Triggering asymmetry for flow past circular cylinder at low Reynolds numbers

The flow past a circular cylinder above some critical Reynolds number (Rec) is known to be asymmetric and, as a consequence, vortex shedding occurs naturally in physical situations. But in numerical simulations, especially in finite difference set up, it is well known that the shedding process needs to be initiated artificially for flows in the threshold regime in the vicinity of Rec. In the present study, we discuss four different techniques, including an untested one that trigger asymmetry into the flow in this regime with the help of a recently developed finite difference scheme for the biharmonic pure stream function form of the Navier–Stokes equations. In particular, we choose Reynolds number Re = 44 and 50; in case of the former, the flow eventually retains its symmetry and for the latter, it settles into a periodic state. We further narrow down the range of Re to establish that the critical Reynolds number resides in the regime 46.5 < Rec ⩽ 47 and finally provide an estimation of Rec as well. In order to ascertain credibility to our numerical simulation, we also compute flows for Re slightly beyond this regime, namely Re = 40 and 80 for which the flow pattern is well established. For Re = 44 and 80, we replicate the streakline patterns of some earlier experiments for which no such numerical simulation are seen before. In all the cases considered here, our numerical results are in excellent match with available experimental and numerical results. Finally, we provide a brief comparison of the four perturbation techniques.

► A new pure stream function based finite difference scheme is used.
► Robustness of 4 perturbation techniques including an untested one is established.
► The techniques trigger asymmetry in the threshold regime in the vicinity of Rec.
► Experimental results are replicated for Re = 44 and 80 by streakline simulation.
► By direct numerical time integration, we have found a very narrow range for Rec.