Three-dimensional Potential Flow Problems Research Articles

Regularized boundary integral methods for three-dimensional potential flows

The three-dimensional potential flow problems are solved by a boundary integral equation in this article. The boundary integral equation is regularized by a subtracting and adding-back technique in global elements. This technique utilizes several identities to eliminate the singularities or near singularities of surface integrals. In test cases, the convergence speed of this method for a smooth body is of the order N−3 in one direction no matter how high-order quadrature is applied. For nearly singular integrals, several extremely oblate spheroids are tested to verify this method. These results illustrate that this method can effectively improve the nearly singular deficit when it exists. For the non-smooth bodies, the present method is applied to solve the mixed boundary value problems inside two kinds of vessels, which are sloshing motions. At last, some tests are compared between the boundary element methods (local elements) and the present method (global elements).

Method of Fundamental Solutions for Three-Dimensional Exterior Potential Flows

AbstractThe method of fundamental solutions for solving three-dimensional potential flow problems with an unbounded domain is developed in this paper. Because the present meshless method is free from treatments of singularities, meshes, and numerical integrations, the computational effort and memory storage required are minimal as compared with other numerical schemes. It is a suitable technique for the potential flow problems in an unbounded domain, because it only requires that the field points be located on the body surface to satisfy the impermeable boundary condition without defining an optimal finite-domain computation. For the flow passing an obstacle, the impermeable boundary condition on the body surface can be dealt with by the linear superposition scheme. With the validations for the uniform flow passing a two-dimensional wing section and some three-dimensional benchmark problems, an application of case study for the flow field in the multiconnected unbounded domain is carried out. From the com...

A Three-Dimensional Desingularized High Order Panel Method Based on Nurbs

A desingularized high order panel method based on Non-Uniform Rational B-Spline (NURBS) was developed to deal with three-dimensional potential flow problems. A NURBS surface was used to precisely represent the body geometry. Velocity potential on the body surface was described by the B-spline after the source density distribution on the body surface had been solved. The collocation approach was employed to satisfy the Neumann boundary condition and Gaussian quadrature points were chosen as both the collocation points and the source points. The singularity was removed by a combined method, so the process of the numerical computation was non-singular. In order to verify the method proposed, the unbounded flow problems of sphere and ellipsoid, the wave-making problem of a submerged ellipsoid were chosen as computational examples. It is shown that the numerical results are in good agreement with analytical solutions and other numerical results in all cases, and sufficient accuracy of numerical solution can be reached with a small number of panels.

A NURBS Panel Method for Three-Dimensional Radiation and Diffraction Problems

A B-spline panel method is developed to solve a boundary integral equation for three-dimensional potential flow problems. In particular, a nonuniform rational B-spline (NURBS) surface is introduced to accommodate a precise geometric description of a given body. For the unknown (potential) description over the surface, uniform B-spline basis functions are used. A collocation approach is adopted for numerical computations, and influence coefficients are evaluated in a robust manner over the surface defined by NURBS. Convergence characteristics of the present method have been investigated in the numerical experiments on the unbounded problem of a sphere, the radiation problem of a floating hemisphere, and the diffraction problem of a submerged spheroid. It is shown that the numerical results are in excellent agreement with analytical solutions in all cases considered. It is concluded that the NURBS panel method is superior to existing panel methods in geometric description of body surface, and convergent solutions can be achieved rapidly with a small number of panels.

Numerical calculation of singular integrals appearing in three-dimensional potential flow problems

Two approximate methods for calculating singular integrals appearing in the numerical solution of three-dimensional potential flow problems are presented. The first method is a self-adaptive, fully numerical method based on special copy formulas of Gaussian quadrature rules. The singularity is treated by refining the partitions of the copy formula in the vicinity of the singular point. The second method is a semianalytic method based on asymptotic considerations. Under the small curvature hypothesis, asymptotic expansions are derived for the integrals that are involved in the calculation of the scalar potential, the velocity as well as the deformation field induced from curved quadrilateral surface elements. Compared to other methods, the proposed integration schemes, when applied to practical flow field calculations, require less computational effort.

Transient, three-dimensional potential flow problems and dynamic response of the surrounding structures. Part I: Description of the fluid dynamics by a singularity method (computer code SING)

In Part I a singularity method—also called boundary integral equation method or panel method—has been developed. It is applicable especially to highly transient internal flow problems with any three-dimensional geometry including walls wetted on both sides. The boundary conditions are prescribed in terms of pressures and/or accelerations. The method is primarily based on a recently developed dipole element treatment for incompressible fluids. Such elements (panels) can be fitted to the fluid boundary or any enveloping surface. Also, point sources may be included. The applicability of the method is demonstrated by two different examples: the incipient flow in a T-joint and the oscillating flow in the pressure suppression system of a boiling water reactor. In Part II the coupling of the transient flow problem with the dynamic behavior of the surrounding structure will be investigated.

Transient, three-dimensional potential flow problems and dynamic response of the surrounding structures. Part II: Simultaneous coupling between fluid and structural dynamics (computer code SING-S)

In Part I a singularity method was described which is applicable especially to highly transient internal flow problems with any three-dimensional geometry including walls wetted on both sides. In Part II, this model is integrated into the equation of motion of the structure which may be obtained from finite-element methods, for instance. In this way, the coupling between fluid and structural dynamics due to common interfaces between fluid regions and structural members is taken into account. Equations of motion are obtained which simultaneously satisfy the conditions of fluid and structural dynamics. Since these equations are of the same type and have the same dimensions as those describing the structural dynamics, the solution of the coupled problem can be obtained by well-known techniques, such as the method of modal superposition which will be applied here. Results are presented for two examples. The second, more practical one deals with vibrations in the pressure suppression system of a boiling water reactor.