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International Heat Transfer Conference 12

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

Numerical Analysis of Unsteady Evaporation of Moderately Large (0.01≤Kn≤0.3) Droplets in Non-Isothermal Multicomponent Gaseous Mixtures

Gabi Ben-Dor
The Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel

Tov Elperin
The Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653 Beer Sheva 84105 Israel

Boris Krasovitov
The Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel

Abstract

In the present study unsteady evaporation of a single moderately large (0.01≤Kn≤0.3, where Kn = λ/R is Knudsen number) droplet in a non-isothermal multicomponent gaseous mixture was analyzed numerically taking into account the effects of temperature and concentration jumps. Following the diffusional-kinetic model (DKM) (Yalamov et al., 1977; Shchukin et al., 1991; Elperin and Krasovitov, 1995) the flow field in the neighborhood of the droplet is divided into the outer region where equations of continuum fluid mechanics can be applied and the inner Knudsen layer where transport processes are kinetically controlled. In the present study DKM is extended to the case of unsteady evaporation of moderately large droplet in non-isothermal multicomponent gaseous mixture with high temperature and concentration gradients in the vicinity of the droplet. The performed analysis is pertinent to slow droplet evaporation when Mach number is small (M<<1). System of unsteady nonlinear energy and mass conservation equations is solved numerically using inelastic approximation. The dependence of the droplet surface temperature on time and the effect of Stefan's flow and radiation on droplet evaporation are taken into account. Numerical calculations are performed for evaporating water and n-heptane droplets. It is found that the effect of temperature and concentration jumps on the evaporation of moderately large droplet during a warming-up period is significant when the temperature and vapor concentration at the droplet surface are relatively low. It is shown that in case of large concentrations at the droplet surface, boundary conditions for the concentration jump obtained from the kinetic theory and those obtained using Fick's law yield almost the same results. It is shown that the kinetic effects cause a significant deviation from the D2-law.

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