| Thermal convection in gases is widespread in nature and industrial applications.When the height difference and temperature difference are small,the flow can be described by the Boussinesq approximation.When the density stratification caused by gravity or temperature difference is large,however the Non-Boussinesq effect becomes significant.This effect is common in atmospheric convection and large industrial heat-exchange equipment.Due to the limitations of experimental methods and accuracy of numerical schemes,most of the current researches focus on the influence of temperature difference,and few studies consider the interaction between density stratification and temperature difference.Aiming at the natural convection problem of the Non-Boussinesq effect caused by density stratification,this study develops a well-balanced Gas Kinetic Scheme that can achieve steady density stratification on machine accuracy,and then studies the thermal convection in gases under the combined effect of density stratification and temperature difference.The main results include:(1)A second-order Well-Balanced Gas Kinetic Scheme is developed for the NavierStokes equations by improving the integral of the source term.This scheme is not only capable of simulating the isothermal equilibrium state,but also capable of simulating the non-isothermal equilibrium state with heat transfer under density stratification.It is also a key tool for studying the thermal convection in gases with large height differences.(2)The problem of natural convection in the cavity is studied using the proposed WellBalanced Gas Kinetics Scheme.The influence of the density stratification and temperature difference is analyzed on the relative growth of the average Nusselt number and the asymmetry of flow field.The range of application of Boussinesq approximation is identified.(3)The influence of the density stratification and temperature difference on the critical Rayleigh number of Rayleigh-Benard convection is studied by the Well-Balanced Gas Kinetic Scheme.It is found that although gravity is an important driving force for RayleighBenard convection,when fluid is a compressible gas,high gravity can stabilize the flow field and delay the onset of convection. |
