Phase lock-on in periodically excited Bingham flow past a confined cylinder

Abstract

The focus of the work is the “phase lock-on”, a well-known phenomenon observed in oscillating dynamical systems where the forcing and output frequencies are synchronized. This phenomenon appears to be universal with the frequencies related by a rational ratio. We considered the case of an incompressible flow past a confined cylinder where the incident bulk flow is subjected to periodic velocity perturbations. While we considered both Newtonian and non-Newtonian (Bingham) fluids, the main interest was on the Bingham case. Numerical simulations were conducted at a fixed Reynolds number of Re = 100 based on the bulk fluid velocity and cylinder diameter. The relative amplitude of the periodic velocity perturbation was considered in the range 0.10–0.30 and the forcing frequency relative to the natural unforced shedding frequency was in the range 1.4–2.3. These choices yielded fixed lock-on periodic states that correspond to the number 2 on the horizontal axis of an Arnold tongue graph. Yield stress effects are shown for Bingham numbers in the range 0–0.5.