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ARTICLE

Modeling the Unsteady Flow of a Newtonian Fluid Originating from the Hole of an Open Cylindrical Reservoir

Andrianantenaina Marcelin Hajamalala^1,*, Ratovonarivo Noarijaona¹, Zeghmati Belkacem²

1 Laboratory of Mechanics Energetic and Environment (LMEE), University of Fianarantsoa, Fianarantsoa, B.P.1264, Madagascar
2 Laboratory of Mathematics and Physics (LA.M.P.S), University of Perpignan Via Domitia, Perpignan, 66860, France

* Corresponding Author: Andrianantenaina Marcelin Hajamalala. Email:

(This article belongs to the Special Issue: Materials and Energy an Updated Image for 2021)

Fluid Dynamics & Materials Processing 2022, 18(6), 1737-1748. https://doi.org/10.32604/fdmp.2022.022047

Received 18 February 2022; Accepted 23 March 2022; Issue published 27 June 2022

Abstract

This work deals with the modeling of the unsteady Newtonian fluid flow associated with an open cylindrical reservoir. This reservoir presents a hole on the right bottom wall. Fluid volume variation, heat and mass transfers are neglected. The unsteady governing equations are based on the conservation of mass and momentum. A finite volume technique is used to solve the non-dimensional equations and related boundary conditions. The algebraic system of equations resulting from the discretization process are solved by means of the THOMAS algorithm. For pressure-velocity coupling, the SIMPLE algorithm (Semi Implicit Method for Pressure Linked Equations) is used. Results for laminar flow (Re < 1000), including the pressure and velocities profiles as well as the streamlines in the reservoir are presented. Moreover, the effects of the D/d and H₀/D ratios and Reynolds number Re on the fluid flow are discussed. It is shown that the velocities and pressure depend essentially on the reservoir size. To validate the model, the present results have been compared with Zhou et al.’s results, Poiseuille’s and Bernoulli’s exact solution.

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Keywords

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