Averaged equations in a Hele-Shaw cell: Hierarchy of models

In contrast to the classical Darcy law, Navier–Stokes–Darcy model of a flow in a Hele‐Shaw cell includes small inertial and viscous forces in the plane of a cell. The displacement of viscous fluid by a less viscous one from a Hele‐Shaw cell is studied numerically using these models. A distinguishing...

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Bibliographic Details
Published in:Acta astronautica 2016-06, Vol.123, p.103-108
Main Author: Logvinov, Oleg A.
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Computer simulation
Depth-averaged equations
Displacement
Fluid flow
Hele‐Shaw cell
Inertial
Mathematical models
Miscible displacement
Peclet number
Viscous fingering
Viscous fluids
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Summary:In contrast to the classical Darcy law, Navier–Stokes–Darcy model of a flow in a Hele‐Shaw cell includes small inertial and viscous forces in the plane of a cell. The displacement of viscous fluid by a less viscous one from a Hele‐Shaw cell is studied numerically using these models. A distinguishing feature is the special microgravity conditions of displacement. Miscibility of fluids together with the high speed of displacement (Peclet number tends to infinity) provides the absence of surface tension on the one hand and minimal manifestation of molecular diffusion on the other. Simulations based on the Darcy law and on the Navier–Stokes–Darcy model have been compared. The Navier–Stokes–Darcy model clearly exhibits a better consistency with the experimental data.
ISSN:0094-5765
1879-2030
DOI:10.1016/j.actaastro.2016.02.022