﻿ 湍流槽道流并行直接求解方法
 哈尔滨工业大学学报  2021, Vol. 53 Issue (1): 163-167  DOI: 10.11918/202001028 0

### 引用本文

XI Lingchu, XIE Jiabin, BAO Yun. Parallel direct method for turbulent channel flow[J]. Journal of Harbin Institute of Technology, 2021, 53(1): 163-167. DOI: 10.11918/202001028.

### 文章历史

Parallel direct method for turbulent channel flow
XI Lingchu, XIE Jiabin, BAO Yun
School of Aeronautics and Astronautics, Sun Yat-Sen University, Guangzhou 510275, China
Abstract: In this study, the direct numerical simulations of turbulent channel flow combined with Parallel Direct Method of DNS (PDM-DNS) are performed, and high parallel efficiency is obtained. A parallel efficiency of over 95% can be achieved on 256 cores of the Tianhe-2 supercomputer. Statistics of four cases with Reτ=176, 544, 960 and 2000 have been compared with the Lee&Moser's results and the reliability is verified. Further, based on the advantage of finite-difference with immersed boundary condition easy to deal with wall boundary condition, a simulation added local burr band at Reτ=176 has been performed to realize research of complex boundary condition. The proposed method provides a new tool for the study of turbulent channel flow with complex boundary condition.
Keywords: immersed boundary condition    channel flow    turbulence    PDM-DNS

1 槽道流的计算方法

1.1 控制方程与其求解

 $\nabla \cdot \overrightarrow u = 0,$ (1)
 $\frac{{\partial \overrightarrow u }}{{\partial t}} + \left( {\overrightarrow u \nabla } \right)\overrightarrow u = - \nabla p + \frac{1}{{Re}}{\nabla ^2}\overrightarrow u .$ (2)

 $\left\{ \begin{array}{l} {F_x} = \left( {Q{{\left( x \right)}_0} - Q{{\left( x \right)}_{n + 1}}} \right) \times {\rm{d}}z, \\ {F_y} = \left( {Q{{\left( y \right)}_0} - Q{{\left( y \right)}_{n + 1}}} \right) \times {\rm{d}}z. \end{array} \right.$ (3)

1.2 直接并行求解方法与并行效率

1.3 湍流的生成方法

 图 1 壁面摩擦系数随着时间的变化 Fig. 1 Variation of wall friction coefficient with time
2 湍流槽道流DNS模拟结果与讨论

2.1 平均速度

 ${U^ + } = \frac{1}{\kappa } \cdot {\rm{log}}\;{z^ + } + B,$ (4)

 图 2 不同雷诺数下的平均速度曲线 Fig. 2 Mean velocity curves at different Reynolds numbers
2.2 雷诺应力张量

 图 3 不同雷诺数下流向方向雷诺正应力 Fig. 3 Mean-squared streamwise velocity fluctuations at different Reynolds numbers

Lozano等人[9]在文章中指出，流向方向的雷诺应力最大值与雷诺应力之间满足以下关系：

 $<{{u'}^2} > _{{\rm{max}}}^ + = 3.66 + 0.642 \cdot {\rm{log}}\left( {R{e_\tau }} \right).$ (5)

3 局部特殊壁面边界条件

 图 4 槽道流加入粗糙毛刺示意图 Fig. 4 Simulation with rough burr in channel flow

 图 5 加入毛刺后不同位置的平均速度曲线 Fig. 5 Mean velocity curves at different positions after adding rough burr

4 结论

4个不同Re数的槽道流计算结果显示，速度剖面都具有粘性底层和对数段分布，并与湍流速度对数段的理论预测值分布一致，雷诺正应力分布合理，所有计算结果与他人的DNS结果吻合.本文提出的计算方法所得到的湍流槽道流计算结果和数据是合理可信的.

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