An Investigation of Parallel Post-Laminar Flow through Coarse Granular Porous Media with the Wilkins Equation
Abstract
:1. Introduction
2. Experiments and Methodology
3. Correction Factors
3.1. Wall Correction
3.2. Tortuosity Correction
3.3. Porosity Correction
4. Data Analysis
5. The Behavior of the Wilkins Coefficients with Independently Varying Media Size and Porosity
6. Numerical Modelling
6.1. Turbulence Modelling
6.2. Model Description
6.3. Meshing
6.4. Boundary Conditions
7. Results and Discussion
7.1. Comparison between the Experimental and Simulation Data and Statistical Validation of the Simulation
7.2. Validation of the Simulated Data Using the Z-Test
8. Conclusions
- The Wilkins equation can be satisfactorily used to represent post-laminar flow through porous media.
- The Wilkins coefficients are found to have a non-deviating nature with varying hydraulic radius. The obtained results from the present study are similar to the results reported in the literature.
- When subjected to variation in media size, the coefficients of the Wilkins equation are constant, given that the porosity is constant. However, variations in the porosity result in small variations of the coefficient W.
- The flow condition inside the experimental set up is simulated with a CFD model in the ANSYS FLUENT software. Trends similar to the experimental ones are obtained from the simulation results. The percentage deviation between the simulation and experimental results are within the acceptable range.
- For further validation, the experimental results are statistically compared with the simulation results using the standard Z-test. The values of Z calculated are found to be within the acceptable region for all the experimental results.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Passing and Retaining Sieve Sizes (cm) | Volume (cm3) | Volume Diameter (cm) | Avg. Surface Area (cm2) | Specific Surface (/cm) |
---|---|---|---|---|
2.50–3.15 | 14.46 | 2.98 | 44.68 | 2.88 |
3.15–3.75 | 23.10 | 3.48 | 58.44 | 2.53 |
3.75–5.00 | 38.55 | 4.16 | 82.11 | 2.13 |
Media Size (mm) | Porosity (%) | W (m-s) | β | γ |
---|---|---|---|---|
29.80 | 40.59 | 6.15 | 0.39 | 0.54 |
43.34 | ||||
45.69 | ||||
34.78 | 41.72 | 5.52 | 0.38 | 0.56 |
44.70 | ||||
46.34 | ||||
41.59 | 41.03 | 5.55 | 0.38 | 0.55 |
43.62 | ||||
46.15 |
Proposed by | Media | Volume Diameter (mm) | Porosity (%) | W (m/s) | β | γ |
---|---|---|---|---|---|---|
Wilkins (1956) [21] | Crushed stone | 51.00 | 40.00 | 5.24 | 0.50 | 0.54 |
Garga et al. (1990) [22] | Crushed stone | 24.60 | 47.00 | 5.39 | 0.50 | 0.53 |
Pradeep Kumar (1994) [27] | Crushed stone | 13.10 | 47.00 | 4.94 | 0.51 | 0.52 |
20.10 | 45.88 | |||||
28.90 | 48.73 | |||||
39.50 | 48.26 |
Parameter | Hydraulic Gradient | Velocity (m/s) at 0.285 m | Velocity (m/s) at 1.11 m |
---|---|---|---|
h1 | 0.005216 | 0.005216 | 0.005216 |
h2 | 0.006937 | 0.006937 | 0.006937 |
h3 | 0.009226 | 0.009226 | 0.009226 |
r21 | 1.33 | 1.33 | 1.33 |
r32 | 1.33 | 1.33 | 1.33 |
0.01992 | 0.01083 | 0.01156 | |
0.01984 | 0.01080 | 0.01159 | |
0.01973 | 0.01077 | 0.01096 | |
P | 1.32772 | 1.30788 | 10.5924 |
0.02010 | 0.01088 | 0.01156 | |
0.02010 | 0.01088 | 0.01163 | |
0.40% | 0.20% | 0.27% | |
0.59% | 0.29% | 5.45% | |
0.86% | 0.45% | 0.01% | |
1.26% | 0.65% | 0.28% | |
1.09% | 0.56% | 0.02% |
Media Size (mm) | Porosity (%) | Range of Velocity (m/s) | Z Value | |||||
---|---|---|---|---|---|---|---|---|
29.80 | 40.59 | 0.01–0.757 | 0.643 | 0.599 | 0.540 | 0.359 | 250 | −0.940 |
43.34 | 0.01–0.757 | 0.586 | 0.606 | 0.497 | 0.517 | 250 | 0.429 | |
45.69 | 0.01–0.757 | 0.554 | 0.535 | 0.464 | 0.446 | 250 | −0.459 | |
34.78 | 41.72 | 0.01–0.757 | 0.565 | 0.554 | 0.463 | 0.452 | 250 | −0.276 |
44.70 | 0.01–0.757 | 0.527 | 0.510 | 0.435 | 0.420 | 250 | −0.425 | |
46.34 | 0.01–0.757 | 0.496 | 0.471 | 0.407 | 0.383 | 250 | −0.694 | |
41.59 | 41.03 | 0.01–0.757 | 0.511 | 0.489 | 0.422 | 0.406 | 250 | −0.574 |
43.62 | 0.01–0.757 | 0.464 | 0.440 | 0.391 | 0.368 | 250 | −0.684 | |
46.15 | 0.01–0.757 | 0.439 | 0.418 | 0.369 | 0.349 | 250 | −0.661 |
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Banerjee, A.; Pasupuleti, S.; Singh, M.K.; Kumar, G.N.P. An Investigation of Parallel Post-Laminar Flow through Coarse Granular Porous Media with the Wilkins Equation. Energies 2018, 11, 320. https://doi.org/10.3390/en11020320
Banerjee A, Pasupuleti S, Singh MK, Kumar GNP. An Investigation of Parallel Post-Laminar Flow through Coarse Granular Porous Media with the Wilkins Equation. Energies. 2018; 11(2):320. https://doi.org/10.3390/en11020320
Chicago/Turabian StyleBanerjee, Ashes, Srinivas Pasupuleti, Mritunjay Kumar Singh, and G.N. Pradeep Kumar. 2018. "An Investigation of Parallel Post-Laminar Flow through Coarse Granular Porous Media with the Wilkins Equation" Energies 11, no. 2: 320. https://doi.org/10.3390/en11020320