Experimental Investigation of Flow Characteristics in Porous Media at Low Reynolds Numbers (Re→0) under Different Constant Hydraulic Heads
Abstract
:1. Introduction
- (1)
- Do varying constant hydraulic heads affect flow regime and hydraulic conductivity?
- (2)
- What are the flow characteristics in low-permeability porous media with very low Re values?
- (3)
- What is the upper boundary of Re for Darcy’s law in porous media with very low Re values?
2. Materials and Methods
2.1. Experimental Setup
2.2. Experimental Media and Scheme
3. Results and Discussion
3.1. Reynolds Numbers of Experimental Media
3.2. Effect of Constant Hydraulic Head on Flow Regime and Hydraulic Conductivity
3.3. Characteristics of the Flow in Porous Media with Weak Permeability at Low Reynolds Numbers (Re→0)
3.4. Upper Limit of the Validity of Darcy’s Law for Porous Media at Low Reynolds Numbers (Re→0)
3.5. Error Analysis on Darcy’s Law and Forchheimer Equation in Non-Darcy Flow
3.6. Limitations, Uncertainties, and Future Work
4. Summary and Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Field Sample Number | Particle Size Analysis (mm) | Coefficient of Uniformity Cu | Effective Grain Size d10 | Average Grain Size d50 | Classification of Soil Naming Standards (GB50021-2001) * | ||||
---|---|---|---|---|---|---|---|---|---|
Sand | Powder | Clay | |||||||
2–0.5 | 0.5–0.25 | 0.25–0.075 | 0.075–0.005 | <0.005 | |||||
% | % | % | % | % | - | mm | mm | ||
1 | 3.3 | 30.7 | 23.6 | 38.2 | 0.5 | 3.10 | 0.062 | 0.124 | Silty sand |
2 | 16.0 | 80.4 | 3.6 | 3.50 | 0.018 | 0.059 | Silt | ||
3 | 18.3 | 49.0 | 16.7 | 15.6 | 0.4 | 5.33 | 0.069 | 0.319 | Medium sand |
4 | 4.3 | 80.8 | 14.9 | 11.67 | 0.003 | 0.025 | Silt |
Group A (170 cm) | Group B (230 cm) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Silty Sand (d0 = 0.124 mm) | Silt-I (d0 = 0.059 mm) | Medium Sand (d0 = 0.319 mm) | Silt-II (d0 = 0.025 mm) | ||||||||
v (cm/s) | J (cm/cm) | Re | v (cm/s) | J (cm/cm) | Re | v (cm/s) | J (cm/cm) | Re | v (cm/s) | J (cm/cm) | Re |
4.45 × 10−5 | 0.10 | 0.000055 | 8.30 × 10−5 | 0.23 | 0.000048 | 1.39 × 10−3 | 0.35 | 0.004378 | 3.86 × 10−5 | 0.57 | 0.0000095 |
1.06 × 10−4 | 0.22 | 0.000130 | 1.63 × 10−4 | 0.44 | 0.000095 | 3.30 × 10−3 | 0.77 | 0.010409 | 8.33 × 10−5 | 1.14 | 0.000021 |
1.43 × 10−4 | 0.30 | 0.000175 | 2.83 × 10−4 | 0.75 | 0.000165 | 4.73 × 10−3 | 1.14 | 0.014933 | 1.09 × 10−4 | 1.62 | 0.000027 |
1.85 × 10−4 | 0.39 | 0.000228 | 4.12 × 10−4 | 1.02 | 0.000241 | 6.10 × 10−3 | 1.52 | 0.019253 | 1.17 × 10−4 | 2.30 | 0.000029 |
2.57 × 10−4 | 0.59 | 0.000316 | 6.20 × 10−4 | 1.51 | 0.000362 | 6.47 × 10−3 | 1.95 | 0.020442 | 1.40 × 10−4 | 2.81 | 0.000035 |
3.12 × 10−4 | 0.84 | 0.000383 | 7.45 × 10−4 | 2.01 | 0.000435 | 7.69 × 10−3 | 2.42 | 0.024287 | 1.49 × 10−4 | 3.27 | 0.000037 |
4.17 × 10−4 | 0.97 | 0.000512 | 8.98 × 10−4 | 2.46 | 0.000525 | 8.83 × 10−3 | 3.06 | 0.027880 | 1.51 × 10−4 | 4.10 | 0.000037 |
4.94 × 10−4 | 1.17 | 0.000607 | 1.13 × 10−3 | 2.83 | 0.000662 | 9.86 × 10−3 | 3.51 | 0.031147 | 1.62 × 10−4 | 4.54 | 0.000040 |
5.64 × 10−4 | 1.38 | 0.000693 | 1.29 × 10−3 | 3.26 | 0.000755 | 1.04 × 10−2 | 3.87 | 0.032839 | 1.53 × 10−4 | 4.88 | 0.000038 |
6.33 × 10−4 | 1.63 | 0.000777 | 1.25 × 10−3 | 3.51 | 0.000729 | 1.03 × 10−2 | 3.85 | 0.032521 | 1.69 × 10−4 | 5.26 | 0.000042 |
8.42 × 10−3 | 4.14 | 0.026586 | 1.59 × 10−4 | 5.58 | 0.000039 |
Experimental Media | Constant Hydraulic Head | Regression Equation | Correlation Coefficient |
---|---|---|---|
Silty sand | Z = 170 cm | v = 0.408 J | R2 = 0.9890 |
Silt-I | v = 0.3802 J | R2 = 0.9901 | |
Medium sand | Z = 230 cm | v = 0.5456 J | R2 = 0.7810 |
Silt-II | v = 0.3594 J | R2 = 0.3130 |
Experimental Media | Constant Hydraulic Head | Regression Equation | Correlation Coefficient |
---|---|---|---|
Medium sand | Z = 230 cm | J = 1.9973 v2 + 1.8024 v | R2 = 0.9072 |
Silt-II | J = 2.3171 v2 − 0.7785 v | R2 = 0.9129 |
Experimental Media | Constant Hydraulic Head | Regression Equation | Correlation Coefficient |
---|---|---|---|
Medium sand | Z = 230 cm | v = 0.409 J | R2 = 0.9961 |
Silt-II | v = 0.6923 J | R2 = 0.9878 |
ID | Method | Experimental Media | Re | Reference |
---|---|---|---|---|
1 | field survey | gravel | 0.9–414 | [4] |
2 | laboratory experiment | loosely consolidated sandstones | 0.4–3 | [18] |
unconsolidated sands and lead shot | 10–1000 | |||
3 | overview | packed particles | 1–100 | [19] |
4 | simulation experiment | cubic arrays of spheres in diameter from 3 mm–10 mm | 30 | [20] |
5 | numerical simulation | disordered porous media | 0.01–0.1 | [21] |
6 | sand columns experiment | quartz sands with different diameters | 22–2752–104 | [22] |
7 | physical model | plexiglass spheres | 0.16–700 | [23] |
8 | flow experiment | porous metal samples | 0.1–0.2 | [48] |
9 | mathematical modeling | unit cell | 3–17 | [49] |
10 | laboratory filtration experiment | silt, silty sand (0.025–0.319 mm) | <0.03 | this study |
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Wang, L.; Li, Y.; Zhao, G.; Chen, N.; Xu, Y. Experimental Investigation of Flow Characteristics in Porous Media at Low Reynolds Numbers (Re→0) under Different Constant Hydraulic Heads. Water 2019, 11, 2317. https://doi.org/10.3390/w11112317
Wang L, Li Y, Zhao G, Chen N, Xu Y. Experimental Investigation of Flow Characteristics in Porous Media at Low Reynolds Numbers (Re→0) under Different Constant Hydraulic Heads. Water. 2019; 11(11):2317. https://doi.org/10.3390/w11112317
Chicago/Turabian StyleWang, Lili, Yunliang Li, Guizhang Zhao, Nanxiang Chen, and Yuanzhi Xu. 2019. "Experimental Investigation of Flow Characteristics in Porous Media at Low Reynolds Numbers (Re→0) under Different Constant Hydraulic Heads" Water 11, no. 11: 2317. https://doi.org/10.3390/w11112317