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A_singular-perturbation_theory_of_the_growth_of_a_bubble_cluster_in_a_superheated_liquid1.pdf

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A_singular-perturbation_theory_of_the_growth_of_a_bubble_cluster_in_a_superheated_liquid1

J . Fluid M c h . (1985), V O ~ . 156, p p . 257-279 Printed in Oreat Britain 257 A singular-perturbation theory of the growth of a bubble cluster in a superheated liquid By GEORGES L. CHAHINE AND HAN LIEH LIU Tracor Hydronautics Inc., 7210 Pindell School Road, Laurel, Maryland (Received 4 October 1983 and in revised form 5 October 1984) The presence and behaviour of vaporous cavities are of major importance in many modern industrial applications where heat transfer, boiling or cavitation are involved. Following a sudden depressurization of a superheated fluid, the bubble growth rate controls the generated transients and heat transfer. Most existing computer modelling and prediction codes are based on individual spherical-bubble-growth studies and neglect possible interactions and collective phenomena. This paper addresses this collective behaviour using a singular-perturbation approach. The method of matched asymptotic expansions is used to describe the bubble growth, taking into account its interaction with a finite number of surrounding bubbles. A computer program is developed and the influence of the various parameters is studied numerically for the particular case of a symmetrical equal-size-bubble configuration and a thermal- boundary-layer approximation. A significant influence of these interactions on bubble growth and heat transfer is observed: compared to an isolated-bubble case, the growth rate of a bubble is reduced in the presence of other bubbles, and the temperature drop at its wall is smaller. As a result the heat loss due to bubble growth is smaller. These effects increase with the number of interacting bubbles. 1. Introduction The presence and behaviour of vaporous cavities are of great importance in many modern industrial applications where heat transfer, boiling, or cavitation are involved. For instance, the rate of heat transfer in nucleate boiling depends essentially on the ability of the heat-transfer surface to