Non-linear friction modelling and simulation of long pneumatic transmission lines

Dynamic modelling and numerical implementation strategies for fluid transmission lines have been studied thoroughly, mainly for the application in hydraulic pipeline networks. Recent interest in energy efficiency has seen a resurgence of this field for compressed air networks, with impact on manufacturing processes, simulation of pneumatic drive components, and other theoretical analysis applications. The effects of long tubes connecting system components are often neglected to increase computational speed and reduce model size. This document highlights existing modelling approaches from practice as well as from fluid dynamic theory. Existing approaches for hydraulic transmission lines are adapted to their use for pneumatic tubes. A low-order model is derived capable to predict the transient behaviour of pressure and mass flow rate distribution within the tube. The model accounts for non-linear turbulent flow conditions, and is designed to be compatible with signal-flow simulation programmes, increasing its usability in large-scale industrial settings. It is numerically well conditioned, and all parameters are determined by physical or empirical relationships. Both its transient and quasi-stationary behaviour are validated against experimental results.