A NUMERICAL OPTIMIZATION TECHNIQUE APPLIED TO THE DESIGN OF TWO- DIMENSIONAL CAVITATING HYDROFOIL SECTIONS

A numerical nonlinear optimization technique is applied to the systematic design of two-dimensional partially or supercavitating hydrofoil sections. The design objective is to minimize the hydrofoil drag for given lift and cavitation number. The hydrodynamic analysis of the cavitating hydrofoil is performed in nonlinear theory, via a low- order potential-based panel method. The effects of viscosity are taken into account via a uniform friction coefficient applied on the wetted foil surface. The total drag, lift, cavitation number, and other quantities involved in the imposed constraints, are expressed in terms of quadratic functions of the main parameters of the hydrofoil geometry, angle of attack, and the cavity length. The optimization is based on the method of multipliers by coupling the Lagrange multiplier terms and the penalty function terms. The robustness and convergence of the method are extensively investigated, and the results are compared with those from applying other design methods.