方腔回流区水流运动特性三维数值分析

3-D numerical simulation of circulating flow in the square cavity

建立了一个三维水动力学模型,对方腔回流区水流运动特性进行了模拟分析。数学模型以三维浅水环流方程为基础,在垂向空间引入σ坐标变换,采用高分辨率半隐有限元离散格式。计算结果与解析解及水槽试验数据吻合良好。应用该模型对方腔回流区的水流运动特性进行了计算分析,进一步揭示了方腔回流运动的非定常非对称不封闭特性、流动结构表现为竖轴环流与立面环流相叠加、流速沿垂线分布相对均匀等流动规律。

A 3-D hydrodynamic model is developed for circulating flow in a square cavity. Based upon the shallow-water equations and by using water depth to scale the vertical coordinate, the governing equations are transformed into the fixed computational domain. A high-resolution finite element scheme is incorporated to rearrange the convective terms, and a semi-implicit solution technique is employed to achieve high efficiency. The model is tested against analytical solutions for the standard cases and used to study flow characteristics of the cavity circulating flow. The numerical results are in good agreement with the analytical and experimental data. The 3-D computation and analysis help to further disclose the flow patterns of the cavity flow, such as the flow behavior of unsteadiness, asymmetry, and unclosedness, the flow structure composed of circulation in both horizontal and vertical plane, and so on.