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采用SIMPLE算法,QUICK差分格式,对底部加热三维长方体腔内空气的自然对流进行了数值模拟。根据模拟结果,探讨了方腔内流体流动与换热的静态分岔与振荡等非线性现象。数值结果显示,在固定的几何尺寸和不同Ra的情况下,当初始场不同时,会出现若干不同的解,即存在解的静态分岔;在固定的几何尺寸和相同的初始场情况下,低Ra时流动和换热处于稳态,当Ra超过某一临界值时,流动和换热就会随时间振荡,并通过倍周期分岔过渡到混沌;当方腔的几何尺寸不同时,分岔点的特征值Ra也发生变化。
The SIMPLE algorithm and the QUICK difference scheme were used to simulate the natural convection of the heated air in the bottom of three-dimensional rectangular parallelepiped. According to the simulation results, the nonlinear phenomena such as static bifurcation and oscillation of fluid flow and heat transfer in the cavity are discussed. Numerical results show that in the case of fixed geometries and different Ra, when the initial field is different, there will be a number of different solutions, that is, the existence of static bifurcation; in the fixed geometry and the same initial field conditions, When Ra is low, the flow and heat transfer are in steady state. When Ra exceeds a critical value, the flow and heat transfer will oscillate with time and transition to chaos through doubling period bifurcation. When the geometrical dimensions of the cavity are different, The characteristic value Ra of the point also changes.