NUMERICAL MODELING OF SPILLWAY FLOW WITH FREE DROP AND INITIALLY UNKNOWN DISCHARGE

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 eith er the boundary or the discharge is not known a priori. It is much mor e difficult to deal with such flow pattern with free drop. In this pap er, by using the analytic functional boundary-value theory and the sub stitution of variables, the nonsingular boundary integral equations in the physical plane are derived. A synchronous iterative method for th e discharge and the flow pattern is presented according to the consist ency between the discharge and the uniform velocity at far upstream. F lows 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 m easured ones.