Instability and transition of flow past two tandem circular cylinders

• Published in: Physics of fluids (1994) 2005-10, Vol.17 (10), p.104107-104107-11
• Main Authors: Mizushima, Jiro, Suehiro, Norihisa
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Nonlinearity (including bifurcation theory); Physics; Rotational flow and vorticity; Separated flows; Transition to turbulence; Turbulent flows, convection, and heat transfer
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.2104689

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.