On numerical simulation of cavitating flows under thermal regime

Abstract

In this work, we investigate closure laws for the description of interfacial mass transfer in cavitating flows under thermal regime. In a first part, we show that, if bubble resident time in the low pressure area of the flow is larger than the inertial/thermal regime transition time, bubble expansion are no longer monitored by Rayleigh equation, but by heat transfer in the liquid phase at bubbles surfaces. The modelling of interfacial heat transfer depends thus on a Nusselt number that is a function of the Jakob number and of the bubble thermal Péclet number. This original approach has the advantage to include the kinetic of phase change in the description of cavitating flow and thus to link interfacial heat flux to interfacial mass flux during vapour production. The behaviour of such a model is evaluated for the case of inviscid cavitating flow in expansion tubes for water and refrigerant R114 using a four equations mixture model. Compared with inertial regime (Rayleigh equation), results obtained considering thermal regime seem to predict lower local gas volume fraction maxima as well as lower gradients of velocity and gas volume fraction. It is observed that global vapour production is closely monitored by volumetric interfacial area (bubble size and gas volume fraction) and mainly by the Jakob number variations. It is found that, in contrast with phase change occurring in common boiling flow, Jakob number variation is influenced by phasic temperature difference but also by density ratio variation with pressure and temperature (Ja∝(ρL/ρG)ΔT).