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Numerical simulation of flow-induced vibration of the one-degree-of-freedom circular cylinder using random vortex-boundary element method at turbulent flow

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Abstract

In this study, the turbulent flow around a circular cylinder in stationary and oscillating states has been simulated two-dimensionally using a Random Vortex-Boundary element method. The results were obtained in the Reynolds number of \(10^{4}\) and the mass and damping ratio of 11 and 0.001, respectively. Also, the reduced velocity is considered to be in the range of 4–14. Comparing the numerical results with the experimental results showed a 1.81% error in the Random vortex-Boundary element method at a Reynolds number of \(10^{4}\). Moreover, this method predicted the flow pattern with higher accuracy compared to the DES turbulence model. Comparing the present results with the results of the DES turbulence model showed that the computational time of the present method is considerably lower than the DES method. Unlike other methods, this method shows the temporal variations in the drag and lift coefficient values in a turbulent flow. Also, it was found that the cylinder displacement amplitude is large in the lock-in region such as \(U_{r} = 7\), and the flow pattern shows the 2P mode. Furthermore, the cylinder displacement range is very limited beyond this region, such as \(U_{r} = 4\), and the flow pattern shows the 2S mode similar to the flow around the stationary cylinder.

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Abbreviations

\(C_{D}\) :

Drag coefficient

\(C_{L}\) :

Lift coefficient

D :

The diameter of the cylinder, \(m\)

\(f_{n}\) :

Natural frequency, \(s^{ - 1}\)

\(f_{\delta }\) :

The core function of discrete vortex blobs

G :

Green function

\(m^{*}\) :

Dimensionless mass ratio

n :

Normal direction

P :

Pressure,\({\text{Nm}}^{ - 2}\)

q :

Potential flow flux perpendicular to the solid boundary

t :

Time, s

U :

Inlet velocity,\({\text{ms}}^{ - 1}\)

\(u\) :

Dimensionless velocity component in x-direction

\(\vec{u}\) :

(u,v), Dimensionless velocity vector

\(U_{r}\) :

Reduced velocity

\(u_{\delta }\) :

Dimensionless velocity at the outer edge of the boundary domain

v :

Dimensionless velocity component in the y-direction

\(y^{*}\) :

Dimensionless displacement in y-direction

\(\dot{y}\) :

The velocity of the cylinder in the y-direction, \({\text{ms}}^{ - 1}\)

\(\ddot{y}\) :

Acceleration of the cylinder in the y-direction, \({\text{ms}}^{ - 2}\)

\(\Delta_{s}\) :

The thickness of the boundary domain

\({\text{Re}}\) :

Reynolds number

\({\text{St}}\) :

Strouhal number

\(\alpha\) :

The angle between two adjacent elements, \(^\circ\)

\(\gamma\) :

Strength of discrete vortex sheets

\(\delta\) :

Discrete vortex blob core

\(\xi\) :

Damping ratio

\(\rho\) :

Density, \({\text{kgm}}^{ - 3}\)

\(\nu\) :

Kinematic viscosity, \({\text{m}}^{2} {\text{s}}^{ - 1}\)

\(\varphi\) :

Potential function, \({\text{m}}^{2} {\text{s}}^{ - 1}\)

\(\psi\) :

Streamfunction, \({\text{m}}^{2} {\text{s}}^{ - 1}\)

\(\omega\) :

Vorticity

\(\Gamma\) :

Circulation

i :

Point in space

j :

Discrete vortex element

p :

Potential flow

R :

2D area

\(\omega\) :

Produced by turbulence

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran

    Saeed Jamshidi, Amin Haghighi Poshtiri & Mohammad Ebrahim Maali

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  1. Saeed Jamshidi
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  3. Mohammad Ebrahim Maali
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Correspondence to Amin Haghighi Poshtiri.

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Jamshidi, S., Haghighi Poshtiri, A. & Maali, M.E. Numerical simulation of flow-induced vibration of the one-degree-of-freedom circular cylinder using random vortex-boundary element method at turbulent flow. J Braz. Soc. Mech. Sci. Eng. 45, 125 (2023). https://doi.org/10.1007/s40430-023-04037-9

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