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部微观湍流场的行为，并研究了湍流涡旋混合引起的动量和能量输运。将Hele-Shaw流动作为多孔介质中的流动模型进行了实验研究。染料排放的流动显示表明，当雷诺数较高时，固体管间的流动变得湍流。根据我们的实验证据，认为Forchheimer流动阻力和弥散与由于孔隙中的间隙涡和固体周围的长距离湍流混合而产生的短距离湍流混合密切相关。接下来，我们研究了狭窄缝隙中一排管子和一排球体的湍流流动，以阐明多孔介质固有的湍流现象。固体基质的阻碍不仅对间隙涡的大小施加了空间限制，而且还会导致流动的扭曲。流体块通过混合长度为数量级的扭曲来输运，产生对间隙涡的额外混合。此外，流动变形的混合主要是由于液块的温差而产生的能量交换。最后，我们检查了湍流动能方程，以阐明多孔介质中的湍流机理。阐明了多孔介质中湍流产生和耗散的内在机制。结果表明，湍流是由固相阻挡产生的涡量引起的。另一方面，耗散的特点是固体基质的阻挡作用使涡旋向间隙涡流扩散，这些涡流往往比它的代表长度大。在此基础上，给出了多孔介质中湍流流动的Kolmogorov长度尺度。

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.