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

首先，我们研究了多孔介质内微观湍流场的行为，考察了湍流涡旋混合引起的动量和能量输运。作为多孔介质流动的模型，对Hele-Shaw管排绕流进行了实验研究。通过染料喷射的流动显示表明，在高雷诺数下，固体管之间的流动变为湍流。从实验结果来看，Forchheimer流动阻力和弥散与孔隙内间隙涡和固体周围长距离间隙涡引起的近距离湍流混合密切相关。接下来，我们研究了窄间隙内湍流流过管组和球组的情况，以阐明多孔介质中固有的湍流现象。固体基质的阻挡不仅对间隙涡的大小产生空间限制，而且会导致流动畸变。混合长度为数量级的畸变对流体块的输送产生了附加混合。此外，由于流体块体的温差，流动畸变的混合主要是产生能量交换。最后，通过对湍流动能方程的分析，阐明了多孔介质中湍流的机理。阐明了多孔介质中湍流的产生和耗散机制。湍流的产生是由于固相的阻碍而产生的涡量。另一方面，耗散的特征在于固体基质的阻碍将趋于变得大于其代表性长度的涡旋耗散为间隙涡旋。此外，Kolmogorov的长度尺度估计的湍流通过多孔介质。

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.