Solution of Flow Field Equations and Verification of Cavitation Problem on Spillway of the dam


Civil Engineering, Khaje Nasir Toosi University of Technology


The main objective of this paper is to formulate a mathematical model for finding flow field and cavitation problem on dam spillways. The Navier-Stokes Equation has been applied for the computation of pressure and velocity field, free water surface profiles and other parameters. Also, for increasing accuracy of the problem, viscosity effect has been considered. Because of internal flows the effect of gravity forces has been ignored. To have more accuracy the continuity and momentum equations have been transformed to a coordinate system with axis tangent and normal to stream flow.Finite differences has been used to solve equations governing the over flow of dam the spillways. To linearize the nonlinear equations the parameters are expressed in terms of products of last step in the new one. Later the remaining derivatives are with finite differences form. Coefficients of convergence as well as a three diagonal system are used for all the grids points. The cavitation phenomena are discussed after determination of velocity and pressure fields, which cause erosion on the spillway shut and side walls.Also, the different types of cavitations and appropriate solutions were considered and a computer program (MANS) was developed Two examples were solved on this basis and the computed results were compared with experimental results. The results show that for flows up to 4000 m3/sec the condition is good, but for flows higher than this value, the water surface shows high uprising and provisions are needed to resist cavitation at these flows. The results also indicate that at flows about 10899 m3/sec secondary flows dominate near the lateral gates and side walls.