# Simulation of nonlinear wave propagation in circular hydraulic pipes

## Dipl.-Ing. Rainer Haas

**Nov. 17, 2009, 2:30 p.m. P 215**

For hydraulic design it is very important to predict wave propagation in pipelines e.g. a fast closing valve can cause cavitation just behind the valve and damage it. Other applications like the hydraulic buck converter deals with wave propagation effects to work efficiently.

Simulation of high pressure systems is quite straight forward. The fluid parameters like density and bulk modulus can be assumed to be constant and as a result of this the flow equations are very simple e.g. the wave speed in a straight round pipe is constant. For low pressure simulations these assumptions are not true any more. For example, air release in low pressure regions generates small air bubbles which cause dramatic changes in the fluid parameters like density and compressibility. As a result, simulations are only accurate for a special operating point with small variations. In the more general case of large pressure variations around a low pressure operating point, wave speed and the

shape of the pressure pulses change as the previously discussed parameters do.

The aim of this presentation is to derive a set of one dimensional equations e.g. conservation equations and a technical useful friction law. Then some standard simulation techniques with their pros and cons are shown. Finally important claims due to the simulation and occurred simulation problems will

be stated and discussed.