Fluid Structure Interactions
Research Group
Numerical Investigation into Potential Flow Around
High-speed Hydrofoil Assisted Craft
ZHONGYU YANG –zy1c08@soton.ac.uk , supervised by Prof G.E HEARN and Dr Z CHEN
Background
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.
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)
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.
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
Numerical simulation of wave deformation of a half 3-D Wigley hull considering the Non-linear free surface

Mathematical Statement
Governing Equation:
•Laplace’s Equation
where Φ is the total velocity potential.
Comparison of pressure coefficients of a 2-D
NACA4412 hydrofoil with different depths
Comparison of wave patterns of a 2-D NACA4412
hydrofoil
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
Numerical simulation of wave deformation of a 3-D NACA4412 hydrofoil considering the Linear free surface
Perturbed Velocity Potential:
Future work
Numerical calculation of wave contour of a 3-D NACA4412 hydrofoil considering the Linear free surface
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.
FSI Away Day 2012