Water hammer analysis using an implicit finite-difference method

ABSTRACT The Implicit Finite-Difference Method (IFDM) for the solution of water hammer in pipe networks is presented. All the equations necessary to calculate the flow and pressure in each node of the network are shown in detail. Section-by-section coupling through the Karney equation allows obtain...

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Autor principal:	Twyman Q.,John
Lenguaje:	English
Publicado:	Universidad de Tarapacá. 2018
Materias:	Pipe replacement element preissman scheme transient friction factor water hammer weighting coefficients
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0718-33052018000200307
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spelling	oai:scielo:S0718-330520180002003072018-06-15Water hammer analysis using an implicit finite-difference methodTwyman Q.,John Pipe replacement element preissman scheme transient friction factor water hammer weighting coefficients ABSTRACT The Implicit Finite-Difference Method (IFDM) for the solution of water hammer in pipe networks is presented. All the equations necessary to calculate the flow and pressure in each node of the network are shown in detail. Section-by-section coupling through the Karney equation allows obtain a system of equations for each pipe section which is easy to solve applying the Thomas' algorithm. Also, there are presented the original expressions in the form of finite differences are presented for: (1) the frictional term of the dynamics equation, (2) the transient friction factor proposed by Brunone-Vítkovsky, and (3) the short pipe replacement elements which allow increase the time step. It is demonstrated that the proposed methodology allows modelling the transient flow with higher level of stability and numerical accuracy in comparison to the Method of Characteristics (MOC), especially when the Courant number (Cn) is less than 1. However, because of IFDM works with weighting coefficients (θ 1 and θ2) which must adopt values generally close to 0.5 depending on the analyzed problem, the achievement of the best near-to-exact solution requires to analyze each case separately, being obligatory to apply a trial/error procedure that can make the analysis cumbersome and time consuming.info:eu-repo/semantics/openAccessUniversidad de Tarapacá.Ingeniare. Revista chilena de ingeniería v.26 n.2 20182018-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0718-33052018000200307en10.4067/S0718-33052018000200307
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Pipe replacement element preissman scheme transient friction factor water hammer weighting coefficients
spellingShingle	Pipe replacement element preissman scheme transient friction factor water hammer weighting coefficients Twyman Q.,John Water hammer analysis using an implicit finite-difference method
description	ABSTRACT The Implicit Finite-Difference Method (IFDM) for the solution of water hammer in pipe networks is presented. All the equations necessary to calculate the flow and pressure in each node of the network are shown in detail. Section-by-section coupling through the Karney equation allows obtain a system of equations for each pipe section which is easy to solve applying the Thomas' algorithm. Also, there are presented the original expressions in the form of finite differences are presented for: (1) the frictional term of the dynamics equation, (2) the transient friction factor proposed by Brunone-Vítkovsky, and (3) the short pipe replacement elements which allow increase the time step. It is demonstrated that the proposed methodology allows modelling the transient flow with higher level of stability and numerical accuracy in comparison to the Method of Characteristics (MOC), especially when the Courant number (Cn) is less than 1. However, because of IFDM works with weighting coefficients (θ 1 and θ2) which must adopt values generally close to 0.5 depending on the analyzed problem, the achievement of the best near-to-exact solution requires to analyze each case separately, being obligatory to apply a trial/error procedure that can make the analysis cumbersome and time consuming.
author	Twyman Q.,John
author_facet	Twyman Q.,John
author_sort	Twyman Q.,John
title	Water hammer analysis using an implicit finite-difference method
title_short	Water hammer analysis using an implicit finite-difference method
title_full	Water hammer analysis using an implicit finite-difference method
title_fullStr	Water hammer analysis using an implicit finite-difference method
title_full_unstemmed	Water hammer analysis using an implicit finite-difference method
title_sort	water hammer analysis using an implicit finite-difference method
publisher	Universidad de Tarapacá.
publishDate	2018
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0718-33052018000200307
work_keys_str_mv	AT twymanqjohn waterhammeranalysisusinganimplicitfinitedifferencemethod
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Water hammer analysis using an implicit finite-difference method

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