Unsteady Buoyancy-Thermocapillary Induced Convection in Rectangular Tank with Phase Change (Evaporation Number, Condensation, Margangoni Effect, Rayleigh-Driven, Numerical Method).

A numerical and experimental study is performed on transient natural convection in an insulated rectangular tank. The liquid is heated by a line source being placed at the center of the free surface to initiate a thermocapillary force. Either evaporation or condensation takes place on the free surface. The equations of motion are cast into a stream function-vorticity form. A finite-difference technique is employed to numerically integrate the unsteady vorticity and heat transport equations. The effect of the dimensionless physical and geometrical parameters on the transport phenomena are determined. It is found that thermocapillary force promotes natural convection in a reduced-gravity environment but suppresses the fluid motion under a normal-gravity condition. The most interesting phenomena is that the effects of heating and evaporation create two thermal regimes in the liquid: one with the temperature higher than the ambient and the other with lower temperature. The domain with temperature lower than the ambient exp and s with the rate of evaporation. Thermocapillary force plays the role of energy carrier to spread the energy from the source toward the walls. The surface tension therefore stabilizes the system while evaporation and buoyancy make it unstable. At low Ma (Marangoni) number, there are three kinds of convection depending on the range of Rayleigh number: Ma-driven convection, mixed convection and Ra-driven convection. The influence of Ev (Evaporation) number and aspect ratio (RHL) is different in three regions. The induced convection is not sensitive to Ev and RHL in the Ma-driven region while is strongly enhanced in the Ra-driven region. For a system with low evaporation rate and large Ma number convection will be dominated by surface tension alone. A system undergoing condensation is essentially stable because warm liquid underneath the interface stabilizes the system. The system may be stabilized by increasing the aspect ratio. The model can be utilized to determine the nature of convection in an open container situated in a space environment. The theory is qualitatively confirmed by experiments.Ph.D.Mechanical engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/160875/1/8600550.pd