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• W2243043670 abstract "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  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  = 100 and the steady streaming structure is identical to that observed at KC << 1. For  =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 ≤  ≤ 550, the streamwise vortices in steady streaming become uneven along the cylinder. For  = 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. Introduction Oscillatory flow around a stationary circular cylinder and flow induced by a circular cylinder oscillating in an otherwise quiescent viscous fluid has been of significant academic and practical interest. This flow is specified as u = Umsin(2t/T), where Um, the maximum speed of the flow, and T, the period of oscillation. Key dimensionless parameters are then the Keulegan -Carpenter number KC and the Reynolds number Re KC = UmT/D and Re = UmD/ (1) where D is the diameter of the cylinder and  is the kinematic viscosity of the fluid. A frequency number given by the ratio of Re and KC is also used frequently, which is written as  = Re/KC = D/ (2) When a periodic oscillatory flow passes around a circular cylinder, the interaction between the flow and the cylinder leads to a non-zero period-averaged flow field. This phenomenon is referred to as steady streaming ([1] and [2]), which has been of great interest in the area of acoustics and hydrodynamics. Most of the work on steady streaming since the early stage of the investigation has been summarized in the review paper of Riley [3]. Most of the previous research work was carried out under the condition of small amplitude oscillation (KC << 1), where the flow remains two-dimensional and analytic solution of steady streaming is achievable ([4] and [5]). In addition steady streaming can also be observed directly in experiments ([4], [6] and [7]). Steady streaming has been demonstrated to exist at high KC numbers, where separated flow and vortex shedding happens ([8] and [9]). An et al. [10] carried out two-dimensional numerical simulations and captured six steady streaming patterns corresponding to the six vortex shedding regimes observed by Williamson [11]. It has been known that oscillatory flow around a circular cylinder remains two-dimensional only when KC and  are lower than certain values, beyond which Honji instability [12] occurs. Honji instability is a three-dimensional instability, which is characterised by mushroom shaped vortex structures. The flow structure of Honji Instability has been known well based on the previous work [12 – 17]. The motivation of the present study is to identify the structure of steady streaming around the cylinder when the Honji instability is present. This question will be addressed by conducting a series of direct numerical simulations. Governing Equations and Numerical method In this study, a sinusoidal oscillatory flow around a fixed circular cylinder is simulated numerically. The governing equations are the non-dimensional Navier-Stokes equations and the continuity equation. The governing equations in Cartesian coordinate system xyz (shown in Figure 1) read: 0 Re 1 1 2 2            " @default.
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• W2243043670 date "2010-01-01" @default.
• W2243043670 modified "2023-09-23" @default.
• W2243043670 title "Direct numerical simulation of 3D steady streaming induced by Honji Instability" @default.
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