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A two-dimensional lattice Boltzmann study of flow past five side-by-side rectangular cylinders

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Abstract

Numerical simulations are performed, in the range of 0.5 ≤ g ≤ 5, where g is the separation ratio between the cylinders at fixed Reynolds number 150 and aspect ratio 2, for flow past five side-by-side rectangular cylinders. A two-dimensional code is developed using the lattice Boltzmann method. The effect of separation ratio on the vortex shedding frequency, time-trace analysis of drag and lift coefficients, power spectra analysis of lift coefficients and force statistics exerted on the cylinders is quantified together with the observed flow structure. Five different flow structures were found and named as nearly symmetric (g = 0.5), flip-flopping (g = 1), modulated (g = 1.5), strongly interactive (g = 2, 2.5 and 3) and weakly interactive (g = 4 and 5) flow structures. It is found that the vortices are generated on the surfaces of the cylinders as width of the cylinder is 2h (h is the width of the rectangular cylinders) and due to this there is modulation in time-history analysis of drag and lift coefficients for all chosen cases except at g = 0.5. The Strouhal number is also calculated using Welch’s method for comparison, and correlation of lift coefficients for different combinations is also given.

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Abbreviations

1:

First cylinder

2:

Second cylinder

3:

Third cylinder

4:

Fourth cylinder

5:

Fifth cylinder

c i :

Velocity directions of particles

C d :

Drag coefficient

C l :

Lift coefficient

C dmean :

Mean drag coefficient

C drms :

Root-mean-square value of the drag coefficient

C lrms :

Root-mean-square value of the lift coefficient

D :

Dimension of space

E :

Energy spectrum

f i :

Particle distribution function

f (eq) i :

Equilibrium particle distribution function

f s :

Vortex shedding frequency

g :

Separation ratio between two cylinders

H :

Height of the computational domain

h :

Height of the rectangular cylinder

L :

Length of the channel

L u :

Upstream distance from inlet to five rectangular cylinders

L d :

Downstream distance from five rectangular cylinders to outlet boundary

Q :

Number of particles

R :

Aspect ratio

Re :

Reynolds number

s :

Surface-to-surface distance between two consecutive cylinders

St :

Strouhal number

T :

Time step

u :

Macroscopic velocity components

U max :

Uniform inflow velocity

w :

Width of the rectangular cylinder

w i :

Weighting coefficients

x :

Position of particle

τ :

Single-relaxation-time parameter

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Author information

Authors and Affiliations

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

    Shams Ul Islam

  2. Department of Mathematics and Statistics, Bacha Khan University, Charsadda, 44000, Pakistan

    Hamid Rahman

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

    Zhou Chao Ying

Authors
  1. Shams Ul Islam
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  2. Hamid Rahman
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  3. Zhou Chao Ying
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Corresponding author

Correspondence to Hamid Rahman.

Additional information

Technical Editor: Jader Barbosa Jr.

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Islam, S.U., Rahman, H. & Ying, Z.C. A two-dimensional lattice Boltzmann study of flow past five side-by-side rectangular cylinders. J Braz. Soc. Mech. Sci. Eng. 40, 321 (2018). https://doi.org/10.1007/s40430-018-1244-z

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  • DOI: https://doi.org/10.1007/s40430-018-1244-z

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