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 number KC. 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 to KC because it is the terms within the governing equation containing KC that dominate the three-dimensional features of the flow. An empirical relationship between KC and 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.

Oscillating cylinder in viscous fluid: calculation of flow patterns and forces

“…1.1, and also in recomputations by Lu and Ling [12] and An et al [15]. Below we shall compare the present computations to those found in [11,12,15]. The roll pattern extends vertically along the cylinder boundary and has a maximum in the plane x = 0.…”

“…For sufficiently large oscillation amplitude (and Keulegan-Carpenter number), roll pattern becomes generated, superposed on this streaming, as experimentally found by Honji [3]; see Sect. 1.1, and also in recomputations by Lu and Ling [12] and An et al [15]. Below we shall compare the present computations to those found in [11,12,15].…”

“…The cylinder motion was given by 1 2 While the present work was in progress, An et al [15] have, by means of a finite-element method, provided detailed simulations and flow visualizations of the Honji vortices, for K = 2 and β ∼ 100-600. They were able to identify steady-streaming structures induced by the Honji rolls.…”

Numerical study on mixed convection from a constant wall temperature circular cylinder in zero-mean velocity oscillating cooling flows

“…Visualizations of (Sarpkaya, 2002(Sarpkaya, , 2006 showed that over the ranges of 0.02 < KC D < 1 and 10 3 < b D < 1.4 Â 10 4 , the flow can be divided into four distinct regimes: stable, marginal, unstable and chaotic flows. It was found by direct numerical simulation (DNS) of An et al (2011), the spacing between Honji vortices is only weakly dependent on the frequency of oscillation but strongly correlated to KC D , which dominates the three dimensional features of the flow. The three dimensional steady streaming structure within the vortices was identified, and it was found that at high frequencies the steady streaming is two dimensional although the instantaneous flow structure is itself fully three dimensional.…”

Numerical study of flow over a circular cylinder in oscillatory flows with zero-mean and non-zero-mean velocities

“…Compared with zeromean velocity oscillatory flow, there have been fewer studies on nonzero-mean velocity oscillatory flow. A few researchers studied whether Morison's equation is applicable to sinusoidal oscillatory flow with a non-zero-mean velocity (Nomura et al, 2003;Chen et al, 2009;An et al, 2011). Meanwhile, Nomura et al (2003) proposed to extend Morison's equation to predict lift force in an oscillatory flow.…”