A numerical estimation of the error on the induced velocity due to a discrete approximation of a twodimensional vortex sheet
Abstract
A two dimensional infinite vortex sheet of the Prandtl type is considered, having along its finite width the same vorticity distribution as from the trailing edge of a symmetrically loaded wing. Four types of discretization are analyzed reproducing the vortex sheet by making use of singularities. The first and second models represent the sheet by discrete vortices, while a piecewise continuous vorticity distribution is posed by the other two models. The error analysis is based on the evaluation of the velocity induced by the discretized vorticity distribution at a certain number of points along a segment of vorticity identified with a normal section of the sheet itself. The velocities induced by each model of discretization are then compared with the corresponding exact values given by an analytical formula. The error is computed as a function of the number of singularities, discrete or continuous, used by each to reproduce the actual vortex sheet.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 June 1979
 Bibcode:
 1979STIN...8026633T
 Keywords:

 Approximation;
 Discrete Functions;
 Error Analysis;
 Flow Velocity;
 Two Dimensional Flow;
 Vortex Sheets;
 Dynamic Models;
 Prandtl Number;
 Spatial Distribution;
 Trailing Edges;
 Vorticity Transport Hypothesis;
 Wing Planforms;
 Fluid Mechanics and Heat Transfer