Numerical Study Of Thermal Convection In Binary Fluid Mixtures In Tilted Rectangular Cavities

Thermal convection is a common phenomenon occurring in the atmospheric and oceanic circulation,in the Earth’s core and mantle convection,etc.,it also plays an important role in many industrial application,including crystal growth,nuclear reactor and cooling of electronic devices.In this paper,by using a high-order and high-resolution numerical method,direct numerical simulations of RayleighBenard convection in binary fluid mixtures in a two-dimensional tilted cell with an aspect ratio of 2 and 12.We investigated the effect of inclination angle,different trends in the variation of the inclination angle,Rayleigh number(r),Prandtl number(Pr),Lewis number(Le),separation ratio(ψ)and aspect ratio(Γ)on the flow and heat-and mass-transfer efficiencies.For a tilted rectangular cavity with an aspect ratio of Γ=2,the heat and mass transfer characterized by the Nusselt number(Nu)and the Sherwood number(Shz)depend strongly on the inclination angle and Rayleigh number.When r ≤1.2,Nusselt number increases first and then decreases with the increase of inclination angle,while Shz remains constant.When r>1.2,Nusselt number first decreases for small β,then gradually increases and finally decreases again,the inclination angle lies in the range of 54°≤β≤64°,where the heat transport peaks.Sherwood number initially decreases,then increases with increasing β,and finally remains constant when the inclination angle is in the interval[25°90°].The different processes for varying the inclination angle may result in different flow patterns,even for the same Rayleigh number and inclination angle,this causes the solution to bifurcate,the range of inclination angle and Rayleigh number for bifurcation depends on the separation ratio.Regardless of inclination angle,the heat-and mass-transfer efficiency always increase exponentially with increasing Rayleigh number.The evolution of the Nusselt number with separation ratio depends on inclination angle,For β∈[9°,51°),Nusselt number increases with increasing separation ratio.Next,Nusselt number decreases with increasing separation ratio for 53°≤β≤90°,we also suggest the Nusselt number as a function of separation ratio and inclination angle.When 0.01 ≤Pr ≤1,the variation of Nu and Shz is independent of the inclination angle,with the increase in Prandtl number,both Nu and Shz increase.when Pr>1,the variation of Nu and Shz is related to the inclination angle.In the range of Lewis number(Le),when 0°≤β≤6°,Nusselt and Sherwood number increase at first,then decrease and finally increase,whenβ>6°,Nusselt number decreases with increasing Le,Sherwood number first increases to the maximum at Le=0.02 and then decreases.For a tilted rectangular cavity with an aspect ratio of Γ=12,when r=1.0,Nusselt number increases at first,then decreases and finally increases.when r≥1.2,Nusselt number first decreases for small β,then gradually increases.With increasing inclination angle in the range 0°≤β≤25°,the steady flow becomes the periodic flow or chaotic flow via a supercritical Hopf bifurcation.when β>25°,the flow structure is always steady flow.The effect of aspect ratio on heat transfer efficiency is related to the inclination angle,when 0°≤β≤5°,Nusselt number increases monotonically with increasing aspect ratio,the curve of Nu is irregular as β varies from 6° to 19°,when 20°≤β≤90°,Nusselt number decreases monotonically.