2000 M.Sc. Graduated Mollabashi Asieh

Water hammer analysis by finite element method

Abstract

Finite element method (FEM) is used widespread in areas such as structure, fluid mechanics, etc. The aim of this study is to use this common method for the solution of water hammer equations. Two methods of standard Galerkin (G) and Petrov- Galerkin .(PG) are used to evaluate flow characteristics for a simple system containing a pipe with a reservoir at upstream and a valve at downstream. In the G method, linear shape functions and weight functions are used, while in PG method, weight functions are added which will force some kinds of artificial viscosities.

When the pipe is closing gradually, the G method models this effect clearly, but when the pipe is suddenly closed, the results are fluctuated as compared to the real and expected ones. Also, some extra time-steps are taken to reach to the real results. The PG method simulates both conditions clearly. In G method, increasing the number of elements causes the fluctuations happen in a short time and reaches sooner to real head. In PG method, by increasing the number of elements, better results will be obtained. In both methods, by decreasing the time-step, better results will be reached. It is shown that the cost of having more elements is higher than decreasing the time-step. After these steps, the use of PG method for a case of series pipes, a downstream reservoir and a real valve has been investigated, which shows desirable results. In all applications, the final results agree well with those of the characteristics method.