Potential flow about two-dimensional hydrofoils

Abstract

This paper describes a very general method for determining the steady two-dimensional potential flow about one or more bodies of arbitrary shape operating at arbitrary Froude number near a free surface. The boundary condition of zero velocity (solid wall) or prescribed velocity (suction or blowing) normal to the body surface is satisfied exactly, and the boundary condition of constant pressure on the free surface is satisfied using the classic small-wave approximation. Calculations made by the present method are compared with analytic results, other theoretical calculations and experimental data. Examples for which no comparison exists are also presented to illustrate the capability of the method.

Application of a 2D harmonic polynomial cell (HPC) method to singular flows and lifting problems

“…23 with the surface of the NACA-4412 hydrofoil at = 5 ∘ and = 1.03 for two submergence depths. In addition, the present results are verified and validated by comparing them with the numerical results reported by Giesing and Smith [13] and the experimental data reported by Ausman [3]. Furthermore, Giesing and Smith [13] assume a 2D linearized potential flow and apply a BEM.…”

“…In addition, the present results are verified and validated by comparing them with the numerical results reported by Giesing and Smith [13] and the experimental data reported by Ausman [3]. Furthermore, Giesing and Smith [13] assume a 2D linearized potential flow and apply a BEM. This study is more consistent with the numerical results reported by Giesing and Smith [13] than with the experimental results.…”

“…(13) and Eq. (14) indicate that the matching condition is met by requiring continuity in the velocity potential on each node and continuity in the normal velocity on matching surfaces,…”

“…Regarding the matching conditions enforced at the matching boundaries, continuity of the velocity potentials at the seven nodes distributed on the matching boundaries is required, as expressed in Eq. (13). Then, the continuity in the normal velocity component, which is described by Eq.…”

“…Furthermore, Giesing and Smith [13] assume a 2D linearized potential flow and apply a BEM. This study is more consistent with the numerical results reported by Giesing and Smith [13] than with the experimental results. In addition, the disagreement mainly occurs with respect to the suction side of the hydrofoil.…”