Small amplitude pressure wave in subsonic and supersonic bubble flows in convergent-divergent nozzles

Abstract

This paper makes a theoretical analysis of the propagation phenomena of the small amplitude pressure wave in the subsonic and supersonic bubble flow with a velocity slip between bubble and liquid in the convergent-divergent nozzle. From an analysis of the time-mean flow, the nondimensional parameter m = {u 2 G ·α(1 − α)ρ lβ(2 − 1/S)/P·[αβS + (1 − α)βS 2 + α(1 − α)]} 1 2 corresponds to Mach number is gasdynamics where u G is the gas velocity, α: the void fraction, ρ L: the liquid density, P: the pressure, S: the velocity ratio of the gas and liquid flows and β: the proportional constant for the virtual mass. From a theoretical analysis of the small disturbance field, it is clarified that the parameter m also plays an essential and important role as Mach number, although the propagation performance of the disturbance is very complicated compared with that in gasdynamics. It is also shown that the pressure waves are divided into four groups depending on the velocity ratio S. Two of them are rather realistic, but the other two are required of a further investigation in future.