The Flows in Weightlessness Generated by Vibrations

Abstract

Vibration phenomena play an important role in many technical processes involving heated interfaces in the microgravity environment. The analysis of vibration effect on non-isothermal fluid in closed cavity is important for planning technological experiments in space. Control and optimization of these processes critically depend on the understanding of liquid response to the vibrations. With this aim the theoretical investigation for two kinds of problems are performed for infinite plane and cylindrical fluid layers. First of all we investigated simple case of the fluid response-thermal vibrational convection in a cylindrical fluid layer with rigid conducting boundaries. It is found that steady modes of thermal vibrational convection are subjected to various bifurcations. Bifurcations cause shay changes in heat transfer. The generalized Lorenz model is modified and used to conduct the analysis of bifurcations caused by the changing of the cavity shape and vibrational Rayleigh number. The shape of steady-state surface in space of {ψ, Rv, γ} is found, where ψ is the streamfunction of mean flow, Rv is the vibrational Rayleigh number, γ is the cavity curvature. The solution correctly illustrates the general view of steady states surface for the parameter values corresponding to the cavity with the curvature close to zero (thin cylindrical layer). The numerical solution of the vibrational convection equations is performed for plane and cylindrical fluid layers. The results of the analysis based on the generalized Lorenz model are compared with the data obtained by direct numerical simulation. It is shown that the steady-state surface is different from that in the Lorenz model. The bifurcation curve with extremum is found. Thus, bifurcations of complex shape could be observed. This is impossible in a Lorenz model. Second set of investigated problems is related to thermo-vibrational flows caused by oscillations of the boundaries. A general class of oscillations of the boundaries is shown to produce specific mechanisms, of mean transport of vorticity in a uniform fluid, and in addition heat/concentration transport in non-uniform fluid. We performed analytical and numerical study of the flow between two infinite cylinders when the axis of the inner one is subjected to high frequency, small amplitude and oscillations of circular polarization. This type of oscillation produces basic Couette-like mean flow in the gap between the cylinders through the diffusion of vorticity generated in the boundary layers near the rigid surfaces (so-called Schlichting mechanism). The linear stability analysis for this flow with and without radial temperature gradient is performed. Non linear regimes are studied numerically by finite difference method. The results of numerical and analytical simulation of fluid motion for both types vibration interactions are discussed as well.