A singular-perturbation theory of the growth of a bubble cluster in a superheated liquid

Abstract

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 manymodern industrial applications where heat transfer, boiling or cavitation are involved.n'oilowing a sudden depressurization of a superheated fluid, the bubble growth ratecontrols the generated transients and heat transfer. Most existing computer modellingand prediction codes are based on individual spherical-bubble-growth studies andneglect possible interactions and collective phenomena. This paper addresses thiscollective behaviour using a singular-perturbation approach. The method of matchedasymptotic expansions is used to describe the bubble growth, taking into account itsinteraction with a finite number of surrounding bubbles. A computer program isdeveloped and the influence of the various parameters is studied numerically for theparticular case of a symmetrical equal-size-bubble configuration and a thermal-boundary-layer approximation. A significant influence of these interactions on bubblegrowth and heat transfer is observed: compared to an isolated-bubble case, the growthrate of a bubble is reduced in the presence of other bubbles, and the temperature dropat its wall is smaller. As a result the heat loss due to bubble growth is smaller. Theseeffects increase with the number of interacting bubbles.1. IntroductionThe presence and behaviour of vaporous cavities are of great importance in manymodern industrial applications where heat transfer, boiling, or cavitation areinvolved. For instance, the rate of heat transfer in nucleate boiling dependsessentially on the ability of the heat-transfer surface to nucleate and support thegrowth of vapour bubbles. The conduction of heat in the liquid is greatly affectedby the absorption and release of latent heat during the phase transition at thebubble-liquid interfaces. Wave propagation in the medium is also significantlyaffected by bubble behaviour and volume changes. Consequently, the study of thebubble dynamics and of the two-phase medium constituted by the host liquid andbubbles of its own vapour is fundamental in the design, analysis, and application ofvarious engineering systems.Many modern processes deal with various fluids in conditions where both heat-transfer effects and inertia contribute in controlling the bubble behaviour. Examplesof such fluids are hydrocarbons, liquid metals, cryogenic fluids, and demineralizedhot water at temperatures as high as 300 oC. Heat transfer, boiling or cavitationappears with these liquids in such applications as high-speed flows of sodium-cooledfast-breeder reactors in nuclear-power engineering, circulation of cryogenic liquidin pumps in aerospace engineering, and flow of hot water nrszzles and tubes in