Computation of potential flows with embedded vortex rings and applications to helicopter rotor wakes
Abstract
A finite difference scheme for solving the motion of a number of vortex rings is developed. The method is an adaptation of the 'cloudincell' technique to axisymmetric flows, and is thus a combined EulerianLagrangian technique. A straightforward adaptation of the cloudincell scheme to an axisymmetric flow field is shown to introduce a grid dependent selfinduced velocity to each vortex ring. To correct this behavior the potential is considered to consist of two parts, a local and a global field. An improved difference formula is derived, allowing the accurate calculation of the potential at points near vortex locations. The local potential is then subtracted before calculating the velocity, leaving only the influences of the remaining vortices. The correct selfinduced velocity is then explicitly added to the vortex velocity. Calculations of the motion of one and two vortex rings are performed, demonstrating the ability of the new method to eliminate the grid dependence of the selfinduced velocity. The application of the method to the calculation of helicopter rotor flows in hover is attempted.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 September 1983
 Bibcode:
 1983STIN...8417526R
 Keywords:

 Computational Fluid Dynamics;
 Helicopter Wakes;
 Potential Flow;
 Rotary Wings;
 Vortex Rings;
 Computational Grids;
 Finite Difference Theory;
 Flow Equations;
 Flow Velocity;
 Hovering;
 Problem Solving;
 Fluid Mechanics and Heat Transfer