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Comparison of wake structures and force measurements behind three side-by-side cylinders

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Abstract

The research presents a numerical investigation of flow past three side-by-side square cylinders using the multi-relaxation-time lattice Boltzmann method. A comparison is made between equal and unequal gap spacings behind the three cylinders. Fluid forces acting on the cylinders, wake structure mechanism, time-trace analysis of drag and lift coefficients and vortex shedding frequencies are investigated systematically for different equal and unequal gap spacings. The Reynolds number is kept at 150 and unequal gap spacings (g 1, g 2) = (0.5, 0.6), (0.6, 0.5), (1.5, 1.6), (1.6, 1.5), (2.5, 2.6), (2.6, 2.5), (4, 4.1) and (4.1, 4) are selected for the investigation. For comparison we have also investigated the effect of equal gap spacings varied from 0.5 to 4. The results show that the wake structure and fluid forces are responsible for a slight change in gap spacing between any two cylinders. It is observed that the effects of unequal gap spacings on force statistics such as drag and lift coefficients, Strouhal number and the vortex shedding mechanism are notable at (g 1, g 2) = (0.5, 0.6), (0.6, 0.5), (1.5, 1.6) and (1.6, 1.5) and are completely different from those at equal gap spacings (g = 0.5 and 1.5). The results further show that at (g 1, g 2) = (4, 4.1) and (4.1, 4) the unequal gap spacing effect almost diminishes and only the primary vortex shedding frequency is observed. The bistable, asymmetric, inphase–antiphase and modulated synchronized flow patterns observed in this study.

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Abbreviations

C d :

Dimensionless drag coefficient

C l :

Dimensionless lift coefficient

D :

Diameter of the cylinder, m

f s :

Vortex shedding frequency, s−1

F d :

Drag force, N

L f :

Lift force, N

L :

Length of the computational domain

H :

Height of the computational domain

Re :

Reynolds number, dimensionless

St :

Strouhal number, dimensionless

C dmean :

Mean drag coefficient

C drms :

Root-mean-square value of drag coefficient

C lrms :

Root-mean-square value of lift coefficient

G :

Equal gap spacing between cylinders, dimensionless

g 1 :

Gap spacing between lower and middle cylinders, dimensionless

g 2 :

Gap spacing between middle and cylinders, dimensionless

c 1 :

Lower cylinder

c 2 :

Middle cylinder

c 3 :

Upper cylinder

ν :

Kinematic viscosity

U ∞ :

Uniform inflow velocity

u :

Velocity component in x-direction

v :

Velocity component in y-direction

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Authors and Affiliations

  1. Mathematics Department, COMSATS Institute of Information Technology, Islamabad, 44000, Pakistan

    Shams Ul Islam & Hamid Rahman

  2. Harbin Institute of Technology, Shenzhen Graduate School, Xili Town, Shenzhen, China

    Zhou Chao Ying

  3. School of Engineering Systems, Queensland University of Technology, Brisbane, QLD, 4001, Australia

    Suvash Chandra Saha

Authors
  1. Shams Ul Islam
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  2. Hamid Rahman
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  3. Zhou Chao Ying
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  4. Suvash Chandra Saha
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Correspondence to Shams Ul Islam.

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Technical Editor: Francisco Ricardo Cunha.

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Ul Islam, S., Rahman, H., Ying, Z.C. et al. Comparison of wake structures and force measurements behind three side-by-side cylinders. J Braz. Soc. Mech. Sci. Eng. 38, 843–858 (2016). https://doi.org/10.1007/s40430-014-0297-x

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  • DOI: https://doi.org/10.1007/s40430-014-0297-x

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