Direct numerical simulation of oscillatory flow around a circular cylinder at low Keulegan–Carpenter number

Abstract

The Honji instability is studied using direct numerical simulations of sinusoidal oscillatory flow around a circular cylinder. The three-dimensional Navier–Stokes equations are solved by a finite element method at a relatively small value of the Keulegan–Carpenter numberKC. The generation and subsequent development of Honji vortices are discussed over a range of frequency parameters by means of flow visualization. It is found that the spacing between Honji vortices is only weakly dependent on the frequency of oscillation, but is strongly correlated toKCbecause it is the terms within the governing equation containingKCthat dominate the three-dimensional features of the flow. An empirical relationship betweenKCand the spacing between neighbouring vortices is proposed. The three-dimensional steady streaming structure within the vortices is identified and it is found that at high frequencies the steady streaming is two-dimensional although the instantaneous flow structure is itself fully three-dimensional.