Transient Modeling of Arbitrary Pipe Networks by a Laplace-Domain Admittance Matrix

Zecchin, Aaron C.; Simpson, Angus R.; Lambert, Martin F.; White, L.B.; Vítkovský, John P.

doi:10.1061/(asce)0733-9399(2009)135:6(538)

Cited by 34 publications

(15 citation statements)

References 27 publications

(28 reference statements)

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“…(74)). Zecchin et al (2009) term the J H matrix a hydraulic admittance matrix, as it maps from pressure to flow. A more in-depth comparison of the element locations common to the formulations can be observed in (32) and (84).…”

Section: Comparison To Steady-state Analysismentioning

confidence: 99%

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Head- and Flow-Based Formulations for Frequency Domain Analysis of Fluid Transients in Arbitrary Pipe Networks

et al. 2011

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Applications of frequency-domain analysis in pipelines and pipe networks include resonance analysis, time-domain simulation and fault detection. Current frequency-domain analysis methods are restricted to series pipelines, single-branching pipelines and single-loop networks and are not suited to complex networks. This paper presents a number of formulations for the frequency-domain solution in pipe networks of arbitrary topology and size. The formulations focus on the topology of arbitrary networks and do not consider any complex network devices or boundary conditions, other than head and flow boundaries. The frequency-domain equations are presented for node elements and pipe elements, which correspond to the continuity of flow at a node and the unsteady flow in a pipe, respectively. Additionally, a pipe-node-pipe and reservoir-pipe pair set of equations are derived. A matrix-based approach is used to display the solution to entire networks in a systematic and powerful way. Three different formulations are derived based on the unknown variables of interest that are to be solved for, being the head-formulation, flow-formulation and the head-flow-formulation. These hold significant analogies to different steady-state network solutions. The frequencydomain models are tested against the method of characteristics (a commonly used timedomain model), with good result. The computational efficiency of each formulation is discussed with the most efficient formulation being the head-formulation.

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Section: Comparison To Steady-state Analysismentioning

confidence: 99%

“…Recently, Zecchin et al (2009) formulated a Laplace-domain network admittance matrix formulation of the fundamental network equations, which shares a similarity to the ĥ -formulation that is derived within this paper.…”

Section: Introductionmentioning

confidence: 97%

Head- and Flow-Based Formulations for Frequency Domain Analysis of Fluid Transients in Arbitrary Pipe Networks

et al. 2011

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“…An alternative method for modelling systems comprised of pipes, junctions and reservoirs was proposed in Zecchin et al [2009] in which an admittance matrix expression relating the nodal pressures to the nodal outflows was derived from the basic fluid equations using graph theory concepts. The significance of this is twofold, (i) the network matrix was shown to have an intuitive and simple structure for which analogies with admittance matrices in electrical circuits was made apparent [Desoer and Kuh, 1969], and (ii) it showed that the entire network state was a function of the reduced variable set of nodal pressures and flows.…”

Section: Background Modelling the Transient Behaviour Of Pipe Networkmentioning

confidence: 99%

“…Firstly, as background for this work, the network admittance matrix for a simple node network is derived [Zecchin et al, 2009]. Based on this, a staged generalisation is presented.…”

Section: Network Formulationmentioning

confidence: 99%

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

et al. 2010

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Frequency-domain modeling of transients in pipe networks with compound nodes using a Laplacedomain admittance matrix Journal of Hydraulic Engineering, 2010; 136(10) AbstractAn 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 frequencydomain 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.

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Leak Detection in a Branched System by Inverse Transient Analysis with the Admittance Matrix Method

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Zecchin

et al. 2017

Water Resour Manage

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The diagnosis of water distribution systems by means of the inverse transient analysis requires efficient and reliable numerical models. In the network admittance matrix method (NAMM) the 1-D waterhammer governing equations are integrated in the frequency domain and organized in a laplacian matrix form. The NAMM is particularly suitable for complex systems because of this structure and can be used for the system diagnosis, including leak sizing and location. In this paper a damaged branched system is considered and the diagnosis is performed by means of the NAMM using experimental data from laboratory transient tests. Two different boundary conditions are used in the implementation of the NAMM and the leak is located and sized with a reasonable approximation. An extended numerical investigation is also presented and allows confirmation of the results for different leak locations. The use of the NAMM for the leak detection and the validation using experimental data on a branched system are the main original contributions of this work. The successful diagnosis indicates promising results for applications in more complex systems.

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Transient Modeling of Arbitrary Pipe Networks by a Laplace-Domain Admittance Matrix

Cited by 34 publications

References 27 publications

Head- and Flow-Based Formulations for Frequency Domain Analysis of Fluid Transients in Arbitrary Pipe Networks

Head- and Flow-Based Formulations for Frequency Domain Analysis of Fluid Transients in Arbitrary Pipe Networks

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

Leak Detection in a Branched System by Inverse Transient Analysis with the Admittance Matrix Method

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