Unsteady threedimensional lifting surface theory with the freesurface effect
Abstract
The unsteady threedimensional linearized lifting surface problem with the free surface effect is solved in a supercritical case using the integral equation method. The kernel originating in the potential of Havelock source is expressed as a Fourier series with respect to the azimuth angle, the coefficients of which are simple integrals. The method of steepest descents provides asymptotic approximations for coefficients of large indices. It is shown that convergence disappears on the free surface downstream from the integration point. An asymptotic approximation for the remainder of the truncated series is used to find the singularity. The integral equation yielding the local lift coefficient is solved by a collocation method. Curves showing the numerical results for horizontal and vertical vibrating plates moving horizontally enable the ranges of the parameters over which the freesurface effects on the hydrodynamic derivatives are significant to be determined.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 October 1985
 Bibcode:
 1985STIN...8622911L
 Keywords:

 Bodies;
 Hydrodynamic Equations;
 Hydrodynamics;
 Hydrofoils;
 Lift Devices;
 Lifting Bodies;
 Singular Integral Equations;
 Three Dimensional Flow;
 Fourier Series;
 Free Vibration;
 Series Expansion;
 Unsteady State;
 Fluid Mechanics and Heat Transfer