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，并检查了湍流涡旋混合引起的动量和能量传输。作为穿过多孔介质的流动模型，对穿过管束的 Hele-Shaw 流进行了实验研究。染料发射的流动可视化表明，实心管之间的流动在高雷诺数下变得湍流。从我们的实验证据来看，福希海默流动阻力和色散与孔隙中的间隙涡和固体周围的长距离涡流引起的短距离湍流混合密切相关。接下来，我们研究了穿过狭窄间隙中的一组管子和一组球体的湍流，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造成空间限制，而且引起流动畸变。流体团块通过混合长度为 量级的扭曲来传输，这对间隙涡流产生了额外的混合。此外，流动畸变的混合主要是由于流体团温差而产生能量交换。最后，我们研究了湍流动能方程，以阐明多孔介质中湍流的机理。我们阐明了多孔介质中湍流产生和耗散的内在机制。其产生特点是湍流是由固相阻碍引起的涡度产生的。另一方面，耗散的特征是固体基质的阻碍将趋于变得大于其代表长度的涡流消散为间隙涡流。此外，还估算了穿过多孔介质的湍流的柯尔莫哥洛夫长度尺度。

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.