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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| Lenguaje: | English |
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Universidad de Tarapacá.
2018
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| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0718-33052018000200307 |
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| Sumario: | 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. |
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