底部加热的两板间水平流动进口段流动特性分析

Analysis of entrance region of horizontal flow between two plates heated from bottom

采用二维流体力学基本方程组对普朗特数 Pr=0.72 的具有水平流动的底部加热两板之间的流动特性进行数值模拟。结果表明,对于给定相对瑞利数 r,随着雷诺数 Re 的增加,底部加热的两板之间依次出现定常对流滚动,均匀行波对流滚动,具有水平流动进口段的局部行波对流滚动及水平流动。对于相对瑞利数 r =3,在雷诺数 9.0<Re<21.0 范围内,系统是局部行波对流滚动,存在水平流动进口段。随着雷诺数增加,水平流动进口段长度增加。对于雷诺数 Re=25.0,在相对瑞利数 4<r<12 范围内,两板之间是局部行波对流滚动,出现水平流动进口段。随着相对瑞利数增加,水平流动进口段长度减小。最后给出了进口段长度随雷诺数或相对瑞利数变化的经验式。

The two-dimensional basic equations of fluid mechanics are used to numerically simulate the characteristics of flow between two plates heated from below with horizontal flows, with the Prandtl number Pr equaling 0.72. The numerical simulation results show that for a given reduced Rayleigh number r, with the increase of the Reynolds number Re, there appear steady convective rolls, uniform traveling wave convective rolls, localized traveling wave convective rolls with the entrance region of the horizontal flow, and the horizontal flows occur successively between two plates heated from the bottom. When the Reynolds number Re is between 9.0 and 21.0 and the reduced Rayleigh number r equals 3, the localized traveling wave convection rolls occur in the system and there exists the entrance region of the horizontal flow. The length of the entrance region of the horizontal flow X0 increases with the increase of the Reynolds number. When the reduced Rayleigh number r is between 4 and 12, and the Reynolds number Re equals 25.0, the localized traveling wave convection rolls occur between two plates and there exists the entrance region of the horizontal flow. The length of the entrance region of the horizontal flow decreases with the increase of the reduced Rayleigh number. And finally, the empirical formulas for the length X0of the entrance region varying with the Reynolds number or the reduced Rayleigh number are given in this paper.