Darcy and post-Darcy flows within different sands

摘要

The subject of non-Darcy flow spans many engineering disciplines. The Authors have presented the results of interesting research on flow through a fine porous media in which high Reynolds numbers were induced. A number of issues can be raised: (ⅰ) In their Abstract the Authors make the rather definitive assertion that non-Darcy flow begins at a Reynolds number of 4.3, and present Fig. 7 to support this claim. In fact, in the section before "Conclusion" on p. 524, the Authors show that the value of 4.3 arises from the arbitrary selection of 0.95 for the ratio of viscosity-induced friction to total friction. They also show that a ratio of 0.99 yields Re = 0.93, instead of Re = 4.3. This is consistent with the fact that it has long been recognized that there is no single value of Re at which it can be said that Darcy's Law breaks down. In this respect the nature of the transition from linear to post-linear flow shown in Fig. 7 is no different than many other such plots that have appeared in the literature, and supports the communis opinio that the transition is gradual. Examples of similar plots can be found in the following references: Rose (1945a,b), Ergun (1952), Arbhabhirama and Dinoy (1973)—a family of curves, McCorquodale et al. (1978)—large unified data-set, and Fand and Thinakaran (1990)—expanding the work of Reichelt (to name just a few). Although these various references often show more scatter about their fitted curves than does the author's Fig. 7, they all show a gradual transition from a linear to a non-linear relationship, regardless of how the friction factor and Reynolds number terms are defined. In fact, even though flow through pipes does go through a well-known and sudden transition (from laminar flow to partially developed turbulent flow), the commonly stated figure of Re = 2000 is also known to be an approximate value. The assertion in the abstract that non-Darcy flow through porous media begins at a Reynolds number of 4.3, made again in the section entitled "Conclusion", is therefore not justified.