长矩形腔体中混合流体的对称对传波

Symmetrical counterpropagating waves of binary fluid mixture in a long rectangular cavity

为了研究分离比ψ=-0.4的混合流体在长高比Γ=40的长矩形腔体内对称对传波的时空特性,利用SIMPLE算法对流体力学基本方程组进行了数值模拟。结果发现,随着对传波对称的向左右两侧传播和两端壁附近对流滚动的消失,中间部位的对流圈拉长,当中间部位的对流局部波数和腔体平均对流波数变的足够小时,中间部位的对流圈保持原有相位,分裂成两个小对流圈。紧接着,在两个小对流圈中间生成一个与其相位相差为180°的新对流圈。中间部位局部波数和腔体的平均对流波数突然变大。随着时间发展,两端壁附近各有一个对流圈消失,中间部位对流圈拉长,系统再次重复对流圈分裂的变化过程。正是由于局部波数和平均波数的小大交替变化,系统周期的产生对传波缺陷。对称对传波存在于相对瑞利数r∈[3.24,3.501]的区间内,对传波缺陷的出现位置和发生周期不随着相对瑞利数变化。

In order to study the spatiotemporal characteristics of symmetrical counterpropagating waves(CPWs)in a long rectangular cavity with an aspect ratio Γ = 40 in binary fluid mixture with a separation ratio ψ =-0.4,the basic equations of fluid mechanics were numerically simulated by using SIMPLE algorithm. The results show that with the symmetrical propagation of CPWs to the left and right sides and the disappearance of convective rolls near the two end walls, the convective roll in the middle part elongates, the local wave number in the middle part and the average convective wave number in the cavity become sufficiently small, and the convective roll in the middle part keeps its original phase and splits into two small convection rolls. Next, a new convective roll with phase difference 180° is generated between the two small convective rolls. The local wave number in the middle part and the average convection wave number of the cavity suddenly increase. As time goes by, a convective roll near each end wall disappears, and convective roll in the middle part elongates. The system repeats the changing process of the convective roll splitting. It is just because the local wave number and the average wave number change alternately from small to large that the system periodically produces the defect of CPWs. The symmetrical CPWs exists in the range of reduced Rayleigh number r∈[3.24,3.501], and the position and period of CPW defects do not vary with the reduced Rayleigh number.