Laminar Condensation on a Moving Drop. Part 1. Singular Perturbation Technique

In this paper, laminar condensation on a spherical drop in a forced flow is investigated. The drop experiences a strong, radial, condensation-induced velocity while undergoing slow translation. In view of the high condensation velocity, the flow field, although the drop experiences slow translation, is not in the Stokes-flow regime. The drop environment is assumed to consist of a mixture of saturated steam (condensable) and air (non-condensable). The study has been carried out in two different ways. In Part 1 the continuous phase is treated as quasi-steady and the governing equations for this phase are solved through a singular perturbation technique. The transient heat-up of the drop interior is solved by the series-truncation numerical method. The solution for the total problem is obtained by matching the results for the continuous and dispersed phases. I n Part 2 both the phases are treated as fully transient and the entire set of coupled equations are solved by numerical means. Validity of the quasi-steady assumption of Part 1 is discussed. Effects due to the presence of the non-condensable component and of the drop surface temperature on transport processes are discussed in both parts. A significant contribution of the present study is the inclusion of the roles played by both the viscous and the inertial effects in the problem treatment. Disciplines Engineering | Mechanical Engineering Comments Suggested Citation: Chung, J.N., Portonovo S. Ayyaswamy and Satwindar S. Sadhal. (1984). Laminar condensation on a moving drop. Part 1. Singular perturbation technique. Journal of Fluid Mechanics. Vol. 139, p. 105-130. Copyright 1984 Cambridge University Press. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/186 J . Fluid Mech. (1984), wol. 139, p p . 105130 Printed in Great Britain 105 Laminar condensation on a moving drop. Part 1. Singular perturbation technique By J. N. CHUNG, Department of Mechanical Engineering, Washington State University, Pullman, WA 99164-2920 P. S. AYYASWAMY Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104 AND s. s. SADHAL Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453 (Received 26 August 1981 and in revised form 7 September 1983) I n this paper, laminar condensation on a spherical drop in a forced flow is investigated. The drop experiences a strong, radial, condensation-induaed velocity while undergoing slow translation. In view of the high condensation velocity, the flow field, although the drop experiences slow translation, is not in the Stokes-flow regime. The drop environment is assumed to consist of a mixture of saturated steam (condensable) and air (non-condensable). The study has been carried out in two different ways. I n Part 1 the continuous phase is treated as quasi-steady and the govcrning equations for this phase are solved through a singular perturbation technique. The transient heat-up of the drop interior is solved by the series-truncation numerical method. The solution for the total problem is obtained by matching the results for the continuous and dispersed phases. I n Part 2 both the phases are treated as fully transient and the entire set of coupled equations are solved by numerical means. Validity of the quasi-steady assumption of Part 1 is discussed. Effects due to the presence of the non-condensable component and of the drop surface temperature on transport processes are discussed in both parts. A significant contribution of the present study is the inclusion of the roles played by both the viscous and the inertial effects in the problem treatment.