Stokes Flow Within Networks of Flow BranchesSource: Journal of Fluids Engineering:;2018:;volume( 140 ):;issue: 012::page 121110DOI: 10.1115/1.4040832Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Stokes flow in the branches of structured looped networks with successive identical square loops and T-junction branches is studied. Analytical expressions of the flow rate in the branches are determined for network of one, two, three, or four loops with junction head loss neglected relative to regular one. Then, a general expression of the flow rate is deduced for networks with more loops. This expression contains particularly a sequence of coefficients obeying to a recurrence formula. This sequence is a part of the fusion of Fibonacci and Tribonacci sequences. Furthermore, a general formula that expresses the quotient of flow rate in successive junction flow branches is given. The limit of this quotient for an infinite number of junction branches is found to be equal to 2+3. When the inlet and outlet flow rates are equal, this quotient obeys to a sequence of invariant numbers whatever the ratio of flow rate in the outlet branches is. Thus, the flow rate distribution for any configuration of inlet and outlet flow rates can be calculated. This study is also performed using Hardy–Cross method and a commercial solver of Navier-Stokes equation. The analytical results are approached very well with Hardy–Cross method. The numerical resolution agrees also with analytical results. However, the difference with the numerical results becomes significant for low flow rate in the junction branches. The flow streamlines are then determined for some inlet and outlet flow rate configurations. They particularly illustrate that recirculation flow takes place in branches of low flow rate.
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contributor author | Hellou, Mustapha | |
contributor author | Lominé, Franck | |
date accessioned | 2019-02-28T10:59:29Z | |
date available | 2019-02-28T10:59:29Z | |
date copyright | 8/16/2018 12:00:00 AM | |
date issued | 2018 | |
identifier issn | 0098-2202 | |
identifier other | fe_140_12_121110.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4251493 | |
description abstract | Stokes flow in the branches of structured looped networks with successive identical square loops and T-junction branches is studied. Analytical expressions of the flow rate in the branches are determined for network of one, two, three, or four loops with junction head loss neglected relative to regular one. Then, a general expression of the flow rate is deduced for networks with more loops. This expression contains particularly a sequence of coefficients obeying to a recurrence formula. This sequence is a part of the fusion of Fibonacci and Tribonacci sequences. Furthermore, a general formula that expresses the quotient of flow rate in successive junction flow branches is given. The limit of this quotient for an infinite number of junction branches is found to be equal to 2+3. When the inlet and outlet flow rates are equal, this quotient obeys to a sequence of invariant numbers whatever the ratio of flow rate in the outlet branches is. Thus, the flow rate distribution for any configuration of inlet and outlet flow rates can be calculated. This study is also performed using Hardy–Cross method and a commercial solver of Navier-Stokes equation. The analytical results are approached very well with Hardy–Cross method. The numerical resolution agrees also with analytical results. However, the difference with the numerical results becomes significant for low flow rate in the junction branches. The flow streamlines are then determined for some inlet and outlet flow rate configurations. They particularly illustrate that recirculation flow takes place in branches of low flow rate. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Stokes Flow Within Networks of Flow Branches | |
type | Journal Paper | |
journal volume | 140 | |
journal issue | 12 | |
journal title | Journal of Fluids Engineering | |
identifier doi | 10.1115/1.4040832 | |
journal fristpage | 121110 | |
journal lastpage | 121110-12 | |
tree | Journal of Fluids Engineering:;2018:;volume( 140 ):;issue: 012 | |
contenttype | Fulltext |