Design and optimization method for a two-dimensional hydrofoil

In this paper, methods for the design and the optimization of two-dimensional hydrofoils are presented. First a previously developed potential flow design method is extended to the viscous flow computations. In this design method, the foil geometry is defined by B-splines, and the RANS method is utilized for the viscous flow computations. The foil is designed based on a prescribed pressure distribution, and the Newton-Raphson method is used to achieve a foil geometry generating the prescribed pressure distribution. In the design method described above, although designers can specify a pressure distribution based on the desired local characteristics, it is hard to know the forces on the desired foil in advance. Therefore, an “optimization method” by using the Lagrange multiplier method is then developed. The optimization problem described in the proposed paper is to satisfy the lift requirement by minimizing the drag force. The design variables are the angle of attack and the “geometry parameters”. In the presented design examples, the camber distribution and the pressure distribution “shape function” are selected as the geometry parameter. Both the “design” and the “optimi- zation” methods can be used as a design tool individually; however, the combination of two methods provides a useful design tool that can not only optimize the global performance, but also design the detailed geometry according to designers' requirements. Design examples are illustrated in the paper, and this design method is proved to be practical and effective.