Nonlinear corrections to the linear theory for the prediction of the cavitating flow around hydrofoils
Abstract
The problem of a partial or supercavitating hydrofoil in linear theory is formulated in terms of integral equations of unknown vortex and cavity source distributions. The general problem is decomposed into one camber, one of thickness, and one of angle of attack. The general solution is given in terms of integrals of known functions over the cavity length for partial or over the chord length for supercavitating hydrofoils. The numerical scheme to compute the integrals is shown to be very accurate and insensitive to the variables of the problem. Cavity shapes obtained from linear and nonlinear theory are compared for certain special cases. Linear theory is shown to be accurate for supercavitating sharpnosed hydrofoils at moderate angles of attack. The effect of the leading edge radius on the partial cavitation of a hydrofoil is introduced by incorporating Lighthill's correction in the linearized formulation of the problem. Results for certain special cases show the significant role of the leading edge radius on the cavitation of hydrofoils, something also confirmed from experiments conducted at the MIT water tunnel.
 Publication:

Massachusetts Inst. of Tech. Report
 Pub Date:
 June 1985
 Bibcode:
 1985mit..reptQ....K
 Keywords:

 Angle Of Attack;
 Cavitation Flow;
 Flow Distribution;
 Hydrofoils;
 Linear Prediction;
 Accuracy;
 Camber;
 Correction;
 Decomposition;
 Flow Theory;
 Formulations;
 Hydraulic Test Tunnels;
 Hydrodynamics;
 Hydrofoils;
 Integral Equations;
 Mathematical Models;
 Nonlinear Systems;
 Numerical Analysis;
 Radii;
 Shapes;
 Sharp Leading Edges;
 Solutions;
 Thickness;
 Vortices;
 Fluid Mechanics and Heat Transfer