# The effect of Reynolds numbers for unequal gap spacings on flow past three square cylinders arranged in-line

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## Abstract

Numerical investigations are carried out to study the effect of Reynolds numbers (*Re*) for unequal gap spacing on the flow past three square cylinders arranged in-line. Three different cases of unequal gap spacing between the cylinders are chosen in this work: the first case is related to the subcritical spacing range (*g* _{1}, *g* _{2}) = (1, 1.5) and (*g* _{1}, *g* _{2}) = (1.5, 1), the second one is related to the post-critical spacing range (*g* _{1}, *g* _{2}) = (4.5, 5) and (*g* _{1}, *g* _{2}) = (5, 4.5) and the third one is related to critical gap spacing (*g* _{1}, *g* _{2}) = (3, 4) and (*g* _{1}, *g* _{2}) = (4, 3). The *Re* values are varied from 75 to 175. Effect of equal gap spacing at *Re* = 150 is also discussed. A two-dimensional single-relaxation time lattice Boltzmann code was employed to simulate the important flow characteristics. In this study, three major cases concerning the behavior of shear layers, emerging from first cylinder, are observed: (a) without reattachment and without roll up, (b) without reattachment and with roll up and (c) with reattachment and with roll up. For equal spacing case, it is found that the critical spacing lies between 2–4. In the subcritical unequal spacing range, the single slender body flow is observed while the reattachment and binary vortex streets are observed in the post-critical unequal spacing range. The mean drag coefficient, Strouhal number, root-mean-square values of drag and lift coefficients are also calculated and compared with the experimental and numerical data in existing literature. It is found that the value of critical *Re* is 75 where maximum changes in the flow characteristics are observed.

## Keywords

Critical spacing Drag coefficient Single-relaxation-time lattice Boltzmann method Reynolds number Shear layers Square cylinder## List of symbols

- AR
Aspect ratio

*C*_{d}Drag coefficient

*C*_{l}Lift coefficient

*c*_{1}Upstream cylinder

*c*_{2}Middle cylinder

*c*_{3}Downstream cylinder

*C*_{dmean}Mean drag coefficient

*C*_{drms}Root-mean-square value of drag coefficient

*C*_{drms1}Root-mean-square value of drag coefficient of upstream cylinder

*C*_{drms2}Root-mean-square value of drag coefficient of middle cylinder

*C*_{drms3}Root-mean-square value of drag coefficient of downstream cylinder

*C*_{lrms}Root-mean-square value of lift coefficient

*C*_{lrms1}Root-mean-square value of lift coefficient of upstream cylinder

*C*_{lrms2}Root-mean-square value of lift coefficient of middle cylinder

*C*_{lrms3}Root-mean-square value of lift coefficient of downstream cylinder

*D*Diameter of the cylinder

*F*_{d}In-line force component

*F*_{l}Transverse force component

*f*_{s}Vortex shedding frequency

*g*Equal gap spacing

*g*_{1}Gap spacing between

*c*_{1}and*c*_{2}*g*_{2}Gap spacing between

*c*_{2}and*c*_{3}*H*Height of the computational domain

*L*Length of the computational domain

*L*_{d}Downstream position

*L*_{u}Upstream position

*Re*Reynolds number

*s*_{1}Surface-to-surface distance between

*c*_{1}and*c*_{2}*s*_{2}Surface-to-surface distance between

*c*_{2}and*c*_{3}*S*_{t}Strouhal number

*U*_{∞}Uniform inflow velocity

## Greek symbols

- ν
Kinematic viscosity

- ρ
Fluid density

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