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Showing papers on "Shell balance published in 1990"


Journal ArticleDOI
TL;DR: In this paper, a mathematical model of an abrupt pressure impact applied to a compressible fluid flowing through a porous medium domain is developed, where a sequence of four reduced forms of mass and momentum balance equations are associated with four time periods following the onset of a pressure change.
Abstract: A mathematical model is developed of an abrupt pressure impact applied to a compressible fluid flowing through a porous medium domain. Nondimensional forms of the macroscopic fluid mass and momentum balance equations yield two new scalar numbers relating storage change to pressure rise. A sequence of four reduced forms of mass and momentum balance equations are shown to be associated with a sequence of four time periods following the onset of a pressure change. At the very first time period, pressure is proven to be distributed uniformly within the affected domain. During the second time interval, the momentum balance equation conforms to a wave form. The behavior during the third time period is governed by the averaged Navier-Stokes equation. After a long time, the fourth period is dominated by a momentum balance similar to Brinkman's equation which may convert to Darcy's equation when friction at the solid-fluid interface dominates.

30 citations