Numerical Investigation into Potential Flow Around High-speed Hydrofoil Assisted Craft ZHONGYU YANG supervised by Prof G.E HEARN and Dr Z Fluid Structure Interactions Research Group FSI Away Day 2012 Currently, hydrofoils are an important element for some high-speed crafts. The role of a hydrofoil is to lift a part or the whole hull above the free surface at a sufficiently accelerated speed so that the waves normally generated by a displaced hull no longer exist. Consequently, with the same engine power, crafts equipped with hydrofoils travel much faster than conventional displacement hulls. Hydrofoils may be surface piercing or fully submerged. The surface piecing system provides good roll, heave and pitch stability because the lifting foil area automatically changes as the craft attitude varies, which makes it self-stabilizing with no control required. The fully submerged foil system offers better sea keeping performance since it suffers much less free surface losses and this makes it more steady in rough seas. The fully submerged hydrofoil is adopted in this investigation to improve potential flow based calculations and numerical simulations around hydrofoil assisted crafts during the transitional take-off stages whilst considering free surface effects. Instead of applying a time dependent simulation, a specific number of quasi-steady state flows are investigated. Background Proposed Numerical Method  Panel (boundary element) Method Panel, or boundary element method is adopted as the numerical simulation method in this investigation. It was developed during the late 1950's and early 1960's by Hess and Smith as a simple numerical tool for calculating potential flows about arbitrarily shaped bodies. The technique consists of discretising the boundary of the structure and associated wakes into a number of elements. From each element a simple flow field is considered to originate from an assigned fluid singularity. The strengths of the fluid singularities are determined by requiring continuity of velocity on the panels. By constraining the assumed complexity of variation of fluid singularity strengths over the panels, the fluid structure in each analysis may be reduced to a set of simultaneous equations solved for these unknown strengths. The panel method exploits the fact that potential fluid flows are governed by Laplace's equation. This feature and the linearity of the associated boundary value problem permits an equivalent integral equation formulation that does not require determination of flow within the interior of the fluid domain. Comparison with the finite element method and the finite difference method readily demonstrates the advantages of the panel method through discretisation of boundaries only. In practice this means that associated volume integrals associated with the Green integral identities used may be removed without introducing approximation. When considering the free surface effect (kinematic and dynamic free surface boundary conditions), the simple Rankine source method is applied instead of an all encompassing Green function which is computationally very complicated. However, the consequence of using the simple Rankine source method is that singularities have to be distributed on the all the boundaries including the free surface. This increases the number of unknowns and the approach is restricted to panel sizes that are small enough compared with the wavelength to ensure no useful information is lost. In addition, special attention has to be paid to guarantee that there are no waves in front of the body, which means no upstream waves. A one-sided, upstream, finite difference operator was applied to ensure that waves do not propagate ahead of the body. Results Future work Numerical investigation considering the non-linear free surface effect remains a challenge when hydrofoil assisted craft go through the take-off stage. It is necessary to implement a numerical simulation of the hydrofoil assisted craft as it picks up the speed to reach full speed with considering the interactions between multiple foils and the displacement hull under the non-linear free surface formulation.  Mathematical Statement Governing Equation: Laplace’s Equation where Φ is the total velocity potential. Boundary Conditions: Steady state body boundary condition where n is a unit outward normal vector on the surface. Kutta condition that requires the velocity on the wake to be finite and in the selected implementation the doublet strength on the wake equals the difference of doublet strengths on the first and the last hydrofoil panels. Non-linear free surface boundary condition Perturbed Velocity Potential: Surface piercing hydrofoil Bras-D’s Or in Canada (60 knots) Fully submerged hydrofoil craft PC(H) High Point produced by U. S. Navy (45 knots) Numerical simulation of wave deformation of a half 3-D Wigley hull considering the Non-linear free surface Comparison of pressure coefficients of a 2-D NACA4412 hydrofoil with different depths Comparison of wave patterns of a 2-D NACA4412 hydrofoil Numerical simulation of wave deformation of a 3-D NACA4412 hydrofoil considering the Linear free surface Numerical calculation of wave contour of a 3-D NACA4412 hydrofoil considering the Linear free surface