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Flow-induced vibration of a circular cylinder in cross-flow at moderate Reynolds number

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Abstract

In this paper, two-dimensional numerical simulations of the incompressible flow around an elastically mounted rigid circular cylinder in cross-flow have been accomplished with the finite difference method. The bluff body immersed in the flow is modeled by the Immersed Boundary Methodology combined with the Virtual Physical Model. The motion of the cylinder is described by the harmonic structural model which is solved using a fourth order Runge–Kutta method. The numerical simulations were performed for Reynolds number 8,000 and 10,000 and for the reduced velocity in the range 1 ≤ V r  ≤ 15. The vortex shedding process, the time evolution of the dynamic coefficients, the cylinder response and the power spectra of the lift coefficient and of the cylinder displacement were investigated. It was found a reasonable agreement with numerical results for R e  = 8,000. On the other hand, for R e  = 10,000, the present results as well as other numerical simulations failed when compared with the experiments in the capture of the so-called upper branch. The absence of that in LES simulations can be explained by the existence of discrepancies between the experiments and the assumptions adopted in the present methodology.

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Abbreviations

A :

Amplitude, m

c :

Structural damping, Ns/m

C d :

Drag mean coefficient, dimensionless

C l :

Lift mean coefficient, dimensionless

C s :

Smagorinsky constant, dimensionless

D :

Cylinder diameter, m

D ij :

Distribution function, m−2

\(E_{{C_{l} }}\) :

Power spectrum of the lift coefficient signal

E y/D :

Power spectrum of the displacement signal in the y direction

\(\varvec{f}\) :

Eulerian force vector, N

f i :

I-th component of the Eulerian force, N/m3

f n :

Natural frequency of the cylinder, Hz

yf o :

Vortex shedding frequency of the stationary cylinder, Hz

f r  = f o /f n :

Response frequency

f v :

Vortex shedding frequency, Hz

\(\varvec{F}\) :

Lagrangean force vector, N

\(\varvec{F}_{a}\) :

Acceleration force vector, N

\(\varvec{F}_{i}\) :

Inertial force vector, N

F l :

Lift force, N

\(\varvec{F}_{p}\) :

Pressure force vector, N

\(\varvec{F}_{v}\) :

Viscous force vector, N

L :

Length, m

m :

Cylinder mass, kg

m * :

Mass ratio, dimensionless

p :

Pressure, N/m2

R e :

Reynolds number, dimensionless

S ij :

Strain rate tensor, s−1

St o :

Vortex shedding frequency of the stationary cylinder, dimensionless

St :

Strouhal number, dimensionless

t :

Physical time, s

T :

Dimensionless time

u i , u j :

Components i and j of the velocity, m/s

U :

Free stream velocity, m/s

υ :

Velocity in the y direction, m/s

V r :

Reduced velocity, dimensionless

\(\varvec{x}\) :

Position vector of an Eulerian point, m

\(\varvec{x}_{k}\) :

Position vector of a Lagrangean point, m

y :

Transversal displacement of the cylinder, m

k :

Spring constant, N/m

ΔS :

Arc length centered in each Lagrangean point, m

Δt :

Time step, s

ρ :

Specific mass, kg/m3

μ :

Dynamic viscosity, kg/(ms)

ν :

Kinematic viscosity, m2/s

ℓ:

Length scale

ν t :

Turbulent viscosity, m2/s

ω n :

Natural angular frequency, Hz

ξ :

Damping ratio, dimensionless

i, j :

Eulerian grid points

k :

Lagrangean grid points

o :

Initial condition, stationary

∼:

Auxiliar variable

n :

Superscript of time, dimensionless

∇:

Nabla vector operator

∇2 :

Laplaciano operator

∂ :

Partial derivate

Δ:

Finite difference

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Acknowledgments

The authors are grateful to the Minas Gerais State Agency FAPEMIG for the financial support to their research activities and the agency of the Ministry of Science, Technology and Innovation—CNPq for the continued support to their research work, especially through research projects by A. M. G. de Lima and A. Silveira-Neto.

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Authors and Affiliations

  1. School of Civil Engineering, Federal University of Uberlândia, Campus Santa Mônica, P. O. Box 593, Uberlândia, MG, CEP 38400-902, Brazil

    A. R. da Silva

  2. School of Mechanical Engineering, Federal University of Uberlândia, Campus Santa Mônica, P. O. Box 593, Uberlândia, MG, CEP 38400-902, Brazil

    A. Silveira-Neto & A. M. G. de Lima

Authors
  1. A. R. da Silva
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  2. A. Silveira-Neto
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  3. A. M. G. de Lima
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Correspondence to A. R. da Silva.

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Technical Editor: Francisco Ricardo Cunha.

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da Silva, A.R., Silveira-Neto, A. & de Lima, A.M.G. Flow-induced vibration of a circular cylinder in cross-flow at moderate Reynolds number. J Braz. Soc. Mech. Sci. Eng. 38, 1185–1197 (2016). https://doi.org/10.1007/s40430-015-0314-8

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  • DOI: https://doi.org/10.1007/s40430-015-0314-8

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