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Numerical simulation of flow interaction between stationary and downstream elastically mounted cylinders in tandem at low Reynolds numbers

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Abstract

Despite the simplicity of the geometry of the circular cylinders, the uniform flow around them is complex, since it may induce unsteady forces on structures associated with vortex shedding. This paper describes the study of two circular cylinders (the downstream one is elastically mounted in transversal direction) in tandem arrangement subject to bi-dimensional uniform laminar flows at low Reynolds numbers. The academic numerical model Ifeinco, which is based on the finite element method and uses a partitioned scheme that considers two-way interaction of fluid flow and structure, has been employed to the analysis. Firstly, both stationary cylinders in tandem arrangement for Re = 100 are analysed for center to center distance between the cylinders, L/D, from 1.5 to 6.0. Results of lift and drag coefficients and Strouhal number are compared with other numerical results and good agreement is found. Secondly, numerical results for L/D = 5.25, considering downstream elastically mounted cylinder, are analysed for Reynolds numbers ranging from 100 to 140. It shows that the resonance occurs for Reynolds numbers between 115 and 120 and the maximum dimensionless amplitude of oscillation is 0.721 for Re = 118.

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Abbreviations

c :

Damping coefficient (kg/s)

c s :

Sound velocity (m/s)

C D :

Drag coefficient

C Dmean :

Mean drag coefficient

C L :

Lift coefficient

C Lrms :

Root mean square lift coefficient

D :

Cylinder diameter (m)

f :

Vortex shedding frequency (Hz)

F :

Dynamic force (N)

f n :

Natural frequency (Hz)

k :

Spring stiffness (N/m)

k s :

Surface roughness parameter

K s :

Stability parameter

L :

Distance between cylinders (m)

L c :

Critical distance between cylinders (m)

m :

Mass (kg)

M :

Mass ratio

p :

Pressure (Pa)

Re :

Reynolds number

St :

Strouhal number

t :

Time (m)

U i :

Momentum per volume (i, j = 1, 2) (kg m/s/m3)

U ∞ :

Free stream velocity (m/s)

v i :

Fluid velocity (i, j = 1, 2) (m/s)

V R :

Reduced velocity

x i :

Coordinate (i, j = 1, 2) (m)

w i :

Mesh velocity (i, j = 1, 2) (m/s)

Y :

Amplitude of cylinder oscillation (m)

y :

Cylinder displacement (m)

\(\dot{y}\) :

Cylinder velocity (m/s)

\({\ddot{y}}\) :

Cylinder acceleration (m/s2)

α :

Parameter of the Newmark method

δ :

Parameter of the Newmark method

τ ij :

Viscous stress tensor (i, j = 1, 2) (Pa)

ω n :

Angular frequency (rad/s)

ρ :

Specific mass (kg/m3)

μ :

Viscosity (kg/ms)

ζ :

Damper ratio

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Acknowledgements

The authors acknowledge the support of Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq, Brazil (project 303765/2012-7) and Fundação de Ciência e Tecnologia-FCT, Portugal (SFRH/BPD/37901/2007).

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Authors and Affiliations

  1. Universidade Federal do Rio Grande (FURG), Avenida Itália km8, Campus Carreiros, 96203-900, Rio Grande, RS, Brazil

    Paulo R. F. Teixeira

  2. Departamento de Hidráulica e Ambiente, Laboratório Nacional de Engenharia Civil (LNEC), Avenida do Brasil, 101, 1700-066, Lisbon, Portugal

    Eric Didier

  3. Departamento de Engenharia Mecânica e Industrial, Universidade Nova de Lisboa (FCT-UNL), Campus da FCT/UNL, 2829-516, Caparica, Portugal

    Eric Didier

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  1. Paulo R. F. Teixeira
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Correspondence to Paulo R. F. Teixeira.

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Technical Editor: Marcio S. Carvalho.

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Teixeira, P.R.F., Didier, E. Numerical simulation of flow interaction between stationary and downstream elastically mounted cylinders in tandem at low Reynolds numbers. J Braz. Soc. Mech. Sci. Eng. 39, 801–811 (2017). https://doi.org/10.1007/s40430-016-0682-8

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