Effects on lift caused by vortices near a flat plate
Date Issued
2010
Date
2010
Author(s)
Lu, Tsung-Yu
Abstract
This article aims to use two-dimensional potential flow theory, to construct a flow field that uniform flow past through a flat plate which has vortices above the plate, so we can simulate and qualitative analyze the variations of lift when vortices generated in the flow field of a flat plate wing. The method in this article is to first use uniform flow, vortex, doublet to establish the complex potential of a circular cylinder flow field, and then map it into a plate flow field by using Joukowski transformation, then use Kutta condition to amend the problem of infinite velocity at the sharp trailing edge, finally we can obtain the lift of the plate by using the Blasius’ integral laws. While the calculating values of lift and drawing the streamlines and the vector filed will be handed over by computer programming (Fortran and Tecplot).
When there is only one vortex above the flat plate, if we fix the horizontal position and change the vertical position, it will produce greater lift if the vortex is close to the plate enough, and it will produce negative lift after a certain distance away from the plate; if we fix the vertical position and change the horizontal position, the maximum lift will occur near the trailing edge at the plate.
The vortex will result in higher lift than no vortex when the vortex is been placed in some areas. When changing the circulation strength of the vortex, if there’s no angle of attack, only near the plate’s upper surface, or near and after the trailing edge region, will produce greater lift than there’s no vortex; if there exists an angle of attack, it will generate additional lift, then the circulation must be over a certain strength so that the Bernoulli effect may be significant, only near the plate’s upper surface, or near and after the trailing edge region will produce the larger lift, too.
Finally, the general solution of the flow field of the plate with multiple vortices will be developed by using the extension of Lagally theorem, we can use this general solution accompanied by a computer program to map out any relevant required flow.
Subjects
potential flow
vortex
flat plate
lift
Type
thesis
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