We consider the motion of shallow two-dimensional gravity currents of a purely viscous and relatively heavy power-law fluid of flow behavior index n in a uniform saturated porous layer above a horizontal impermeable boundary, driven by the release from a point source of a volume of fluid increasing with time like t^α. The equation of motion for power-law fluids in porous media is a modified Darcy’s law taking into account the nonlinearity of the rheological equation. Coupling the flow law with the mass balance equation yields a nonlinear differential problem which admits a self-similar solution describing the shape of the current, which spreads like t^(α+n )/(2+n), generalizing earlier results for Newtonian fluids. For the particular values α = 0 and 2, closed-form solutions are derived; else, a numerical integration is required; the numerical scheme is tested against the analytical solutions. Two additional analytical approximations, valid for any α, are presented. The space-time development of the gravity current is discussed for different flow behavior indexes.

Similarity solutions for spreading of a two-dimensional non-Newtonian gravity current in a porous layer / V., Di Federico; R., Archetti; Longo, Sandro Giovanni. - In: JOURNAL OF NON-NEWTONIAN FLUID MECHANICS. - ISSN 0377-0257. - 177-178:(2012), pp. 46-53. [10.1016/j.jnnfm.2012.04.003]

Similarity solutions for spreading of a two-dimensional non-Newtonian gravity current in a porous layer

LONGO, Sandro Giovanni
2012-01-01

Abstract

We consider the motion of shallow two-dimensional gravity currents of a purely viscous and relatively heavy power-law fluid of flow behavior index n in a uniform saturated porous layer above a horizontal impermeable boundary, driven by the release from a point source of a volume of fluid increasing with time like t^α. The equation of motion for power-law fluids in porous media is a modified Darcy’s law taking into account the nonlinearity of the rheological equation. Coupling the flow law with the mass balance equation yields a nonlinear differential problem which admits a self-similar solution describing the shape of the current, which spreads like t^(α+n )/(2+n), generalizing earlier results for Newtonian fluids. For the particular values α = 0 and 2, closed-form solutions are derived; else, a numerical integration is required; the numerical scheme is tested against the analytical solutions. Two additional analytical approximations, valid for any α, are presented. The space-time development of the gravity current is discussed for different flow behavior indexes.
2012
Similarity solutions for spreading of a two-dimensional non-Newtonian gravity current in a porous layer / V., Di Federico; R., Archetti; Longo, Sandro Giovanni. - In: JOURNAL OF NON-NEWTONIAN FLUID MECHANICS. - ISSN 0377-0257. - 177-178:(2012), pp. 46-53. [10.1016/j.jnnfm.2012.04.003]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2412562
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