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采用低马赫数近似的厅法来对大温差驱动的自然对流问题进行数值模拟。低马赫数近似是通过将全可压的Navier-Stokes方程中声波进行过滤,从而在马赫数较低的流动中忽虑声波对流场的影响。声波过滤后的方程具有不可压缩N-S方程的特点,但可以求解温度和密度变化较大的问题。首先,通过对盖顶驱动流的数值模拟,验证了本文方法的可靠性。本文对常重力下,瑞利数为10~6的大温差驱动自然对流进行数值模拟,并且与简单不可压方程的结果进行比较,发现在大温差的情况下Boussineq假设并不能给出很精确的结果。
A low Mach number approximation Hall method is used to simulate the natural convection problem driven by large temperature difference. The low Mach number is approximated by filtering the acoustic waves in a fully-compressible Navier-Stokes equation so that the effects of acoustic waves on the flow field are ignored in the lower Mach flow. The sonic filtered equation has the characteristics of an incompressible N-S equation, but it can solve the problem of large changes in temperature and density. First of all, the numerical simulation of the roof-driven flow validates the reliability of the proposed method. In this paper, the numerical simulation of natural convection driven by large temperature difference with Rayleigh number of 10 ~ 6 under constant gravity is compared with that of simple incompressible equation. It is found that the Boussineq assumption does not give a very accurate result.