论文标题
准周期开发的宏观尺度描述
A macro-scale description of quasi-periodically-developed flow
论文作者
论文摘要
我们提出了通道中准周期性流动流的宏观尺度描述，该流量依赖于双重体积平均。我们表明，准开发的宏尺度流的特征是速度模式在主要流动方向上呈指数衰减。我们证明，闭合力可以由由两个部分组成的精确渗透性张量表示。第一部分是由于开发的宏观流动引起的，到处都是均匀的，除了在侧壁区域外，它受到宏观尺度速度曲线及其滑动长度的影响。第二部分表示对速度模式的电阻，因此随着流量的发展而呈指数衰减。它满足了数组的横向行上的特定封闭问题。从这些属性中，我们评估了体积平均流动方程的经典闭合问题的有效性。我们表明，其所有基本假设部分因流量发展过程中的错误误差而部分侵犯。此外，我们表明，当它应用于重建宏观流量时，它会修改准开发流的特征值，模式和开始点。通过直接的数值模拟和流动的显式过滤，对具有等距的在线正方形圆柱的高孔隙率阵列进行了高孔隙率阵列的高孔隙率阵列进行了说明。特别是，我们提出了雷诺数字的经典闭合问题的广泛解决方案，最多600，孔隙率在0.2到0.95之间，以及0至45度之间的流动方向，尽管该通道高度与圆柱体间距相等。将这些封闭溶液与孔隙率在0.75至0.94之间的圆柱阵列的通道中的实际闭合力进行了比较，雷诺数最高为300。
We present a macro-scale description of quasi-periodically developed flow in channels, which relies on double volume-averaging. We show that quasi-developed macro-scale flow is characterized by velocity modes which decay exponentially in the main flow direction. We prove that the closure force can be represented by an exact permeability tensor consisting of two parts. The first part, which is due to the developed macro-scale flow, is uniform everywhere, except in the side-wall region, where it is affected by the macro-scale velocity profile and its slip length. The second part expresses the resistance against the velocity mode, so it decays exponentially as the flow develops. It satisfies a specific closure problem on a transversal row of the array. From these properties, we assess the validity of the classical closure problem for the volume-averaged flow equations. We show that all its underlying assumptions are partly violated by an exponentially vanishing error during flow development. Furthermore, we show that it modifies the eigenvalues, modes, and onset point of quasi-developed flow, when it is applied to reconstruct the macro-scale flow. The former theoretical aspects are illustrated for high-aspect-ratio channels with high-porosity arrays of equidistant in-line square cylinders, by means of direct numerical simulation and explicit filtering of the flow. In particular, we present extensive solutions of the classical closure problem for Reynolds numbers up to 600, porosities between 0.2 and 0.95, and flow directions between 0 and 45 degrees, though the channel height has been kept equal to the cylinder spacing. These closure solutions are compared with the actual closure force in channels with cylinder arrays of a porosity between 0.75 and 0.94, for Reynolds numbers up to 300.
