Analytical, Numerical 1D and 3D Water Hammer Investigations in a Simple Pipeline Apparatus

Abstract

This paper deals with the analytical and numerical simulation of a water hammer in the reservoir-pipeline-valve (RPV) system. An analytical solution of the water hammer equations with unsteady friction term was derived for transient laminar pipe flow in a RPV system. For simulation of an arbitrary flow situation a number of one-dimensional (1D) numerical methods have been developed. The physically based method of characteristics proved to be computationally efficient and can handle complex boundary conditions. The accuracy of the 1D numerical model is increased by introducing terms that take into account 3D effects (example of an unsteady skin friction). The 3D model predicts these influences directly and represents an excellent tool for researching multidimensional properties of fluids (numerical laboratory). Calculation results based on 1D and 3D numerical models are in good agreement with the results of measurements taking into account adequate prediction and modelling of influential physical parameters during laminar and low-Reynolds number turbulent water hammer events. Quantitative comparison analysis yields up to 2 % difference in maximum head at the valve and up to 5 % relative difference in pressure head drop at the midpoint of the pipeline monitored over the first four positive pressure pulses.