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Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

机译：天然和可变梯度粒料填充床中的非线性流动行为

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摘要

Under certain flow conditions, fluid flow through porous media starts to deviate from the linear relationship between flow rate and hydraulic gradient. At such flow conditions, Darcy's law for laminar flow can no longer be assumed and nonlinear relationships are required to predict flow in the Forchheimer regime. To date, most of the nonlinear flow behavior data is obtained from flow experiments on packed beds of uniformly graded granular materials (C-u = d(60)/d(10) < 2) with various average grain sizes, ranging from sands to cobbles. However, natural deposits of sand and gravel in the subsurface could have a wide variety of grain size distributions. Therefore, in the present study we investigated the impact of variable grain size distributions on the extent of nonlinear flow behavior through 18 different packed beds of natural sand and gravel deposits, as well as composite filter sand and gravel mixtures within the investigated range of uniformity (2.0 < C-u < 17.35) and porosity values (0.23 < n < 0.36). Increased flow resistance is observed for the sand and gravel with high C-u values and low porosity values. The present study shows that for granular material with wider grain size distributions (C-u > 2), the d(10) instead of the average grain size (d(50)) as characteristic pore length should be used. Ergun constants A and B with values of 63.1 and 1.72, respectively, resulted in a reasonable prediction of the Forchheimer coefficients for the investigated granular materials.
机译：在某些流动条件下，流经多孔介质的流体开始偏离流量与水力梯度之间的线性关系。在这种流动条件下，不能再假定达西定律用于层流，并且需要非线性关系来预测福希海默状态下的流动。迄今为止，大多数非线性流动行为数据是从均布不同粒度（从沙子到鹅卵石）的均等梯度颗粒材料（C-u = d（60）/ d（10）<2）的填充床上的流动实验获得的。但是，地下的沙子和砾石的自然沉积物可能具有各种各样的粒度分布。因此，在本研究中，我们研究了可变粒度分布对通过18种不同填充床的天然砂和砾石沉积物以及复合滤砂和砾石混合物在研究的均匀性范围内非线性流动行为程度的影响（ 2.0 2）的颗粒材料，应使用d（10）代替平均粒度（d（50））作为特征孔径。 Ergun常数A和B的值分别为63.1和1.72，可以合理预测所研究颗粒材料的Forchheimer系数。

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