Direct numerical simulation of 3D steady streaming induced by Honji Instability

Direct numerical simulation of sinusoidal oscillatory flow around a circular cylinder is carried out to study the Honji Instability. Three-dimensional Navier-Stokes equations are solved by finite element method. Numerical study is performed at KC number of 2 and β number ranging from 100 to 600 with an interval of 50. The steady streaming is calculated by averaging the velocity component over one oscillatory flow period. It is found that the flow is two-dimensional at β = 100 and the steady streaming structure is identical to that observed at KC << 1. For β =150 and 200, regularly distributed Honji vortices are observed around the cylinder. Three-dimensional steady streaming for these two β numbers is characterized by evenly distributed streamwise vortex-pairs. For 250 ≤ β ≤ 550, the streamwise vortices in steady streaming become uneven along the cylinder. For β = 600, the flow transition to turbulent happens while the streamwise vortices still exist in the steady streaming. For case with unstable Honji vortices or turbulent flow, the steady streaming is time dependent because the flow is aperiodic. The intensity of streamwise vortices in the steady streaming decreases with the increase of the number of flow periods over which the steady streaming is calculated.