Numerical simulation of the water hammer phenomenon taking into account the hydraulic friction of the pipeline by the control point method

Abstract

The calculations of dynamic processes in the pipeline are necessary for modeling the processes of fluid movement in the pipeline, for example, for predicting loads on the pipeline when compression and rarefaction waves move in it. These tasks are reduced to solving systems of partial differential equations. The calculation of the phenomenon excluding hydraulic friction can be carried out by the method of characteristics, however, the calculation, taking into account the friction forces, is complicated for known methods, such as the finite difference method and the final element method. The article provides a brief description and an example of using the control point method for the task of modeling the water hammer phenomenon, taking into account the hydraulic friction forces of the pipeline. The main idea of the proposed method is to reduce the solution of these systems of equations to solving linear programming problems. The purpose of this work is to solve the problem of water hammerwith friction by the control point method. This method, developed jointly with A.S. Maksimov by the authors of this article at the Melentiev Energy Systems Institute, has shown good results in solving systems of partial differential equations of a periodic heat exchanger with ceramic ball filling. Moreover, heat transfer inside these elements was taken into account. With large values of thermal conductivity coefficients, this system is also rigid, which complicates its solution by the control volume method, but the control point method has shown good results. This gives reason to consider it promising in calculations of hydraulic friction. The results of modeling a hydraulic shock to a pipe filled with an incompressible liquid at different friction coefficients have been obtained. The results make it possible to make a numerical assessment of the effect of the o hydraulic friction coefficient on the attenuation of oscillatory processes during a hydraulic shock.