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The separated flow of an inviscid fluid around a moving flat plate

The separated flow of an inviscid fluid around a moving flat plate
The separated flow of an inviscid fluid around a moving flat plate
In this study we consider the separated flow of an inviscid fluid around a moving flat plate. The motion of the plate, which is initially started from rest, is prescribed and unconstrained and we set ourselves the task of fully characterizing the resulting motion in the surrounding fluid. To do this we use a boundary integral representation for the complex-conjugate velocity field $\Phi(z,t)$ and require that the force and torque on the plate be determined as part of the solution. The flow solution is assumed to consist of a bound vortex sheet coincident with the plate and two free vortex sheets that emanate from each of the plate's two sharp edges. The time evolution of these vortex sheets is then considered in general. For physical reasons, the flow solution is required to satisfy the unsteady Kutta condition, which states that $\Phi(z,t)$ must be bounded everywhere, and the rigorous imposition of this condition then yields two types of additional constraint. The first governs the rate at which circulation is shed from the plate's edges and the second ensures that the free vortex sheets are shed tangentially. In fact, all the familiar flow characteristics associated with the imposition of the steady Kutta condition are rigorously shown to have exact parallels in the unsteady case. In addition, explicit expressions for the normal force and torque on the plate are derived. An asymptotic solution to the full system of evolution equations is developed for small times $t > 0$ and a simplified version of this solution is used as an initial condition for a desingularized numerical treatment of the full problem. A fast numerical algorithm is proposed and implemented and the results of several example calculations are presented. The featured examples are limited to high effective angles of attack due to the occurrence of a specific type of event that prevents further time-integration of the evolution equations using the current numerical method. The event corresponds physically to a situation in which a Lagrangian point placed at one of the plate's edges moves onto instead of away from the edge.
flat plate, separation, vortex sheets, aerodynamics, insect flight
0022-1120
405-441
Jones, Marvin A.
9a7aac34-f43b-4ea9-a6fb-f08d0515a411
Jones, Marvin A.
9a7aac34-f43b-4ea9-a6fb-f08d0515a411

Jones, Marvin A. (2003) The separated flow of an inviscid fluid around a moving flat plate. Journal of Fluid Mechanics, 496, 405-441. (doi:10.1017/S0022112003006645).

Record type: Article

Abstract

In this study we consider the separated flow of an inviscid fluid around a moving flat plate. The motion of the plate, which is initially started from rest, is prescribed and unconstrained and we set ourselves the task of fully characterizing the resulting motion in the surrounding fluid. To do this we use a boundary integral representation for the complex-conjugate velocity field $\Phi(z,t)$ and require that the force and torque on the plate be determined as part of the solution. The flow solution is assumed to consist of a bound vortex sheet coincident with the plate and two free vortex sheets that emanate from each of the plate's two sharp edges. The time evolution of these vortex sheets is then considered in general. For physical reasons, the flow solution is required to satisfy the unsteady Kutta condition, which states that $\Phi(z,t)$ must be bounded everywhere, and the rigorous imposition of this condition then yields two types of additional constraint. The first governs the rate at which circulation is shed from the plate's edges and the second ensures that the free vortex sheets are shed tangentially. In fact, all the familiar flow characteristics associated with the imposition of the steady Kutta condition are rigorously shown to have exact parallels in the unsteady case. In addition, explicit expressions for the normal force and torque on the plate are derived. An asymptotic solution to the full system of evolution equations is developed for small times $t > 0$ and a simplified version of this solution is used as an initial condition for a desingularized numerical treatment of the full problem. A fast numerical algorithm is proposed and implemented and the results of several example calculations are presented. The featured examples are limited to high effective angles of attack due to the occurrence of a specific type of event that prevents further time-integration of the evolution equations using the current numerical method. The event corresponds physically to a situation in which a Lagrangian point placed at one of the plate's edges moves onto instead of away from the edge.

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More information

Submitted date: 3 September 2002
Published date: 2003
Keywords: flat plate, separation, vortex sheets, aerodynamics, insect flight

Identifiers

Local EPrints ID: 29402
URI: http://eprints.soton.ac.uk/id/eprint/29402
ISSN: 0022-1120
PURE UUID: 0504f248-007e-4013-a709-06d11e73e5eb

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Date deposited: 11 May 2006
Last modified: 27 Apr 2022 08:45

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Author: Marvin A. Jones

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