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

首先，我们研究了多孔介质固有的微观湍流场的行为，并考察了湍流涡旋混合引起的动量和能量输运。本文将Hele-Shaw流作为多孔介质流动模型进行了实验研究。染料发射的流动可视化表明，固体管之间的流动在高雷诺数时变得湍流。从我们的实验证据来看，Forchheimer流动阻力和弥散与孔内间隙涡旋和固体周围长距离涡旋引起的短距离湍流混合密切相关。接下来，我们研究了一排管子和一排球体在狭窄间隙中的湍流，以阐明多孔介质固有的湍流现象。固体基质的阻塞不仅对间隙涡的大小施加了空间限制，而且引起了流动畸变。混合长度为数量级的变形将液块输运，产生间隙涡的额外混合。此外，流动畸变的混合主要是由于液块的温差引起的能量交换。最后，我们通过紊流动能方程来阐明多孔介质中紊流的机理。阐明了多孔介质湍流产生和耗散的机理。紊流的产生特点是由固相的阻塞所引起的涡量产生。另一方面，耗散的特征是固体基体的阻塞将涡流耗散到间隙涡流中，而涡流往往比其代表长度更大。此外，还估计了多孔介质湍流的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.