Numerical Study Of Natural Convection With Non-Oberbeck-Boussinesq Effects

Thermal convection with non-Oberbeck-Boussinesq (NOB) effects is ubiquitous in na-ture and industrial application. There are two categories of NOB effects. The first one comes from temperature dependence of physical variables, such as density, isobaric thermal expan-sion coefficient, dynamic viscosity, conductivity and so on. The other is the one that including compressibility led by large temperature difference. Up to date, much work has been con-centrated on NOB-Ⅰ effects which could affect the flow patterns, heat transfer and dynamic behaviour. In this study, it is focused on the influence of NOB effects on the flow instability and nonlinear evolution of thermal convection with relatively low Rayleigh numbers.First, the influence of NOB-Ⅱ effects on thermal convection in a differentially side-heated cube has been studied. For the Rayleigh numbers 103≤Rα≤106, much attention has been focused on influences on the average Nusselt number Nu, Reynolds number Re and the distributions of temperature and velocity in the mid plane. It is shown that influence of NOB-II effects on Nu and Re is small whereas rather large for temperature and velocity dis-tributions. With increasing NOB-Ⅱ effects, the distributions move in the direction of negative y-axis, i.e. approaching to cold wall. For the Rayleigh numbers 107≤Rα≤108, the mech-anism to second unsteady instability are proposed in this paper. Two travelling waves merges near the transverse middle plane x=0.5 and then the reflection symmetry with respect to the transverse middle plane is broken only if the two vortex with the same sign.Secondly, the influence of NOB-Ⅱ effects on Rayleigh-Benard convection in a square cavity has been studied. The NOB-Ⅱ effects on the multiple solutions are first studied. Then newly-found flow reversals led by NOB-Ⅱ effects are revealed. Thanks to the vorticity trans-port equation from low-Mach-number momentum equations, the flow reversals are attributed to the imbalance of buoyancy force between corner roll and the bulk. Further, it is demon-strated that the asymmetry of isobaric expansion coefficient in buoyancy force is responsible for the imbalance.Thirdly, the influence of NOB-II effects on Rayleigh-Benard convection in three dimen-sional thin cavity with various ratios of depth to height has been studied. The ratios F=D/H are 1/10,1/4,1/3 and 1/2= For the ratios of 1/10 and 1/3, the influence of NOB-Ⅱ effects is great because new flow pattern are born or eliminated. Whereas for the other two ratios, the influence is quantitatively small.