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Influences of spray and operating parameters on penetration of vaporizing fuel droplets in a gas turbine combustor
Applied Thermal Engineering 21 (2001) 1755±1768
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In¯uences of spray and operating parameters on penetration of vaporizing fuel droplets in a gas turbine combustor N.Y. Sharma 1, A. Datta 2, S.K. Som * Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721 302, India Received 10 August 2000; accepted 22 January 2001
Abstract The eects of inlet spray and operating parameters on penetration and vaporization histories of fuel droplets of a liquid fuel spray injected into a turbulent swirling ¯ow of air through a typical can type gas turbine combustor, have been evaluated from numerical solutions of the conservation equations in gas and droplet phases. The computational scheme is based on the typical stochastic separated ¯ow model of the gas-droplet ¯ow within the combustor. A j±e model with wall function treatment for near wall region has been adopted for the solution of conservative equations in gas phase. The initial spray parameters are speci®ed by a suitable PDF size distribution and a given spray cone angle. It has been recognized that the penetration of vaporizing droplets is reduced with an increase in inlet air swirl and spray cone angle. An increase in inlet air pressure or a decrease in inlet air temperature also results in a reduction in droplet penetration. The inlet air pressure and spray cone angle are found to be the most in¯uencing parameters in this regard. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Gas turbine; Penetration histories; Spatial dispersions; Swirl number; Cone angle
1. Introduction Extensive research works in the area of gas turbine combustion have gone on over the last two decades in order to improve the design of both stationary gas turbines for power generation and aero-propulsion gas turbines. The principal objectives of these research works are to improve the combustion process in order to achieve higher combustion eciency with a uniform *
Corresponding author. Tel.: +91-3222-8-2978; fax: +91-3222-5-5303. E-mail address: [email protected] (S.K. Som). 1 On leave from Department of Mechanical and IP Engineering, Manipal Institute of Technology, Manipal, India. 2 Department of Power Plant Engineering, Jadavpur University, Calcutta, India.
1359-4311/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 1 ) 0 0 0 1 5 - 1
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Nomenclature b cp Cfs Cj d di dmin i dmax i D Deff m Nu p Pr Re r S S Sc Sh Sc
size parameter of Rosin±Rammler function speci®c heat at constant pressure mean fuel vapor concentration at the droplet surface mean concentration of jth species droplet diameter droplet diameter of ith class of droplet minimum diameter of ith droplet class maximum diameter of ith droplet class combustor diameter eective mass diusivity mass Nusselt number pressure Prandtl number Reynolds number radial location Swirl number gas phase mass source term due to droplets Schmidt number Sherwood number gas phase species conservation equation source term
SE SM t T Ui Uz Vi z Greek aeff b leff lt q w
gas phase energy conservation equation source term gas phase momentum source term due to momentum exchange with the droplets time mean temperature mean velocity in xi direction mean axial velocity velocity in xi direction axial location letters eective thermal diusivity transfer number eective viscosity eddy viscosity gas phase density spray cone angle
Subscripts i initial/index of tensor notation j index of tensor notation in inlet Superscripts d droplet phase g gas phase
exit temperature, allowable liner wall temperature and to reduce the combustion-generated pollutants. A host of articles, both numerical and experimental in nature, is available in literature for combustion studies. The relevant numerical works as those of Ramos [1], Raju and Sirignano [2], Ma et al. [3], Sokolov et al. [4], Tolpadi [5] and Amin et al. [6], are based on the analysis of either axisymmetric or asymmetric reacting ¯ow in combustor and predict mainly the ¯ow structure and temperature pro®les in dierent zones within the combustor. The pertinent experimental works as those of Kevin et al. [7], Jones and Toral [8], Heitor and Whitelaw [9], Bicen et al. [10] and Cameron et al. [11], focus mainly on the in¯uence of some important parameters like inlet swirl, air-fuel ratio, inlet pressure and inlet temperature on ¯ow and combustion characteristics in the combustor. Most of the experimental works reported in literature were conducted with gaseous
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fuels. The work of Raju and Sirignano [2] is based on the numerical computation of gas-droplet ¯ow on an Eularian±Lagrangian plane and predict the trajectories of vaporizing droplets and velocity and temperature ®elds of the gas phase. But their work did not report the in¯uences of various operating parameters namely the inlet pressure, swirl as well as spray parameters on the trajectories of vaporizing droplets. Datta and Som [12,13] have recently reported from their computational studies on gas-droplet ¯ow, the in¯uences of operating parameters like inlet pressure, swirl and spray parameters on dierent combustion characteristics of the process. They have reported a contrasting trend of inlet air swirl with combustion eciency at higher and lower combustion pressures. In spite of a large number of articles in the ®eld, it has been felt that further studies are required to understand the in¯uences of (i) operating parameters, namely, the inlet pressure, temperature and swirl and (ii) spray parameters, namely, the mean drop size and spray cone angle, on the penetration histories of a polydisperse vaporizing spray in a turbulent swirling ¯ow through a typical gas turbine combustor. The success of combustion in a gas turbine combustor depends primarily on eective mixing between air and fuel vapor in the region of high temperature primary zone. This brings about a higher combustion eciency and desirable combustion characteristics like, distribution of temperature along liner wall and at combustor exit. The proper mixing of fuel vapor with air depends mainly on the rate of vaporization of liquid fuel droplets, which in turn, is greatly in¯uenced by the dispersion and penetration of fuel droplets in the stream of swirling air in the combustor. Thus the information on penetration histories of vaporising fuel droplets with pertinent operating parameters helps in the physical understanding of the combustion phenomenon within the combustor and of the in¯uences of operating conditions on the combustion characteristics like combustion eciency, temperature distribution at liner wall and at combustor exit. The present paper therefore attempts in predicting the penetration and vaporizing histories of fuel droplets of various size classes comprising the atomized fuel spray that is injected into a gas turbine combustor under dierent operating conditions and spray parameters. The predictions have been made from the numerical computation of gas-droplet ¯ow. 2. Theoretical formulation 2.1. Physical statement and assumptions The physical model refers to the evaporation of a continuously injected liquid-fuel spray in a can type combustor (Fig. 1). The air supply to the combustor is split among the swirler at entry and through two radial jets in the form of secondary and dilution air. The vane swirler at entry is of helicodial type. The vane angle a, at any radial height r, has been considered to be related to the vane tip angle a0 , given by tana r=R tana0 where R is the radius of the vane swirler. Fuel spray is injected from an atomizer located at the hub of the swirler. The fuel is considered to be n-hexane (C6 H14 ). The following assumptions have been made. · The problem is considered to be axisymmetric. Hence the radial jets of air are taken to be uniform over the periphery. This assumption is justi®ed since the geometry of the combustor is
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Fig. 1. A physical model of the combustor.
azimuthally symmetric and also the inlet ¯ow of gas and liquid droplets are symmetrical in nature. However asymmetricity may be induced downstream of the combustor due to introduction of secondary and dilution air through radial holes. But this has negligible in¯uence on the symmetric gas droplet ¯ow in the upstream primary zone of the combustor. · Body forces and buoyancy forces are neglected. · Virtual mass force and Basset force on liquid particles are not considered due to high density ratio between the phases. · The droplet collisions and interactions are neglected and spray is assumed to be dilute in nature. 2.2. Numerical model The numerical model is based on a typical Eularian gas phase and Lagrangian droplet phase formulation following a particle-source-in-cell (PSIC) modeling technique [14], where the coupling between two phases is taken care of through interactive source terms, generated from the droplet phase information on a Lagrangian frame. 2.2.1. Gas phase conservation equations The average gas phase equations are as follows: Continuity: oq o qUi S_ ot oxi Momentum: o o qUi Uj qUi ot oxj
1 op0 o oUi oUj _ i S_ Mi SU leff oxj oxj oxj oxi
2
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where, leff l lt l cl q
k2 e
3
2 2 oUj p0 p qk leff 3 3 oxj
4
Turbulent kinetic energy (j): o o o qj qUi j ot oxi oxi
lt oj rk oxi
P
_ qe Sj
5
where, turbulent kinetic energy production rate P is given by P lt
oUi oUj oxj oxi
oUi oxj
2 oUi oUi qj lt 3 oxi oxi
Turbulent kinetic energy dissipation rate (e): o o o lt oe e qe qUi e c1e P ot oxi oxi re oxi j
6
qc2e
e2 _ Se j
7
Typical constants for standard j±e method are taken as: cl 0:09;
c1e 1:44;
c2e 1:92;
rk 1:0; and re 1:3
Individual species conservation:
o o o oCj _ j qCj qUi Cj qDeff S_ Cj SC ot oxi oxi oxi
8
Since the present problem pertains to the evaporation of fuel spray without burning, the species conservation equation is solved for fuel-vapor only, while the concentration of oxygen is found from the dierence. Energy:
o o o oT g g g g g g qcp Ui T qcp aeff qcp T ot oxi oxi oxi
S_ E cgp T g S_
9
The Energy source term SE is the energy absorbed by the liquid droplets during their heating up period calculated from the interphase transport process. 2.2.2. Generation of droplet phase information The fuel spray injected continuously into the combustor is considered to be speci®ed by an initial droplet size distribution function along with an initial velocity and temperature, same for all droplets. The velocity, mass and temperature history of all droplet classes along their
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trajectories are obtained from the respective conservation equations on a Lagrangian frame as follows: Droplet velocity: md
dVi d p 2 qd CD j Vi g 8 dt
Vi d j Vi g
Vi d
10
Drag coecient CD is computed following the standard drag law of Clift et al. [15]. The eect of gas phase turbulence on the droplet motion is simulated using a stochastic approach. The instantaneous gas phase velocity (Vi g ) is obtained by computing the ¯uctuating velocity component from the turbulent kinetic energy in consideration of isotropic turbulence, and using a normally distributed random number, f r 2j g 11 V i Ui f 3 Droplet mass: dmd dt
qm bpd 2 Cfs
Cf
12
where, qm is the density of the gas phase at the droplet surface. Droplet temperature: md Cpd
dT d hpd 2 T g dt
dmd Td DHv dt
13
where, DHv is the enthalpy of vaporization of the liquid fuel at droplet temperature. Mass transfer coecient b and heat transfer coecient h in Eqs. (12) and (13) are evaluated from the standard correlations, 0:33 Nu 1 B 2 0:6 Re0:5 d Pr
14
0:33 Sh 1 B 2 0:6 Re0:5 d Sc
15
where B is the transfer number. Eqs. (10), (12) and (13) are solved for Vi d , md and T d with appropriate initial conditions. The initial drop size distribution of liquid fuel spray is assumed to follow a realistic fourparameter Rosin±Rammler distribution function given by, G0 di
n exp bdin exp bdmax i n n exp bdmin i exp bdmax i
16
where, G0 di is the mass fraction of the spray having diameter above di . The dispersion parameter n is taken as 3 following Mugele and Evans [16].
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3. Method of solution 3.1. Numerical scheme The numerical code consisted of two dierent modules, one for gas phase computation and the other for calculation of the droplet phase. The gas phase conservation equations were solved with appropriate boundary conditions following explicit ®nite dierence technique. The conservation equations were ®rst non-dimensionalized against reference quantities and then discretized following a staggered grid arrangement. The reference length was taken to be the combustor diameter (D), the reference velocity to be the axial velocity through the swirler (Uz in ), the reference temperature to be the ambient temperature (Ta 300 K), and the reference time as D=Uz in . The diusion and convective terms were discretized by central and hybrid dierencing schemes respectively. The coupling between pressure and velocity was accomplished using a MAC-based SOLA algorithm after Hirt and Cook [17]. Energy and species conservation equations were solved in a coupled form with the continuity and momentum equations to account for the variation in density with temperature and concentration. The solution procedure in this module continued till a steady state convergence was obtained. The ordinary dierential equations of the droplet phase were solved by a fourth order Runge± Kutta method to generate droplet information required for the gas phase source terms. The solution in this module continued until all the representative droplets of dierent classes extinguished in the process of evaporation. The modules were invoked alternately to solve the respective equations until a ®nal convergence was arrived at. This was considered to be achieved when the result of any module did not alter the result of the other module. 3.2. Numerical mesh A numerical mesh of 89 31 grid nodes was used after several experiments, which showed that further re®nement in either direction did not change the result (maximum dierence in velocity and other scalar functions in the carrier phase) by more than 2%. The grid spacings in axial and radial directions were changed smoothly to minimize the deterioration of the formal accuracy of the ®nite dierence scheme due to variable grid spacing and in such a way that a higher concentration of nodes occurs near the swirler and the radial holes. 3.3. Operating parameters and boundary conditions The total air ¯ow to the combustor was split among the swirler and the two radial jets according to a ratio of 5:7:8, following Cameron et al. [11]. An air-fuel ratio of 90 was used. Swirl number was calculated assuming a solid body type rotation generated by the helicoidal vanes in the swirler. The air entering the combustor was considered to be at 600 K. The fuel spray was considered to comprise eight droplet classes as recommended by Faeth [18] with representative droplet diameters as shown in Table 1 below. A zero axial gradient was prescribed at the outlet for all variables. Standard logarithmic law of wall was considered at the solid walls.
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Table 1 Droplet size classi®cation Droplet classes Size (lm)
A
B
C
D
E
F
G
H
18
33
48
63
78
93
108
123
4. Results and discussion The droplet penetration along with the life histories of fuel droplets within the combustor, under the in¯uences of spray and dierent inlet operating parameters, have been reported in this section. The penetration of a class of droplets of given diameter is de®ned as the axial distance traversed by the droplet class in the surrounding ambience from the plane of injection, before it vaporizes completely. The experimental validation of the present numerical model is somewhat dicult, since experimental information on non-reacting gas-droplet ¯ow is sparse in literature. The available experimental results on gas droplet ¯ow pertain mostly to the dierent combustion characteristics of a gas turbine combustor. Moreover, the relevant information available in the existing works do not reproduce explicitly all input parameters required to generate the output data of the present model for the purpose of validation. There is in fact very little experimental information on the stochastic Lagrangian path of liquid droplets in a turbulent swirling ¯ow of gas. Therefore comparison of predicted droplet penetration with experimental results in case of a gas-droplet ¯ow could not be made. However, the present numerical model has been calibrated through a comparison of the axial and tangential velocity distributions predicted by the model, in case of an axisymmetric sudden expansion swirling ¯ow, with the computational work of Chang and Chen [19] and the experimental results of Dallenback [20] under a similar situation. Fig. 2(a) and (c) shows a fair agree-
Fig. 2. Comparisons of predicted axial and tangential velocity distributions with Chang and Chen [19] and Dallenback [20]: (±) present computation, ( ) Chang and Chen, () Dallenback. (a) Z=D 0:75, (b) Z=D 4:0, (c) Z=D 0:75, (d) Z=D 4:0.
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ment of the predicted axial and tangential velocity pro®les near the inlet region (z 0:75) with the computations of Chang and Chen and the empirical values of Dallenback. However it is observed from Fig. 2(b) and (d) that the present numerical results and the computations of Chang and Chen being in agreement with each other do not conform well with the experimental results of Dallenback for the tangential velocity distribution at far down stream from the inlet (z 4:0) and mainly near the axis. This was explained by Chang and Chen in the light of under-prediction of the length of central toroidal recirculation zone by the standard j±e model. Therefore the theoretical model predicts a relatively lower strength of swirl at the down stream location. The trajectory of a particular droplet class, in the present work, has been determined on the basis of time averaged spatial locations of the droplets of that class. The in¯uences of the pertinent parameters on the penetration histories of the droplet classes are discussed below.
4.1. In¯uence of inlet air swirl Fig. 3(a) and (b) shows the variation of diameters of dierent droplet classes (speci®ed by initial class diameter) with their axial displacements in the combustion chamber at dierent swirl numbers (S), while Fig. 4(a) and (b) shows the axial and radial dispersions of dierent droplet classes within the combustor. It is observed that the penetration of a droplet class increase with an increase in its initial class diameter. It is obvious, since, for coarser droplets the drag per unit mass is lower while the time for complete vaporization is much longer. However, it is observed from Fig. 4(a) and (b) that the coarser droplets suer relatively small radial dispersions as compared to that of ®ner ones. This is due to the fact that the coarser droplets have been assumed to be injected from a relatively lower radial location as compared to that of smaller droplets from the plane of injection. This assumption has been made in accordance with the typical atomization process by conventional atomizers, as reported earlier [21], where the lower droplets remain at the outer skirt of the atomized spray while the coarser droplets remain in the core. Fig. 3(a) and (b) shows a decrease in droplet penetration with an increase in swirl number. An increase in inlet swirl causes a relatively stronger recirculatory ¯ow in the upstream part of the combustor, and thus decreases
Fig. 3. Penetration histories of vaporizing fuel droplets at dierent inlet swirls (P 1 bar, T 600 K, w 60°, Rein 52 400) (a) S 0:37, (b) S 1:11.
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Fig. 4. Spatial dispersions of vaporizing fuel droplets at dierent inlet swirls (P 1 bar, T 600 K, w 60°, Rein 52 400) (a) S 0:37, (b) S 1:11.
Fig. 5. Velocity ®eld in the combustor (P 1 bar, T 600 K, S 0:37, w 60°, Rein 52 400).
the droplet penetration. However, the decrease in penetration is marginal for ®ner droplets, while it is considerable for coarser ones. The ¯ow ®eld in the combustor at a given set of operating conditions is shown in the Fig. 5. It is observed that there exist recirculation zones both near the wall and near the axis of the combustor. Fig. 6(a) and (b) shows the fuel vapor concentration ®elds in the gas phase at steady state condition in the absence of burning. It is found that, at increased swirl number, a relatively vapor rich zone exists in an upstream region closer to the plane of fuel injection. 4.2. In¯uence of inlet air pressure Fig. 7(a) and (b) shows the penetration histories of vaporizing fuel droplets at a pressure of 10 bar and at swirl number of S 0:37 and S 1:11. A comparison of Fig. 7 with Fig. 3, shows that an increase in combustor pressure from 1 to 10 bar reduces the droplet penetration considerably. This can be attributed to the higher values of drag forces experienced by the moving droplets due to higher density of the high-pressure ambient gas within the combustor. The rate of vaporization of droplets is also reduced at higher pressure, because of a reduction in mole fraction of the fuel vapor at droplet surface with an increase in the local pressure at a given local temperature. However the reduction in droplet velocities associated with larger drag dominates over the
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Fig. 6. Fuel vapor mass concentration contour plots (P 1 bar, T 600 K, w 60°, Rein 52 400) (a) S 0:37, (b) S 1:11.
Fig. 7. Penetration histories of vaporizing fuel droplets with dierent inlet swirls at higher pressure (P 10 bar, T 600 K, w 60°, Rein 52 400) (a) S 0:37, (b) S 1:11.
reduction in vaporization rate and ®nally results in a lower penetration of the fuel droplets. The most interesting feature in this context as observed from Figs. 3 and 7, is that the in¯uence of inlet swirl in reducing the droplet penetration is more pronounced at a higher pressure of 10 bar as compared to that at 1 bar. It is found (Fig. 8(a)) that the radial dispersions are suppressed at higher pressure within the combustor. However a little larger radial dispersions are obtained at a higher swirl number as seen from Fig. 8(b) because of a stronger o-axis recirculatory ¯ow. 4.3. In¯uence of inlet temperature It is found from Figs. 9 and 10 that, both the axial penetrations and radial dispersions of fuel droplets increase with an increase in inlet air temperature. This can be attributed to a reduction in the density of air due to an increase in air temperature, ®nally resulting in a reduced drag on moving droplets. These droplet classes have been assumed to stick to the wall for the remaining part of their vaporization process, according to the stick model for wall impingement as employed in the numerical scheme of the present work. This is exhibited by straight vertical lines (Fig. 10 (b)) in the later part of the diameter penetration histories of these droplet classes.
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Fig. 8. Spatial dispersions of vaporizing fuel droplets with dierent inlet swirls at higher pressure (P 10 bar, T 600 K, w 60°, Rein 52 400) (a) S 0:37, (b) S 1:11.
Fig. 9. Penetration histories of vaporizing fuel droplets at dierent inlet air temperatures (P 1 bar, S 0:37, w 60°, Rein 52 400) (a) T 600 K, (b) T 800 K.
Fig. 10. Spatial dispersions of vaporizing fuel droplets at dierent inlet air temperatures (P 1 bar, S 0:37, w 60°, Rein 52 400) (a) T 600 K, (b) T 800 K.
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Fig. 11. Penetration histories of vaporizing fuel droplets at dierent inlet spray cone angles (P 1 bar, T 600 K, S 0:37, Rein 52 400) (a) w 60°, (b) w 100°.
Fig. 12. Spatial dispersions of vaporizing fuel droplets at dierent inlet spray cone angles (P 1 bar, T 600 K, S 0:37, Rein 52 400) (a) w 60°, (b) w 100°.
4.4. In¯uence of spray cone angle An increase in spray cone angle shows a drastic reduction in the penetration of the spray (Fig. 11), with an increase in its radial dispersion (Fig. 12). A spray of higher cone angle with a given ¯ow rate is required to be injected from a larger ori®ce diameter of a conventional duplex nozzle. This causes a reduction in the initial axial velocity of droplets along with an increase in their initial tangential velocity, and ®nally results into a radially dispersed spray with a poor penetration.
5. Conclusion The penetration and vaporization histories of fuel droplets of a liquid fuel spray injected into a turbulent swirling ¯ow of air through a gas turbine combustor under dierent operating parameters and spray have been predicted from numerical computations of gas-droplet ¯ow based on two phase separated ¯ow model. It has been observed that a decrease in spray penetration takes place with an increase in inlet air swirl and inlet air pressure and with a decrease in inlet air temperature. The in¯uence of inlet swirl on penetration is more prominent at higher pressure as
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compared to that at lower pressure. The radial dispersions are drastically suppressed at higher air pressure. An increase in spray cone angle results in a drastic reduction in droplet penetration with signi®cant increase in radial dispersions. References [1] J.I. Ramos, A numerical study of swirl stabilized combustors, J. Non-Equlib. Thermodynamics 10 (1985) 263. [2] M.S. Raju, W.A. Sirignano, Spray computations in a centerbody combustor, ASME J. Engng. Gas Turbine Power 111 (1989) 710. [3] H.K. Ma, F.H. Lee, M.W. Wang, Numerical study on heat and mass transfer in a liquid-fueled gas turbine combustor, Int. J. Heat Mass Transfer 36 (13) (1993) 3271. [4] K.Y. Sokolov, A.G. Tumanovskiy, M.N. Gutnik, A.V. Sudarev, Y.I. Zakharov, E.D. Winogradov, Mathematical modeling of an annular gas turbine, ASME J. Engng. Gas Turbine Power 117 (1995) 94. [5] A.K. Tolpadi, Calculation of two-phase ¯ow in gas turbine combustor, ASME J. Engng. Gas Turbine Power 117 (1995) 695. [6] E.M. Amin, G.E. Andrews, M. Pourkishnian, A. Williams, R.A. Yetter, A Computational study of pressure eects on pollutant generation in gas turbine combustors, ASME J. Engng. Gas Turbine Power 119 (1997) 76. [7] F.K. Owen, I.J. Spadaccini, C.T. Bowman, Pollutant Formation and Energy Release in Con®ned Turbulent Diusion Flames, Sixteenth Symposium (International) on Combustion, The Combustion Institute, 1977, p. 105. [8] W.P. Jones, H. Toral, Temperature and composition measurement in a research gas turbine combustion chamber, Combustion Sci. Technol. 31 (1983) 249. [9] M.V. Heitor, J.H. Whitelaw, Velocity temperature and species characteristics of ¯ow in a gas turbine combustor, Cumbust. Flame 64 (1986) 1. [10] A.M. Bicen, M. Senda, J.H. Whitelaw, Scalar characteristics of combusting ¯ow in a model annular combustor, ASME J. Engng. Gas Turbine Power 111 (1989) 90. [11] C.D. Cameron, J. Brouwer, C.P. Wood, G.S. Samuelson, A detailed characteristics of the velocity and thermal ®elds in a model can combustor with wall jet injection, ASME J. Engng. Gas Turbine Power 111 (1989) 31. [12] A. Datta, S.K. Som, Eects of spray characteristics on combustion performance of a liquid fuel spray in a gas turbine combustor, Int. J. Energy Res. 23 (1999) 217. [13] A. Datta, S.K. Som, Combustion and emission characteristics in a gas turbine combustor at dierent pressure and swirl conditions, Appl. Thermal Engng. 19 (1999) 949. [14] C.T. Crowe, M.P. Sharma, D.E. Stock, The particle-source-in-cell (PSI-Cell) model for gas droplet ¯ows, ASME J. Fluids Engng. 99 (1977) 325. [15] R. Clift, J.R. Grace, M.E. Weber, Bubbles, Drops and Particles, Academic Press, New York, 1978. [16] R.A. Mugele, H.D. Evans, Droplet size distribution in sprays, Ind. Engng. Chem. 43 (1951) 1317. [17] C.W. Hirt, J.L. Cook, Calculating three dimensional ¯ows around structures and over rough terrain, J. Comput. Phys. 10 (1972) 324. [18] G.M. Faeth, Evaporation and combustion of sprays, Prog. Energy Combust. Sci. 9 (1983) 1. [19] K.C. Chang, C.S. Chen, Development of a hybrid j±e turbulence model for swirling recirculating ¯ows under moderate to strong swirl intensities, Int. J. Numer. Meth. Fluids 16 (1993) 421. [20] P.A. Dallenback, Heat Transfer and Velocity Measurements in Turbulent Swirling Flow through an Abrupt Axisymmetric Expansion. Ph.D. Thesis. Arizona State University, Tempe, 1986. [21] K.-J. Wu, R.D. Reitz, F.V. Bracco, Measurement of drop size at the spray edge near the nozzle in atomising liquid jets, Phys. Fluids 29 (4) (1986) 941±951.
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In¯uences of spray and operating parameters on penetration of vaporizing fuel droplets in a gas turbine combustor N.Y. Sharma 1, A. Datta 2, S.K. Som * Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721 302, India Received 10 August 2000; accepted 22 January 2001
Abstract The eects of inlet spray and operating parameters on penetration and vaporization histories of fuel droplets of a liquid fuel spray injected into a turbulent swirling ¯ow of air through a typical can type gas turbine combustor, have been evaluated from numerical solutions of the conservation equations in gas and droplet phases. The computational scheme is based on the typical stochastic separated ¯ow model of the gas-droplet ¯ow within the combustor. A j±e model with wall function treatment for near wall region has been adopted for the solution of conservative equations in gas phase. The initial spray parameters are speci®ed by a suitable PDF size distribution and a given spray cone angle. It has been recognized that the penetration of vaporizing droplets is reduced with an increase in inlet air swirl and spray cone angle. An increase in inlet air pressure or a decrease in inlet air temperature also results in a reduction in droplet penetration. The inlet air pressure and spray cone angle are found to be the most in¯uencing parameters in this regard. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Gas turbine; Penetration histories; Spatial dispersions; Swirl number; Cone angle
1. Introduction Extensive research works in the area of gas turbine combustion have gone on over the last two decades in order to improve the design of both stationary gas turbines for power generation and aero-propulsion gas turbines. The principal objectives of these research works are to improve the combustion process in order to achieve higher combustion eciency with a uniform *
Corresponding author. Tel.: +91-3222-8-2978; fax: +91-3222-5-5303. E-mail address: [email protected] (S.K. Som). 1 On leave from Department of Mechanical and IP Engineering, Manipal Institute of Technology, Manipal, India. 2 Department of Power Plant Engineering, Jadavpur University, Calcutta, India.
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Nomenclature b cp Cfs Cj d di dmin i dmax i D Deff m Nu p Pr Re r S S Sc Sh Sc
size parameter of Rosin±Rammler function speci®c heat at constant pressure mean fuel vapor concentration at the droplet surface mean concentration of jth species droplet diameter droplet diameter of ith class of droplet minimum diameter of ith droplet class maximum diameter of ith droplet class combustor diameter eective mass diusivity mass Nusselt number pressure Prandtl number Reynolds number radial location Swirl number gas phase mass source term due to droplets Schmidt number Sherwood number gas phase species conservation equation source term
SE SM t T Ui Uz Vi z Greek aeff b leff lt q w
gas phase energy conservation equation source term gas phase momentum source term due to momentum exchange with the droplets time mean temperature mean velocity in xi direction mean axial velocity velocity in xi direction axial location letters eective thermal diusivity transfer number eective viscosity eddy viscosity gas phase density spray cone angle
Subscripts i initial/index of tensor notation j index of tensor notation in inlet Superscripts d droplet phase g gas phase
exit temperature, allowable liner wall temperature and to reduce the combustion-generated pollutants. A host of articles, both numerical and experimental in nature, is available in literature for combustion studies. The relevant numerical works as those of Ramos [1], Raju and Sirignano [2], Ma et al. [3], Sokolov et al. [4], Tolpadi [5] and Amin et al. [6], are based on the analysis of either axisymmetric or asymmetric reacting ¯ow in combustor and predict mainly the ¯ow structure and temperature pro®les in dierent zones within the combustor. The pertinent experimental works as those of Kevin et al. [7], Jones and Toral [8], Heitor and Whitelaw [9], Bicen et al. [10] and Cameron et al. [11], focus mainly on the in¯uence of some important parameters like inlet swirl, air-fuel ratio, inlet pressure and inlet temperature on ¯ow and combustion characteristics in the combustor. Most of the experimental works reported in literature were conducted with gaseous
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fuels. The work of Raju and Sirignano [2] is based on the numerical computation of gas-droplet ¯ow on an Eularian±Lagrangian plane and predict the trajectories of vaporizing droplets and velocity and temperature ®elds of the gas phase. But their work did not report the in¯uences of various operating parameters namely the inlet pressure, swirl as well as spray parameters on the trajectories of vaporizing droplets. Datta and Som [12,13] have recently reported from their computational studies on gas-droplet ¯ow, the in¯uences of operating parameters like inlet pressure, swirl and spray parameters on dierent combustion characteristics of the process. They have reported a contrasting trend of inlet air swirl with combustion eciency at higher and lower combustion pressures. In spite of a large number of articles in the ®eld, it has been felt that further studies are required to understand the in¯uences of (i) operating parameters, namely, the inlet pressure, temperature and swirl and (ii) spray parameters, namely, the mean drop size and spray cone angle, on the penetration histories of a polydisperse vaporizing spray in a turbulent swirling ¯ow through a typical gas turbine combustor. The success of combustion in a gas turbine combustor depends primarily on eective mixing between air and fuel vapor in the region of high temperature primary zone. This brings about a higher combustion eciency and desirable combustion characteristics like, distribution of temperature along liner wall and at combustor exit. The proper mixing of fuel vapor with air depends mainly on the rate of vaporization of liquid fuel droplets, which in turn, is greatly in¯uenced by the dispersion and penetration of fuel droplets in the stream of swirling air in the combustor. Thus the information on penetration histories of vaporising fuel droplets with pertinent operating parameters helps in the physical understanding of the combustion phenomenon within the combustor and of the in¯uences of operating conditions on the combustion characteristics like combustion eciency, temperature distribution at liner wall and at combustor exit. The present paper therefore attempts in predicting the penetration and vaporizing histories of fuel droplets of various size classes comprising the atomized fuel spray that is injected into a gas turbine combustor under dierent operating conditions and spray parameters. The predictions have been made from the numerical computation of gas-droplet ¯ow. 2. Theoretical formulation 2.1. Physical statement and assumptions The physical model refers to the evaporation of a continuously injected liquid-fuel spray in a can type combustor (Fig. 1). The air supply to the combustor is split among the swirler at entry and through two radial jets in the form of secondary and dilution air. The vane swirler at entry is of helicodial type. The vane angle a, at any radial height r, has been considered to be related to the vane tip angle a0 , given by tana r=R tana0 where R is the radius of the vane swirler. Fuel spray is injected from an atomizer located at the hub of the swirler. The fuel is considered to be n-hexane (C6 H14 ). The following assumptions have been made. · The problem is considered to be axisymmetric. Hence the radial jets of air are taken to be uniform over the periphery. This assumption is justi®ed since the geometry of the combustor is
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Fig. 1. A physical model of the combustor.
azimuthally symmetric and also the inlet ¯ow of gas and liquid droplets are symmetrical in nature. However asymmetricity may be induced downstream of the combustor due to introduction of secondary and dilution air through radial holes. But this has negligible in¯uence on the symmetric gas droplet ¯ow in the upstream primary zone of the combustor. · Body forces and buoyancy forces are neglected. · Virtual mass force and Basset force on liquid particles are not considered due to high density ratio between the phases. · The droplet collisions and interactions are neglected and spray is assumed to be dilute in nature. 2.2. Numerical model The numerical model is based on a typical Eularian gas phase and Lagrangian droplet phase formulation following a particle-source-in-cell (PSIC) modeling technique [14], where the coupling between two phases is taken care of through interactive source terms, generated from the droplet phase information on a Lagrangian frame. 2.2.1. Gas phase conservation equations The average gas phase equations are as follows: Continuity: oq o qUi S_ ot oxi Momentum: o o qUi Uj qUi ot oxj
1 op0 o oUi oUj _ i S_ Mi SU leff oxj oxj oxj oxi
2
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where, leff l lt l cl q
k2 e
3
2 2 oUj p0 p qk leff 3 3 oxj
4
Turbulent kinetic energy (j): o o o qj qUi j ot oxi oxi
lt oj rk oxi
P
_ qe Sj
5
where, turbulent kinetic energy production rate P is given by P lt
oUi oUj oxj oxi
oUi oxj
2 oUi oUi qj lt 3 oxi oxi
Turbulent kinetic energy dissipation rate (e): o o o lt oe e qe qUi e c1e P ot oxi oxi re oxi j
6
qc2e
e2 _ Se j
7
Typical constants for standard j±e method are taken as: cl 0:09;
c1e 1:44;
c2e 1:92;
rk 1:0; and re 1:3
Individual species conservation:
o o o oCj _ j qCj qUi Cj qDeff S_ Cj SC ot oxi oxi oxi
8
Since the present problem pertains to the evaporation of fuel spray without burning, the species conservation equation is solved for fuel-vapor only, while the concentration of oxygen is found from the dierence. Energy:
o o o oT g g g g g g qcp Ui T qcp aeff qcp T ot oxi oxi oxi
S_ E cgp T g S_
9
The Energy source term SE is the energy absorbed by the liquid droplets during their heating up period calculated from the interphase transport process. 2.2.2. Generation of droplet phase information The fuel spray injected continuously into the combustor is considered to be speci®ed by an initial droplet size distribution function along with an initial velocity and temperature, same for all droplets. The velocity, mass and temperature history of all droplet classes along their
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trajectories are obtained from the respective conservation equations on a Lagrangian frame as follows: Droplet velocity: md
dVi d p 2 qd CD j Vi g 8 dt
Vi d j Vi g
Vi d
10
Drag coecient CD is computed following the standard drag law of Clift et al. [15]. The eect of gas phase turbulence on the droplet motion is simulated using a stochastic approach. The instantaneous gas phase velocity (Vi g ) is obtained by computing the ¯uctuating velocity component from the turbulent kinetic energy in consideration of isotropic turbulence, and using a normally distributed random number, f r 2j g 11 V i Ui f 3 Droplet mass: dmd dt
qm bpd 2 Cfs
Cf
12
where, qm is the density of the gas phase at the droplet surface. Droplet temperature: md Cpd
dT d hpd 2 T g dt
dmd Td DHv dt
13
where, DHv is the enthalpy of vaporization of the liquid fuel at droplet temperature. Mass transfer coecient b and heat transfer coecient h in Eqs. (12) and (13) are evaluated from the standard correlations, 0:33 Nu 1 B 2 0:6 Re0:5 d Pr
14
0:33 Sh 1 B 2 0:6 Re0:5 d Sc
15
where B is the transfer number. Eqs. (10), (12) and (13) are solved for Vi d , md and T d with appropriate initial conditions. The initial drop size distribution of liquid fuel spray is assumed to follow a realistic fourparameter Rosin±Rammler distribution function given by, G0 di
n exp bdin exp bdmax i n n exp bdmin i exp bdmax i
16
where, G0 di is the mass fraction of the spray having diameter above di . The dispersion parameter n is taken as 3 following Mugele and Evans [16].
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3. Method of solution 3.1. Numerical scheme The numerical code consisted of two dierent modules, one for gas phase computation and the other for calculation of the droplet phase. The gas phase conservation equations were solved with appropriate boundary conditions following explicit ®nite dierence technique. The conservation equations were ®rst non-dimensionalized against reference quantities and then discretized following a staggered grid arrangement. The reference length was taken to be the combustor diameter (D), the reference velocity to be the axial velocity through the swirler (Uz in ), the reference temperature to be the ambient temperature (Ta 300 K), and the reference time as D=Uz in . The diusion and convective terms were discretized by central and hybrid dierencing schemes respectively. The coupling between pressure and velocity was accomplished using a MAC-based SOLA algorithm after Hirt and Cook [17]. Energy and species conservation equations were solved in a coupled form with the continuity and momentum equations to account for the variation in density with temperature and concentration. The solution procedure in this module continued till a steady state convergence was obtained. The ordinary dierential equations of the droplet phase were solved by a fourth order Runge± Kutta method to generate droplet information required for the gas phase source terms. The solution in this module continued until all the representative droplets of dierent classes extinguished in the process of evaporation. The modules were invoked alternately to solve the respective equations until a ®nal convergence was arrived at. This was considered to be achieved when the result of any module did not alter the result of the other module. 3.2. Numerical mesh A numerical mesh of 89 31 grid nodes was used after several experiments, which showed that further re®nement in either direction did not change the result (maximum dierence in velocity and other scalar functions in the carrier phase) by more than 2%. The grid spacings in axial and radial directions were changed smoothly to minimize the deterioration of the formal accuracy of the ®nite dierence scheme due to variable grid spacing and in such a way that a higher concentration of nodes occurs near the swirler and the radial holes. 3.3. Operating parameters and boundary conditions The total air ¯ow to the combustor was split among the swirler and the two radial jets according to a ratio of 5:7:8, following Cameron et al. [11]. An air-fuel ratio of 90 was used. Swirl number was calculated assuming a solid body type rotation generated by the helicoidal vanes in the swirler. The air entering the combustor was considered to be at 600 K. The fuel spray was considered to comprise eight droplet classes as recommended by Faeth [18] with representative droplet diameters as shown in Table 1 below. A zero axial gradient was prescribed at the outlet for all variables. Standard logarithmic law of wall was considered at the solid walls.
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Table 1 Droplet size classi®cation Droplet classes Size (lm)
A
B
C
D
E
F
G
H
18
33
48
63
78
93
108
123
4. Results and discussion The droplet penetration along with the life histories of fuel droplets within the combustor, under the in¯uences of spray and dierent inlet operating parameters, have been reported in this section. The penetration of a class of droplets of given diameter is de®ned as the axial distance traversed by the droplet class in the surrounding ambience from the plane of injection, before it vaporizes completely. The experimental validation of the present numerical model is somewhat dicult, since experimental information on non-reacting gas-droplet ¯ow is sparse in literature. The available experimental results on gas droplet ¯ow pertain mostly to the dierent combustion characteristics of a gas turbine combustor. Moreover, the relevant information available in the existing works do not reproduce explicitly all input parameters required to generate the output data of the present model for the purpose of validation. There is in fact very little experimental information on the stochastic Lagrangian path of liquid droplets in a turbulent swirling ¯ow of gas. Therefore comparison of predicted droplet penetration with experimental results in case of a gas-droplet ¯ow could not be made. However, the present numerical model has been calibrated through a comparison of the axial and tangential velocity distributions predicted by the model, in case of an axisymmetric sudden expansion swirling ¯ow, with the computational work of Chang and Chen [19] and the experimental results of Dallenback [20] under a similar situation. Fig. 2(a) and (c) shows a fair agree-
Fig. 2. Comparisons of predicted axial and tangential velocity distributions with Chang and Chen [19] and Dallenback [20]: (±) present computation, ( ) Chang and Chen, () Dallenback. (a) Z=D 0:75, (b) Z=D 4:0, (c) Z=D 0:75, (d) Z=D 4:0.
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ment of the predicted axial and tangential velocity pro®les near the inlet region (z 0:75) with the computations of Chang and Chen and the empirical values of Dallenback. However it is observed from Fig. 2(b) and (d) that the present numerical results and the computations of Chang and Chen being in agreement with each other do not conform well with the experimental results of Dallenback for the tangential velocity distribution at far down stream from the inlet (z 4:0) and mainly near the axis. This was explained by Chang and Chen in the light of under-prediction of the length of central toroidal recirculation zone by the standard j±e model. Therefore the theoretical model predicts a relatively lower strength of swirl at the down stream location. The trajectory of a particular droplet class, in the present work, has been determined on the basis of time averaged spatial locations of the droplets of that class. The in¯uences of the pertinent parameters on the penetration histories of the droplet classes are discussed below.
4.1. In¯uence of inlet air swirl Fig. 3(a) and (b) shows the variation of diameters of dierent droplet classes (speci®ed by initial class diameter) with their axial displacements in the combustion chamber at dierent swirl numbers (S), while Fig. 4(a) and (b) shows the axial and radial dispersions of dierent droplet classes within the combustor. It is observed that the penetration of a droplet class increase with an increase in its initial class diameter. It is obvious, since, for coarser droplets the drag per unit mass is lower while the time for complete vaporization is much longer. However, it is observed from Fig. 4(a) and (b) that the coarser droplets suer relatively small radial dispersions as compared to that of ®ner ones. This is due to the fact that the coarser droplets have been assumed to be injected from a relatively lower radial location as compared to that of smaller droplets from the plane of injection. This assumption has been made in accordance with the typical atomization process by conventional atomizers, as reported earlier [21], where the lower droplets remain at the outer skirt of the atomized spray while the coarser droplets remain in the core. Fig. 3(a) and (b) shows a decrease in droplet penetration with an increase in swirl number. An increase in inlet swirl causes a relatively stronger recirculatory ¯ow in the upstream part of the combustor, and thus decreases
Fig. 3. Penetration histories of vaporizing fuel droplets at dierent inlet swirls (P 1 bar, T 600 K, w 60°, Rein 52 400) (a) S 0:37, (b) S 1:11.
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Fig. 4. Spatial dispersions of vaporizing fuel droplets at dierent inlet swirls (P 1 bar, T 600 K, w 60°, Rein 52 400) (a) S 0:37, (b) S 1:11.
Fig. 5. Velocity ®eld in the combustor (P 1 bar, T 600 K, S 0:37, w 60°, Rein 52 400).
the droplet penetration. However, the decrease in penetration is marginal for ®ner droplets, while it is considerable for coarser ones. The ¯ow ®eld in the combustor at a given set of operating conditions is shown in the Fig. 5. It is observed that there exist recirculation zones both near the wall and near the axis of the combustor. Fig. 6(a) and (b) shows the fuel vapor concentration ®elds in the gas phase at steady state condition in the absence of burning. It is found that, at increased swirl number, a relatively vapor rich zone exists in an upstream region closer to the plane of fuel injection. 4.2. In¯uence of inlet air pressure Fig. 7(a) and (b) shows the penetration histories of vaporizing fuel droplets at a pressure of 10 bar and at swirl number of S 0:37 and S 1:11. A comparison of Fig. 7 with Fig. 3, shows that an increase in combustor pressure from 1 to 10 bar reduces the droplet penetration considerably. This can be attributed to the higher values of drag forces experienced by the moving droplets due to higher density of the high-pressure ambient gas within the combustor. The rate of vaporization of droplets is also reduced at higher pressure, because of a reduction in mole fraction of the fuel vapor at droplet surface with an increase in the local pressure at a given local temperature. However the reduction in droplet velocities associated with larger drag dominates over the
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Fig. 6. Fuel vapor mass concentration contour plots (P 1 bar, T 600 K, w 60°, Rein 52 400) (a) S 0:37, (b) S 1:11.
Fig. 7. Penetration histories of vaporizing fuel droplets with dierent inlet swirls at higher pressure (P 10 bar, T 600 K, w 60°, Rein 52 400) (a) S 0:37, (b) S 1:11.
reduction in vaporization rate and ®nally results in a lower penetration of the fuel droplets. The most interesting feature in this context as observed from Figs. 3 and 7, is that the in¯uence of inlet swirl in reducing the droplet penetration is more pronounced at a higher pressure of 10 bar as compared to that at 1 bar. It is found (Fig. 8(a)) that the radial dispersions are suppressed at higher pressure within the combustor. However a little larger radial dispersions are obtained at a higher swirl number as seen from Fig. 8(b) because of a stronger o-axis recirculatory ¯ow. 4.3. In¯uence of inlet temperature It is found from Figs. 9 and 10 that, both the axial penetrations and radial dispersions of fuel droplets increase with an increase in inlet air temperature. This can be attributed to a reduction in the density of air due to an increase in air temperature, ®nally resulting in a reduced drag on moving droplets. These droplet classes have been assumed to stick to the wall for the remaining part of their vaporization process, according to the stick model for wall impingement as employed in the numerical scheme of the present work. This is exhibited by straight vertical lines (Fig. 10 (b)) in the later part of the diameter penetration histories of these droplet classes.
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Fig. 8. Spatial dispersions of vaporizing fuel droplets with dierent inlet swirls at higher pressure (P 10 bar, T 600 K, w 60°, Rein 52 400) (a) S 0:37, (b) S 1:11.
Fig. 9. Penetration histories of vaporizing fuel droplets at dierent inlet air temperatures (P 1 bar, S 0:37, w 60°, Rein 52 400) (a) T 600 K, (b) T 800 K.
Fig. 10. Spatial dispersions of vaporizing fuel droplets at dierent inlet air temperatures (P 1 bar, S 0:37, w 60°, Rein 52 400) (a) T 600 K, (b) T 800 K.
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Fig. 11. Penetration histories of vaporizing fuel droplets at dierent inlet spray cone angles (P 1 bar, T 600 K, S 0:37, Rein 52 400) (a) w 60°, (b) w 100°.
Fig. 12. Spatial dispersions of vaporizing fuel droplets at dierent inlet spray cone angles (P 1 bar, T 600 K, S 0:37, Rein 52 400) (a) w 60°, (b) w 100°.
4.4. In¯uence of spray cone angle An increase in spray cone angle shows a drastic reduction in the penetration of the spray (Fig. 11), with an increase in its radial dispersion (Fig. 12). A spray of higher cone angle with a given ¯ow rate is required to be injected from a larger ori®ce diameter of a conventional duplex nozzle. This causes a reduction in the initial axial velocity of droplets along with an increase in their initial tangential velocity, and ®nally results into a radially dispersed spray with a poor penetration.
5. Conclusion The penetration and vaporization histories of fuel droplets of a liquid fuel spray injected into a turbulent swirling ¯ow of air through a gas turbine combustor under dierent operating parameters and spray have been predicted from numerical computations of gas-droplet ¯ow based on two phase separated ¯ow model. It has been observed that a decrease in spray penetration takes place with an increase in inlet air swirl and inlet air pressure and with a decrease in inlet air temperature. The in¯uence of inlet swirl on penetration is more prominent at higher pressure as
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compared to that at lower pressure. The radial dispersions are drastically suppressed at higher air pressure. An increase in spray cone angle results in a drastic reduction in droplet penetration with signi®cant increase in radial dispersions. References [1] J.I. Ramos, A numerical study of swirl stabilized combustors, J. Non-Equlib. Thermodynamics 10 (1985) 263. [2] M.S. Raju, W.A. Sirignano, Spray computations in a centerbody combustor, ASME J. Engng. Gas Turbine Power 111 (1989) 710. [3] H.K. Ma, F.H. Lee, M.W. Wang, Numerical study on heat and mass transfer in a liquid-fueled gas turbine combustor, Int. J. Heat Mass Transfer 36 (13) (1993) 3271. [4] K.Y. Sokolov, A.G. Tumanovskiy, M.N. Gutnik, A.V. Sudarev, Y.I. Zakharov, E.D. Winogradov, Mathematical modeling of an annular gas turbine, ASME J. Engng. Gas Turbine Power 117 (1995) 94. [5] A.K. Tolpadi, Calculation of two-phase ¯ow in gas turbine combustor, ASME J. Engng. Gas Turbine Power 117 (1995) 695. [6] E.M. Amin, G.E. Andrews, M. Pourkishnian, A. Williams, R.A. Yetter, A Computational study of pressure eects on pollutant generation in gas turbine combustors, ASME J. Engng. Gas Turbine Power 119 (1997) 76. [7] F.K. Owen, I.J. Spadaccini, C.T. Bowman, Pollutant Formation and Energy Release in Con®ned Turbulent Diusion Flames, Sixteenth Symposium (International) on Combustion, The Combustion Institute, 1977, p. 105. [8] W.P. Jones, H. Toral, Temperature and composition measurement in a research gas turbine combustion chamber, Combustion Sci. Technol. 31 (1983) 249. [9] M.V. Heitor, J.H. Whitelaw, Velocity temperature and species characteristics of ¯ow in a gas turbine combustor, Cumbust. Flame 64 (1986) 1. [10] A.M. Bicen, M. Senda, J.H. Whitelaw, Scalar characteristics of combusting ¯ow in a model annular combustor, ASME J. Engng. Gas Turbine Power 111 (1989) 90. [11] C.D. Cameron, J. Brouwer, C.P. Wood, G.S. Samuelson, A detailed characteristics of the velocity and thermal ®elds in a model can combustor with wall jet injection, ASME J. Engng. Gas Turbine Power 111 (1989) 31. [12] A. Datta, S.K. Som, Eects of spray characteristics on combustion performance of a liquid fuel spray in a gas turbine combustor, Int. J. Energy Res. 23 (1999) 217. [13] A. Datta, S.K. Som, Combustion and emission characteristics in a gas turbine combustor at dierent pressure and swirl conditions, Appl. Thermal Engng. 19 (1999) 949. [14] C.T. Crowe, M.P. Sharma, D.E. Stock, The particle-source-in-cell (PSI-Cell) model for gas droplet ¯ows, ASME J. Fluids Engng. 99 (1977) 325. [15] R. Clift, J.R. Grace, M.E. Weber, Bubbles, Drops and Particles, Academic Press, New York, 1978. [16] R.A. Mugele, H.D. Evans, Droplet size distribution in sprays, Ind. Engng. Chem. 43 (1951) 1317. [17] C.W. Hirt, J.L. Cook, Calculating three dimensional ¯ows around structures and over rough terrain, J. Comput. Phys. 10 (1972) 324. [18] G.M. Faeth, Evaporation and combustion of sprays, Prog. Energy Combust. Sci. 9 (1983) 1. [19] K.C. Chang, C.S. Chen, Development of a hybrid j±e turbulence model for swirling recirculating ¯ows under moderate to strong swirl intensities, Int. J. Numer. Meth. Fluids 16 (1993) 421. [20] P.A. Dallenback, Heat Transfer and Velocity Measurements in Turbulent Swirling Flow through an Abrupt Axisymmetric Expansion. Ph.D. Thesis. Arizona State University, Tempe, 1986. [21] K.-J. Wu, R.D. Reitz, F.V. Bracco, Measurement of drop size at the spray edge near the nozzle in atomising liquid jets, Phys. Fluids 29 (4) (1986) 941±951.