Numerical investigation on flow transition of two tandem circular cylinders in an X arrangement: Effects of spacing ratio and transverse inclination angle

This paper reports on a numerical study of the effects of five spacing ratios (L/D = 3-5) and eight transverse inclination angles (alpha = 0 degrees-30 degrees) on force coefficients and wake patterns of two tandem circular cylinders in an X arrangement, at a subcritical Reynolds number Re = 3900. It also addresses the mutual wake interference between the cylinders and the critical parameters determining the flow transition (FT) from the reattachment to the co-shedding regime. The main findings are: (1) the FT from the reattachment to the co-shedding regimes was identified for the considered range of L/D and alpha. The flow transition induces a sharp rise in force coefficients, especially for the downstream cylinder. FT can be triggered by the critical spacing ratio (L/D)(c) at different alpha, as well as excited by the critical transverse inclination angle alpha(c) at different L/D. (2) When alpha = 0 degrees (i.e., two tandem vertical cylinders), FT occurs at (L/D)(c) = 4.5-5. As alpha increases to 5 degrees, 15 degrees, and 25 degrees, (L/D)(c) gradually drops to 4-4.5, 3.5-4, and 3-3.5, respectively. From another perspective, with fixed spacing ratios of L/D = 3.5, 4, and 4.5, FT appears at alpha(c) = 20 degrees-25 degrees, 12.5 degrees-15 degrees, and 0 degrees-5 degrees, respectively. Additionally, in the case of L/D = 3 and 5, the flow pattern, respectively, remains in the reattachment and co-shedding regimes. (3) The formation of the co-shedding regime requires sufficient gap space between two crossing cylinders. A nondimensional center spacing ratio on the top view between the cylinders (CS*(top view)), was proposed to reflect the variation of gap space. The critical value of CS*(top view) to excite FT falls within the range of 3.5-5, which is a function of alpha and L/D. The mathematical expression of (CStop view*) points to the predominant role of L/D on the FT when compared with alpha. In addition, it also accounts for the fact that the transverse inclination angle has an inverse effect on the critical value of the spacing ratio and vice versa. These findings provide new insight into understanding the flow transition and wake interference of two crossing cylinders in an X arrangement.