STUDY OF FLOW-INDUCED MOTION CHARACTERISTICS OF THREE TANDEM CIRCULAR CYLINDERS IN PLANAR SHEAR FLOW1)

doi:10.6052/0459-1879-18-348

Abstract

Abstract:

Flow-induced motions of three elastically mounted circular cylinders subjected to the planar shear flow in tandem arrangement at $Re =100$ were numerically investigated by using semi-implicit characteristics-based split (CBS) finite element algorithm. Firstly, the results are compared with the existing data in the literature to verify the accurateness of the method. Then, the influence of some key parameters, such as shear ratio ($k$), natural frequency ratio ($r$) and reduced velocity ($U_{\rm r}$) on the characteristics of flow-induced dynamic responses and flow field of three circular cylinders with tandem arrangement was analyzed. The numerical results show that the shear ratio, natural frequency ratio and reduced velocity play an important role in the amplitude and trajectory of motion. The change of maximum amplitude of the upstream cylinder is similar to that of an isolated cylinder case with the increasing of $k$. The maximum amplitudes of the midstream and downstream cylinders increase, and the dual resonance is observed. Meanwhile, the increasing of $k$ causes the extension of the resonance region. With the increasing of $r$, the lock-in region of the upstream cylinder reduces in the in-line direction. However, for the midstream and downstream ones, the dual-lock-in region broadens. On the other hand, the prominent $X-Y$ trajectories of three circular cylinder resemble figure-eight shape and irregular one in the uniform flow. With the change of $k$, the motion orbit transforms from figure-eight to the raindrop shape in the lock-in region. In the larger shear ratio and higher natural frequency ratio case, the dual-raindrop is observed in the $X-Y$ vibrating trajectory of the midstream cylinder. Finally, the flow-induced motion mechanism of three tandem circular cylinders exposed to planar shear flow is revealed according to the analysis of the characteristic of the flow field.

Key words: planar shear flow, three tandem circular cylinders, flow induced motion, dynamic response, flow characteristics

CLC Number:

O357.1

Jiahuang Tu, Xiaoling Tan, Xuhui Deng, Xiaogang Guo, Jingqun Liang, Ping Zhang. STUDY OF FLOW-INDUCED MOTION CHARACTERISTICS OF THREE TANDEM CIRCULAR CYLINDERS IN PLANAR SHEAR FLOW¹⁾[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 787-802.

Figures/Tables 16

Fig. 1 Model schematic of validation study

Fig. 2 The comparisons of the variation of vibration amplitudes with $U_{\rm r}$

Fig. 3 The computational model and boundary conditions

Table 1 Grid independence test: the results for the three circular cylinders in the tandem arrangement at ${Re}=100$, $k=0$, $r=1.0$, $ U_{\rm r} =5.5$

Fig. 4 Schematic of the computational mesh

Fig. 5 The variation of the maximum vibrating amplitudes with reduced velocity under different shear ratios ($r =1.0$)

Fig. 6 The variation of the maximum vibrating amplitudes with reduced velocity under different shear ratios ($r =1.5$)

Fig. 7 Time history of streamwise displacements ($X/D)$ and the drag coefficients ($C_{\rm D})$ at different reduced velocities ($k =0.05$, $ r =1.5$)

Fig. 8 The variation of the maximum vibratin amplitudes with reduced velocity under different shear ratios ($r =2.0$)

Fig. 9 The variation of frequency ratios with reduced velocities under different shear ratios ($r =1.0$)

Fig. 10 The variation of frequency ratios with reduced velocitiesunder different shear ratios ($r =1.5$)

Fig. 11 The variation of frequency ratios with reduced velocities under different shear ratios ($r =2.0$)

Fig. 12 The variation of $X$-$Y$ trajectories with reduced velocities at different cases

Fig. 13 Power spectral density (PSD) of the flow force coefficients($C_{\rm D}$, $C_{\rm L})$ and displacements ($X/D$, $Y/D)$ of midstream cylinder under different shear ratios ($r =1.0$, $U_{\rm r} =6$

Fig. 14 Power spectral density (PSD) of the flow force coefficients ($C_{\rm D}$, $C_{\rm L})$ and displacements ($X/D$, $Y/D)$ of midstream cylinder under different shear ratios ($r =2.0$, $U_{\rm r} =6$)

Fig. 15 Time-history curve of displacement of midstream and downstream cylinders under different shear ratio cases and vorticity contours and instantaneous pressure contours at different times ($r =1.0$, $U_{\rm r} =8$)

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STUDY OF FLOW-INDUCED MOTION CHARACTERISTICS OF THREE TANDEM CIRCULAR CYLINDERS IN PLANAR SHEAR FLOW¹⁾

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References 33

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