Nonlinear dynamics of flow in piping trees using projection methods

Simple methods for the steady‐state analysis of a flow network are readily available, but the dynamic behavior of a large‐scale flow network is difficult to study due to the complex differential‐algebraic equation system resulting from its modeling. It is the aim of this paper to present two simple methods for the dynamic analysis of large‐scale flow networks and to demonstrate their use by examining the dynamics of a self‐similar branching tree network.

Two numerical projection methods are proposed for one‐dimensional dynamic analysis of large piping networks. Both are extensions of that suggested by Chorin for the nonlinear differential‐algebraic system resulting from the Navier‐Stokes equations. Each numerical algorithm is discussed and verified for turbulent flow in a nonlinear, self‐similar, branching tree network with constant friction factor for which an exact solution is available.

The dynamics of this network are calculated for more realistic friction factors and described as system parameters are varied. Self‐excited oscillations due to laminar‐turbulent transition are found for some parameter values and dynamic component behavior is observed in the network which is not observable in components apart from it.

It is shown that the dynamics of a flow network can exhibit unexpected behavior, reinforcing the need for simple methods to perform dynamic analysis.

This paper presents two numerical projection schemes for dynamic analysis of large‐scale flow networks to aid in their study and design.