Instability and transition of flow past two tandem circular cylinders

Abstract

The instability and transition of flow past two circular cylinders arranged in tandem are investigated numerically. A steady symmetric flow is realized at small Reynolds numbers, but the flow becomes unstable above a critical Reynolds number and makes a transition to an oscillatory flow. We obtained the symmetric flow numerically and analyze its stability by applying linear stability theory. The nonlinear oscillatory flow arising from the instability is obtained not only by numerical simulation but also by direct numerical calculation of the equilibrium solution, and the bifurcation diagram for the nonlinear equilibrium solution is depicted. We focused our attention on the effect of the gap spacing between the two cylinders on the stability and transition of the flow. The transition of the flow from a steady state to an oscillatory state is clarified to occur due to a supercritical or subcritical Hopf bifurcation depending upon the gap spacing. We found that there is a certain range of the gap spacing where physical quantities such as the drag and lift coefficients and the Strouhal number show an abrupt change when the gap spacing is continuously changed. We identified the origin of the abrupt change as the existence of multiple stable solutions for the flow.

Hysteretic mode exchange in the wake of two circular cylinders in tandem

“…Performing a series of experiments by incrementing ⌫ in steps of 0.1, such a hysteretic mode exchange is observed for 4.6ഛ⌫ഛ5.0. Note that this range of ⌫ is shifted in our experiment in comparison to the values observed in the numerical analysis 11 where it takes place for 3.05Ͻ⌫Ͻ3.4. The finite size of the cylinders is certainly at the origin of this discrepancy between the experiment and the 2D simulation.…”

“…These modes correspond to the modes that were computed in the numerical study of Mizushima and Suehiro. 11 The transition between the slow and fast vortex shedding mode is abrupt. The values of Re that this occurs at depends on ⌫.…”

“…In the present experimental study, we confirm the existence and their hysteretic exchange of the two vortex shedding regimes past two tandem circular cylinders as observed in the results of the bidimensional numerical calculation of Mizushima and Suehiro. 11 Flow patterns at each Reynolds number are observed by visualization using fluorescent dye for increasing and decreasing Re, and for different values of ⌫. An ultrasonic velocity profiler ͑UVP͒ has also been employed to measure the velocities and their fluctuation profiles in the near wake.…”

“…These results were further confirmed by Ohmi and Imaichi 8 and by the recent numerical simulations of Meneghini et al 9 and Sharman et al 10 To our knowledge, the most complete description of the tandem cylinder wake at low Reynolds numbers was recently given by Mizushima and Suehiro. 11 Using both linear stability analysis and direct numerical simulation, they investigated the instability of the two-dimensional wake of two tandem cylinders, which were arranged as shown in Fig. 1.…”

Numerical investigation of fluid-solid interaction for flow around three square cylinders

“…[1][2][3] Several analytic and numerical studies have been conducted to study the characteristics of Newtonian as well as non-Newtonian fluid flows. [4][5][6] Also numerous experimental and numerical studies have been carried out for the flow past inline circular cylinders; some representative works are those of Zdravkovich, 7 Williamson, 8 Mizushima and Suehiro, 9 Sumner et al, 10 and Lam et al 11 These researchers found that the gap spacing between cylinders play an important role because it strongly affects the flow patterns and also flow induced forces.…”