The Application of Boundary Elements to Steady and Unsteady Potential Fluid Flow Problems in Two and Three Dimensions

Abstract

The Boundary Element Method is applied to both steady and unsteady potential flow of a compressible liquid inside a fixed volume. For steady flow the velocity potential satisfies the Laplace or Poisson equation. This potential can be found by solving the linear equations resulting from a discretisation of the boundary integral equation.

The velocity potential for unsteady fluid flow can be found by solving the three-dimensional wave equation. The potential at a certain point and moment can be expressed in an integral over the boundary of the values of the potential at the retarded time plus a (inhomogeneous) source term.

The computer code BEREPOT (Boundary Element Retarded Potential Technique) has been developed to calculate the potential successively. This code can handle boundaries consisting of a rigid structure and non-reflecting openings representing infinitely long pipes.

This method has been applied to the flow of liquid sodium in cooling components of Liquid-Metal Fast Breeder Reactors. Special attention will be paid to the pressure wave propagation resulting from a sodium-water reaction following a tube rupture in a LMFBR steam generator. The boundary is given by (parts of) the s.g. walls and the connections with the piping system. The validity of the potential flow model and of the solution method, the boundary conditions and other applications will be discussed. Some results will be compared with the results from analytical solutions and from other numerical methods.