June 22-27, 2014
An attempt is made in this study to quantify the effect of convergence on macroscopic scale in the case of flow through porous media. Experiments are conducted separately on specially conceived parallel flow permeameter and converging flow permeameter keeping identical inlet and outlet conditions, using eight sizes of coarse granular media and water as the fluid medium. The media is sieved through sieves of different sizes to separate the crushed rock into sizes of 3.25 mm, 4.73 mm, 10.00 mm, 11.64 mm, 13.10 mm, 20.10 mm, 28.90 mm and 39.50 mm and glass spheres of 15.41 mm, 18.03 mm and 28.37 mm. As the effect of convergence is predominant in non- Darcian zones of flow, such as flow near the well, flow through rock fills, filters etc.,, the scope of the present work is restricted to flow regime with Re > 10. (After Kovacs) Forchheimer’s equation ( i = aV + bV2 ) is applied to analyze the experimental data. Equations are derived for Darcy parameter (a) and Non-Darcy parameter (b) of the Forchheimer’s equation for the crushed rock and glass spheres by relating to size of the media (d) in both parallel flow condition and converging flow condition. From the results it is inferred that for a given rate of flow through a known size of aquifer having predetermined grain size, the resistance to flow is higher in the parallel flow compared to similar media conditions in converging flow configurations. A comparison is then made between the coefficients of the equation, computed for parallel and converging configurations of flow. The difference in these values is expressed in terms of a factor called ‘Integrated Convergence factor (Cfi)’. It is concluded that the convergence of stream lines of seepage flow has a clear and profound influence on the relationship between resistance and regime. In order to make the findings reliable and suitable to field applications, the derived expressions are subjected to corrections for porosity effect, wall effect and tortuosity effect. Expressions for integrated convergence factor for crushed rocks and glass spheres are Cfi = 1.095 d - 0.079 and Cfi = 0.802 d - 0.25 respectively.
Srinivas Pasupuleti, Pradeep Kumar, and K. Jayachandra, "Quantification of effect of convergence in porous media flow" in "5th International Conference on Porous Media and Their Applications in Science, Engineering and Industry", Prof. Kambiz Vafai, University of California, Riverside; Prof. Adrian Bejan, Duke University; Prof. Akira Nakayama, Shizuoka University; Prof. Oronzio Manca, Seconda Università degli Studi Napoli Eds, ECI Symposium Series, (2014). http://dc.engconfintl.org/porous_media_V/20