Micro- and macroscopic investigation and mathematical modeling of heat transfer within a porous medium layer

广泛应用于多孔介质研究的局部体积平均理论（即VAT）的概念被提出，用于研究由小型元件组成的复杂热流体流动设备内的流动和换热，这些设备不希望网格化。例如，紧凑型热交换器中的热流体通道和冷流体通道可被视为具有高度各向异性渗透率的两种不同的多孔介质。首先，对微观流体流动方程和传热方程进行体积平均，建立宏观控制方程；研究表明，雷诺数平均必须先于体积平均，因为必须首先对孔隙内较小的涡流进行建模。其次，预先建立了亚尺度固体单元（以各向异性多孔介质为模型）的流动阻力和流动流体与亚尺度单元之间的传热的亚控制体积模型。对孔隙尺度下的微观数值结果进行处理，提取体积平均量下的宏观水动力和热特性。研究发现，渗透率张量（控制低雷诺数范围内的粘性阻力）的主轴与Forchheimer张量（控制高雷诺数范围内的形式阻力）的主轴明显不同。研究还表明，定向界面换热系数随宏观流动角的变化与定向渗透率的变化相似。利用PIV系统进行了实验研究，阐明了多孔介质中最终导致湍流过渡的非定常流动特性。

The concept of local volume-averaging theory, namely, VAT, widely used in the study of porous media has been proposed to investigate the flow and heat transfer within complex heat and fluid flow equipment consisting of small scale elements which one does not want to grid. For example, the hot and cold fluid passages in a compact heat exchanger can be treated as two distinct porous media with highly anisotropic permeabilities. Firstly, the set of macroscopic governing equations was established by carrying out volume averaging over the microscopic fluid flow and heat transfer equations. It has been revealed that the Reynolds averaging must precede the volume averaging, since smaller eddies within a pore must be modeled first. Secondly, the sub-control volume models were established beforehand for the flow resistance associated with subscale solid elements (modeled as an anisotropic porous medium) and the heat transfer between the flowing fluid and the subscale elements. The microscopic numerical results obtained at a pore scale were processed to extract the macroscopic hydrodynamic and thermal characteristics in terms of the volume-averaged quantities. It has been found that the principal axes of the permeability tensor (which controls the viscous drag in the low Reynolds number range) differ significantly from those of the Forchheimer tensor (which controls the form drag in the high Reynolds number range). The study also reveals that the variation of the directional interfacial heat transfer coefficient with respect to the macroscopic flow angle is analogous to that of the directional permeability. Experimental investigation using PIV system was also conducted to elucidate unsteady flow characteristics in porous media, which eventually would lead to turbulence transition.