Point vortex model of the unsteady separated flow past a semi-infinite plate with transverse motion

Abstract

Two-dimensional unsteady separated flow past a semi-infinite plate with transverse motion is considered. The rolling-up of the separated shear-layer is modelled by a point vortex whose time-dependent circulation is predicted by an unsteady Kutta condition. A power-law starting flow is assumed along with a power law for the transverse motion. The effects of the motion of the plate on the starting vortex circulation and trajectory are presented. A suitable vortex shedding mechanism is introduced and a class of flows involving several vortices is presented. Finally, some possibilities for actively controlling the production of circulation by moving the plate are discussed

An unsteady point vortex method for coupled fluid–solid problems

“…In the following, we simply refer to these vortices as unsteady point vortices. This method was previously used to study the vortex shedding past a finite or semi-infinite plate with prescribed orthogonal translation [14][15][16]-the purpose of the present work is to generalize the method to arbitrary motions of a general body, including rotation, and to formulate the fully coupled problem of the fluid and solid motions.…”

“…The intensity of the vortices varies monotonically to represent the irreversible nature of the vortex roll-up. A new vortex is shed when the intensity reaches a maximum, representing a new roll-up in the vortex sheet [16,20,27]. This method has been previously applied to study the shedding of vorticity from a finite or semi-infinite plate exposed to a prescribed uniform flow with no rotation [14,16] and compared to continuous shedding methods [15].…”

“…A new vortex is shed when the intensity reaches a maximum, representing a new roll-up in the vortex sheet [16,20,27]. This method has been previously applied to study the shedding of vorticity from a finite or semi-infinite plate exposed to a prescribed uniform flow with no rotation [14,16] and compared to continuous shedding methods [15]. The originality of the present work is to generalize the method to arbitrary body shapes and motions and to couple the vortex model to the solid dynamics.…”

“…In Sect. 4, the small-time analysis of the equations is performed generalizing the work of [16]. In Sect.…”

Falling cards and flapping flags: understanding fluid–solid interactions using an unsteady point vortex model

“…At each time step, the intensity of this vortex is adjusted to cancel exactly the velocity singularity at the corresponding corner, rather than creating a new element of vorticity at each time step as in a continuous vortex sheet approach [1,13,14]. To include the irreversible nature of the vortex sheet roll-up in this model, when a vortex reaches a maximum intensity, its intensity becomes frozen and a new vortex is started from the generating corner [9].…”