A relatively heavy, non-Newtonian power-law fluid of flow behavior index n is released from a point source into a saturated porous medium above an horizontal bed; the intruding volume increases with time as t^alpha. Spreading of the resulting axisymmetric gravity current is governed by a non-linear equation amenable to a similarity solution, yielding an asymptotic rate of spreading proportional to t^((alpha+n)/(3+n)). The current shape factor is derived in closed-form for an instantaneous release (alpha = 0), and numerically for time-dependent injection (alpha not 0). For the general case alpha not 0, the differential problem shows a singularity near the tip of the current and in the origin; the shape factor has an asymptote in the origin for n>=1 and alpha not 0. Different kinds of analytical approximations to the general problem are developed near the origin and for the entire domain (a Frobenius series and one based on a recursive integration procedure). The behavior of the solutions is discussed for different values of n and alpha. The shape of the current is mostly sensitive to alpha and moderately to n; the case alpha = 3 acts as a transition between decelerating and accelerating currents.

V. Di Federico, R. Archetti, S. Longo (2012). Spreading of axisymmetric non-Newtonian power-law gravity currents in porous media. JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 189-190, 31-39 [10.1016/j.jnnfm.2012.10.002].

Spreading of axisymmetric non-Newtonian power-law gravity currents in porous media

DI FEDERICO, VITTORIO;ARCHETTI, RENATA;
2012

Abstract

A relatively heavy, non-Newtonian power-law fluid of flow behavior index n is released from a point source into a saturated porous medium above an horizontal bed; the intruding volume increases with time as t^alpha. Spreading of the resulting axisymmetric gravity current is governed by a non-linear equation amenable to a similarity solution, yielding an asymptotic rate of spreading proportional to t^((alpha+n)/(3+n)). The current shape factor is derived in closed-form for an instantaneous release (alpha = 0), and numerically for time-dependent injection (alpha not 0). For the general case alpha not 0, the differential problem shows a singularity near the tip of the current and in the origin; the shape factor has an asymptote in the origin for n>=1 and alpha not 0. Different kinds of analytical approximations to the general problem are developed near the origin and for the entire domain (a Frobenius series and one based on a recursive integration procedure). The behavior of the solutions is discussed for different values of n and alpha. The shape of the current is mostly sensitive to alpha and moderately to n; the case alpha = 3 acts as a transition between decelerating and accelerating currents.
2012
V. Di Federico, R. Archetti, S. Longo (2012). Spreading of axisymmetric non-Newtonian power-law gravity currents in porous media. JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 189-190, 31-39 [10.1016/j.jnnfm.2012.10.002].
V. Di Federico; R. Archetti; S. Longo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/129613
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