Fluid structure interaction problem for flow past three unequal sized square cylinders at different Reynolds numbers

Abstract

The flow past three square cylinders of unequal size placed in an inline arrangement is studied using the lattice Boltzmann method at different Reynolds numbers [Re = (u∞ d)/ν] within the range of Re = 120, 150, 160, 175, and 200 for various gap spacings (g = s/d), ranging from 1 to 6. This study focused on the symmetric examination of flow behavior for various gap spacing within the three unequal-sized square cylinders. The main objective of this study was to investigate the effects of Reynolds numbers and gap spacing for flow structure mechanism and vortex shedding suppression in between the gap and down-stream position of all three cylinders. Results are obtained in terms of vorticity contours visualization, drag and lift coefficients, Strouhal number, and physical parameters. In vorticity contour visualization, different flow behaviors are observed, known as flow regimes, and are named according to their characteristics, and they are (i) steady flow regime, (ii) shear layer reattachment flow regime (SLR), (iii) fully developed vortex shedding flow regime, (iv) two-row fully developed vortex shedding flow regime, and (v) fully developed irregular vortex shedding flow regime. The present study also includes a discussion on aerodynamic forces, namely the mean drag coefficient (Cdmean), root mean square of the lift coefficient (Clrms), and Strouhal numbers (St) for three cylinders with sizes d = 20, d1 = 15, and d2 = 10, respectively. The maximum value of Cdmean for the first cylinder (C1) is obtained at (Re, g) = (200, 3) that is, 1.5156, where the existing flow regime is the SLR flow regime, while for C2 and C3, the maximum Cdmean values are examined at critical flow behaviors, where the existing flow regime is a fully developed irregular vortex shedding flow regime. Negative values of Cdmean are also examined for cylinders C2 and C3 at some combinations of (Re, g), attributed to the effect of thrust. Furthermore, it is noticed that the values of Strouhal number are increased with an increment in values of gap spacing. The highest value of the Strouhal number for all three cylinders is observed for C1 at (Re, g) = (120, 5), reaching 0.1556 along with a two-row fully developed flow regime. Furthermore, it is investigated from the present problem that the position of unequal sized square cylinders strongly influenced the flow structure mechanism. The information found and discussed in this study could be effective for structure designing arrangement in the case of three square cylinders of unequal size placed in a horizontal arrangement.