Thin-Flame Theory for the Combustion of a Moving Liquid Drop: Effects Due to Variable Density

The combustion of a moving liquid fuel drop has been investigated. The drop experiences a strong evaporation-induced radial velocity while undergoing slow translation. In view of the high evaporation velocity, the flow field is not in the Stokes regime. The combustion process is modelled by an indefinitely fast chemical reaction rate. While the flow and the transport in the continuous phase and the drop internal circulation are treated as quasisteady, the drop heat-up is regarded as a transient process. The transport equations of the continuous phase require analysis by a singular perturbation technique. The transient heat-up of the drop interior is solved by a series-truncation numerical method. The solution for the total problem is obtained by coupling the results for the continuous and dispersed phases. The enhancement in the mass burning rate and the deformation of the flame shape due to drop translation have been predicted. The initial temperature of the drop and the subsequent heating influence the temporal variations of the flamefront standoff ratio and the flame distance. The friction drag, the pressure drag and the drag due to interfacial momentum flux are individually predicted, and the total drag behaviour is discussed. The circulation inside the drop decreases with evaporation rate. A sufficiently large non-uniform evaporation velocity causes the circulation to reverse. Disciplines Engineering | Mechanical Engineering Comments Suggested Citation: Gogos, George S., et. al. (1986) Thin-flame theory for the combustion of a moving liquid drop: effects due to variable density. Journal of Fluid Mechanics, Volume 171, p. 121-144. Copyright 1986 Cambridge University Press. This article is also available at http://dx.doi.org/10.101/ S0022112086001398 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/182 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/182 J . Fluid Me&. (1986), vol. 171, p p . 121-144 Printed in Great Britain 121 Thin-flame theory for the combustion of a moving liquid drop: effects due to variable density By GEORGE GOGOS, University of Pennsylvania, Philadelphia, PA 19104, USA S. S. SADHAL, University of Southern California, Los Angeles, CA 90089-1453, USA P. S. AYYASWAMY AND T. SUNDARARAJAN Department of Mechanical Engineering and Applied Mechanics, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104, USA (Received 11 December 1984 and in revised form 14 March 1986) The combustion of a moving liquid fuel drop has been investigated. The drop experiences a strong evaporation-induced radial velocity while undergoing slow translation. In view of the high evaporation velocity, the flow field is not in the Stokes regime. The combustion process is modelled by an indefinitely fast chemical reaction rate. While the flow and the transport in the continuous phase and the drop internal circulation are treated as quasisteady, the drop heat-up is regarded as a transient process. The transport equations of the continuous phase require analysis by a singular perturbation technique. The transient heat-up of the drop interior is solved by a series-truncation numerical method. The solution for the total problem is obtained by coupling the results for the continuous and dispersed phases. The enhancement in the mass burning rate and the deformation of the flame shape due to drop translation have been predicted. The initial temperature of the drop and the subsequent heating influence the temporal variations of the flamefront standoff ratio and the flame distance. The friction drag, the pressure drag and the drag due to interfacial momentum flux are individually predicted, and the total drag behaviour is discussed. The circulation inside the drop decreases with evaporation rate. A sufficiently large non-uniform evaporation velocity causes the circulation to reverse.