Numerical modelling of spillway flow with free drop and initially unknown discharge

Abstract

The difficulties in solving the spillway flow arise not only from the determination of the critical point, which has been used to divide the subcritical and supercritical flows, but also from the fact that either the boundary or the discharge is not known a priori. It is much more difficult to deal with such flow pattern with free drop. In this paper, by using the analytic functional boundary-value theory and the substitution of variables, the nonsingular boundary integral equations in the physical plane are derived. A synchronous iterative method for the discharge and the flow pattern is presented according to the consistency between the discharge and the uniform velocity at far upstream. Flows over different spillway profiles are treated. The discharge, the profiles of the free drop and the pressure distributions on the walls are calculated. The numerical results are in good agreement with the measured ones.