Computation Of Partial Cavitation Characteristcs Over Two-Dimensional Symmetric Hydrofoils Using A Newly Proposed Boundary Element Algorithm (original) (raw)
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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.
Boundary Element Method and Its Applications of Non-Linear Analysis of Flow around Hydrofoils
M.Sc. Thesis, 2007
Cavitation is one of the most important problems in hydrodynamic applications which causes a noticeable deterioration of the machine performance. Thus, accurate prediction of cavitation is very important in estimating the hydrodynamic performance of pumps, marine propellers and high speed hydrofoils. For this reason, substantial efforts have been taken by many researchers to develop capabilities to predict the extent of cavitation for various types of geometries. Several researchers have successfully analyzed the cavitation phenomenon and its application. They used different analytical and numerical methods to determine the shape and the size of the cavity and to know the velocities and/ or pressure along the boundaries. Due to the complexity of the cavitation problem and due to the difficulty to obtain analytical solutions many researchers prefer numerical methods. The most popular numerical technique for analyzing cavitation problems is the boundary element method (BEM). Boundary element method has gained its popularity from its simplified nature and many other reasons that will be encountered through the thesis. The boundary element method was used herein as a mathematical tool to solve the cavity flow around hydrofoils. Two major difficulties meet the researcher in this field of study. These difficulties are the determination of the cavity free surface and the potential at the leading point. In the present thesis, these difficulties are solved by a new suggested technique and it gives excellent results. Also, the new technique saves the time and effort needed by previous techniques. The algorithm is applied to solve the different symmetric hydrofoil NACA sections with studying the effect of three different parameters. Excellent agreement was obtained with the available existing results.
Some Remarks on the Three Dimensionality of Hydrofoil Cavitation
2017
As it is well-known that cavitation is a very important physical phenomenon that affects significantly the performance of three-dimensional hydrofoils. Prediction of cavitation on three-dimensional hydrofoils is very important in the design stage. In this study, some approaches have been verified for hydrofoil cavitation. The main aim of this paper is to compare the mid-section pressure distribution of three-dimensional cavitating rectangular hydrofoil for increasing aspect ratios, with the pressure distribution of two-dimensional cavitating hydrofoil having the same section geometry as in the three-dimensional hydrofoil. In this study, a boundary element (panel) method (BEM) has been applied to investigate the hydrofoil cavitation for both two- and three-dimensional cases. Two-dimensional analytical solution in case of cavitating flat-plate has also been applied for comparison. It has been shown that the pressure distributions on the mid-section of three-dimensional cavitating and ...
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.
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.
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.
A numerical wave tank model for cavitating hydrofoils
Computational Mechanics, 2003
In this paper, an iterative boundary element method (IBEM) for both 2-D and 3-D cavitating hydrofoils moving steadily inside a numerical wave tank (NWT) is presented and some extensive numerical results are given. The cavitating hydrofoil part, the free surface part and the wall parts of NWT are solved separately, with the effects of one on the others being accounted for in an iterative manner. The cavitating hydrofoil surface, the free surface, the bottom surface and the side walls are modelled by a low-order potential based panel method using constant strength dipole and source panels. Second-order correction on the free surface in 2-D are included into the calculations by the method of small perturbation expansion both for potential and for wave elevation. The source strengths on the free surface are expressed in terms of perturbation potential by applying first-order (linearized) and second-order free surface conditions. The IBEM is applied to a 2-D (NACA16006 and NACA0012) and a 3-D rectangular cavitating hydrofoil and the effect of number of iterations, the effect of the depth of the hydrofoil from finite bottom and the effect of the walls of NWT, on the results are discussed.
Investigation of cavitation inception characteristics of hydrofoil sections via a viscous approach
Journal of Marine Science and Technology, 2004
incipient cavitation number becomes more important for high-performance lifting surfaces, especially in highspeed conditions, where cavitation can occur and cause acoustic and vibration problems. Cavitation also damages the lifting surface devices in severe conditions. Avoiding cavitation is one of the most important issues in designing lifting surfaces at high speed, as discussed by Yamaguchi et al. 1 The cavitation inception characteristics are usually represented by the cavitation bucket diagram (Fig. 1), where a is the angle of attack (in degrees), and C p min is the minimum pressure coefficient. Region A represents the back-cavitation near the leading edge, which occurs on the suction side of the foil at high angles of attack, while region C represents the face-cavitation near the leading edge, which occurs on the pressure side of the foil at low angles of attack. Region B is the area of backbubble cavitation near the design angle of attack, and occurs on the suction side of the foil. The cavitation-free zone, region D, is bounded by the curving envelope of regions A, B, and C. Cavitation inception is a physical phenomenon which is influenced by flow characteristics such as the nuclei content in the water, boundary layer growth, etc. Traditionally, panel methods based on potential theory, e.g., Eppler and Somers 2 and Scherer and Stairs, 3 are applied to investigate the minimum pressure, pressure distribution, and lift on hydrofoil sections. However, no value for drag can be obtained because viscosity is neglected in the potential theory. Empirical formulations are often incorporated to give a reasonable drag prediction. Another widely used approach, instead of using problem-dependent, empirical correlations and to predict drag more self-containedly, is to combine a viscous boundary layer calculation and an inviscid panel method in an iterative manner, e.g., Eppler and Shen, 4,5 Drela, 6 and Yamaguchi. 7 The outer pressure distribution of the boundary layer is predicted by potential computations, while the boundary-layer calculations give the outer shape of the inviscid foil