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Numerical analysis of hydrodynamic forces and flow modes variation around a cluster of four cylinders

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Abstract

This work describes the results of numerical computations of fluid flow around four-square cylinders, forming a square cluster, using the lattice Boltzmann method. The purpose of this study is to analyze the transitions in flow modes and variations in hydrodynamic drag and lift forces under the effects of changing Reynolds number (Re) and gap ratio (G) between cylinders. Reynolds number is varied from 1 to 200 with two configurations of cylinders depending on the gap ratios: G = 0 (closely packed) and G = 7 (wide spacing). The results indicate three different flow modes, namely: the steady, transient and unsteady flow mode. At G = 0, the steady flow mode is found in the range 1 ≤ Re ≤ 39, transient mode in the range 40 ≤ Re ≤ 54 and unsteady mode for 55 ≤ Re ≤ 200. While at G = 7, the flow remains steady for 1 ≤ Re ≤ 34, becomes transient for 35 ≤ Re ≤ 37 and completely unsteady in the range 38 ≤ Re ≤ 200. The unsteady mode further exhibits different flow patterns categorized as the extended body vortex shedding, stable shielding flow, wiggling shielding flow and binary vortex shedding. Results indicate a strong influence of spacing values as well as a strong effect of both the proximity and wake interference on flow structure mechanism and flow induced hydrodynamic forces.

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Data availability statement

The data associated with graphs presented in this paper will be provided upon demand.

Abbreviations

G :

Gap ratio between the cylinders

Re :

Reynolds number

AR :

Aspect ratio

B :

Blockage ratio

c1 :

First cylinder

c2 :

Second cylinder

c3 :

Third cylinder

c4 :

Fourth cylinder

CD :

Drag coefficient

CD 1 :

Drag coefficient of first cylinder

CD 2 :

Drag coefficient of second cylinder

CD 3 :

Drag coefficient of third cylinder

CD 4 :

Drag coefficient of fourth cylinder

CL :

Lift coefficient

CL 1 :

Lift coefficient of first cylinder

CL 2 :

Lift coefficient of second cylinder

CL 3 :

Lift coefficient of third cylinder

CL 4 :

Lift coefficient of fourth cylinder

St :

Strouhal number

St 1 :

Strouhal number of first cylinder

St 2 :

Strouhal number of second cylinder

St 3 :

Strouhal number of third cylinder

St 4 :

Strouhal number of fourth cylinder

d :

Dimension

D :

Size of the cylinder

CD mean :

Mean drag coefficient

CL rms :

Root mean square value of Cl

CD rms :

Root mean square value of Cd

SRT :

Single relaxation time

LBM :

Lattice Boltzmann method

FVM :

Finite volume method

FEM :

Finite element method

FDM :

Finite difference method

\(\rho\) :

Density

\(\nu\) :

Kinematic viscosity

\(P\) :

Pressure

\(f\) :

Distribution function

f eq :

Equilibrium distribution function

\(c\) :

Velocity direction of the particle

t :

Time

θ:

Cylinder inclination

\(\tau\) :

Relaxation time factor

\(c_s\) :

Lattice speed of sound

\(w_i\) :

Weighting coefficients

U ∞ :

Inflow velocity

u :

Velocity vector

S:

Surface to surface distance between the cylinders

Lu :

Upstream length

Ld :

Downstream length

L:

Length of the computational domain

H:

Height of the computational domain

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Authors and Affiliations

  1. Department of Mathematics, Air University, Islamabad, Pakistan

    Waqas Sarwar Abbasi & Ramsha Jameel

  2. Department of Mathematics and Statistics, Women University Swabi, Swabi, Pakistan

    Hamid Rahman

  3. Department of Mathematics, COMSATS University, Islamabad, Pakistan

    Shams Ul Islam

Authors
  1. Waqas Sarwar Abbasi
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  2. Ramsha Jameel
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  3. Hamid Rahman
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  4. Shams Ul Islam
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Correspondence to Waqas Sarwar Abbasi.

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Abbasi, W.S., Jameel, R., Rahman, H. et al. Numerical analysis of hydrodynamic forces and flow modes variation around a cluster of four cylinders. J Braz. Soc. Mech. Sci. Eng. 45, 394 (2023). https://doi.org/10.1007/s40430-023-04327-2

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