Nonlinear evolution of non-Boussinesq thermal convection in three-dimensional differentially heated cavity
We study numerically the nonlinear evolution of non-Boussinesq thermal convection with constant Prandtl number(Pr = 0.71) in three-dimensional(3D) closed,differentially heated cavity having aspect ratio of unity(= Height/Lenth) by DNS.Second-order Adams-Bashforth Crank-Nicolson(AB-CN) mixed scheme is used for time integration,while a fractional-step method is exploited to split momentum equations.A consistent pressure update equation is given so that overall accuracy of the scheme are second order.Rich and complex buoyancy-driven flow phenomena different from those under Boussinesq approximation are rendered by virtue of the power spectrum and phase portrait.When simulation is performed,with increasing Rayleigh number(Ra),the predicted flow is found to evolve from the conduction-dominated state to the convection-dominated state,which is steady and symmetrical about middle plane(x=0.5).Firstly,compared with Boussinesq ones,we find under non-Boussinesq condition that the velocity profiles near boundary lose symmetry at Rayleigh numbers under consideration,such as 104,which could be explained by strongly temperature-dependent fluid properties.Secondly,it is found that the convection patterns of the resulting flow are determined not only by Rayleigh number,but also by which is a measure of dimensionless temperature difference far from Boussinesq limit in our study.Finally,a new interesting phenomenon is found that while Rayleigh number goes around 6 × 107,the flow could bifurcate from periodic state(Ra = 5×107) to aperiodic one followed then by asymptotical steady state (Ra = 7 × 107),and finally back to periodic state (Ra = 8 × 107 - 9 × 107) with a different fundamental frequency.
Non-Boussinesq AB-CN Fractional-Step broken symmetry bifurcation
Shu-Ning Xia Hai-Hua Yang Kun Jia De-Jun Sun
Department of Modern Mechanics, University of Science and Technology of China,Hefei 230027, China
国际会议
The 8th International Conference of Computational Fluid Dynamics, (ICCFD8)(第八届国际计算流体力学会议)
成都
英文
1-11
2014-07-25（万方平台首次上网日期，不代表论文的发表时间）