Frequency-Domain Modeling of Transients in Pipe Networks with Compound Nodes Using a Laplace-Domain Admittance Matrix

An alternative to modeling the transient behavior of pipeline systems in the time domain is to model these systems in the frequency domain using Laplace transform techniques. A limitation with traditional frequency-domain pipeline models is that they are only able to deal with systems of a limited class of configuration. Despite the development of a number of recent Laplace-domain network models for arbitrarily configured systems, the current formulations are designed for systems comprised only of pipes and simple node types such as reservoirs and junctions. This paper presents a significant generalization of existing network models by proposing a framework that allows not only complete flexibility with regard to the topological structure of a network, but also, encompasses nodes with dynamic components of a more general class (such as air vessels, valves, and capacitance elements). This generalization is achieved through a novel decomposition of the nodal dynamics for inclusion into a Laplace-domain network admittance matrix. A symbolic example is given demonstrating the development of the network admittance matrix and numerical examples are given comparing the proposed method to the method of characteristics for 11-pipe and 51-pipe networks.