A Computational framework to design optimally loaded supercavitating hydrofoils by differential evolution algorithm and a new viscous lifting line method

The engineering design of a three dimensional submerged hydrofoil operating at very high speeds is obtained leveraging a Differential Evolution (DE) approach. The final goal is to identify the optimal load distribution over the span of a super-cavitating hydrofoil by using a design by optimization approach driven by hydrodynamic analysis of complex, turbulent, multi-phase flows. We achieve this goal by modeling the load distribution over the hydrofoil by means of a B-spline curve, which provides a rigorous parametric description of the hydrofoil operating conditions through the points of the load distribution control polygon. The parametric model includes design variables representing the most relevant hydrofoil shape parameters. We predict hydrodynamic performance by means of a Viscous Lifting Line method specifically conceived for the application targeted in the present study. This computational model accounts for the strong non-linear hydrodynamic characteristics of super-cavitating hydrofoils. We demonstrate the validity of the proposed design by optimization framework for high speed super-cavitating hydrofoils showcasing two design applications, namely a fully submerged hydrofoil operating close to a rigid boundary and a surface-piercing hydrofoil with variable dihedral angle. A statistical analysis of DE algorithm is performed to assess its performance on such an engineering design problem.