New insights into numerical simulations of flow around two tandem square cylinders

Abstract

Flows around tandem square cylinders at Re = 100 are numerically studied using a characteristic-based penalty operator splitting finite element method based on a multistep algorithm. The validation of the code and numerical method is performed for flows around single square cylinders. L/D effects (with L being the center-to-center distance and D being the square cylinder width) on the flow structures and parameters are investigated for 1.5 ≤ L/D ≤ 9.0. The flow structures, especially far downstream of the square cylinder, indicate six distinct flow regimes. The two-layered vortex formation (TVF) and secondary vortices formation (SVF) modes are defined, and their mechanisms are analyzed. The evolution of TVF into SVF proceeds through the combination of single and binary vortex formations. Variations in the physical flow parameters, including the coefficients of fluctuating lift (CL′), time-averaged drag (C̄D), and amplitude lift (CLA), as well as the Strouhal number and phase lag (ϕ), are analyzed for various L/D values. Obvious jumps in the flow parameters occur at both square cylinders for L/D = 4.4–4.5 because of vortex impingement. Finally, insight into the physics underlying the relationship between CL−upA, CL−up′, and ϕ is derived from the simulation results. The local maximum and minimum of CL−upA and CL−up′ occur at ϕ = 2π and 3π, respectively, corresponding to in-phase and anti-phase vortex shedding by the cylinders. The pressures on the upper and lower sides of the upstream square cylinder decrease and increase, respectively, leading to reductions in CL−upA and CL−up′ as the flow pattern changes from in-phase to anti-phase.

Analysis of the wake mechanism in external flow around tandem bluff bodies with different aspect ratios

“…Zdravkovich (1987) also classified such a flow pattern as a single slender body occurring in the range between 1 < G < 1.8 for coupled inline circular cylinders. This kind of flow pattern is also known as an isolated blunt body (Shui et al, 2021). Figure 3B presents the pressure and streamline contour for this flow pattern-it is obvious that the pressure is higher on the leading surface area of the C 1 and lower at the rear side of the C 2 .…”

“…The critical Reynolds number significantly influenced by the ratio of the upstream cylinder's diameter to the downstream cylinder's diameter. Shui et al (2021) Two tandem square cylinders, finite element method (FEM)…”

“…In the case of multiple obstacles, gap spacing (G) is another important parameter which significantly affects flow characteristics. Several studies have examined the combined effects of Re and G on fluid flows around two inline circular or square or rectangular cylinders (Shiraishi et al, 1986;Su et al, 2002;Su et al, 2004;Kuo et al, 2008;Huang et al, 2012;Mithun and Tiwari, 2014;Gnatowska et al, 2020;Rajpoot et al, 2021;Shui et al, 2021;Wang et al, 2022). Important findings of these studies are highlighted in Table 1.…”

Extensive study of flow characters for two vertical rectangular polygons in a two-dimensional cross flow

“…Specifically, for Re = 145 and 150, a discontinuity in the St is observed at 0.5 ≤ AR ≤ 0.6. In a study by Shui, Q., et al (Shui et al, 2021), numerical simulations were employed to investigate the flow characteristics across a pair of square cylinders arranged in tandem at Re = 100. Their research involved an in-depth exploration of the flow structures within the far-wake regions behind the downstream square cylinders, enabling the identification of the mechanisms responsible for their formation.…”

Numerical Simulation and Deep Neural Network Revealed Drag Reduction of Microstructured Three-Dimensional Square Cylinders at High Reynolds Numbers

“…Square cylinders are widely used in the engineering field, and they are common structures in fishways. A square cylinder can be regarded as a bluff body structure with a rectangular cross section, such as cylinders, beams, and fences in the building structure (Chen, 2019;Shui et al, 2021;Yang et al, 2021). In fluid mechanics, the flow around a square cylinder is a classic problem of flow around a bluff body, which contains complex phenomena such as impact, separation, reattachment, orbiting, and vortex often encountered in various fields (Lahaye et al, 2014;Vikram et al, 2020).…”