Numerical Study Of Double-Diffusive Convection With Soret Effect In Rectangular Cavities

Double-diffusive convection is a common phenomenon occurring in oceanic circulation,the earth's mantle convection,and has a wide range of engineering applications including the chemical vapor deposition,crystal growth,metal solidification etc.Due to its great importance in nature and many industrial processes,the double-diffusive convection problem has been the topic of intensive researches for many years.In this paper,based on the idea of dispersion-relation-preserving optimization,a class of high-order high-resolution upwind compact schemes and their consistent boundary schemes are proposed for the solution of the governing equations of the two-dimensional double-diffusive convection.The asymptotic stability analysis and numerical verification of the numerical method are carried out.The presented method is adopted to numerically simulate the double-diffusive convection in rectangular cavities and the double-diffusive convection in rectangular cavities with Soret effect respectively.The dependence of the flow motion and the strength of thermal and compositional recirculations on buoyancy ratio,Rayleigh number(Ra),Prandtl number(Pr),Lewis number(Le)and height-to-width aspect ratio are discussed.The main conclusions include following aspects:(1)For the double-diffusive convection,the steady flow becomes the periodic flow,chaotic flow via a supercritical Hopf bifurcation when the buoyancy ratio changes.With the increase of Prandtl number,when 0<Pr<1,the flow structure changes from periodic flow or chaotic flow to steady flow,the heat and mass transfer becomes higher and higher in the oscillation.When Pr ? 1,the flow structure is always steady flow,the heat and mass transfer hardly changes.With the increase of Lewis number,the flow structure is steady flow all the time,the heat and mass transfer becomes higher and higher for low Rayleigh number(Ra=104).The steady flow changes from steady flow to periodic flow or chaotic flow,the heat and mass transfer increases with oscillation for high Rayleigh number(Ra=105).In the range of height-to-width aspect ratio studied in this paper,the heat and mass transfer decreases with the increase of height-to-width aspect ratio.(2)For the double-diffusive convection with Soret effect,with the increase of buoyancy ratio,the bifurcation phenomenon is similar to that without Soret effect,but the bifurcation point varies with different Soret number.With the increase of Prandtl number,when 0<Pr<1,the flow structure evolution and heat and mass transfer are the same as those without Soret effect.When Pr? 1,no matter for positive or negative Soret number,the flow structure evolution and heat and mass transfer at low Rayleigh number are the same as those without Soret effect.At high Rayleigh number,negative Soret number has great influence on the flow structure and heat and mass transfer,and the flow structure is no longer steady flow.With the increase of Lewis number,for low Rayleigh number,the flow structure is not always steady flow under positive and negative Soret number.The heat and mass transfer is similar to that without Soret effect with the increase of height-to-width aspect ratio.Given other parameters,the heat and mass transfer gets lower and lower when the Soret number changes from-1 to 1.