A numerical wave tank model for cavitating hydrofoils (original) (raw)
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Numerical Analysis of 2-D and 3-D Cavitating Hydrofoils Under a Free Surface
Journal of Ship Research
A method which models two- or three-dimensional cavitating hydrofoils moving with constant speed under a free surface is described. An integral equation is obtained by applying Green's theorem on all surfaces of the fluid domain. This integral equation is divided into two parts: (i) the cavitating hydrofoil problem, and (ii) the free-surface problem. These two problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The cavitating hydrofoil surface and the free surface are modeled with constant strength dipole and source panels. The source strengths on the free surface are expressed in terms of the second derivative of the potential with respect to the horizontal axis by applying the linearized free-surface conditions. 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. In order to prevent upstream waves the source strengths fro...
Second-Order Free Surface Effect on Cavitating 3-D Hydrofoils
The iterative method which is originally developed before for the three-dimensional cavitating hydrofoils moving with constant speed under a free surface is extended to include the second-order free surface effect into the calculations. The iterative nonlinear method is based on the Green's theorem and allows separating the cavitating hydrofoil problem and the free surface problem. These two problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The cavitating hydrofoil surface and the free surface are modeled with constant strength dipole and constant strength source panels. The second-order free surface effect is included into the calculations by the technique of small perturbation expansion both for the potential and for the wave elevation on the free surface. The source strengths on the free surface are expressed in terms of perturbation potential by applying first-order (linearized) and second-order free surface cond...
Numerical simulation of flow around two- and three-dimensional partially cavitating hydrofoils
2014
A new method is developed for the prediction of cavity on two-dimensional (2D) and three-dimensional (3D) hydrofoils by a potential-based Boundary Element Method (BEM). In the case of specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained by the dynamic boundary condition on the cavity surface and the kinematic boundary condition on the whole foil surface including the cavity. For a given cavitation number the cavity length of 2D hydrofoil is determined according to the minimum error criterion among different cavity lengths. In the 3D case, the prediction of cavity is exactly the same as in the case of 2D method in span wise locations by the transformation of the pressure distribution from analysis of 3D to 2D. The 3D effects at each span-wise location are considered by the multiplication of the cavitation number by a coefficient. The pressure recovery and termination wall models are used as cavity termination. For the 2D case the NACA 16006 and NACA 16012 hydrofoil sections are investigated for two angles of attack using different cavity termination models. For 3D analysis an application for a rectangular hydrofoil with NACA16006 section is carried out. The results are compared with those of other potential based boundary element codes and a commercial CFD code (FLUENT). The effects of different Reynolds numbers (R n ) on the cavitation behavior are also investigated. The results developed from present method are in a good agreement with those obtained from the others.
A BEM for the prediction of free surface effects on cavitating hydrofoils
Computational Mechanics, 2002
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.
In the present paper, the boundary element method (BEM) is used with a new numerical algorithm to predict the cavitation characteristics over two-dimensional symmetric hydrofoils. Two main difficulties encountered when predicting the cavitation over the hydrofoil, namely: (1) The free surface location is not known in advance and should be determined, (2) The potential at the leading point is not known. The present algorithm overcomes these difficulties through some mathematical manipulation by tracing the free surface. In addition to the above-mentioned difficulties, four main working parameters and their effect on the cavitation characteristics are also investigated. The present algorithm was first tested on some existing results and an execllent agreement was obtained, then more computations and results were performed.
In the present paper, the boundary element method (BEM) is used with a new numerical algorithm to predict the cavitation characteristics over two-dimensional symmetric hydrofoils. Two main difficulties encountered when predicting the cavitation over the hydrofoil, namely: (1) The free surface location is not known in advance and should be determined, (2) The potential at the leading point is not known. The present algorithm overcomes these difficulties through some mathematical manipulation by tracing the free surface. In addition to the above-mentioned difficulties, four main working parameters and their effect on the cavitation characteristics are also investigated. The present algorithm was first tested on some existing results and an execllent agreement was obtained, then more computations and results were performed
Journal of Fluid Mechanics, 1993
The partially cavitating two-dimensional hydrofoil problem is treated using nonlinear theory by employing a low-order potential-based boundary-element method. The cavity shape is determined in the framework of two independent boundary-value problems; in the first, the cavity length is specified and the cavitation number is unknown, and in the second the cavitation number is known and the cavity length is to be determined. In each case, the position of the cavity surface is determined in an iterative manner until both a prescribed pressure condition and a zero normal velocity condition are satisfied on the cavity. An initial approximation to the nonlinear cavity shape, which is determined by satisfying the boundary conditions on the hydrofoil surface rather than on the exact cavity surface, is found to differ only slightly from the converged nonlinear result. The boundary element method is then extended to treat the partially cavitating three-dimensional hydrofoil problem. The three-dimensional kinematic and dynamic boundary conditions are applied on the hydrofoil surface underneath the cavity. The cavity planform at a given cavitation number is determined via an iterative process until the thickness at the end of the cavity at all spanwise locations becomes equal to a prescribed value (in our case, zero). Cavity shapes predicted by the present method for some three-dimensional hydrofoil geometries are shown to satisfy the dynamic boundary condition to within acceptable accuracy. The method is also shown to predict the expected effect of foil thickness on the cavity size. Finally, cavity planforms predicted from the present method are shown to be in good agreement to those measured in a cavitating three-dimensional hydrofoil experiment, performed in MIT's cavitation tunnel.
Numerical Study of Unsteady Behavior of Partial Cavitation on Two Dimensional Hydrofoils
2012
Abstract: This paper deals with time dependent performance characteristics of cavitating hydrofoils, the flow around which has been simulated using pressure-based finite volume method. A bubble dynamics cavitation model was used to investigate the unsteady behavior of cavitating flow and describe the generation and evaporation of vapor phase. For choosing the turbulence model and mesh size a non cavitating study was conducted.