Simulation of normal vortex–cylinder interaction in a viscous fluid

Abstract

A computational study of three-dimensional vortex–cylinder interaction is reported for the case where the nominal orientation of the cylinder axis is normal to the vortex axis. The computations are performed using a new tetrahedral vorticity element method for incompressible viscous fluids, in which vorticity is interpolated using a tetrahedral mesh that is refit to the Lagrangian computational points at each timestep. Fast computation of the Biot-Savart integral for velocity is performed using a box-point multipole acceleration method for distant tetrahedra and Gaussian quadratures for nearby tetrahedra. A moving least-square method is used for differentiation, and a flux-based vorticity boundary condition algorithm is employed for satisfaction of the no-slip condition. The velocity induced by the primary vortex is obtained using a filament model and the Navier–Stokes computations focus on development of boundary-layer separation from the cylinder and the form and dynamics of the ejected secondary vorticity structure. As the secondary vorticity is drawn outward by the vortex-induced flow and wraps around the vortex, it has a substantial effect both on the essentially inviscid flow field external to the boundary layer and on the cylinder surface pressure field. Cases are examined with background free-stream velocity oriented in the positive and negative directions along the cylinder axis, with free-stream velocity normal to the cylinder axis, and with no free-stream velocity. Computations with no free-stream velocity and those with free-stream velocity tangent to the cylinder axis exhibit similar secondary vorticity structures, consisting of a vortex loop (or hairpin) that wraps around the primary vortex and is attached to the cylinder boundary layer at two points. Computations with free-stream velocity oriented normal to the cylinder axis exhibit secondary vorticity structure of a markedly different character, in which the secondary eddy remains close to the cylinder boundary and has a quasi-two-dimensional form for an extended time period.

Two-Step Method for Static Topological Reanalysis

“…This assumption is supported by the computational results of Ref. 9, which cover the time period during which the ejected vorticity wraps approximately one time around the primary vortex. The result [Eq.…”

“…In the Ref. 9 computations the ejection velocity of the vortex sheet from the cylinder face is observed to maintain a nearly constant value V E » D 0:44 0=D, which is comparable to, but slightly larger than, the velocity 0:380=D induced by the columnar vortex (in isolation) evaluated at the ejection point. Estimating°0 using the correlation for the inviscid slip velocity W at the separation point gives°0 » D max.¡W / D 0:22 0=S.…”

Underlying mechanisms of propeller wake interaction with a wing

“…The approaching phase is characterised by a complex deformation mechanism of the tip vortex, which undergoes a considerable progressive bending while it is advected towards the stagnation point, similarly to what was observed in the interaction of a line vortex with a circular cylinder (see, e.g., Marshall & Yalamanchili 1994;Gossler & Marshall 2001) or with a wing with equivalent thickness and impact parameters (see, e.g., Johnston & Sullivan 1993;Marshall & Yalamanchili 1994).…”

Numerical Study of the Instability and Flow Transition in a Vortex-Ring/Wall Interaction

“…Moreover, it is observed from Figs. 2(d) and 2(e) that a series of loop-like vortices (Krishnamoorthy and Marshall 1998;Krishnamoorthy et al 1999;Gossler and Marshall 2001) and hair-pin vortices (Hon and Walker 1991;Adrian 2007;Liu and Chen 2011) wrapping around the vortex rings are formed. With the evolution of vortical structures, it is seen that the strength and number of the wrapping vortices are increased con-siderably as shown in Figs.…”