THERMAL AND DYNAMIC EVOLUTION OF A SPHERICAL BUBBLE MOVING STEADILY IN A SUPERHEATED OR SUBCOOLED LIQUID

The heat transfer rate and the hydrodynamic forces experienced by a si ngle vapor bubble of variable radius moving in a superheated or subcoo led liquid are studied by means of numerical simulation. For that purp ose the full Navier-Stokes equations and the temperature equation are solved in a frame of reference where the bubble surface is steady. The time evolution of the bubble radius is determined by solving the ener gy balance at the bubble surface. The numerical method is first valida ted by comparing present predictions with previous asymptotic or numer ical results in the ease where no relative motion between the liquid a nd the bubble exists. Then the situation where a constant relative vel ocity exists is considered. Effects of the mean flow on the heat trans fer rate and on the bubble radius evolution are first discussed. Two d ifferent stages are generally observed in the computations. First, the radial motion induced by the displacement of the bubble surface domin ates and the bubble evolution is essentially identical to the one obse rved in a liquid at rest. Then the ratio between the radial velocity a nd the translatory velocity decreases and the heat transfer rate becom es governed by streamwise advection effects. In this second stage a su bstantial increase of the growth or collapse rate of the bubble is obs erved, compared to the case of a liquid at rest. For a growing bubble it is shown that the complete process is successively described by the analytical solutions given by Scriven [Chem. Eng. Sci. 10, 1 (1959)] and Ruckenstein [Chem. Eng. Sci. 10, 22 (1959)]. The situation is much less simple for a collapsing bubble and the reasons of this increased complexity are discussed. It is found that, when the heat transfer me chanism is dominated by streamwise advection, the bubble evolution and the collapse time predicted by the simulations agree well with the ex perimental results obtained by Chen and Mayinger [Int. J. Multiphase F low 18, 877 (1992)]. Based on the present results, a general correlati on giving the collapse time as a function of the characteristic parame ters of the problem is proposed. The second contribution of the presen t work concerns the hydrodynamic force experienced by the bubble. Usin g a general decomposition procedure, the added mass effect and the vis cous contribution are separately identified. It is first shown that th e added mass coefficient is strictly constant and equal to one half, w hatever the Reynolds number and the relative magnitude of the radial v elocity. The viscous drag is then systematically compared with the qua sisteady viscous drag corresponding to the instantaneous value of the Reynolds number. In situations of boiling, effects due to unsteadiness are found to exist during the first stages of the motion if the initi al Reynolds number is not very large. In contrast, for a collapsing bu bble, such effects remain significant all along the process because th e relative importance of viscous phenomena increases in time. In both cases it is shown that the time variations of the bubble radius may af fect deeply the viscous drag force. For example, when the radial veloc ity is high enough, the viscous drag force is found to be identical to the one corresponding to a potential flow, even if the instantaneous Reynolds number is low. These effects are discussed with the help of t wo asymptotic expressions of this force derived recently by Magnaudet and Legendre [Phys. Fluids 10, 550 (1998)] for a bubble with a time-de pendent radius. (C) 1998 American Institute of Physics.