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

  • Shams Ul-Islam
  • Waqas Sarwar Abbasi
  • Aftab Khan


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.


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

List of symbols


Aspect ratio


Drag coefficient


Lift coefficient


Upstream cylinder


Middle cylinder


Downstream cylinder


Mean drag coefficient


Root-mean-square value of drag coefficient


Root-mean-square value of drag coefficient of upstream cylinder


Root-mean-square value of drag coefficient of middle cylinder


Root-mean-square value of drag coefficient of downstream cylinder


Root-mean-square value of lift coefficient


Root-mean-square value of lift coefficient of upstream cylinder


Root-mean-square value of lift coefficient of middle cylinder


Root-mean-square value of lift coefficient of downstream cylinder


Diameter of the cylinder


In-line force component


Transverse force component


Vortex shedding frequency


Equal gap spacing


Gap spacing between c 1 and c 2


Gap spacing between c 2 and c 3


Height of the computational domain


Length of the computational domain


Downstream position


Upstream position


Reynolds number


Surface-to-surface distance between c 1 and c 2


Surface-to-surface distance between c 2 and c 3


Strouhal number


Uniform inflow velocity

Greek symbols


Kinematic viscosity


Fluid density


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2015

Authors and Affiliations

  • Shams Ul-Islam
    • 1
  • Waqas Sarwar Abbasi
    • 1
  • Aftab Khan
    • 1
  1. 1.Mathematics DepartmentCOMSATS Institute of Information TechnologyIslamabadPakistan

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