Finite Difference Analysis of Pressure Surge at the Valve of a Closed Pipeline

Jonathan Tsetimi; Ebimene James Mamadu

doi:https://doi.org/10.14445/22315373/IJMTT-V68I5P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 5 | Year 2022 | Article Id. IJMTT-V68I5P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I5P505

Finite Difference Analysis of Pressure Surge at the Valve of a Closed Pipeline

Jonathan Tsetimi, Ebimene James Mamadu

Received	Revised	Accepted	Published
19 Mar 2022	02 May 2022	19 May 2022	06 Jun 2022

Citation :

Jonathan Tsetimi, Ebimene James Mamadu, "Finite Difference Analysis of Pressure Surge at the Valve of a Closed Pipeline," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 5, pp. 22-35, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I5P505

Abstract

Water hammer is very essential for risk analysis and operation of pipeline system. This work studies the effects of steady friction factor, wall constraint, pipe diameter and liquid density for the analysis of water hammer in a pipeline system with special emphasis on the finite difference method (FDM) due to its accurate and reliable evaluation of the water hammer problems. We model water hammer for pipe made from polymeric material by two partial differential equations (PDEs). The PDEs are then discretized along the spatial dimension to give a set of ordinary differential equations, ODEs. For a given set of parameters, we then solve the resulting ODEs numerically and plot the pressure dynamics at the valve to determine the water hammer characteristics. It was observed that the model with steady friction factor is appropriate for the simulation of water hammer in pressurized pipes made from polymers such as Polyvinyl Chloride. The maximum pressure amplitude simulated by the model is estimated accurately. The pipe wall constraint, liquid density, pipe diameter has a significant influence on obtained results. The lower the values of Pipe diameterΑd, effective modulus of system Ds and cross-sectional area , the lower the amplitudes as presented graphically. Also, during the stimulation, the experimental pressure runs shows the pressure increases after the valve closure linearly. Numerical validation of the FDM demonstrates that the FDM performs well and is as good as the method of characteristics in terms of computational speed and accuracy.

Keywords

Darcy-Weisbach equation, Finite difference method, Partial differential equation, Reynold number, Water hammer.

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