Forced streamwise oscillations of a circular cylinder: Locked-on modes and resulting fluid forces

A computational study of laminar, incompressible flow past a cylinder oscillating in the streamwise direction is performed using the two-dimensional unsteady Navier-Stokes equations in nonprimitive variables. The method of solution is based on a conjugating Fourier spectral analysis with finite-difference approximations. The numerical simulations are conducted at a fixed Reynolds number, R = 200, and at displacement amplitude-to-cylinder diameter of A = 0.1 and 0.3. Results show the existence of symmetric/asymmetric modes of vortex formation in the cylinder wake at different values of unsteady loading on the cylinder, which is characterized by the ratio of oscillation frequency, f, to Kármán vortex-shedding frequency, f₀. For this paper, the frequency ratio is chosen from f / f₀ = 0.5 to 3, where switching from asymmetric to symmetric vortex shedding is observed. The relation between these vortex-shedding modes and fluid forces on the cylinder surface is discussed. An analysis of the locked-on modes via Lissajous patterns of unsteady lift coefficient is also included. Previously computed and observed flow fields as well as fluid forces are compared to current numerical results and agreement is found to be excellent.