Numerical analysis of thermal and thermosolutal vibrational convection and its effects on heat and mass transport.

摘要

A numerical method based on a pseudospectral technique has been adapted for the solution of the 'Thermovibrational Mean Flow' (TMF) Equations developed by Gershuni in 1963. The types of vibration considered correspond to the sinusoidal translations of a rigid cavity at a fixed frequency. The fluid filling the cavity is assumed to be Newtonian, obeys the Boussinesq approximation and is subject to an applied temperature gradient. In the frame of reference of the translating cavity, a 'vibrational force' emerges in the equation of motion when non-uniformities of both the density and the pulsation velocity field exist simultaneously. The response of the system to vibration applied along different directions with respect to the applied temperature gradient is examined. The case of compositional variations in the cavity in connection with directional solidification of the fluid is also investigated. The latter necessitated the development of a modified set of TMF equations that accounted for compositional contributions to buoyancy.; It is established, through extensive comparisons with time averaged solutions to the Navier-Stokes-Boussinesq equations, that the inequality 2PrRav O must be satisfied for the TMF equations to produce a valid result.; Interaction between natural convection and thermal vibrational convection has also been studied. The ability of applied vibration to enhance or suppress flow is investigated by varying the orientation of vibration with respect to temperature gradient. Simulation under weightless conditions further demonstrates the underlying features of thermovibrational convection.; The modified TMF equations that account for compositional contributions to buoyancy are applied to a directional solidification problem with g fitter effect under micro-gravity condition. The response of heat, mass and solute transport in a Sn-Bi binary alloy crystal growth is investigated and the significance of solutal contributions to the flow is investigated. A comparison of solutions obtained using the mean flow equations with time averaged solutions obtained using the NSB equations shows that the former are indeed successful in predicting the mean transport properties of the system.