Forchhenimer Flow Resistance and Thermal Dispersion in Porous Media at High Reynolds Number

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First, We have made a study on the behavior of the microscopic turbulent field intrinsic to porous media, and examined the momentum and energy transports due to the turbulent vortex mixing. The Hele-Shaw flow across the tube banks was experimentally studied as a model of flow through porous media. The flow visualizations by dye emissions show that the flow between the solid tubes become turbulent at high Reynolds number. Judging from our experimental evidences, it is considered that the Forchheimer flow resistance and the dispersion have a close relevance to the short-distance turbulent mixing due to the interstitial vortex in pore and the long-distance one around the solid.Next, we examines the turbulent flow across a bank of tubes as well as a bank of spheres in a narrow gap to clarify the turbulent phenomena intrinsic to porous media. The obstruction of solid matrix not only imposes spatial restrictions on the magnitude of interstitial vortices, but also induces the flow distortion. The fluid lump is transported by the distortion with mixing length of order of, which produces the additional mixing to that of the interstitial vortex. Furthermore, the mixing of flow distortion can mainly produce the energy exchange owing to the temperature difference of fluid lump.Finally, we examine the turbulent kinetic-energy equation to clarify the mechanism of turbulence in porous media. We clarify the mechanism of the production and the dissipation intrinsic to the turbulence in porous media. The production characterizes that the turbulence is produced by the vorticity which is induced by the obstruction of the solid phase. On the other hand, the dissipation characterizes that the obstruction of a solid matrix dissipates the eddies, which tend to become larger than its representative length, to the interstitial eddies. Furthermore, the Kolmogorov's length scale is estimated for the turbulent flow through porous media.