Description: |
Solution of flow field equations and verification of cavitation problem on spillway of the dam
The main objective of this paper is to formulate a mathematical model for finding a flow field and cavitation problem on dam spillways. The Navier-Stokes equation is applied for the computation of pressure and velocity field, free water surface profiles and other parameters. Also, for increasing accuracy, the viscosity effect is considered. Because of internal flows the effect of gravity forces is ignored. To have more accuracy, the continuity and momentum equations are transformed to a coordinate system with axis tangent and normal to stream flow. par Finite differences are 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 expressed in finite difference form. The coefficients of convergence as well as a three-diagonal system are used for grids points. The cavitation phenomena are discussed after determination of velocity and pressure fields, which cause erosion on the spillway shut and side walls. par Also, different types of cavitations and appropriate solutions are considered, and a computer program { t MANS} is developed. Two examples are solved on this basis, and the computed results are compared with experimental results. The results show that for flows up to 4000,m\(^3\)/s the condition is good, but for flows higher than this value, the water surface shows high uprising, and provisions are needed to resist the cavitation at these flows. The results also indicate that for flows about 10899,m\(^3\)/s secondary flows dominate near the lateral gates and side walls. |