Abstract
The small open area available at the slots of underdrains in pressurized granular bed filters for drip irrigation implies: (1) the existence of a region with non-uniform flow, and (2) local values of modified particle Reynolds number >500. These flow conditions may disagree with those accepted as valid for common pressure drop-flow rate correlations proposed for packed beds. Here, we carried out detailed computational fluid dynamics (CFD) simulations of a laboratory filter to analyze the results obtained with five different equations of head losses in porous media: (1) Ergun, (2) Darcy-Forchheimer, (3) Darcy, (4) Kozeny-Carman and (5) power function. Simulations were compared with experimental data at different superficial velocities obtained from previous studies. Results for two silica sand media indicated that all equations predicted total filter pressure drop values within the experimental uncertainty range when superficial velocities <38.3 m h−1. At higher flow rates, Ergun equation approximated the best to the observed results for silica sand media, being the expression recommended. A simple analytical model of the pressure drop along flow streamlines that matched CFD simulation results was developed.
Highlights
World annual freshwater extraction for municipal, industrial, and agricultural needs is approximately 3928 km3 y−1 [1]
We carried out detailed computational fluid dynamics (CFD) simulations of a laboratory filter to analyze the results obtained with five different equations of head losses in porous media: (1) Ergun, (2) Darcy-Forchheimer, (3) Darcy, (4) Kozeny-Carman and (5) power function
Particle Reynolds number Rep at vs = 22.9 m h−1 (=0.2 L s−1) ranged from 4.1 to 5.9, which were above the expected limit (Rep ≤ 1) assumed to ignore inertial effects in porous media equations
Summary
World annual freshwater extraction for municipal, industrial, and agricultural needs is approximately 3928 km y−1 [1]. Some 44% of this water (1716 km y−1) is consumed, mainly for irrigating farmland (38% of freshwater extraction), and the remainder (56%, 2212 km y−1) is primarily released to environment in the form of wastewater, industrial effluents or agricultural drainage water [1]. Reclaimed water for crop irrigation must meet a minimum of quality standards to avoid any health hazard, but the cost of additional treatments and wastewater discharge taxes may compromise its financial viability [3]. Drip irrigation methods are very efficient in water consumption terms [4] and avoid the contact between plant leaves or fruits and wastewater, which is advisable to further reduce contamination risks in some crops [5]. Drip irrigation with reclaimed water might be an appropriate method to cope with forthcoming water scarcity issues
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