This paper investigates flow through variable permeability, two-dimensional circular cylinders using a pseudospectral numerical model. Two types of permeability (K) distributions are considered: constant with a lower permeability blockage, and constant with a higher permeability duct. Boundary conditions set by external flow with high Reynolds number lead to streamwise flow asymmetry and more short length scale variability within the cylinder when compared to conditions set by potential flow. High permeability belts are observed to guide flow around regions of lower permeability, while low permeability belts are observed to impede flow from reaching areas surrounded by the low permeability region. Inward surface flux is used to quantify changes in flow through variable permeability cylinders relative to the constant permeability cylinder. For blocking cases, the relationship between and the largest possible change in relative surface flux is nearly linear. In ducting simulations, where to , this relationship is no longer linear. Simple polynomial fits are derived for both situations, allowing for the calculation of the change in permeability required to achieve a given increase or reduction in inward flux. Finally, the numerical results are contrasted with theoretical perturbation results for the case of azimuthal variations in permeability, which lead to a fundamentally different pressure distribution.
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November 2021
Research Article|
November 17 2021
Numerical simulations of flow through a variable permeability circular cylinder
Jared Penney
;
Jared Penney
a)
Department of Applied Mathematics, University of Waterloo
, Waterloo, Ontario N2L 3G1, Canada
a)Present address: Northwest Atlantic Fisheries Centre, Fisheries and Oceans Canada, St. John's, Newfoundland and Labrador A1C 5X1, Canada. Author to whom correspondence should be addressed: [email protected]
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Marek Stastna
Marek Stastna
b)
Department of Applied Mathematics, University of Waterloo
, Waterloo, Ontario N2L 3G1, Canada
Search for other works by this author on:
Jared Penney
a)
Marek Stastna
b)
Department of Applied Mathematics, University of Waterloo
, Waterloo, Ontario N2L 3G1, Canada
a)Present address: Northwest Atlantic Fisheries Centre, Fisheries and Oceans Canada, St. John's, Newfoundland and Labrador A1C 5X1, Canada. Author to whom correspondence should be addressed: [email protected]
b)
Electronic mail: [email protected]
Physics of Fluids 33, 117113 (2021)
Article history
Received:
August 10 2021
Accepted:
October 30 2021
Citation
Jared Penney, Marek Stastna; Numerical simulations of flow through a variable permeability circular cylinder. Physics of Fluids 1 November 2021; 33 (11): 117113. https://doi.org/10.1063/5.0066415
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