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

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 < L/D < 2), reattachment of the shear layer (2 < L/D < 3.5), and vortex impact (3.5 < L/D < 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 < L/D < 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.