On numerical simulation of cavitating flows under thermal regime

Abstract

International audienceIn this work, we investigate closure laws for the description of interfacial mass transfer in cavitating flowsunder thermal regime. In a first part, we show that, if bubble resident time in the low pressure area of theflow is larger than the inertial/thermal regime transition time, bubble expansion are no longer monitoredby Rayleigh equation, but by heat transfer in the liquid phase at bubbles surfaces. The modelling of inter-facial heat transfer depends thus on a Nusselt number that is a function of the Jakob number and of thebubble thermal Péclet number. This original approach has the advantage to include the kinetic of phasechange in the description of cavitating flow and thus to link interfacial heat flux to interfacial mass fluxduring vapour production. The behaviour of such a model is evaluated for the case of inviscid cavitatingflow in expansion tubes for water and refrigerant R114 using a four equations mixture model. Comparedwith inertial regime (Rayleigh equation), results obtained considering thermal regime seem to predictlower 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 (bubblesize and gas volume fraction) and mainly by the Jakob number variations. It is found that, in contrast withphase change occurring in common boiling flow, Jakob number variation is influenced by phasic temper-ature difference but also by density ratio variation with pressure and temperature

A Review of Models for Bubble Clusters in Cavitating Flows

“…Regarding models for cryogenic cavitation Tseng et al [194] and Zhu et al [220] solve for the enthalpy equation assuming both gas and liquid as incompressible substances while Gnanaskandan [82] solves for the internal energy equation to show results on the cavitating flow around a cylinder [83,84]. Saito et al [172] and more recently Goncalves and coworkers [86,85,36] use formulations that include the equation for the total energy of the mixture (derived from Eq. 4).…”

“…Most of these models [194,220,82,172] still resort to the calculation of the mass transfer flux through the semi-empirical models described above. Only the recent work of Colombet et al [36] makes a first attempt to impose the condition obtained from the energy balance across the interface (Eq. 12) to obtain the total mass transfer flux from the heat flux at the interface and the enthalpy of vaporization neglecting any temperature gradient inside the gas/vapor phase.…”

“…Goncalves & Patella [86] compares the use of this methodology with an ad-hoc barotropic EOS where the averaged density and pressure are directly related through the barotropic relation proposed in [53]. Remarkably, the authors find that the barotropic EOS performs better than the mixture of EOS for cavitation in standard liquids [86,85] while the barotropic EOS model fails reproducing experimental results when thermal effects are relevant [36]. This is consistent with the conclusions extracted from the linear oscillation of vapor bubbles presented above where we have concluded that in those regions where transient heat transfer effects control the dynamic response of bubbles a barotropic EOS will have troubles to correctly reproduce the response of the gas/vapor mixture.…”

“…Using this approach, typically known as Monocally Integrated LES (MILES) [66,67], there is no need to include any physical model capturing the influence of unresolved structures on the numerical solution. In the context of cavitating flows some examples include those in [178,153,179,17,102,36].…”

Combined suppression effects on hydrodynamic cavitation performance in Venturi-type reactor for process intensification

“…The Jakob number, which is a reciprocal of the B factor mathematically, compares the ratio between the latent heat needed to generate bubbles through a phase change and the sensible heat available in the volumes of liquid regarding the bubble volumes . As reported by [33] , the B factor is usually employed when investigating cavitation with the thermal effect, while a Jakob number is often used to study phase change in boiled fluids. Additionally, the C factor, was proposed by [34] , which can associate the thermodynamic effects with the thermal transition time during cavitation of different thermo-fluids.…”