Abstract
Article describes simulation of unsteady flow during water hammer with two programs, which use different numerical approaches to solve ordinary one dimensional differential equations describing the dynamics of hydraulic elements and pipes. First one is Matlab-Simulink-SimHydraulics, which is a commercial software developed to solve the dynamics of general hydraulic systems. It defines them with block elements. The other software is called HYDRA and it is based on the Lax-Wendrff numerical method, which serves as a tool to solve the momentum and continuity equations. This program was developed in Matlab by Brno University of Technology. Experimental measurements were performed on a simple test rig, which consists of an elastic pipe with strong damping connecting two reservoirs. Water hammer is induced with fast closing the valve. Physical properties of liquid and pipe elasticity parameters were considered in both simulations, which are in very good agreement and differences in comparison with experimental data are minimal.
Highlights
Unsteady flow in pipeline systems is well known phenomenon
The other software is called HYDRA and it is based on the Lax-Wendroff numerical method, which serves as a tool to solve the momentum and continuity equations
Relationship between mass fraction and content of air according to SimHydraulics can described by equation (7), which is valid for little volume of free air
Summary
It is possible to describe it by momentum and continuity equations, which can be simplified to solve one dimensional problem. Behaviour of pipeline system is defined by many factors and sound speed is one of them, probably, one of the most important, see equation 1. As hydraulic systems does not consist only of fluid, it is necessary to consider pipe properties (Young’s modulus, diameter and thickness of the wall), which reduce bulk modulus and so sound speed. When static pressure is low enough it is good idea to consider influence of undissolved gas in fluid. Influence of air on sound speed in water was measured by [6] and [7] and analytical derivation is published in [8]
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