Hydrodynamic instability of fluid flow through homogeneous porous media

An analytical investigation of the mechanisms contributing to large scale spatial instability of flow within homogeneous porous media is conducted. The volumetric phase averaged fluid equations with the retention of the macroscopic convective and Brinkman diffusion terms are considered. Closure of the viscous and inertial stress and the pressure correlations is made with the conventional Ergun empirical drag expression. The fluid is assumed to be homogeneous and incompressible and a complex exponential form of the streamfunction is introduced for the first order, two-dimensional, unsteady disturbance system.; The results for temporal and spatial instability indicate that the flow processes exponentially damped solutions. However, degenerate eigenvalues are found to exist which allow the disturbance to exhibit local algebraic spatial growth for steady flows. The transverse wavelength for the degenerate modes, the streamwise length and growth rate of the disturbance depend principally on the resistance coefficients in the Ergun drag formula. The Brinkman viscous term attenuates the disturbance at lower Reynolds numbers and higher transverse wavenumbers.; To examine mechanisms for the production of large-amplitude, steady disturbances at elevated Reynolds number, the effective porosity of the medium is reconsidered. Experimental results and detailed microscale flow simulations indicate that significant regions of flow separation exist around and downstream of the contact points of the particles in the porous medium. This results in a decrease in the effective porosity of the medium as Reynolds number is increased, insofar as transport of mass and momentum are concerned, and this phenomenon has not been addressed in prior experimental or computational studies. A new porosity-based streamfunction transformation is introduced, similar in aspects to the density-based transformations used in compressible flows. The porosity is then assumed to be a function of flow Reynolds number. The equation for the linearized disturbance streamfunction then depends on the derivative of porosity with respect to pore Reynolds number evaluated at the mean flow conditions. Flow in the porous media system is found to be spatially unstable for relatively small negative values of the porosity derivative, thus providing a new potential mechanism for observed instabilities.