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Numerical investigation of the flow characteristics around two sequential cylinders with circular and square cross-sections

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Abstract

Many efforts have been dedicated to examining the flow characteristics around a pair of cylinders. Despite the straightforward geometry, the flow dynamics around a cylinder prove to be intricate. The practical applications of this phenomenon extend across various engineering domains, including oil and gas transmission lines, heat exchangers, pipelines, and the construction of successive skyscrapers. The current investigation delves into the examination of the critical distance ratio, fluctuating velocity, flow pattern, and drag surrounding two sequential circular and square cylinders. The governing equations are solved using the finite volume method (FVM). For momentum, turbulent kinetic energy, and turbulent dissipation rate equations, the upwind second-order discretization is used. The findings, acquired at a Reynolds number of 32,000 for distance ratios ranging from 0.25 to 10, are then compared with those from single-cylinder cases. The results highlight the significant influence of both geometry and the distance between cylinders on the observed flow patterns. The critical distance ratio is obtained as \(s_{c}\) = 2 and 2.5 for the case of two sequential circular and square cylinders, respectively, while for the case of combined circular and square cylinders, it is calculated as \(s_{c}\) = 3. The non-dimensional fluctuating velocity decreases by 7%, 26%, and 38% in the case of two sequential circular cylinders with distance ratios of S* = 1, 2, and 3 at the first station, respectively, compared to a single circular cylinder. The drag coefficient is 50% lower in the two sequential circular and square cylinders case compared to the single square cylinder.

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Abbreviations

\(C_{D}\) :

Drag coefficient

\(C_{P}\) :

Pressure coefficient

CFl:

Courant number

D :

Diameter(mm)

\(F_{D}\) :

Drag force (kg \({\text{ms}}^{ - 2}\))

K :

Kinetic turbulent energy (\({\text{m}}^{2} {\text{s}}^{ - 2}\))

P :

Static pressure (kg \({\text{m}}^{ - 1} {\text{s}}^{ - 2}\))

\(p_{\infty }\) :

Ambient pressure (kg \({\text{m}}^{ - 1} {\text{s}}^{ - 2}\))

S :

Cylinders’ distance (mm)

\(s^{*}\) :

Cylinder distance to diameter ratio (mm)

\(s_{c}\) :

Critical distance ratio

St:

Strouhal number

T :

Time (s)

\(u_{i}{\prime}\), \(u_{j}{\prime}\) :

Fluctuating velocity components (m/s)

\(\overline{{u_{i}{\prime} u_{j}{\prime} }}\) :

Reynolds shear stress (\({\text{m}}^{2} {\text{s}}^{ - 2}\))

\(\overline{{u_{i} }}\), \(\overline{{u_{j} }}\) :

Mean velocity components (m/s)

\(U_{0}\) :

Inlet velocity (m/s)

\(\Delta x\) :

Spatial step (m)

\(\Delta t\) :

Time step (s)

\(\mu\) :

Dynamic viscosity (kg \({\text{m}}^{ - 1} {\text{s}}^{ - 1}\))

\(\vartheta\) :

Kinematic viscosity (\({\text{m}}^{2} {\text{s}}^{ - 1}\))

\(\rho\) :

Density (kg \({\text{m}}^{ - 3}\))

\(\sigma_{\omega }\) :

Effective diffusivity of k and ω

\(\omega\) :

Turbulence dissipation rate (\({\text{s}}^{ - 1}\))

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hakim Sabzevar University, Sabzevar, Iran

    M. Sadeghi & A. Bak Khoshnevis

  2. Department of Mechanical Engineering, Esfarayen University of Technology, Esfarayen, Iran

    M. Yadegari

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  1. M. Sadeghi
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Correspondence to A. Bak Khoshnevis.

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Sadeghi, M., Yadegari, M. & Khoshnevis, A.B. Numerical investigation of the flow characteristics around two sequential cylinders with circular and square cross-sections. J Mar Sci Technol (2024). https://doi.org/10.1007/s00773-024-00987-4

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