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NUMERICAL SIMULATION OF A STEADY HOLLOW-CONEMETHANOL SPRAY FLAME WITHIN AN ANNULAR AIR JETWOO TAE KIM a , KANG Y. HUH a , JACOB A. FRIEDMAN b & METIN RENKSIZBULUT ca Department of Mechanical Engineering, Pohang University of Science & Technology,Pohang, Kyungbuk, Republic of Koreab Department of Mechanical Engineering, Ryerson Polytechnic University, Toronto, Ontario,Canadac Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada

Version of record first published: 03 Apr 2007.

To cite this article: WOO TAE KIM, KANG Y. HUH, JACOB A. FRIEDMAN & METIN RENKSIZBULUT (2001): NUMERICAL SIMULATIONOF A STEADY HOLLOW-CONE METHANOL SPRAY FLAME WITHIN AN ANNULAR AIR JET, Combustion Science and Technology,171:1, 119-139

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Combust. Sci. andTech.. 171:llS-139, 2001 Copyright 0 2001 Taylor & Francis 0010-2202101 $12.00 +.oo

NUMERICAL SIMULATION OF A STEADY HOLLOW-CONE METHANOL SPRAY FLAME WITHIN AN ANNULAR AIR JET

W O O TAE K I M AND KANG Y. HUH* Department of Mechanical Engineering, Pohang University of Science &Technology, Pohang, Kyungbuk, Republic of Korea

JACOB A. FRIEDMAN Department of Mechanical Engineering, Ryerson Polytechnic University, Toronto, Ontario, Canada

METlN RENKSIZBULUT Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada

Numerical simulations are performed to investigate a reacting steady hollow- cone methanol spray interacting with an annular air jet. Eulerian conservation equations are solved for gas flow while a stochastic Lagrangian method is used for sprays in KIVA-3 (Amsden 1993). Initial conditions for injected droplet parcels are sampled stochastically from the distribution functions based on measured liquid volume flux and Sauter mean diameter. Coupling between turbulent flow and chemistry is treated by the conserved scalar approach with a beta function probability density function for the mixture fraction. Mean gas temperature, OH concentration, Sauter mean diameter, and liquid volume flux are in reasonable agreement with measurements for three different air flow rates. It is shown that the annular air jet tends to deflect droplets toward the axis, providing a narrower and shorter reaction

Received 18 October 2000; accepted 20 July 2001. This paper is original work not previously published and not being considered else-

where for publication, and that if accepted for publication it will not be published elsewhere in the same form, in any language, without the consent of editors and publisher.

*Corresponding author E-mail: huh@postech.ac.kr

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zone suitable for a more compact combustion chamber. Discrepancy for the no air jet case is attributed to the isotropic turbulent dispersion model for droplet-eddy interaction. Other possible reasons may be the k - c model for gas flow, improper input conditions for injected droplet parcels, and inaccu- rate correlations for exchange of mass, momentum, and energy between droplets and gas.

Keywnrd.~: Annular air jet; combustion; numerical simulation; spray

INTRODUCTION

Liquid fuel is introduced in the form of a spray in many energy con- version systems such as industrial furnaces, power plants, home heating systems, and internal combustion engines. Enhanced performance and low en~issions of these applications demand optimized control of the atomized droplet sizes, their spatial distribution, and interaction with surrounding gas. One of many atomizing systems available is the pres- sure-swirl, or simplex, atomizer, which injects swirling liquid in a thin hollow-cone sheet, which subsequently breaks up into droplets (Lefebvre, 1989). It has been found that a hollow-cone spray in the wake or recir- culation region of a bluff body enhances the low load performance by redistributing droplets in space (Li and Tankin, 1991). The recirculation zone provides a region of low mean velocity and high turbulence intensity for more stable combustion. Stability of the flame, as well as the overall flame shape, soot, and pollutant formation are strongly influenced by these flow characteristics.

A considerable amount of experimental work has been performed on the wake flow of a bluff body (Chigier and Be&, 1964; Dur lo and Whitelaw, 1978; Taylor and Whitelaw, 1984) and interaction with a fuel jet or a spray under nonreacting as well as reacting conditions (Beer, Chigier, and Lee, 1963; Li and Tankin, 1987; Li and Tankin, 1989). Li and Tankin (1989) examined the spray shapes and parameters to study the behavior of a spray in an annular air jet. Phase Doppler Interferometry (PDI) is capable of rapid simultaneous measurement of droplet sizes and velocities for detailed characterization of a spray (McDonell, Adachi, and Samuelsen, 1993; Friedman and Renksizbulut, 1994; Sommerfeld and Qiu, 1998). Planar laser-induced fluorescence (PLIF) has been used to produce two-dimensional maps of various species concentrations in spray flames (Allen et al., 1995; Cessou and Stepowski, 1996: Friedman and Renksizbulut, 1999). Friedman and Renksizbulut recently investi-

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gated interaction of a methanol spray flame with an annular air jet by PDI and PLIF, the database of which is employed for validation in this paper. Hollmann and Gutheil (1998) numerically investigated turbulent methanollair sprays under both nonreacting and reacting conditions. They concluded that detailed input conditions a t the nozzle were required to properly represent the spray characteristics. Sommerfeld (1998) pre- sented both experimental and numerical results on stationary turbulent sprays by the EulerlLagrange approach. Although these few previous predictions have shown qualitative agreement, more validation work has been needed against a consistent set of data for practical spray com- bustion systems.

MATHEMATICAL MODELS

Liquid Spray Model

The standard spray models in KIVA (Amsden et al., 1989) are used for mass, momentum, and energy exchange with gas phase. Breakup is assumed to occur completely at the nozzle exit to avoid uncertainties in the atomization and collision/coalescence models. The droplet accelera- tion, F, due to aerodynamic drag is given as

3 p I t i + u U - v l F = - - (t i + u" - v)CD 8 pd r

The drag coefficient, CD, is given by (Putnam, 1961)

where Red is the droplet Reynolds number based on the droplet diameter, p is the mean gas density, pd is the liquid density, r is the droplet radius, ic is the Favre average gas velocity, u" is the turbulent fluctuation velocity, and v is the droplet velocity. Relevant thermophysical properties are evaluated at the reference temperature according to the one-third rule (Sparrow and Gregg, 1958). The vaporization rate of each droplet is described by the Frossling correlation (Faeth, 1977) as,

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where 9, is the mean mass fraction of fuel vapor, p f / p , and yI* is the mean mass fraction of fuel vapor at droplet surface. The Sherwood number, Shd, is given by

where SC,/ is the Schmidt number and Bd = (3 - Y I ) / ( I - f i ) . The rate of change of the droplet temperature is determined from energy balance,

where cl is the specific heat of liquid fuel, L(Td) is the latent heat of vaporization, Td is the droplet temperature, and Q,/ is the rate of heat conduction to the droplet per unit area. Qd is given by the Ranz-Marshall correlation (Faeth, 1977) as

where Kai, is gas conductivity. The Nusselt number, Nud, is given by

where Prd is the Prandtl number. An isotropic interaction model is used to account for the effect of gas turbulence on turbulent droplet dispersion (Shirolkar et al., 1996). The droplet-eddy interaction time is determined as the minimum of the two time scales, eddy-life time and eddy-transit time, as

where c,, is an empirical constant, given the value of 0.164 (Amsden, O'Rourke, and Butler, 1989) here. Each component of u" is obtained by

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randomly sampling a Gaussian P D F with a standard deviation of ( 2 ~ 1 3 ' ' ~ ) (Gosman and Ioannides, 1981).

Turbulent Combustion Model

For gas flow the equations for mean and variance of the mixture fraction are solved in addition to the equations for mass, momentum, energy, turbulent kinetic energy, and its dissip~tion rate. The Favre mean and variance of the mixture fraction, 5 and ( / I 2 , satisfy the following transport equations,

where p" is the rate of mass transfer from droplets to gas. The Schmidt numbers, ScF and Sc- , are assigned a constant value of 0.7 (Launder and

W. T. KIM ET AL.

('4)

FLFM(5*), p S L F M ( ( * ) and q L F M ( ( ' ) are given from the stationary laminar flamelet model (Kim, Huh, and Liu, 2000b) with a low strain rate of 1 s-' and the detailed reaction mechanism for methanol (Peters, 1993). It turns out that equilibrium assumption leads to erroneous results in rich mixtures of methanol. It is because methanol includes an oxygen atom and is not in the thermodynamic equilibrium state by itself (Kin], Huh, and Liu). Figure I shows the functional shapes of Y , ? ~ ~ ~ ( ( * ) for major reactant and product species from the stationary laminar flamelet model. The Favre PDF, P(t*;x), is parameterized as a beta function (Libby and Williams, 1994) as

Mixture Fraction Variable

Figure I . Mess fractions of the major species with respect to the mixture fraction

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where cc = ~ ( I / S - I), = a(1/4 - l ) , and S = [(/'*/;(I - ?)I. The effects of radiative heat loss are ignored as negligible for nonluminous methanol flames.

NUMERICAL METHOD

Spray calculation is performed by the stochastic discrete particle method in KIVA-3 (Amsden 1993). Each computational parcel represents a number of droplets of the identical size, location, velocity, temperature, etc. The initial conditions for the injected droplet parcels are specified as follows. First the measured radial distribution of the liquid volume flux near the nozzle is converted to a distribution function with respect to the injection angle in Figure 2. The injection direction of each parcel is determined stochastically according to the P D F in terms of the normal- ized liquid volume flow rate. A random number c, between 0 and 1 is generated for each parcel to determine the injection angle 0, from the cumulative distribution function. The droplet size is again stochastically determined from the drop size distribution function (Lefebvre, 1989) based on the measured Sauter mean diameter (SMD) in the given injec- tion direction. The factor 6 in the Rosin-Rammler distribution is set equal to 4.0, as an average value of available data (Friedman and Renksizbulut, 1999). The injection speed is fixed as constant for all parcels injected in different directions. Previous study (Kim et al., 2000a) has

- Injection Angle (degrees) Figure 2. Normalized liquid volume Row rate and its cumulative distribution function.

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shown good agreement of the calculated and measured radial profiles of mean droplet velocity near the nozzle.

Statistical averaging is performed for the spray parameters of interest a t selected probing planes perpendicular to the axis. A single cell on the probing plane is selected as a probing volume, while the bottom face of a probing volume is selected as a probing area. Spray parcels are collected over a few thousand computational time steps after the steady-state is reached. Convergence to the steady-state is checked in terms of the total number of spray parcels in the domain and the fractional differences of mean pressure and velocity components between consecutive time steps. The Sauter mean diameter and average volume flux are obtained as

Sauter mean diameter = (g - :$) ~ T C ~ N , D ;

volume flux = Aprobetprobe

where Ni and Di represent the number and the diameter of droplets in the ith parcel. Aprobc and t,,,b, are the probing area and the total probing time. Summation is over all parcels that pass through the probing area during the probing time.

DESCRIPTION OF THE PROBLEM

A typical configuration of a hollow-cone spray flame surrounded by an annular air jet is shown in Figure 3 (Chigier, 1981). The primary reaction zone exists outside the spray sheath between the recirculation zone and the external air jet. A larger secondary reaction zone is located down- stream of the recirculation zone. Rapid evaporation of fuel droplets occurs in the hot primary and secondary reaction zones.

The nozzle assembly consists of a hollow brass cylinder fitted with the standard Delavan 0.75-60"A pressure-swirl nozzle. Air is guided through the annular region between the removable outer sleeve and the inner cylinder to form an annular jet. The air flow rate is varied as 0,4770, and 9520 cm3/s a t the atmospheric pressure and temperature. The flow rate of methanol is fixed a t 0.42 g/s. The inner diameter of the annulus is

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Liquid Fuel

TI- Annulus

Air I 1 ,Spray Nozzle

Primary Reaction Zone

. . . . . . . . Spray Sheath

. . . . . . . . . . . Boundaries

Secondary Gas Flow Streamlines Visible Flame

/Boundary

Axis Figure 3. A typical configuration of spray flames (Chigier, 1981).

5.04 cm, while the outer diameter is 6.36 cm. The air jet velocities are 0, 404, and 806 cm/s for the three different air flow rates.

The computational domain is a rectangle with the radius of 7 cm and the length of 10 cm. An axisymmetric 2-D sector mesh is used with a nonuniform structured grid of 41 x 61 in the radial and axial direction, which gives the grid independent results (Figure 4). The circumferential angle of the sector mesh is specified as 0.5 degree with periodic boundary conditions on the front and rear faces. The degenerate left face is the axis of the cylinder with a symmetric boundary condition. A solid wall boundary condition is imposed on the bluff-body while an inflow velocity boundary condition is imposed a t the inlet of an annular air jet. A continuative inflow boundary condition is imposed on the remaining part of the top face. Constant pressure is assumed on the right and bottom faces of the computational domain.

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Figure 4. Computational grid

RESULTS AND DISCUSSION

Figure 5 shows the gas flow fields with three different air flow rates. Flow is induced only by the momentum of injected spray droplets with no air jet in Figure 5(a). As the air flow rate increases, a jet-driven recirculating flow interferes with the downward flow induced by spray droplets. The wake flow behind the bluff-body is divided into two distinct recirculating regions with a strong air jet. Figure 6 shows distributions of droplets, the sizes of which are proportional to the SMDs of the parcels. Note that these are overlapped images in the circumferential direction of an axi- symmetric sector mesh. They are different from a planar image since a small number of parcels near the axis may represent a large number density per unit volume. For the case with no air jet, some small droplets escape the initial spray envelope and float outward due to turbulent entrainment in Figure 6. Most droplets in the spray decelerate fast and move slowly with gas at a downstream location. The annular air jet helps to prevent droplets from escaping the initial spray envelope as shown in Figure 6. Droplets are deflected toward the axis by a larger deflection angle as the air flow rate increases. The recirculation pocket between the

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0 2 4 6 r(cmJ

(a) Qc = 0 cm3/s (b) Qc: = 4770 cm3/s Figure 5. Gas velocity fields.

0 2 4 6 r (cm)

(c) Qc = 9520 cm3/s

edge of the spray and the bluff-body is strong enough to entrain droplets in Figure 6(c). These entrained droplets first move upward and then follow the streamlines of recirculating flow. Most large droplets exist around the periphery of the spray, since they are not much affected by the air jet due to their larger mass and momentum.

Figures 7 and 8 show contours of mean and variance of the mixture fraction. Contours of the mean mixture fraction are the combined effects

i i i o i i i r lcm) r (cm)

(a) Qc = 0 cm3/s (b) Qc = 4770 cm3/s (c) Qc: = 9520 cm3/s Figure 6. Distributions of spray droplets.

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130 W. T. KIM ET AL.

Figure 7. Contours of mean mixture fraction

of droplet distribution mixing with an air jet, resulting in different combustion characteristics. As the air flow rate increases, the maximum mean mixture fraction in the recirculation region also increases. In Figure 7 , the upstream contour of the stoichiometric mean mixture fraction moves from the fuel nozzle toward the air inlet as the air flow rate increases. On the other hand, the downstream contour of the stoichio- metric mean mixture fraction approaches the axis a t a higher air flow

Figure 8. Contours of variance of the mixture fraction.

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rate. Contours of the scalar fields, such as mean density, temperature, and species mole fractions in Figures 9-10 and 12-13 are direct con- sequences of the distributions of mean and variance of the mixture fraction. Note a steep gradient of mean gas temperature near the reaction region a t the stoichiometric mean mixture fraction. A higher air flow rate results in a steeper gradient of mean gas density and temperature in the reaction region. Figures 10 and 11 show contours of the predicted O H mole fraction and composite fluorescence images of OH averaged over one hundred shots in experiment (Friedman and Renksizbulut, 1999). The O H radical has a longer lifetime in burned gas of premixed flames, whereas it quickly disappears on either side of the reaction zone in nonpremixed flames (Cessou and Stepowski, 1996). The O H radical may, therefore, be considered as a tracer of reactivity in the present spray flame. Calculation shows a proper qualitative trend for distribution of mean O H concentration except for the case with no air jet. One possible reason for such discrepancy seems to be the turbulent dispersion model of droplets. Several authors (Chen and Pereira, 1996; Adeniji-Fashola and Chen, 1990) reported in nonreacting spray calculations that the predicted droplet mass flux tends to accumulate unrealistically near the axis in a cylindrical geometry. Macinnes and Bracco (1992) showed that small droplets tend to be depleted from the region of high turbulence intensity and accumulate in the region of the minimum turbulence intensity in inhomegeneous particle-laden flows. This mechanism may have caused

(a) Q c = 0 cm3/s (b) Q c = 4770 cm3/s (c) Q c = 9520 cm3/s

Figure 9. Contours o f mean gas temperature.

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0 2 4 6 o i i i r k m ) r (cm)

(b) QG = 4770 cm3/s (c) QG = 9520 crn3/s Figure 10. Contours of mean OH mole fraction

small droplets to move toward the axis, resulting in the maximum mean mixture fraction on the axis. The experimentally observed double reac- tion zones may be recovered, if the maximum mean mixture fraction occurs in the spray cone angle. The maximum mean mixture fraction occurs in the recirculating region adjacent to the bluff-body with a strong air jet in Figure 7(b)-(c). The turbulent dispersion model of droplets has much weaker influence in these mean flow structures. The predicted OH concentrations turn out to be twice as high as the measurement with the

(a) QG = 0 cmys (b) &G = 4770 cm3/s (c) QG = 9520 cmys Figure I I . Coniposite OH fluorescence images averaged over one hundred shots in experi- ment (Friednian and Renksizhulut. 1999).

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Figure 12. Contours of mean mole fraction of CH,OH

reported uncertainty level of about 50 percent (Friedman and Renksiz- bulut, 1999). The predicted O H concentrations are from the stationary laminar flamelet solution with a low strain rate, which is close to ther- modynamic equilibrium. Figures 12-13 show contours of mean mass fractions of the major species, C H 3 0 H and COz.

Calculated SMD's at z = 2.5 cm and z = 8.0 cm are compared with the measurements in Figure 14. The same size distribution function is

r (cm)

(a) Qc = 0 cm3/s I (cml

(b) QG = 4770 cm3/s

Figure 13. Contours of mean mole fraction of C 0 2

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80

P a 0

% 2 4 6 0 2 4 6 0 2 4 Radius (cm) Radius (cm) Radius (cm)

(a) z = 2.5 cm 80

0

Radius (cm) Radius (cm) Radius (cm) (b) z = 8.0 cm

Figure 14. Radial profiles of the Sauter mean diameter at z = 2.5 cm and z = 8.0 cm; 0 , ex- periment (Friedman and Renksizbulut. 1999); 0, calculation.

prescribed for all cases, since the annular air jet is not likely to have any direct influence on injected droplet sizes. The S M D profiles at z = 2.5 cm are not as much affected by the air flow rate as those at z = 8.0 cm. The calculated S M D profiles at z=8.0 cm with an air jet have steeper radial gradients than the measurements. It is because many small droplets are entrained toward the axis in calculation as the air flow rate increases. The corresponding profiles of the liquid volume flux are given at the same locations in Figure 15. Calculation results show reasonable agreement with the measured liquid volume fluxes, which involve considerable uncer- tainty owing to measurement difficulties (Friedman and Renksizbulut, 1999). Discrepancy for the air flow rate of 4770 cm3/s in Figure 15(a) is

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Q, = 0 cm'ls

Radius (cm) ,b&l& Radius (cm) Radius ( a n )

(a) z = 2.5 cm

'A Q, = 0 cm'ls $0.003

Radius (cm)

Q, = 4770 cm'ls

Radius (cm) (b) 2 = 8.0 cm

Figure 15. Radial profiles of the liquid volume flux at z = 2.5 cm and z = 8.0 cm; a, experi- ment (Friedman and Renksizbulut, 1999); 0 calculation.

due to methanol emerging as a vapor jet from the bluff-body heated by flame impingement (Friedman and Renksizbulut). The flame along the stoichiometric mean mixture fraction is attached to the bluff-body in Figure 7(b). Note also the underpredicted liquid volume fluxes a t a downstream location and on the axis with no air jet in Figure 15(b). These may be partly due to inaccurate correlations for exchanges of mass, momentum, and energy between droplets and gas (Renksizbulut, Buss- mann, and Li, 1992). The downstream liquid volume fluxes are much lower than the upstream values, as most liquid droplets evaporate fast. Figure 16 shows good agreement for radial profiles of the Favre mean temperature except for the case with no air jet. Predicted mean

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136 W. T. KIM ET AL.

OOOXCO 00 CCCC

Radius (cm) Radius (cm) Radius (cm) (a) z = 2.5 cm

2500

500

' 0 2 4 6 0 2 4 6 0 2 4 Radius (cm) Radius (cm) Radius (cm)

(b) 2 = 8.0 cm Figure 16. Radial profiles of the mean gas temperature at z = 2.5 cni and : = 8.0 cm; .,ex- periment (Friedman and Renksizbulut 1999); 0, calculation.

temperature distributions are the direct consequences of the distributions of mean and variance of the mixture fraction in Figures 7-8. The overpredicted temperatures on the axis seem to be partly related to onlission of gas phase cooling due to evaporation of droplets. All the computation results here are based on the adiabatic assumption with the temperature and other thermodynamic variables given as a function of the mixture fraction.

CONCLUSION An axisymmetric two-dimensional simulation has been performed for a steady hollow-cone spray flame of methanol interacting with an annular

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air jet. The annular air jet produces a recirculation region and exerts a shielding effect by deflecting droplets toward the axis. It tends to confine the spray shape in a narrower and shorter reaction zone suitable for a more compact con~bustion chamber. Calculation results show good comparison with the measured radial profiles of SMD and liquid volume flux for three different air flow rates. The radial profiles of mean tem- perature are also in good agreement with some discrepancy on the axis and near the peaks for the case with no air jet. This is attributed to the isotropic turbulent dispersion model of droplets, which tends to drift too many droplets toward the axis. There may be other possible reasons that require further investigation, such as the gas phase turbulence model, improper injection conditions at the nozzle, and inaccurate cor- relations for exchange of mass, momentum, and energy between droplets and gas.

REFERENCES Adeniji-Fashola, A. and Chen, C.P. (1990) Modeling of confined turbulent fluid-

particle flows using Eulerian and Lagrangian schemes. 1111. J. Mass Truttsfer, 33, 691-701.

Allen, M.G., McManus, K.R., Sonnenfroh, D.M. and Paul, P.H. (1995) Planar laser-induced fluorescence imaging measurements of OH and hydrocarbon fuel fragments in high pressure spray flame combustion, Applied Optics, 34, 6287-6300.

Amsden, A.A. (1993) KIVA-3: A K I V A Progrunt tvirh Block-Structured Mesh for Comp1e.r Geometries. Los Alamos National Laboratory Report LA-12503- MS.

Amsden, A.A., O'Rourke, P.J. and Butler, T.D. (1989) KIVA-11: A Computer Program for Chemically Reactive Flo~vs with Sprays. Los Alamos National Laboratory Report LA-1 1560-MS.

Beer, J.M., Chigier, N.A. and Lee, K.B. (1963) Modeling of the double concentric burning jets. Proc. Combust. Int., 9, 892-900.

Cessou, A. and Stepowski, D. (1996) Planar laser induced fluorescence mea- surement of [OH] in the stabilization stage of a spray jet flame. Cornbust. Sci. Technol., 118, 361-381.

Chen, X.Q. and Pereira, J.C.F. (1996) Computation of turbulent evaporating sprays with well-specified measurements: A sensitivity study on droplet properties. Inr. J. Heur Mass Transfer, 39, 441 -454.

Chigier, N.A. (1981) Energy, Combusrion and Environment, McGraw Hill: New York.

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] at 1

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138 W. T. KIM ET AL.

Chigier, N.A. and Be&, J.M. (1964) The flow region near the nozzle in double concentric jets. J . Basic Eng., 797-804.

Durio, D.F.G. and Whitelaw, J.H. (1978) Velocity characteristics of the flow in the near wake of a disk. J . Fluid Mech., 85, 369-385.

Faeth, G.M. (1977) Current status of droplet and liquid combustion. Prog. En- ergy Conihust. Sci., 3, 191 -224.

Friedman, J.A. and Renksizbulut, M. (1994) Interaction of an annular air jet with a non-evaporating liquid spray, Part. Part. Syst. Cl~aract., l I , 442-452.

Friedman, J.A. and Renksizbulut, M . (1999) Investigating a methanol spray flame interacting with an annular air jet using phase-Doppler interferometry and planar laser-induced fluorescence. Conlhust. Flume, 117, 661-684.

Gosman, A.D. and loannides, E. (1981) Aspects of computer simulation of liquid-fueled compustors. AlAA Paper 81-0323.

Hollmann, C. and Gutheil, E. (1998) Flamelet-modeling of turbulent spray dif- fusion flames based on a laminar spray flame library. Comhusr. Sci. Technol., 135, 175-192.

Jones, W.P. and Whitelaw, J.H. (1982) Calculation methods for reacting turbu- lent flows: A review. Conthust. Flatne, 48, 1-26.

Kim, S.H., Huh, K.Y. and Liu, T. (2000b) Application of the elliptic conditional moment closure model to a two-dimensional nonpremixed methanol bluff body flame. Conthust. Flame, 120, 75-90.

Kim, W.T., Huh, K.Y., Friedman, J.A. and Renksizbulut, M. (2000a) Numerical investigation of a steady nonevaporating hollow-cone spray interacting with an annular air jet. Atotniz. Sprays, 11, in press.

Launder, B.E. and Spalding, D.B. (1972) Lectures in Mathematical Models of Tirrhttlence. Academic Press: London.

Lefebvre, A.H. (1989) Arotnization and Sprays. Hemisphere Publishing Cor- poration: U.S.A.

Li, X. and Tankin, R.S. (1987) A study of cold and combusting flow around bluff body combustors. Comhust. Sci. Technol., 52, 173-206.

Li, X . and Tankin, R.S. (1989) Spray behaviour in annular air streams. Comhust. Sci. Technol., 64, 141 - 165.

Li, X. and Tankin, R.S. (1991) Spray behaviour in non-swirling and swirling annular air flows. Alomiz. and Sprays, 1 , 319-336.

Libby, P.A. and Williams, F.A. (1994) Fundamental aspects and a review. Tur- brrleut Reacting Flows, In P.A. Libby and F.A. Williams (eds.), Academic Press: London, pp. 2-61.

Macinnes, J.M. and Bracco, F.V. (1992) Stochastic particle dispersion modeling and the tracer-particle limit. Pltys. Fluids A, 4 , 2809-2824.

McDonell, V.G., Adachi, M. and Samuelson, G.S. (1993) Structure of reacting and non-reacting, non-swirling, air assisted sprays, Part 2: Drop behavior. Atoniiz. and Sprays, 3, 41 1-436.

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