Drag/lift coefficients of flow around two circular cylinders at low Reynolds numbers and high Knudsen numbers

doi:10.16085/j.issn.1000-6613.2025-0183

Abstract

Abstract:

Flow around two cylinders is a fundamental model for a deep understanding of the flow around complex structures, which has been extensively studied by numerous researchers, yet scarcely touches upon the flow at low Reynolds numbers and high Knudsen numbers. In this study, pseudo-particle modeling was employed to simulate the drag and lift forces on the flow around two circular cylinders in both side-by-side and tandem arrangements under the conditions of 0.5≤Re≤5 and 0.1≤Kn≤1.5. The results were as follows: for side-by-side cylinders, the drag coefficient increased with the increase of the distance between them, and once the distance exceeded a critical value, the drag coefficient approached that of the flow around a single cylinder. This critical value decreased with the increase of Re and was independent of Kn; the lift coefficient initially increased and then gradually decreased to zero as the distance widened, with the peak value corresponding distance influenced by both Re and Kn. The minimum distance required for the lift coefficient to approach zero decreased with the increase of Re and Kn. For tandem cylinders, the drag coefficients of both the upstream and downstream cylinders decreased; the drag coefficient of the upstream cylinder first decreased and then increased with the widening of the distance; the drag coefficient of the downstream cylinder increased with the distance and was significantly affected by the upstream cylinder, which was consistent with the situation in the continuous flow region; Kn affected the distance at which the upstream cylinder influenced the downstream cylinder, as the smaller the Kn, the greater the interference distance.

Key words: fluid mechanics, computer simulation, microfluidics, flow around two cylinders, low Reynolds number, high Knudsen number

摘要：

双圆柱绕流是深入理解复杂结构周围流动的基础模型，已有众多研究者进行了广泛研究，但鲜有涉及低雷诺数高克努森数的流动。本文采用拟颗粒模型，模拟研究0.5≤Re≤5和0.1≤Kn≤1.5条件下，并排及串排双圆柱绕流的阻力及升力情况。研究发现，圆柱并排时，阻力系数随间距增大而增大，并在间距超过临界值后，阻力系数接近单圆柱绕流结果，该临界值随Re增大而减小且与Kn无关；升力系数随间距增大先增大再逐渐减小趋于0，峰值所对应的间距受Re和Kn的影响，升力系数趋于0所需的最小间距随Re和Kn的增大而减小。圆柱串排时，上下游圆柱阻力系数均会降低；上游圆柱阻力系数随间距增大先减小后增大；下游圆柱阻力系数随间距增大而增大，且受上游圆柱影响明显，与连续流区域情况相符；Kn会影响上游圆柱对下游圆柱产生干扰的距离，表现为Kn越小，干扰距离越大。

关键词: 流体力学, 计算机模拟, 微流体, 双圆柱绕流, 低雷诺数, 高克努森数

CLC Number:

O355

LONG Kai, CHEN Feiguo, XIONG Qingang. Drag/lift coefficients of flow around two circular cylinders at low Reynolds numbers and high Knudsen numbers[J]. Chemical Industry and Engineering Progress, 2025, 44(8): 4526-4535.

龙凯, 陈飞国, 熊勤钢. 低雷诺数高克努森数下的双圆柱绕流阻力/升力系数[J]. 化工进展, 2025, 44(8): 4526-4535.

Figures/Tables 11

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雷诺数Re	克努森数Kn	圆柱直径D	模拟区域L×W×H	区域划分	拟颗粒数	来流速度U	密度ρ	剪切黏度μ	声速c	圆柱间距S/D
0.5	0.5	24.72	3213×1606×401	6×2×1	3.20×10⁷	0.0116	0.0196	0.0113	0.0772	0、0.5、1、2、 5、10、15、25
0.5	1.0	24.67	3207×1603×400		1.56×10⁷	0.0229	0.00985	0.0113	0.0759
0.5	1.5	24.44	3156×1578×394		1.02×10⁷	0.0345	0.00661	0.0112	0.0754
1.0	0.25	24.32	2652×1326×331		2.45×10⁷	0.0122	0.0384	0.0114	0.0799
1.0	0.5	24.51	2691×1345×336		1.30×10⁷	0.0234	0.0196	0.0113	0.0772
1.0	1.0	24.56	2694×1347×336		8.98×10⁶	0.0462	0.00978	0.0113	0.0759
2.0	0.1	24.99	2493×1246×311		2.94×10⁷	0.0107	0.0885	0.0118	0.0873
2.0	0.25	23.00	2300×1150×287		1.06×10⁷	0.0243	0.0407	0.0114	0.0802
2.0	0.5	26.59	2639×1319×329		7.08×10⁶	0.0470	0.0180	0.0113	0.0770
5.0	0.1	25.39	1770×885×221		1.47×10⁷	0.0266	0.0874	0.0118	0.0872
5.0	0.25	24.59	1717×858×214		1.05×10⁷	0.0603	0.0383	0.0114	0.0799
5.0	0.5	24.51	1713×856×214		7.97×10⁶	0.117	0.0195	0.0113	0.0772

雷诺数Re	克努森数Kn	圆柱直径D	模拟区域L×W×H	区域划分	拟颗粒数	来流速度U	密度ρ	剪切黏度μ	声速c	圆柱间距S/D
0.5	0.5	24.72	3213×1606×401	6×2×1	3.20×10⁷	0.0116	0.0196	0.0113	0.0772	0、0.5、1、2、 5、10、15、25
0.5	1.0	24.67	3207×1603×400		1.56×10⁷	0.0229	0.00985	0.0113	0.0759
0.5	1.5	24.44	3156×1578×394		1.02×10⁷	0.0345	0.00661	0.0112	0.0754
1.0	0.25	24.32	2652×1326×331		2.45×10⁷	0.0122	0.0384	0.0114	0.0799
1.0	0.5	24.51	2691×1345×336		1.30×10⁷	0.0234	0.0196	0.0113	0.0772
1.0	1.0	24.56	2694×1347×336		8.98×10⁶	0.0462	0.00978	0.0113	0.0759
2.0	0.1	24.99	2493×1246×311		2.94×10⁷	0.0107	0.0885	0.0118	0.0873
2.0	0.25	23.00	2300×1150×287		1.06×10⁷	0.0243	0.0407	0.0114	0.0802
2.0	0.5	26.59	2639×1319×329		7.08×10⁶	0.0470	0.0180	0.0113	0.0770
5.0	0.1	25.39	1770×885×221		1.47×10⁷	0.0266	0.0874	0.0118	0.0872
5.0	0.25	24.59	1717×858×214		1.05×10⁷	0.0603	0.0383	0.0114	0.0799
5.0	0.5	24.51	1713×856×214		7.97×10⁶	0.117	0.0195	0.0113	0.0772

雷诺数Re	C_D
雷诺数Re	L/D=20	L/D=40	L/D=70	L/D=110	L/D=130	L/D=160
0.5	7.9069	7.3499（Δ=7.04%）	7.0056（Δ=4.68%）	6.9288（Δ=1.10%）	6.8963（Δ=0.47%）	6.8955（Δ=0.01%）
1.0	5.5314	5.1371（Δ=7.13%）	4.9681（Δ=3.29%）	4.8843（Δ=1.69%）	4.8855（Δ=0.02%）	4.8849（Δ=0.01%）
2.0	4.6628	4.2706（Δ=8.41%）	4.0840（Δ=4.37%）	4.0722（Δ=0.29%）	4.0718（Δ=0.01%）	4.0721（Δ=0.01%）
5.0	3.2061	2.8564（Δ=10.91%）	2.7014（Δ=5.43%）	2.7009（Δ=0.02%）	2.7012（Δ=0.01%）	2.7010（Δ=0.01%）

雷诺数Re	C_D
雷诺数Re	L/D=20	L/D=40	L/D=70	L/D=110	L/D=130	L/D=160
0.5	7.9069	7.3499（Δ=7.04%）	7.0056（Δ=4.68%）	6.9288（Δ=1.10%）	6.8963（Δ=0.47%）	6.8955（Δ=0.01%）
1.0	5.5314	5.1371（Δ=7.13%）	4.9681（Δ=3.29%）	4.8843（Δ=1.69%）	4.8855（Δ=0.02%）	4.8849（Δ=0.01%）
2.0	4.6628	4.2706（Δ=8.41%）	4.0840（Δ=4.37%）	4.0722（Δ=0.29%）	4.0718（Δ=0.01%）	4.0721（Δ=0.01%）
5.0	3.2061	2.8564（Δ=10.91%）	2.7014（Δ=5.43%）	2.7009（Δ=0.02%）	2.7012（Δ=0.01%）	2.7010（Δ=0.01%）

(Re, Kn)	热适应系数α	参考值^[3,37]	PPM	相对偏差Δ
(0.5, 0.50)	0.7	12.992	12.792	1.5%
(1.0, 0.25)	0.7	8.815	8.829	0.2%
(1.0, 0.50)	0.7	7.415	7.508	1.3%
(5.0, 0.25)	0.7	3.439	3.306	3.9%