Shock waves in porous media

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Abstract

Balance equations of mass, momentum and energy for a compressible Newtonian fluid and a thermoelastic solid are introduced in their microscopic forms. Macroscopic balance equations are derived from the microscopic ones, in order to describe the interaction of the fluid and solid phases in saturated porous media. These yield Forchheimer terms presenting the exchange between the phases through the solid-fluid interfaces. Nondimensional investigation of the phases' macroscopic balance equations, yields four evolution periods associated with different dominant balance equations obtained following an abrupt change the in fluid's pressure and temperature. During the second time interval, compaction wave equations are formed. Various analytical solutions of these nonlinear wave equations are described for the 1-D case. Comparison with literature and verifications with shock tube experiments, prove the superiority of the developed theory.

Original languageEnglish
Pages (from-to)215-254
JournalINTERNATIONAL SERIES ON ADVANCES IN FLUID MECHANICS
Volume13
StatePublished - 1 Jan 1997
Externally publishedYes

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