Thermal Damping in Cavitating Nozzle Flows

Abstract

Recent investigations of bubbly cavitating nozzle flows by Wang and Brennen (1998) and by Delale et al. (2001), where various damping effects are lumped together in an adhoc manner, have shown flow instabilities that lead to flashing flow solutions. Here, we investigate the stabilizing effect of thermal damping on these instabilities. For this reason we consider the energy equation within the bubble, assumed to be composed of vapor and gas, in the uniform pressure approximation (similar to that given by Nigmatulin et al., 1981 and by Prosperetti, 1991). The partial vapor pressure is fixed by the vapor saturation pressure corresponding to the interface temperature, which is evaluated by the Plesset-Zwick$^5$ formula assuming the thin boundary layer approximation within the liquid. Consequently, the partial gas pressure is evaluated by its relation to the heat flux through the interface in the uniform pressure approximation. The model is then coupled to the steady-state cavitating nozzle flow equations employed by Wang and Brennen and by Delale et al., replacing the previously assumed polytropic law for the partial gas pressure. The instabilities arising from the use of the polytropic law for the gas pressure in steady cavitating nozzle flows are seen to be stabilized by thermal damping with or without the occurrence of bubbly shock waves.