Modeling and Simulation of a Hydraulic Network for Leak Diagnosis

Bermúdez, J.R.; López‐Estrada, Francisco‐Ronay; Besançon, Gildas; Valencia‐Palomo, Guillermo; Torres, Lizeth; León, Héctor Ricardo Hernández-De

doi:10.3390/mca23040070

Cited by 22 publications

(23 citation statements)

References 13 publications

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“…For example, ruptures of pipes with leakage can be detected using the Hardy Cross method because every single-point disturbance affects the general distribution of flow and pressure [37,38]. This paper has the purpose of illustrating the very beginning of modelling of gas or water pipe networks.…”

Section: Discussionmentioning

confidence: 99%

Short Overview of Early Developments of the Hardy Cross Type Methods for Computation of Flow Distribution in Pipe Networks

Brkić

Praks

2019

Applied Sciences

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P.P.) Dejan Brkić: https://orcid.org/0000-0002-2502-0601, Pavel Praks https://orcid.org/0000-0002-3913-7800 #Dejan Brkić was on short visit funded by IT4Innovations, VŠB -Technical Abstract: Hardy Cross originally proposed a method for analysis of flow in networks of conduits or conductors in 1936. His method was the first really useful engineering method in the field of pipe network calculation. Only electrical analogs of hydraulic networks were used before the Hardy Cross method. A problem with flow resistance versus electrical resistance makes these electrical analog methods obsolete. The method by Hardy Cross is taught extensively at faculties, and it remains an important tool for the analysis of looped pipe systems. Engineers today mostly use a modified Hardy Cross method which considers the whole looped network of pipes simultaneously (use of these methods without computers is practically impossible). A method from a Russian practice published during the 1930s, which is similar to the Hardy Cross method, is described, too. Some notes from the work of Hardy Cross are also presented. Finally, an improved version of the Hardy Cross method, which significantly reduces the number of iterations, is presented and discussed. We also tested multi-point iterative methods, which can be used as a substitution for the Newton-Raphson approach used by Hardy Cross, but in this case this approach did not reduce the number of iterations. Although many new models have been developed since the time of Hardy Cross, the main purpose of this paper is to illustrate the very beginning of modelling of gas and water pipe networks and ventilation systems. As a novelty, a new multi-point iterative solver is introduced and compared with the standard Newton-Raphson iterative method.

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Section: Discussionmentioning

confidence: 99%

Short Overview of Early Developments of the Hardy Cross Type Methods for Computation of Flow Distribution in Pipe Networks

Brkić

Praks

2019

Applied Sciences

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“…Ruptures of pipes with leakage can be detected using the Hardy Cross method because every single-point disturbances affects the general distribution of flow and pressure [28,29].…”

Section: Discussionmentioning

confidence: 99%

Hardy Cross Method for Pipe Networks

Brkić¹,

Praks²

2019

Preprint

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Hardy Cross originally proposed a method for analysis of flow in networks of conduits or conductors in 1936. His method was the first really useful engineering method in the field of pipe network calculation. Only electrical analogs of hydraulic networks were used before the Hardy Cross method. A problem with the flow resistance versus the electrical resistance makes these electrical analog methods obsolete. The method by Hardy Cross is taught extensively at faculties and it still remains an important tool for analysis of looped pipe systems. Engineers today mostly use a modified Hardy Cross method which threats the whole looped network of pipes simultaneously (use of these methods without computers is practically impossible). A method from the Russian practice published during 1930s, which is similar to the Hardy Cross method, is described, too. Some notes from the life of Hardy Cross are also shown. Finally, an improved version of the Hardy Cross method, which significantly reduces number of iterations, is presented and discussed. Also we tested multi-point iterative methods which can be used as substitution for the Newton-Raphson approach used by Hardy Cross, but this approach didn’t reduce number of required iterations to reach the final balanced solution. Although, many new models have been developed since the time of Hardy Cross, main purpose of this paper is to illustrate the very beginning of modeling of gas and water pipe networks or ventilation systems.

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“…The here presented methods can be easily readapted for detection of a position of leakage in a pipe network [42,43]. A to E and a to e -auxiliary symbols Subscripts: n -normal w -water g -gas a -absolute Constants: π≈3.1415…”

Section: Figure 3 Main Conceptual Difference Between the Hardy Crossmentioning

confidence: 99%

An Efficient Iterative Method for Looped Pipe Network Hydraulics

Brkić¹,

Praks²

2019

Preprint

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Original and improved version of the Hardy Cross iterative method with related modifications are today widely used for calculation of fluid flow through conduits in loops-like distribution networks of pipes with known node fluid consumptions. Fluid in these networks is usually natural gas for distribution in the municipalities, water in waterworks or hot water in district heating system, air in the case of ventilation systems in buildings or mines, etc. Since, the resistances in these networks depend of flow, problem is not linear like in electrical circuits, and iterative procedure must be used. In both version of the Hardy Cross method, in original and in the improved one, initial results of calculation in iteration procedure is not flow, but rather the correction of flow. Unfortunately, these corrections should be added to or subtracted from a flow calculated in previous iteration according to complicate algebraic rules. After the here presented node-loop method, final results in each of the iterations is flow directly rather than flow correction. In that way complex algebraic scheme for sign of flow correction is avoided, while the final results still remain unchanged. Numbers of required iterations for the same results are comparable with the improved Hardy Cross method.All methods from this paper assume equilibrium between pressure and friction forces in steady and incompressible flow. As a result, they cannot be successfully used in unsteady and compressible flow calculations with large pressure drop where inertia force is important. Gas flow in a municipal distribution network [5], air flow in a ventilation system in buildings and mines [6], and of course water flow in waterworks [7] or district heating systems [8] and cooling systems [8] can be treated as incompressible flow since the pressure drop in these kinds of networks are minor even to compress significantly natural gas or air. The same applies to pipelines for distribution of mixed natural gas and hydrogen [9]. Overview of existing methods for calculation of flow distribution in a looped network of pipes Loop-oriented methods; Original and improved Hardy Cross methodThe Hardy Cross method [1] introduced in 1936 is the first useful procedure for the calculation of flow distribution in looped networks of pipes. Further step was made by introduction of the modification in the original Hardy Cross method in 1970 by Epp and Fowler [2]. The original Hardy Cross method [1] as a sort of single adjustment method, first of all, as an intermediate step in calculation, determines correction of flow for each loop independently and then applies this corrections to compute new flow in each conduit. It is not efficient as the improved Hardy Cross method [2,3] that considers entire system simultaneously. The improved Hardy Cross method [2], still firstly as an intermediate step, determines corrections for each loop but treated all network system simultaneously, and then applies this correction to compute new flow in each conduit such as in the original version [1...

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Modeling and Simulation of a Hydraulic Network for Leak Diagnosis

Cited by 22 publications

References 13 publications

Short Overview of Early Developments of the Hardy Cross Type Methods for Computation of Flow Distribution in Pipe Networks

Short Overview of Early Developments of the Hardy Cross Type Methods for Computation of Flow Distribution in Pipe Networks

Hardy Cross Method for Pipe Networks

An Efficient Iterative Method for Looped Pipe Network Hydraulics

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