Zhu, M.; Rogg, B. Modelling and simulation of sprays in laminar flames. (English) Zbl 0887.76097 Meccanica 31, No. 2, 177-193 (1996). Summary: We model and numerically simulate steady, laminar, premixed spray flames. The gas phase is described in Eulerian form by the equations governing the conservation of overall mass, momentum, energy and species mass. The liquid phase is described in Lagrangian form by the overall continuity equation, which reduces to an equation for the droplet size, the equations of motion, the energy equation and a droplet density function transport equation. The latter is the so-called ‘spray equation’, which, at any position in the chemically reacting flow field, describes the joint distribution of droplet size, droplet velocity and droplet temperature. Herein the spray equation is solved using a Monte Carlo method. Detailed models of the exchange of mass, momentum and energy between the gaseous and the liquid phase are taken into account. The results are presented for an octane-air flame, where small amounts of liquid octane in form of a liquid spray are added to a fresh, unburnt gaseous octane-air mixture. MSC: 76V05 Reaction effects in flows 76T99 Multiphase and multicomponent flows 76M25 Other numerical methods (fluid mechanics) (MSC2010) Keywords:conservation laws; Eulerian equations; Lagrangian equation; gas phase; liquid phase; transport equation; Monte Carlo method; octane-air flame PDFBibTeX XMLCite \textit{M. Zhu} and \textit{B. Rogg}, Meccanica 31, No. 2, 177--193 (1996; Zbl 0887.76097) Full Text: DOI References: [1] Williams, F.A., ?Progress in spray-combustion analysis?. In Eighth Symposium on Combustion, The Combustion Institute, 1962, pp. 50-69. [2] Lin, T.H., Law, C.K. and Chung, S.H., ?Theory of laminar flame propergation in off-stoichiometric dilute sprays?, Int. J. Heat Mass Transfer, 31 (1988) 1023-1034. [3] Lin, T.H. and Sheu, Y.Y., ?Theory of laminar flame propergation in near-stoichiometric dilute sprays?, Combust. and Flame, 84 (1991) 333-342. [4] Polymeropoulos, C.E., ?Flame propagation in a one-dimensional liquid fuel spray?, Combust. Sci. and Tech., 9 (1974) 197-207. [5] Burgoyne, J.H. and Cohen, L., ?The effect of drop size on flame propagation in liquid aerosol?, Proc. Royal Society, A 225 (1954) 375-392. [6] Hayashi, S., Kumagai, S. and Sakai, T., ?Propagation velocity and structure of flames in droplet-vapor-air mixtures?, Combust. Sci. and Tech., 15 (1976) 169-177. [7] Silverman, I., Greenberg, J.B. and Tambour, Y., ?Asymptotic analysis of a premixed polydisperse spray flame?, SIAM J. Appl. Math, 50, (5) (1991) 1284-1303. · Zbl 0744.76110 [8] Silverman, I., Greenberg, J.B. and Tambour, Y., ?Stoichiometry and polydisperse effects in premixed spray flames?, Combust. and Flame, 93 (1993) 97-118. [9] Westbrook, C.K. and Dryer, F.L., ?Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames?, Combust. Sci. and Tech., 27 (1981) 31-43. [10] Williams, F.A., Combustion Theory, Benjamin/Cummings, Menlo Park, 2nd edition, 1985. [11] Crowe, C.T., Sharma, M.P. and Stock, D.E., ?The Particle-source-in-cell (PSI-CELL) model for gas-droplet flows?, Transactions of the ASME, Journal of Fluids Engineering, June 1977, 325-332. [12] Abramzon, B. and Sirignano, W.A., ?Droplet vaporization model for spray combustion calculation?, Int. J. Heat Mass Transfer, 32 (9) (1989) 1605-1618. [13] Faeth, G.M., ?Current status of droplet and liquid combustion?, Prog. Energy Combust. Sci., 3 (1977) 191-224. [14] Adeniji-Fashola, A. and Chen, C.P., ?Modelling of confined turbulent fluid-particle flows using Eulerian and Lagrangian schemes?, Int. J. Heat Mass Transfer, 33 (4) (1990) 691-701. [15] Rogg, B., RUN-1DL: A Computer Program for the Simulation of One-Dimensional Chemically Reacting Flows, Technical Report CUED/A-THERMO/TR39, University of Cambridge, Department of Engineering, April 1991. [16] Rogg, B., RUN-1DL: ?The Cambridge universal laminar flamelet computer code?. In: Peters, N. and Rogg, B. (editors) Reduced Kinetic Mechanisms for Applications in Combustion Systems, Appendix C. Springer-Verlag, Berlin, Heidelberg, 1993. [17] Rogg, B., RUN-1DL: The Universal Laminar Flame and Flamelet Code, Technical report, 1994. [18] Reid, R.C., Prausnitz, J.M. and Poling, B.E., The Properties of Gases and Liquids, McGraw-Hill, New York, 4th edition, 1987. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.