Numerical study of flow past four square-arranged cylinders using spectral element method

• Flow around four square-arrayed cylinders at Re = 200 are numerically studied.
• The spectral element code is tested by flow past one- and two-tandem cylinders.
• The flow incidence angles are α = 0° and 45° and the spacing ratios from 1.5 to 4.0.
• Smaller spacing ratios can produce single-bluff body hydrodynamics.
• Four vortex streets can be observed at larger spacing ratios.

In this paper, flow past around four cylinders which are arranged as a square shape at a Reynolds number of 200 is numerically investigated with a spectral element method. To validate the numerical method for incompressible Navier–Stokes equations, benchmark problems of flow past a single and two tandem cylinders are employed, with the numerical results in a good agreement with the available literatures. Then the study concentrates on the flow characteristics of two groups of cases, respectively, with incidence angle α = 0° and α = 45°. By changing the spacing ratios L/D from 1.5 to 4.0 (L is the center-to-center distance and D the cylinder diameter), the flow characteristics, including the flow patterns, statistical force parameters such as the drag and lift coefficients as well as wake oscillation frequencies (Strouhal numbers) are investigated. Numerical results show that in each case there are around three wake flow patterns which are more related with the spacing ratio. In addition, the force parameters are highly affected by the flow patterns.