Direct Numerical Simulation Of Double Diffusive Convection In A Rectangular Enclosure With Height-to-length Ratio Equal To 8

In this paper,the Navier-Stokes equations of double diffusive convection system is solved by using the high-order compact finite difference scheme.The convection terms are discretized with 7th-order upwind compact scheme,the diffusive terms are discretized with6th-order accurate symmetrical compact difference scheme,a three stage third order Runge-Kutta method are employed for time advancement schemes,the stream possion is discretized with 4th-order accurate symmetrical compact scheme,and solved by SOR method.Using the above algorithm,the paper presents a direct numerical simulation of the dou-ble diffusive convection system of the cavity with hight-to-width aspect ration of 8.We should consider the case with the thermal Rayleigh number of 10~5,the Pradtle number of 1,the Lewis number of 2,the buoyancy ratio of composition to temperature being in the range of[0,2].By calculating the simulation,it can capture the small changes of the multi-scale flow field well and get the real physical process of the flow field motion.The numerical simulation results mainly consist of two aspects:(1)Along with the increase of the buoyancy will experience a series of complex changes in the flow field,the stable laminar flow through the Hopf bifurcation become unstable flu-id,then the periodic flow,chaos and other oscillatory motion occurred.What's more,there are two types of periodic flow,one is simple periodic flow with single fundamental fre-quency,and another is complex periodic flow with multiple.In a special stage,there is a sub-harmonic and multi-times FFs coexist periodical flow in multi-times FF periodical flow,which contains the fundamental frequency and multiple fundamental frequency8)FF.In ad-dition,some lower frequency sub-harmonic waves are excited.This process is illustrated by using time-velocity histories,Fourier frequency spectrum analysis and the phase-space trajectories.(2)In the process of double diffusive convection system,a variety of flow field struc-tures are presented,including the center symmetric flow field with laminar flow and periodic symmetric structure,asymmetric flow field,and multi-cell flow structure.In addition,we also found a special structure:the odd couple exchange symmetric flow.The emergence of multiple flow field structures accelerate the diffusion of heat and concentration in the double diffusive convection system.