Numerical investigation of the patterns of the flow past nine cylinders at low Reynolds number

Jian-Jun Yin,Feng Xiao,Tao Jia,Di Gao

doi:10.1063/5.0015541

Abstract

Numerical investigations of the flow patterns around nine cylinders under the condition of Reynolds number around 200 are carried out. The change in the mean lift coefficient, the mean drag coefficient, Strouhal number, and mean streamwise velocity with the change in the pitch ratio is revealed. The Shannon entropy is calculated in the sample region to qualitatively measure the randomness of the velocity field in the region. It is shown that in flow regimes there are three patterns, including shield flow (1.1 &lt; L/D &lt; 2), reattachment of the shear layer (2 &lt; L/D &lt; 3.5), and vortex impact (3.5 &lt; L/D &lt; 5). The gap flow under different wake patterns has different effects on the change in hydrodynamic characteristics. The mean streamwise velocity is not strictly symmetrical about y/D when 2 &lt; L/D &lt; 3.5, and this asymmetry becomes more obvious as the pitch ratio increases. This asymmetry phenomenon is caused by deflection wake and instability of the shear layer falling from the surface of the upper and lower cylinders. The Shannon entropy of the velocity field decreases with an increase in the pitch ratio.

Highlights

From academic and practical perspectives, the flow around bluff bodies is an important engineering issue
Numerical simulation of fluid flow past four cylinders arranged in diamondshape under the condition of a low Reynolds number was conducted by solving the incompressible Navier–Stokes equation through SIMPLE algorithm
In the regimes under the condition of 1.1 < L/D < 2, due to the small spacing between the cylinders, the free shear layer on the upper side of the C1 cylinder surface completely shields its downstream cylinders without being attached to the downstream, while the lower shear layer is attached to the surface of the downstream cylinders

Summary

Introduction

From academic and practical perspectives, the flow around bluff bodies is an important engineering issue. The experimental investigation of the flow past four cylinders in a square configuration was carried out under the condition that the longitudinal and lateral pitch ratios were enlarged in equal proportions.[18] According to the flow field characteristics in the cases of different pitch ratios, the flow field is divided into three states: stable shielding flow state, swing shielding flow state, and vortex shedding flow state Both large eddy simulation and experimental studies were conducted to investigate the behavior of the turbulent flow around cylinders at high Reynolds number,[19,20] and it was found that the flow spectrum analysis could reveal the influence of the pitch ratio and subcritical Reynolds number on the flow pattern. Two-dimensional numerical simulations on the fluid flow around four cylinders under conditions of low Reynolds numbers have been extensively studied.[21,22,23,24,25,26,27]

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Conclusion