A BEM for the prediction of free surface effects on cavitating hydrofoils

Abstract

In this paper, a boundary element method (BEM) for cavitating hydrofoils moving steadily under a free surface is presented and its performance is assessed through systematic convergence studies, comparisons with other methods, and existing measurements. The cavitating hydrofoil part and the free surface part of the problem are solved separately, with the effects of one on the other being accounted for in an iterative manner. Both the cavitating hydrofoil surface and the free surface are modeled by a low-order potential based panel method using constant strength dipole and source panels. The induced potential by the cavitating hydrofoil on the free surface and by the free surface on the hydrofoil are determined in an iterative sense and considered on the right hand side of the discretized integral equations. The source strengths on the free surface are expressed by applying the linearized free surface conditions. In order to prevent upstream waves the source strengths from some distance in front of the hydrofoil to the end of the truncated upstream boundary are enforced to be equal to zero. No radiation condition is enforced at the downstream boundary or at the transverse boundary for the three-dimensional case. First, the BEM is validated in the case of a point vortex and some convergence studies are done. Second, the BEM is applied to 2-D hydrofoil geometry both in fully wetted and in cavitating flow conditions and the predictions are compared to those of other methods and of the measurements in the literature. The effects of Froude number, the cavitation number and the submergence depth of the hydrofoil from free surface are discussed. Then, the BEM is validated in the case of a 3-D point source. The effects of grid and of the truncated domain size on the results are investigated. Lastly, the BEM is applied to a 3-D rectangular cavitating hydrofoil and the effect of number of iterations and the effect of Froude number on the results are discussed.

Prediction of wave pattern and wave resistance of surface piercing bodies by a boundary element method

“…The number of panels used on the hydrofoil surface is NXH * NYH = 40 * 20 (NXH is the number of panels on the hydrofoil surface in the chordwise direction, NYH number of panels in the spanwise direction), the number of panels used on the free surface NXFS * (NYFSI+NYFSII) = 100 * (10+10). In Figures 6 and 7, the perspective views of half of cavity shapes by calculated present IBEM are shown as compared with those of method given in [30]. Note that the results of the present IBEM and the method given in [30] are converged to the same values.…”

“…In Figures 6 and 7, the perspective views of half of cavity shapes by calculated present IBEM are shown as compared with those of method given in [30]. Note that the results of the present IBEM and the method given in [30] are converged to the same values. This can be seen much clearly in Figure 8 that the cavity planforms are shown.…”

A numerical wave tank model for cavitating hydrofoils

“…The cavitating hydrofoil influence on the free surface and the free surface influence on the cavitating hydrofoil were considered via potential. Some convergence tests carried out and extensive results, including the comparisons with the experiments of this IBEM were given (Bal and Kinnas, 2002a).In the present study, the effects of walls (side and bottom) of the NWT on both 2-D and 3-D cavitating hydrofoils and the effect of second-order free surface condition are included in the calculations. More results of this method can be found (Bal and Kinnas, 2002b).…”

Cloud Cavitating Flow That Surrounds a Vertical Hydrofoil Near the Free Surface

“…Faltingsen proposed a numerical method for calculating free surface and steady super cavity based on the potential flow theory and analyzed the important parameters that influence the cavity shape development [24,25]. Bals and Kinnas used the boundary element method to investigate the cavitation problems of submerged and surface piercing hydrofoils as well as to validate his experimental results [26][27][28]. Wang et al conducted an experiment and simulation to examine the characteristics of unsteady cloud cavitation evolution on the surface of a projectile, and then analyzed the interaction between the free surface and cavitation [29].…”