Fluid Flows from Axisymmetric Orifices and Valves

Abstract

The present finite element analysis seeks an approximate solution for the minimization of a functional which is related to the axisymmetric irrotational flow of an ideal fluid as it passes through orifices, valves, or nozzles and emerges as a free-surface jet. The resulting set of linear equations for the nodal values of the velocity potential is symmetric and banded, which can be efficiently solved by the computer. Location of the free surface profile requires the use of an iterative scheme, which is apparently always convergent. Then velocity and pressure distributions can subsequently be evaluated quickly. Curvilinear interior solid boundaries cause no computational difficulties, although results near a convex surface tend to be less accurate than results in other regions. The method can produce good accuracy for such quantities as free surface profiles, and contraction and discharge coefficients; in most, but not all, flow regions it will also produce good results for velocity and pressure distributions. Computer execution time is generally modest.