A numerical nonlinear analysis of two-dimensional ventilating entry of surface-piercing hydrofoils with effects of gravity

Abstract

The presence of the free surface adds an element of difficulty to the development of numerical and theoretical methods for the performance prediction of surfacepiercing hydrofoils. Existing methods of analysis for two-dimensional surface-piercing hydrofoils or blade sections of a surface-piercing propeller solve either a linear problem, assuming a thin section and ventilated surface along with linear free-surface boundary conditions, or a nonlinear problem in a self-similar setting. Both these approaches cannot be used when the effects of gravity are important, which is the case when a craft is operating at low speeds. A two-dimensional boundary-elementmethod-based numerical scheme is presented here that overcomes these drawbacks by solving the fully ventilated flow past a surface-piercing hydrofoil of finite dimensions and includes the whole gamut of nonlinear free-surface interactions. The unique aspect of the numerical scheme is that fully nonlinear boundary conditions are applied on the free surface which allows for the accurate modelling of the jet generated on the wetted boundary and the ventilated surface formed on the suction side as a result of the passage of the hydrofoil through the free surface. Moreover, the effects of gravity can be considered to take into account the influence of the Froude number. Ventilated-surface shapes predicted by the present scheme are compared with existing experimental results and are shown to be in good agreement.

Hydroelastic analysis of surface piercing hydrofoil during initial water entry phase

“…8 -middle) and the computed pressure coefficient Cp shown in Fig.8 (right), matches well with the results of BEM simulation by Vinayan [14].…”

“…Yim [13] was the first to present 2D analytical method for simulation of fully ventilated water entry and exit of a thin infinite symmetric wedge based on Wagner theory [11]. Vinayan [14] prepared a 2D BEM code to consider the nonlinear nature of the free surface pattern. He investigated the symmetric oblique wedge studied by Cox [15] and provided the pressure curves and free surface patterns.…”

“…The effects of mesh size on the solution are investigated by considering four different meshing options of 0.4 (Vinayan [14]), 0.5, 0.6, and 0.7 million cells. It is shown that increasing the cell numbers beyond 0.5 million has less than 1% effect on the resultant forces.…”

Spurious solutions in a Fredholm integral equation of the second kind with a Cauchy kernel

“…63-64], [11,12]. We are also going to mention briefly the piecewise-linear singularity-sheet distribution as appears in more detail in [13,17,14,23,24], [1, Section 10].…”

“…In a fashion similar to [1, Section 10], [14,23,24], the contour of integration is divided into small segments where linear interpolation has been employed for both the singularity-sheet as well as the body interface geometry at each element. Upon integration, the first-order scheme can be written as:…”