction of kerosene spray ame.

Fig. 2(b) shows the variation of predicted soot volume fractionusing the modied empirical constants as a function of radial dis-tance at a height of 100 mm from the inlet plane. The correspond-ing experimental data measured by Wen et al. [23] is also plotted.The results indicate qualitative agreement showing the peak vol-ume fraction away from the axis. The predicted peak volume frac-tion value comes quite close to the experimental peak. In fact theagreement between the peak volume fractions in the distributionis much better than those in the work of Wen et al. Thus the modelof soot for the kerosene ame justies its applicability.

5.2. Validation of numerical model

Subsequent to the selection of the soot model parameters, wehave computed the spray combustion of kerosene fuel in themodel combustor considering the soot formation in ame. Exper-iments have been performed in the model combustor under thesame ow and spray conditions as in computation and with one

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(a)Fig. 2. Comparison of predicted and measured soot volume fractions along the (a)centerline and (b) radial direction at 100 mm above inlet of Wen et al. ame.-0.05

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(m) No. of elements = 254720

No. of elements = 324394

No. of elements = 462875

(a)

(b)

Fig. 3. Comparison of predicted values of (a) wall temperature along the length ofthe combustor, (b) exit gas temperature across the radial direction for threedifferent grid congurations.

air ow split (50:50 between primary and secondary). Validationof the model predictions has been made by comparing the pre-dicted temperature distributions along the wall and across theexit plane against the experimental values. A grid independencetest is rst done by rening the grid over the computational do-main and by observing the variation in predicted temperaturesalong the wall (Fig. 3a) and over the exit plane (Fig. 3b). Anunstructured, quadrilateral mesh conguration is chosen with254,720, 324,394 and 462,875 elements in the domain. It is foundfrom the gures that with the rst renement of the grid (from254,720 to 324,394 elements) the maximum changes in the walltemperature and the exit gas temperature are found to be 5.6%and 8.2%, respectively. While with further renement (from324,394 to 462,875 elements), the above two peak variationscome down to 2.2% and 1.2%, respectively. Considering these,we have nally chosen the grid conguration with 324,394 ele-ments in the mesh for further computation.

The variations in temperature along the combustor wall(Fig. 4a) and in the exit gas (Fig. 4b) with the chosen grid congu-ration agree quite well with the measured values. A discrepancy inthe temperature prediction is noticed on the wall around the amezone, and may be attributed to the variation in radiative heattransfer from the ame. The predicted temperature distributionin the exhaust gas agrees very well with the experiments overthe entire cross-section of the combustor. Overall considering allthe compared variations of temperature, it can be concluded thatthe adopted spray combustion model predicts the parameters rea-sonably well in the combustor.

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Fig. 4. Comparison of predicted and measured values of (a) wall temperature alongthe length of the combustor, (b) exit gas temperature across the radial direction.5.3. Velocity and temperature distributions in the combustor

We have applied the spray combustion model to predict resultswith different air ow splits between the primary and secondarystreams. The total air and fuel ow rates are maintained samewhile, three different primary air to secondary air ow ratios(30:70, 40:60 and 50:50) have been considered. As the primaryair fraction is increased the stoichiometry in the ame region be-comes leaner. This alters the structure of the ame and the velocityand temperature distributions in the ame region. However, thecorresponding reduction in the secondary air ow rate reducesthe momentum in the ow adjacent to the combustor wall, affect-ing the ow mixing and the convective cooling of the combustorwall.

Fig. 5(ac) shows the mean velocity and temperature distribu-tions in the vertical plane passing through the axis of the combus-tor for the three different air ow splits. The axial distance in thegures has been measured from the plane of the swirler/atomizer,where x = 0 is considered. The highest temperature zones in thegures, adjacent to the fuel injector, depict the ame regions. Itis clearly evident from the gures that the ame becomes shorterin size with the increase in the primary air. The primary air isadmitted in the combustor with a swirling motion casuing a toroi-dal recirculating zone about the axis adjacent to the fuel injector.When the primary air ow rate increases the tangential momen-tum in the inlet stream also increases, and it generates a strongercentral recirculation zone. Under the inuence of the strong swirl-ing motion, the mixing process intensies in the ame zone. Thekinetics of the reactions is considered to be very fast and thereforethe overall combustion rate is controlled by the rates of physicalprocesses. At higher primary air ow, the increased rates of thephysical processes, like vaporization and mixing, increase the over-all reaction rate in the combustor. As a result, the ame becomesshorter with increase in the primary air. When the primary air frac-tion is 50% of the total ow rate, the central recirculation bubble isso strong that it breaks the ame bubble on the axis and the high-est temperature ame zone is conned within an annulus close tothe inlet (refer Fig. 5(c)). The ame is short and intense in this casedue to the increased rates of the physical processes. All the temper-ature contours further show that there is only a little deviationfrom axi-symmetry within the combustor. A closer look revealsthat the deviation somewhat increases with the increase in pri-mary air fraction in the combustor.

Fig. 6 compares the centerline temperature variations in thecombustor for the three different air ow splits. It is seen that inall the cases, the temperature at the plane of the atomizer (x = 0)is somewhat high. It rst decreases over a very short length inthe downstream direction and then increases to reach a peak value.Subsequently, the temperature decreases again till the combustorexit plane is reached. The temperature on the atomizer surface ishigh because of the incident radiation from the ame. The peakcenterline temperature is the maximum for the 40:60 ow splitcase, though in the 30:70 ow split case the maximum tempera-ture is reached at a further downstream location. In case of50:50 air ow split, the maximum centerline temperature is muchlower and occurs closer to the inlet plane. This variation in the cen-terline distributions can be clearly explained from the respectivetemperature contour plots. For the 30:70 and 40:60 air ow splits,the maximum temperature zones are located on the centerline. Onthe other hand, in the 50:50 case, the maximum temperature zoneoccurs in an annulus, which is away from the center, and the peakcenterline temperature is much less.

The variation in gas temperature at the combustor exit often

and Mass Transfer 74 (2014) 143155has signicance. In case of gas turbine, the exit gas temperaturedistribution depicts the combustor pattern factor. A low patternfactor, signifying more uniform exit gas temperature, is desirable

HeatP. Ghose et al. / International Journal offor the health of the turbine. Fig. 7 shows the radial variation of thegas temperature at the exit to the combustor for the three differentair ow splits. More uniform temperature variation is obtainedwhen the air ow split is 50:50. As the primary air fraction is less,the peak temperature at the exit plane, occurring at the axis of thecombustor, increases and the non-uniformity in the temperaturedistribution becomes more. This is because of the fact that in thecase of 30:70 air ow split, the ame is longer and the maximumtemperature in the combustor occurs closer to the exit plane.Therefore, the distance available to transport the energy in the lat-eral direction becomes considerably shorter. As a result, greaternon-uniformity in the temperature distribution prevails at the exitplane. When the primary air fraction increases to 40% of the totalair ow, the ame shortens in length and the maximum tempera-

Fig. 5. Velocity vector and Temperature distributions across the vertical plane through thstreams (a) 30:70, (b) 40:60 and (c) 50:50.

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Fig. 6. Variation of centerline temperature along the length of the combustor fordifferent air ow splits between primary and secondary streams.and Mass Transfer 74 (2014) 143155 151ture on the centerline occurs earlier along the combustor. The tem-perature variation attens at the exit due to increased transport ofenergy in the radial direction. In the third case of 50% primary air,the maximum temperature is reached even earlier and at an off-axis location. Therefore, not only the axial length available for en-ergy transport is more but also the radial distance over which en-ergy has to be transported becomes less. As a result, the mostuniform exit temperature distribution among the three cases is ob-tained with the 50:50 air ow split.

5.4. Soot distribution in the combustor

The soot distributions in the combustor are plotted in Fig. 8(ac) for the three different air ow splits. The soot laden zone is pro-

e combustor axis for three different air ow splits between primary and secondary

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Fig. 7. Variation of exit gas temperature from the combustor at three different airow splits between primary and secondary streams.

usto

152 P. Ghose et al. / International Journal of HeatFig. 8. Soot volume fraction distributions across the vertical plane through the comb30:70, (b) 40:60 and (c) 50:50.longed and the peak soot volume fraction is more when the pri-mary air fraction is less. This is due to the fact that with the lowerprimary air, the soot precursor concentration in the ame regionincreases. The higher precursor concentration along with the ex-tended high temperature zone results in increased formation ofsoot over the combustor. It is further to be noted from the soot dis-tribution patterns that, under all the three cases, the maximumsoot volume fraction occurs on the centerline of the combustor.

Fig. 9 shows the variation of soot volume fraction on the center-line of the combustor for three different air ow splits. The peaksoot volume fraction on the centerline is about 9 times higher inthe 30:70 split case and more than 5 times higher in the 40:60 splitcase, compared to the 50:50 split case. Furthermore, it is seen fromthe soot contours that the concentration of soot near the fuel

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Fig. 9. Variation of soot volume fraction along the combustor centerline for threedifferent air ow splits between primary and secondary streams.r axis for three different air ow splits between primary and secondary streams (a)and Mass Transfer 74 (2014) 143155injector (x = 0) remains quite high. This results in the depositionof considerable soot on the atomizer body after continuous opera-tion, which is also evident in the experiments. The higher soot vol-ume fraction near the atomizer with lower primary air results infaster build up of soot on the atomizer surface. When the soot buildup becomes large, the atomization quality of the fuel suffers andthe combustion gets affected.

5.5. Temperature and incident radiative heat ux on combustor walland fuel injector

The soot laden gas at high temperature causes increased radia-tion from the ame zone. The concentration of soot in the amezone is dependent on the quantity of primary air supplied to thecombustor. On the other hand, the secondary air, which entersalong the outer wall of the combustor, helps to keep the wall sur-face cool. Therefore, the split between the primary and secondaryair ow into the combustor will have an effect on the combustorwall and fuel injector surface temperatures.

This is evident in Fig. 10(a), which plots the variation of incidentradiative heat ux on the combustor peripheral wall for the threedifferent air ow splits. Taking into account that there is not muchdeviation from symmetry in the temperature distribution, the plothas been made only along a line in the axial direction. The corre-sponding wall surface temperatures are plotted in Fig. 10(b). It isclearly evident from Fig. 10(a) that the highest radiative ux onthe wall is incident around the ame close to the inlet to the com-bustor. This is caused by the high temperature of the ame and thehigh luminous radiation from the soot present in the ame zone. Atthe downstream location, the radiative ux on the wall is mostlyfrom the participating gases in the ow. The maximum incidentheat ux due to radiation on the peripheral wall is achieved whenthe primary air ow is 30% of the total air ow. The soot volume

fraction in the ame is much higher in this case, which is the primereason of the increased radiative ux. The maximum incident radi-ation decreases by more than 50% when the primary air fraction isincreased to 50% of the total ow. However, the peripheral wall ofthe combustor is cooled convectively by the ow of secondary airadjacent to the wall. The secondary air enters the combustor co-axially with the primary air ow and grazes along the wall, whileexchanging energy with the high temperature core as well as withthe combustor wall. When the primary air fraction is more, thefraction of the secondary air is less and it gives less convectivecooling of the wall. Fig. 10(b) shows the distribution of wall tem-perature along the length of the combustor. The wall temperatureis seen to increase along the combustor length in all the threecases. However, the highest wall temperature is attained withthe 50:50 air ow split and the lowest with 30:70 split. This isattributed to the fact that even with a much higher incident radi-ation in the 30:70 ow split case, the higher convective coolingdue to increased secondary air ow keeps the wall at a lower tem-perature. On the contrary, though in the 50:50 case, the maximumradiative ux incident on the wall is low, but the wall temperaturereaches a higher value as the secondary air ow adjacent to thewall is less.

It is also signicant to study the incident heat ux and the sur-face temperature on the fuel injector considering the life of theinjector. Figs. 11 and 12 show the incident radiation ux and sur-face temperature, respectively, on the swirlerinjector assembly atthe inlet to the combustor for the three different cases of air owsplits. It is clearly seen that the fuel injector is the more critical partthan the swirler as it receives more radiative heat ux and attains a

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(b)Fig. 10. Variation of (a) incident radiation, (b) outer wall temperature along thecombustor length for three different air ow splits.

Fig. 11. Distributions of incident radiation on the swirlerinjector planes for three differ(c) 50:50.

Fig. 12. Temperature distributions across the swirlerinjector plane for three different a50:50.

P. Ghose et al. / International Journal of Heat and Mass Transfer 74 (2014) 143155 153higher temperature. On the other hand, the primary air, which di-rectly ows over the swirler keeps the surface of the swirler cool.The incident radiation on the fuel injector is the highest for thecase of lowest primary air fraction (Fig. 11(a)) due to increasedradiation from the ame. This is attributed to the higher soot con-

ent air ow splits between primary and secondary streams (a) 30:70, (b) 40:60 andir ow splits between primary and secondary streams (a) 30:70, (b) 40:60 and (c)

laboratory.The model combustor under consideration has an air ow split

eatbetween primary and secondary streams entering co-axially. Theeffect of air ow distribution on different combustor parametershas been investigated by considering three primary to secondaryow rates as 30:70, 40:60 and 50:50. The results show that asthe proportion of the primary air increases from 30% to 50% ofthe total air ow, the ame becomes more compact. This leads toless soot production in the ame zone and a more uniform temper-ature pattern factor at the combustor exit. With the reduction insoot formation, the incident radiative heat ux decreases withthe increase in primary air fraction. The increase in primary airfrom 30% to 50% of the total air ow reduces the maximum inci-dent heat ux on the peripheral wall by more than 50%. However,reduction in the air ow rate near the combustor wall leads tohigher wall temperature, particularly close to the inlet. In addition,the lower soot formation in the ame at higher primary air fractiondecreases the radiative heat ux from the ame on the injector sur-face by more than 25%. However, the convective heat transfer tocentration in the ame in this case. The high incident radiationcauses the fuel injector surface temperature to reach a value above1100 K in this case (Fig. 12(a)). The incident radiation ux on theinjector surface reduces as the primary air fraction is increased(Fig. 11(b and c)). However, the surface temperature distributionson the injector (Fig. 12(b and c)) do not show a decrease in valuefor the corresponding cases. This may be attributed to the strongerconvective heat transfer with the increase in primary air fraction.When the primary air ow rate increases, the central recirculationzone established on the combustor axis becomes more intensied.As a result, the high temperature gas from the downstream owsback with a higher velocity towards the injector. The resultinghigher convective heat transfer offsets the lower incident radiativeheat ux and maintains the injector nearly at the same high tem-perature for all the three cases. Thus the fuel injector remains asthe more critical component of the combustor and its materialhas to be selected properly to save it from failure.

6. Conclusions

In the present work, a numerical model has been developed forsimulating spray combustion in a model gas turbine combustor.The model includes sub-models for soot formation and radiationheat transfer both from the ame and the soot particles. A Favre-averaged transport model is used for the turbulent ow with tur-bulence modeled by realizable ke model. Turbulent combustionis represented using equilibrium presumed probability densityfunction and BrookesMoss model was adopted for the soot forma-tion with model parameters suited for kerosene ame. The solutionfor radiative exchange has been done using discrete ordinate mod-el and the non-gray behavior of the gases has been accounted byweighted sum gray gas model (wsggm). Lagrangian approach hasbeen used for modeling the liquid phase transport using expres-sions pertinent to isolated droplets for drag, heat transfer andevaporation. The spray formation from a pressure-swirl atomizerwas modeled using Linearized Instability Sheet Atomization (LISA)model for primary atomization. The initial size distribution of thedroplets in the spray following atomization is considered usingthe RosinRammler distribution function. The droplet diameterfollowing breakup (do) is considered as the size parameter of thedistribution function, while a xed value (3.5) is used for the dis-persion parameter. The model was validated with experimental re-sults both from the literature and obtained from a rig in our

154 P. Ghose et al. / International Journal of Hthe injector surface counterbalances the variation in radiative heatux and the injector surface temperature remains nearly the sameunder all the three air ow splits.Conict of interest

I, on behalf of my co-authors, certify that there is no conict ofinterest with any organization regarding the material discussed inthis manuscript.

Acknowledgment

This work has been supported by the Gas Turbine ResearchEstablishment, Govt. of India under the GATET scheme (Grant No.GTRE/GATET/CA07/1012/026/11/001).

References

[1] P. Moin, S.V. Apte, Large-eddy simulation for realistic gas turbine combustors,AIAA J. 44 (4) (2006) 698708.

[2] K. Luo, H. Pitsch, M.G. Pai, O. Desjardins, Direct numerical simulations andanalysis of three-dimensional n-heptane spray ames in a model swirlcombustor, Proc. Combust. Inst. 33 (2011) 21432152.

[3] C. Hollmann, E. Gutheil, Modelling of turbulent spray diffusion amesincluding detailed chemistry, Combust. Inst. (1996) 17311738. TwentySixth Symp. (Int) on Combustion.

[4] A. Datta, S.K. Som, Combustion and emission characteristics in a gas turbinecombustor at different pressure and swirl conditions, Appl. Therm. Eng. 19(1999) 949967.

[5] H. Watanabe, Y. Matsushita, H. Aoki, T. Miura, Numerical simulation ofemulsied fuel spray combustion with pufng and micro-explosion, Combust.Flame 157 (2010) 839852.

[6] G. Hsiao, H.C. Mongia, Swirl cup modeling part 3: grid independent solutionwith different turbulence models, in: 41st Aerospace Sciences Meeting andExhibit, AIAA Paper 2003-1349, 2003.

[7] D. Joung, K.Y. Huh, Numerical simulation of non-reacting and reacting ows ina 5 MW commercial gas turbine combustor, ASME Paper No. GT 2009-59987,2009.

[8] V.M Karim, M. Bart, D. Erik, Comparative study of k-e turbulence models ininert and reacting swirling ows, in: 33rd AIAA Fluid Dynamics Conferenceand Exhibit, Paper No. AIAA 2003-3744, 2003.

[9] G.M. Faeth, Mixing, transport and combustion in sprays, Prog. Energy Combust.Sci. 13 (1987) 293345.

[10] Kenneth K. Kuo, Ragini Acharya, Fundamentals of Turbulent and MultiphaseCombustion, John Wiley & Sons Inc., 2012, pp. 509575.

[11] M. Hallmann, M. Scheurlen, S. Wittig, Computation of turbulent evaporatingsprays: Eulerian versus Lagrangin approach, ASME J. Eng. Gas Turbines Power117 (1) (1995) 112119.

[12] H. Richter, J.B. Howard, Formation of polycyclic aromatic hydrocarbos andtheir growth to soot a review of chemical reaction pathways, Prog. EnergyCombust. Sci. 26 (2000) 565608.

[13] Z.A. Mansurov, Soot formation in combustion processes, Combust. Explo.Shock Waves 41 (6) (2005) 727744.

[14] H. Richter, S. Granata, W.H. Green, J.B. Howard, Detailed modeling of PAH andsoot formation in laminar preliminary mixture benzene/oxygen/argon at lowpressure ame, Proc. Combust. Inst. 30 (2004) 13971405.

[15] C.S. McEnally, L.D. Pfefferle, B. Atakan, K. Kohse-Hoinghaus, Studies ofaromatic hydrocarbon formation mechanisms in ames: progress towardsclosing the fuel gap, Prog. Energy Combust. Sci. 32 (2006) 247294.

[16] I.M. Kennedy, W. Kollmann, J.Y. Chen, A model for the soot formation inlaminar diffusion ame, Combust. Flame 81 (1990) 7385.

[17] K.M. Leung, R.P. Lindstedtand, W.P. Jones, A simplied reaction mechanism forsoot formation in nonpremixed ames, Combust. Flame 87 (1991) 289305.

[18] J. B Moss, C.D. Stewart, K.J. Young, Modeling soot formation and burnout in ahigh temperature laminar diffusion ame burning under oxygen-enrichedconditions, Combust. Flame 101 (1995) 491500.

[19] S.J. Brookes, J.B. Moss, Predictions of soot and thermal radiation properties inconned turbulent jet diffusion ames, Combust. Flame 116 (1999) 486503.

[20] K.B. Lee, M.W. Thring, J.M. Beer, On the rate of combustion of soot in a laminarsoot ame, Combust. Flame 6 (1962) 137145.

[21] J. Nagle, R.F. Strickland-Constable, Fifth Carbon Conference 1 (1962) 154164.[22] C.P. Fenimore, G.W. Jones, Oxidation of soot by hydroxyl radicals, J. Phys.

Chem. 71 (1967) 593597.[23] Z. Wen, S. Yun, M.J. Thomson, M.F. Lightstone, Modeling soot formation in

turbulent kerosene/air jet diffusion ames, Combust. Flame 135 (2003) 323340.

[24] J.B. Moss, I.M. Aksit, Modelling soot formation in a laminar diffusion ameburning a surrogate kerosene fuel, Proc. Combust. Inst. 31 (2007) 31393146.

[25] A.B. Al-Omari, K. Kawajiri, T. Yonesawa, Soot processes in a methane-fueledfurnace and their impact on radiation heat transfer to furnace walls, Int. J. HeatMass Transfer 44 (2001) 25672581.

[26] S.C. Paul, M.C. Paul, Radiative heat transfer during turbulent combustionprocess, Int. Commun. Heat Mass Transfer 37 (2010) 16.

and Mass Transfer 74 (2014) 143155[27] D. Byun, S.W. Baek, Numerical investigation of combustion with non-graythermal radiation and soot formation effect in a liquid rocket engine, Int. J.Heat Mass Transfer 50 (2007) 412422.

[28] L. Tesse, F. Dupoirieux, J. Taine, Monte Carlo modeling of radiative transfer in aturbulent sooty ame, Int. J. Heat Mass Transfer 47 (2004) 555572.

[29] G.D. Raithby, E.H. Chul, A nite volume method for predicting radiant heattransfer in enclosures with participating media, J. Heat Transfer 112 (1990)415423.

[30] T.H. Shih, W.W. Liou, A. Shabbir, Z. Yang, J. Zhu, A new k-e eddy viscositymodel for high Reynolds number turbulent ows, Comput. Fluids 24 (3) (1995)227238.

[31] D.P. Schmidt, I. Nouar, P.K. Senecal, C.J. Rutland, J.K. Martin, R.D. Reitz, Pressureswirl atomization in the near eld, SAE Paper No. 1999-01-0496, SAE, 1999.

[32] S.H. Bafekr, M. Shams, R. Ebrahimi, A. Shadaram, Numerical simulation ofpressure-swirl spray dispersion by using EulerianLagrangian method, J.Dispersion Sci. Technol. 32 (2011) 4755.

[33] S.H. Park, H.J. Kim, H.K. Suh, C.S. Lee, Atomization and spray characteristics ofbioethanol and bioethanol blended gasoline fuel injected through a directinjection gasoline injector, Int. J. Heat Fluid Flow 30 (2009) 11831192.

[34] P.K. Senecal, D.P. Schmidt, I. Nouar, C.J. Rutland, R.D. Reitz, M.L. Corradini,Modeling high-speed viscous liquid sheet atomization, Int. J. Multiph. Flow 25(1999) 10731097.

[35] A.H. Lefebvre, X.F. Wang, Mean drop sizes from pressure-swirl nozzles, J.Propul. Power 3 (1) (1987) 1118.

[36] S.A. Morsi, A.J. Alexander, An investigation of particle trajectories in two phaseow system, J. Fluid Mech. 55 (2) (1972) 193208.

[37] W.E. Ranz, W.R. Marshall Jr., Evaporation from drops, part I and part II, Chem.Eng. Prog. 48 (4) (1952) 173180.

[38] D. Joung, K.Y. Huh, 3D RANS simulation of turbulent ow and combustion in a5 MW reverse-ow type gas turbine combustor, J. Eng. Gas Turbines Power132 (11) (2010) 111504.

[39] M.F. Modest, Radiative Heat Transfer, McGraw-Hill, 1993.[40] H. Watanabe, R. Kurose, S. Komori, H. Pitsch, Effects of radiation on spray ame

characteristics and soot formation, Combust. Flame 152 (2008) 213.[41] T.F. Smith, Z.F. Shen, J.N. Friedman, Evaluation of coefcients for the weighted

sum of gray gases model, J. Heat Transfer 104 (1982) 602608.[42] A. Basak, J. Patra, R. Ganguly, A. Datta, Effect of transesterication of vegetable

oil on liquid ow number and spray cone angle for pressure and twin uidatomizers, accepted for publication in Fuel.

P. Ghose et al. / International Journal of Heat and Mass Transfer 74 (2014) 143155 155

Effect of air flow distribution on soot formation and radiative heat transfer in a model liquid fuel spray combustor firing kerosene1 Introduction2 Model2.1 Gas phase flow models2.2 Spray atomization model2.3 Liquid phase flow model2.4 Equilibrium presumed probability density function model2.5 Soot model2.6 Radiation model

3 Numerical model, operating parameters and boundary conditions4 Experimental5 Results and discussion5.1 Validation of soot model5.2 Validation of numerical model5.3 Velocity and temperature distributions in the combustor5.4 Soot distribution in the combustor5.5 Temperature and incident radiative heat flux on combustor wall and fuel injector

6 ConclusionsConflict of interestAcknowledgmentReferences