Numerical study on fluid-structure interaction of a cylinder-flexible thin beam under an axial magnetic field

doi:10.7523/j.ucas.2025.029

Abstract

Abstract:

This paper conducts a numerical study on the problem of flow-induced vibration under an axial magnetic field. The finite element method is used to simulate the velocity field of the metal fluid under the combined effects of the magnetic field and the vibration of a cylinder-flexible beam. This research analyzes the influence of magnetic field intensity and flexible beam length on the amplitude， vibration frequency of the flexible beam， and the flow characteristics of the flow field. The results indicate that the flexible beam undergoes periodic vibrations due to vortex shedding effects， and the dominant vibration mode exhibits a close resemblance to the first-order natural mode of an Euler-Bernoulli beam. As the magnetic field intensity increases， the unsteady flow in the flow field is suppressed， resulting in a decrease in the amplitude of the flexible beam. Increasing the length of the flexible beam decreases the vibration frequency， while the amplitude shows a nonlinear relationship that first increases and then decreases. Regarding the vortex shedding characteristics of the flow field， an increase in magnetic field intensity promotes vortex dissipation， and reduces the frequency of vortex shedding. Additionally， the longer the flexible beam， the greater the energy dissipation during its interaction with the cylinder shear layer， which significantly changes the vortex shedding pattern； the critical Hartmann number for the transition from vortex shedding flow to steady flow decreases with the increase in the flexible beam length.

Key words: magneto-fluid-structure interaction, cylinder-flexible thin beam, flow pattern, flow-induced vibration

CLC Number:

O361.3

Qilong ZHANG, Jie WANG, Nianmei ZHANG. Numerical study on fluid-structure interaction of a cylinder-flexible thin beam under an axial magnetic field[J]. Journal of University of Chinese Academy of Sciences, 2026, 43(5): 694-705.

Figures/Tables 13

Fig.1 Schematic diagram of the cylinder-flexible beam in the insulated channel

Table 1 Physical and geometric parameters for numerical simulation

符号	含义	数值
ρ_f	流体密度/(kg/m³)	6 360
σ	电导率/(S/m)	3.1×10⁶
ν	运动黏度/(m²/s)	2.98×10^-7
U₀	平均来流速度/(m/s)	0.040 4
d	圆柱直径/mm	6
G	圆柱与底板间隙/mm	9
ρ_s	柔性薄梁密度/(kg/m³)	2 150
h	柔性薄梁厚度/mm	1
L	柔性薄梁长度/mm	12、24、36、48、60
w	柔性薄梁宽度/mm	3
E	弹性模量/(N/m²)	1×10⁶
μ	泊松比	0.42
B₀	磁感应强度/T	0.2～1.5
b	沿磁场方向的半宽/mm	20

Table 2 Comparison of the flow quantities for four grid sets

网格编号	网格数量	$C d ¯$	C_l-rms	St
M1	56 658	0.961	0.297	0.193
M2	73 470	0.957	0.299	0.191
M3	91 280	0.952	0.296	0.188
M4	144 462	0.952	0.296	0.188

Table 2 Comparison of the flow quantities for four grid sets

网格编号	网格数量	$C d ¯$	C_l-rms	St
M1	56 658	0.961	0.297	0.193
M2	73 470	0.957	0.299	0.191
M3	91 280	0.952	0.296	0.188
M4	144 462	0.952	0.296	0.188

Fig.2 Comparison of time history of drag force and lift force with Turek［36］

Table 3 Comparison of the maximum value of drag force and lift force with Turek［36］

	验证结果	Turek^[36]	误差/%
阻力最大值/(N/m)	477.71	482.17	0.92
升力最大值/(N/m)	147.76	151.86	2.70

Fig.3 Variations in tip displacement at the tip of flexible thin beam and vibration frequency of flexible thin beamswith magnetic field intensity and beam length

Fig.4 Variation of tip displacement with time for flexible thin beams of different lengths（Ha=242.4）

Fig.5 Instantaneous deformations of the flexible thin beams of different lengths（Ha=242.4）

Fig.6 Instantaneous deformations and frequency spectrum of the first POD mode of flexible thin beams with beam length（Ha=242.4）

Fig.7 Variations in amplitude and vibration frequency of flexible thin beams with magnetic intensity and beam length

Fig.8 Wake modes for cylinder-flexible thin beams with different magnetic field intensities and beam lengths

Fig.9 Wake modes for cylinder-flexible thin beams with different beam lengths（Ha=242.4）

Fig.10 Map of wake modes in the （L/d， Ha） phase space

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