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Fluid Dynamics of Flow Around Side-by-Side Arranged Cylinders

  • Research Article-Mechanical Engineering
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Abstract

Flow past four side-by-side identical square cylinders arranged normal to the flow have been found to show interesting and important flow features which are very difficult to get through experiments. Lattice Boltzmann method (LBM) is used for numerical simulations of two-dimensional (2D) flow around four side-by-side arranged cylinders. In this study, the Reynolds number (Re) is chosen to be 60, 80, 100, 120 and 140 and the spacing ratio g* (= g/D, where D is the size of cylinder and g is the distance between the cylinders) is set at 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.5, 3, 3.5 and 4. Based on the flow characteristics, seven distinct and unique flow regimes are identified for different ranges of Re and g*. Physical features of each flow regime such as wake structures, vortex dynamics, gap flow behavior, time histories of lift coefficients, shedding frequencies and hydrodynamic forces are thoroughly discussed. The Reynolds numbers strongly affect the flow, especially at 0 ≤ g* ≤ 2, in terms of vortex-shedding frequency. A significant secondary frequency is also found other than the primary frequency in the base-bleed and flip-flopping flow regimes. It is observed that for g* ≥ 2.5 primary shedding frequency strongly affects the flow dynamics and the mutual interaction of the wakes behind the cylinders decreases with an increase in the Reynolds number. The Strouhal value is same for the outer and inner cylinders in inphase–antiphase weak interaction flow regime and different for base-bleed and flip-flopping flow regimes. In inphase asynchronous weak interaction flow regime, the Strouhal number is same for all four cylinders.

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Abbreviations

C 1 :

First cylinder from bottom to top

C 2 :

Second cylinder from bottom to top

C 3 :

Third cylinder from bottom to top

C 4 :

Fourth cylinder from bottom to top

c :

Speed of sound

C D :

Drag coefficient

C L :

Lift coefficient

C Dmean :

Mean drag coefficient

C D1mean :

Mean drag coefficient of first cylinder

C D2mean :

Mean drag coefficient of second cylinder

C D3mean :

Mean drag coefficient of third cylinder

C D4mean :

Mean drag coefficient of fourth cylinder

C Drms :

Root mean square of drag coefficient

C D1rms :

First cylinder rms of drag coefficient

C D2rms :

Second cylinder rms of drag coefficient

C D3rms :

Third cylinder rms of drag coefficient

C D4rms :

Fourth cylinder rms of drag coefficient

C Lrms :

Root mean square of lift coefficient

C L1rms :

First cylinder rms of lift coefficient

C L2rms :

Second cylinder rms of lift coefficient

C L3rms :

Third cylinder rms of lift coefficient

C L4rms :

Fourth cylinder rms of lift coefficient

D :

Size of the cylinder

f i :

Particle distribution function

f (eq) i :

Equilibrium distribution function

f s :

Vortex-shedding frequency

g* :

Dimensionless separation ratio

g :

Distance between the cylinders

L x :

Length of the computational domain

L y :

Height of the computational domain

Ma:

Mach number

Re:

Reynolds number

St:

Strouhal number

St1:

First cylinder Strouhal number

St2:

Second cylinder Strouhal number

St3:

Third cylinder Strouhal number

St4:

Fourth cylinder Strouhal number

t :

Dimensionless time

U ∞ :

Uniform inflow velocity

u :

Velocity components

v :

Kinematic viscosity of fluid

ω i :

Weighting coefficients

x :

Position of particles

ρ :

Density of fluid

τ :

Single-relaxation-time parameter

e i :

Velocity particles

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Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Park Road, Tarlai Kalan, Islamabad, 45550, Pakistan

    Shams-ul-Islam & Naqib Ullah

  2. Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen University Town, Shenzhen, 518055, China

    Chao Ying Zhou

Authors
  1. Shams-ul-Islam
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  2. Naqib Ullah
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  3. Chao Ying Zhou
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Correspondence to Shams-ul-Islam.

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Shams-ul-Islam, Ullah, N. & Zhou, C.Y. Fluid Dynamics of Flow Around Side-by-Side Arranged Cylinders. Arab J Sci Eng 45, 5907–5923 (2020). https://doi.org/10.1007/s13369-020-04603-6

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  • DOI: https://doi.org/10.1007/s13369-020-04603-6

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