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On the solution of a class of polydisperse spray problems

Published online by Cambridge University Press:  26 September 2008

F. Anidjar ,
J. B. Greenberg  and
Y. Tambour
F. Anidjar
Affiliation:
Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
J. B. Greenberg
Affiliation:
Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Y. Tambour
Affiliation:
Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
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Abstract

A general method is presented to facilitate the solution of a class of polydisperse spray problems in which a cloud of droplets can be described using a sectional or group model. The procedure involves replacing the original coupled droplet sectional variables conservation equations by a set of uncoupled sectional equations for auxiliary variables. The form of these latter equations is identical to that of the single spray equation for a quasi-monodisperse spray, solutions of which are more readily attainable even for multidimensional spray problems. Thus, these ready-made solutions can be exploited directly for the auxiliary variables, from which solutions can then be constructed in a straightforward manner for the desired original sectional variables. Three illustrative examples for spray diffusion flames with different features of complexity highlight the potential applicability of the proposed method, and indicate the sensitivity of flame characteristics to initial spray conditions and in-spray related phenomena.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 1 , February 1996 , pp. 75 - 96
Copyright
Copyright © Cambridge University Press 1996

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References

[1] Williams, A. 1973 Combustion of droplets of liquid fuel: a review. Combustion and Flame 21, 1–31.CrossRefGoogle Scholar
[2] Bellan, J. & Harstad, K. 1987 The details of the convective evaporation of dense and dilute clusters of drops. Int. J. Heat Mass Transfer 30, 1083–1093.CrossRefGoogle Scholar
[3] Chiu, H. H. & Liu, T. M. 1977 Group combustion of liquid droplets. Combustion Science and Technology 17, 127–142.Google Scholar
[4] Chiu, H. H., Kim, H. Y. & Croke, E. J. 1980 Internal group combustion of liquid droplets. In 19th Symposium (International) on Combustion. The Combustion Institute, pp 971–980.Google Scholar
[5] Correa, S. M. & Sichel, M. 1982 The group combustion of a spherical cloud of monodisperse fuel droplets. In I9th Symposium (International) on Combustion. The Combustion Institute, pp 981–991.Google Scholar
[6] Labowsky, M. & Rosner, D. E. 1978 Group combustion of droplets in fuel clouds: quasi-steady predictions. In Evaporation – Combustion of Fuels. American Chemical Society, pp 63–79.Google Scholar
[7] Labowsky, M. 1980 Calculation of the burning rates of interacting fuel droplets. Combustion Science and Technology 22, 217–226.Google Scholar
[8] Tal, R., Lee, D. L. & Sirignano, W. A. 1983 Hydrodynamics and heat transfer in sphere assemblages – cylindrical cell models. Int. J. Heat Mass Transfer 26, 1265–1273.Google Scholar
[9] Tambour, Y. 1980 A sectional model for evaporation and combustion of sprays of liquid fuels. Israel Journal of Technology 18, 47–56.Google Scholar
[10] Chen, G. & Gomez, A. 1992 Counterflow diffusion flames of quasi-monodisperse electrostatic sprays. In 24th Symposium (International) on Combustion, pp 1531–1539.Google Scholar
[11] Lacas, F., Darabiha, N., Versaevel, P., Rolon, J. C. & Candel, S. 1992 Influence of droplet number density on the structure of stained laminar spray flames. In 24th Symposium (International) on Combustion, pp 1523–1529.Google Scholar
[12] Levy, Y. & Bulzan, D. L. 1991 Laminar spray combustion. In International Conference on Liquid Atomization and Spray Systems. Gaithersburg, MD.Google Scholar
[13] Li, S. C., Libby, P. A. & Williams, F. A. 1992 Experimental and theoretical studies of counterflow spray diffusion flames. In 24th Symposium (International) on Combustion, pp 1503–1512.Google Scholar
[14] Li, S. C., Libby, P. A. & Williams, F. A. 1993 Spray structure in counterflowing streams with and without a flame. Combustion and Flame 94, 161–177.Google Scholar
[15] Chen, N.-H., Rogg, B. & Bray, K. N. C. 1992 Modelling laminar two-phase counterflow flames with detailed chemistry and transport. In 24th Symposium (International) on Combustion, pp 1513–1521.Google Scholar
[16] Greenberg, J. B., Albagli, D. & Tambour, Y. 1986 An opposed-jet quasi-monodisperse spray diffusion flame. Combustion Science and Technology 50, 255–270.CrossRefGoogle Scholar
[17] Greenberg, J. B. & Cohen, R. 1992 Spatial distortion of spray diffusion flames. Atomisation and Sprays 2, 275–293.CrossRefGoogle Scholar
[18] Greenberg, J. B. & Sarig, N. 1993 Coupled evaporation and transport effects in counterflow spray flames. Combustion Science and Technology 92, 1–33.Google Scholar
[19] Greenberg, J. B. & Shpilberg, I. 1993 Transient phenomena in laminar spray combustion. In Collection of Papers of the 33rd Israel Annual Conference on Aviation and Astronautics. Israel, pp 430–438.Google Scholar
[20] Amsden, A. A., O'Rourke, P. J. & Butler, T. D. 1989 KIVA-1I: A computer program for chemically reactive flows with sprays. Los Alamos National Laboratory, Los Alamos, New Mexico, Report No. LA-11560-MS.Google Scholar
[21] Tambour, Y. 1984 Vaporization of polydisperse fuel sprays in a laminar boundary layer: a sectional approach. Combustion and Flame 58, 103–114.CrossRefGoogle Scholar
[22] Tambour, Y. 1985 A Lagrangian sectional approach for simulating droplet size distribution of vaporizing fuel sprays in a turbulent jet. Combustion and Flame 60, 15–28.Google Scholar
[23] Tambour, Y. 1985 Coalescence of vaporizing kerosene fuel sprays in a turbulent jet. Atomisation and Spray Technology 1, 125–146. (See also Simulation of coalescence and vaporization of kerosene fuel sprays in a turbulence jet: a sectional approach. AIAA/ASME/ASEE 21st Joint Propulsion Conference, Monterey, CA, 1985, AIAA Paper No. 85–1315.Google Scholar
[24] Williams, F. A. 1985 Combustion Theory. Benjamin/Cummings.Google Scholar
[25] Greenberg, J. B., Silverman, I. & Tambour, Y. 1993 On the origins of spray sectional conservation equations. Combustion and Flame 93, 90–96.CrossRefGoogle Scholar
[26] Avital, G., Greenberg, J. B., Tambour, Y. & Timnat, Y. M. 1990 Spray dynamics and fuel vapor distributions in a spinning combustion chamber. Progress in Astronautics and Aeronautics 132, 187–204.Google Scholar
[27] Greenberg, J. B. & Tambour, Y. 1986 Far-field coalescence effects in polydisperse spray jet diffusion flames. In 21st Symposium (International) on Combustion, The Combustion Institute, pp 655–663.Google Scholar
[28] Katoshevski, D. & Tambour, Y. 1993 A theoretical study of polydisperse liquid sprays in a shear-layer flow. Physics of Fluids A 5 (12), 3085–3098.CrossRefGoogle Scholar
[29] Khosid, S. & Tambour, Y. 1993 New closed-form analytical solutions of the discrete coagulation equation with simultaneous evaporation and their use for validation of sectional solutions. Atomization and Sprays 3, 223–248.Google Scholar
[30] Tambour, Y., Greenberg, J. B. & Albagli, D. 1985 Vaporization and coalescence of sprays in a three-dimensional axisymmetric stagnation flow. In ICLASS-85: 3rd International Conf. on Liquid Atomisation and Spray Systems. Institute of Energy, London, VIA/2/1-VIA/2/15.Google Scholar
[31] Greenberg, J. B. 1989 The Burke-Schumann diffusion flame revisited – with fuel spray injection. Combustion and Flame 77, 229–240.CrossRefGoogle Scholar
[32] Chigier, N. A. 1981 Energy Combustion and Environment. McGraw-Hill.Google Scholar
[33] Harsha, P. T. & Edelman, R. B. 1984 Analytical modeling of a spray diffusion flame. AIAA Paper 84–1317.CrossRefGoogle Scholar
[34] Burke, S. P. & Schumann, T. E. W. 1928 Diffusion flames. Ind. Eng. Chem. 20, 998–1004.CrossRefGoogle Scholar
[35] Chigier, N. A. & Tambour, Y. 1994 The structure of sprays produced by air-assist swirl and non-swirl atomizers. In Adv. in Spray Combustion, Kuo, K., Ed. (to appear).Google Scholar
[36] Yule, A. J., Ereant, P. R. & Ungut, A. 1983 Droplet sizes and velocities in vaporizing sprays. Combustion and Flame 54, 15–22.Google Scholar
[37] Greenberg, J. B. 1993 Multisize droplet effects inspray diffusion flames. AIAA/SAE/ASME/ASEE 29th Joint Propulsion Conf., Monterey, CA.Google Scholar
[38] Raju, M. S. & Sirignano, W. A. 1990 Interaction between two vaporizing droplets in an intermediate Reynolds number flow. Physics of Fluids A 2 (10), 1780–1796.Google Scholar
[39] Chung, S. H. & Law, C. K. 1984 Burke-Schumann flame with streamwise and preferential diffusion. Combustion Science and Technology 37, 21–46.Google Scholar
[40] Greenberg, J. B. & Shpilberg, I. 1993 Lewis number and vaporization effects in spray diffusion flames. Atomization and Sprays 3, 437–462.Google Scholar
[41] Greenberg, J. B. 1989 Influence of initial nonuniform spray patterns on quasi-monodisperse droplet diffusion flames. In 26th ASME National Heat Transfer Conference, HTD-Vol. 106, Heat Transfer Phenomena in Radiation, Combustion and Fires, pp 543–549.Google Scholar