低雷诺数下冷圆柱绕流的数值研究

doi:10.7523/j.ucas.2024.036

摘要/Abstract

摘要：

通过对恒定雷诺数Re=80、理查森数Ri范围为-5≤Ri≤-0.5的冷圆柱绕流开展三维数值模拟，研究冷圆柱绕流尾迹结构的形成机理及浮力对尾迹结构的影响。结果表明，在-2.5≤Ri≤-0.5范围内，冷圆柱绕流的尾迹结构受到浮力作用呈现出一致的循环模式，当Ri达到一定值（如Ri=-5）时，冷圆柱绕流的循环模式发生改变。随着Ri减小冷圆柱尾迹结构整体向重力方向偏转，肋部结构数量呈现非单调变化，柱体尾迹的贴壁流动增强，当Ri减小到一定值时流动尾迹仅从圆柱下方发生分离。圆柱表面的升力系数、阻力系数和努塞尔数随Ri的减小而单调增加。

关键词: 冷圆柱, 雷诺数, 理查森数, 循环模式, 流动分离

Abstract:

This article utilizes three-dimensional numerical simulations on the flow around a cold cylinder with a constant Reynolds number （Re=80） and a Richardson number （Ri） ranging from -5 to -0.5， to investigate the formation mechanism of the wake structure and the influence of buoyancy on the wake structure. The results indicate that within the range of -2.5≤Ri≤-0.5， the wake structure around the cold cylinder exhibits a consistent cyclic pattern due to the influence of buoyancy. As $R i$ reaches a certain threshold （e.g.， Ri=-5）， the cyclic pattern of the cold cylinder flow undergoes a change. With the decrease of Ri， the overall wake structure of the cold cylinder deflects in the direction of gravity， while the number of rib structures exhibits a non-monotonic variation， and the wall-attached flow of the cylinder wake intensifies. When Ri decreases to a certain threshold， flow separation occurs solely from beneath the cylinder. The lift and drag coefficients， along with the Nusselt number on the cylinder’s surface， increase monotonically as Ri decreases.

Key words: cold cylinder, Re, Ri, cyclical mode, flow separation

中图分类号:

O357

张睿达, 陈龙. 低雷诺数下冷圆柱绕流的数值研究[J]. 中国科学院大学学报, 2026, 43(2): 173-185.

Ruida ZHANG, Long CHEN. Numerical study on the flow around a cold cylinder at low Reynolds numbers[J]. Journal of University of Chinese Academy of Sciences, 2026, 43(2): 173-185.

图/表 19

图1 WCLL包层示意图

Fig.1 View of the WCLL blanket design

图2 计算模型

Fig.2 Calculation model

表1 圆柱表面升、阻力系数和努塞尔数对比

Table 1 Comparison among Cd， Cl， and Nu of a cylinder

	C_d	C_l	Nu
文献[8]	1.196	-1.129	6.366
本文	1.259	-1.183	6.473
误差/%	2.3	3.1	1.7

图3 双O型网格分布

Fig.3 Distribution of double O-type grids

表2 网格参数对流动特性的影响

Table 2 Effects of grid parameters on flow characteristics

	C_d	C_l	Nu
G₁	1.472	-0.025	2.004
G₂	1.474	-0.025	2.005
G₃	1.476	-0.025	2.006

图4 点（2.5，0，0）处轴向速度Uz 随时间的变化及频谱分析

Fig.4 Temporal variation of axial velocity Uz at the point （2.5，0，0） and spectral analysis

图5 不同Ri下温度等值面Θ=0.1（等值面由流向速度着色）

Fig.5 Iso-thermal surfaces （Θ=0.1） for various Ri values（colored by streamwise velocity）

图6 不同Ri下y=0截面在t/T=0时刻的温度场和速度场

Fig.6 Temperature and velocity fields on the cross section y=0 at t/T=0for different Ri values

图7 t/T=0时不同Ri下zoy平面温度等值线图

Fig.7 Temperature field contours at t/T=0 for different Ri values

图8 Re=80时x=0.51截面不同物理量分布

Fig.8 Distribution of baroclinic vorticity and streamwise vorticity on the cross section x=0.51 for Re=80

图9 Ri=-1时一个周期内流向涡量（ωx=0.2）三维等值面

Fig.9 Numerically calculated iso-vorticity surfaces（ ωx=0.2） for Ri=-1

图10 Ri=-2.5时一个周期内流向涡量（ωx=0.4）三维等值面

Fig.10 Numerically calculated iso-vorticity surfaces（ ωx=0.4） for Ri=-2.5

图11 Ri=-1时y=0截面速度矢量图（矢量线由温度着色）

Fig.11 Velocity vectors at y=0 for Ri=-1（colored by temperature）

图12 Re=80，Ri=-1时y=0截面流向速度等值线图

Fig.12 Velocity contours on the cross section y=0 for Re=80 and Ri=-1

图13 t/T=1/4时刻Re=80，Ri=-1不同截面速度等值线图

Fig.13 Velocity contours at t/T=1/4 for Re=80 and Ri=-1 on the cross sections y=（a）0.5，（b）-0.5

图14 t/T=0时羽流内外温度等值线和速度矢量图

Fig.14 Contours of temperature fields and velocity vectors of the plume at t/T=0

图15 不同Ri下t/T=0时圆柱表面流线（蓝色）和分离线（黑色）

Fig.15 Skin lines （blue） and separation lines （black） on cylinder at t/T=0 for different Ri values

图16 平均升、阻力系数值随Ri的变化

Fig.16 Variation of time-averaged lift and drag coefficients with Ri values

图17 圆柱表面平均努塞尔数随Ri的变化

Fig.17 Variation of average Nu on cylinder with Ri values

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