[en] Shallow reservoirs are often used as sediment traps or storage basins, in which sedimentation depends on the flow pattern: Short rectangular reservoirs reveal a straight jet from inlet to outlet with on both sides identical recirculation zones. In longer reservoirs, the main jet reattaches to the side of the reservoir leading to a small and a large recirculation zone.
Previous studies found an empirical geometric relation describing the switch between these two flow patterns. In this study, we demonstrate, with a simple analytical model, that this switch coincides with a maximization of energy dissipation in the shear layer between the main jet and recirculation zones: Short reservoirs dissipate more energy when the flow pattern is symmetric, while longer reservoirs dissipate more energy with an asymmetric pattern.
This approach enables to predict the flow patterns without detailed knowledge of small scale processes, potentially useful in the early phase of reservoir design.
Research center :
UEE - Urban and Environmental Engineering - ULiège
Disciplines :
Civil engineering
Author, co-author :
Westhoff, Martijn ; Vrije Universiteit Amsterdam, Amsterdam, The Netherlands > Department of Earth Science, Earth and Climate cluster
Erpicum, Sébastien ; Université de Liège > Scientifiques attachés au Doyen (Sc.appliquées)
Archambeau, Pierre ; Université de Liège > Département ArGEnCo > HECE (Hydraulics in Environnemental and Civil Engineering)
Pirotton, Michel ; Université de Liège > Département ArGEnCo > HECE (Hydraulics in Environnemental and Civil Engineering)
Dewals, Benjamin ; Université de Liège > Département ArGEnCo > Hydraulics in Environmental and Civil Engineering
Language :
English
Title :
Maximum energy dissipation to explain velocity fields in shallow reservoirs
Publication date :
2018
Journal title :
Journal of Hydraulic Research
ISSN :
0022-1686
eISSN :
1814-2079
Publisher :
International Association for Hydraulic Research, Delft, Netherlands
Camnasio, E., Erpicum, S., Archambeau, P., Pirotton, M., & Dewals, B., (2014). Prediction of mean and turbulent kinetic energy in rectangular shallow reservoirs. Engineering Applications of Computational Fluid Mechanics, 8(4), 586–597. doi: 10.1080/19942060.2014.11083309
Camnasio, E., Erpicum, S., Orsi, E., Pirotton, M., Schleiss, A. J., & Dewals, B., (2013). Coupling between flow and sediment deposition in rectangular shallow reservoirs. Journal of Hydraulic Research, 51(5), 535–547. doi: 10.1080/00221686.2013.805311
Camnasio, E., Orsi, E., & Schleiss, A. J., (2011). Experimental study of velocity fields in rectangular shallow reservoirs. Journal of Hydraulic Research, 49(3), 352–358. doi: 10.1080/00221686.2011.574387
Carnot, S., (1824). Réflexions sur la puissance motrice du feu et sur les machines propres a développer cette puissance. Paris: Bachelier.
Choufi, L., Kettab, A., & Schleiss, A. J., (2014). Bed roughness effect on flow field in rectangular shallow reservoir [effet de la rugosité du fond d'un réservoir rectangulaire à faible profondeur sur le champ d'écoulement]. La Houille Blanche, 5, 83–92. doi: 10.1051/lhb/2014054
Dewals, B., Erpicum, S., Archambeau, P., & Pirotton, M., (2012). Experimental study of velocity fields in rectangular shallow reservoirs. Journal of Hydraulic Research, 50(4), 435–436. doi: 10.1080/00221686.2012.702856
Dewals, B. J., Kantoush, S. A., Erpicum, S., Pirotton, M., & Schleiss, A. J., (2008). Experimental and numerical analysis of flow instabilities in rectangular shallow basins. Environmental Fluid Mechanics, 8(1), 31–54. doi: 10.1007/s10652-008-9053-z
Dominic, J. A., Aris, A. Z., Sulaiman, W. N. A., & Tahir, W. Z. W. M., (2016). Discriminant analysis for the prediction of sand mass distribution in an urban stormwater holding pond using simulated depth average flow velocity data. Environmental Monitoring and Assessment, 188(3), 1–15. doi: 10.1007/s10661-016-5192-8
Dufresne, M., Dewals, B. J., Erpicum, S., Archambeau, P., & Pirotton, M., (2010a). Classification of flow patterns in rectangular shallow reservoirs. Journal of Hydraulic Research, 48(2), 197–204. doi: 10.1080/00221681003704236
Dufresne, M., Dewals, B. J., Erpicum, S., Archambeau, P., & Pirotton, M., (2010b). Experimental investigation of flow pattern and sediment deposition in rectangular shallow reservoirs. International Journal of Sediment Research, 25(3), 258–270. doi: 10.1016/S1001-6279(10)60043-1
Dufresne, M., Dewals, B. J., Erpicum, S., Archambeau, P., & Pirotton, M., (2011). Numerical investigation of flow patterns in rectangular shallow reservoirs. Engineering Applications of Computational Fluid Mechanics, 5(2), 247–258. doi: 10.1080/19942060.2011.11015368
Hergarten, S., Winkler, G., & Birk, S., (2014). Transferring the concept of minimum energy dissipation from river networks to subsurface flow patterns. Hydrology and Earth System Sciences, 18(10), 4277–4288. doi: 10.5194/hess-18-4277-2014
Howard, A. D., (1990). Theoretical model of optimal drainage networks. Water Resources Research, 26(9), 2107–2117. doi: 10.1029/WR026i009p02107
Kantoush, S. A., (2008). Experimental study on the influence of the geometry of shallow reservoirs on flow patterns and sedimentation by suspended sediments (PhD thesis 4048). EPFL Lausanne, Switzerland.
Kantoush, S. A., Bollaert, E., & Schleiss, A. J., (2008). Experimental and numerical modelling of sedimentation in a rectangular shallow basin. International Journal of Sediment Research, 23(3), 212–232. doi: 10.1016/S1001-6279(08)60020-7
Kleidon, A., (2016). Thermodynamic foundations of the earth system. Cambridge: Cambridge University Press.
Kleidon, A., & Renner, M., (2013). Thermodynamic limits of hydrologic cycling within the earth system: Concepts, estimates and implications. Hydrology and Earth System Sciences, 17(7), 2873–2892. doi: 10.5194/hess-17-2873-2013
Kleidon, A., Zehe, E., Ehret, U., & Scherer, U., (2013). Thermodynamics, maximum power, and the dynamics of preferential river flow structures at the continental scale. Hydrology and Earth System Sciences, 17(1), 225–251. doi: 10.5194/hess-17-225-2013
Langbein, W., & Leopold, L., (1966). River meanders–theory of minimum variance (Tech. Rep. No. 422-H). Washington, DC: USGS.
Lorenz, R. D., Lunine, J. I., Withers, P. G., & McKay, C. P., (2001). Titan, Mars and Earth: Entropy production by latitudinal heat transport. Geophysical Research Letters, 28, 415–418. doi: 10.1029/2000GL012336
Michalec, B., (2014). The use of modified annandale's method in the estimation of the sediment distribution in small reservoirs: A case study. Water (Switzerland), 6(10), 2993–3011.
Paltridge, G. W., (1979). Climate and thermodynamic systems of maximum dissipation. Nature, 279, 630–631. doi: 10.1038/279630a0
Peltier, Y., Erpicum, S., Archambeau, P., Pirotton, M., & Dewals, B., (2014). Experimental investigation of meandering jets in shallow reservoirs. Environmental Fluid Mechanics, 14(3), 699–710. doi: 10.1007/s10652-014-9339-2
Peng, Y., Zhou, J. G., & Burrows, R., (2011). Modeling free-surface flow in rectangular shallow basins by using lattice boltzmann method. Journal of Hydraulic Engineering, 137(12), 1680–1685. doi: 10.1061/(ASCE)HY.1943-7900.0000470
Potter, M. C., Wiggert, D. C., Hondzo, M., Shih, T. I. P., & Chaudhry, K. K., (2010). Mechanics of fluids (3rd ed.). Stamford, CT: Cengage Learning.
Rinaldo, A., Rodríguez-Iturbe, I., Rigon, R., Bras, R. L., Ijjasz-Vasquez, E., & Marani, A., (1992). Minimum energy and fractal structures of drainage networks. Water Resources Research, 28(9), 2183–2195. doi: 10.1029/92WR00801
Rodriguez-Iturbe, I., Rinaldo, A., Rigon, R., Bras, R. L., Ijjasz-Vasquez, E., & Marani, A., (1992). Fractal structures as least energy patterns: The case of river networks. Geophysical Research Letters, 19(9), 889–892. doi: 10.1029/92GL00938
Rodríguez-Iturbe, I., Rinaldo, A., Rigon, R., Bras, R. L., Marani, A., & Ijjász-Väsquez, E., (1992). Energy dissipation, runoff production, and the three-dimensional structure of river basins. Water Resources Research, 28(4), 1095–1103. doi: 10.1029/91WR03034
Secher, M., Hervouet, J. M., Tassi, P., Valette, E., & Villaret, C., (2014). Numerical modelling of two-dimensional flow patterns in shallow rectangular basins. In P. Gourbesville, J. Cunge, & G. Caignaert (Eds.), Advances in hydroinformatics: Simhydro 2012–new frontiers of simulation (pp. 499–510). Singapore: Springer Singapore.
Tarpagkou, R., & Pantokratoras, A., (2013). Cfd methodology for sedimentation tanks: The effect of secondary phase on fluid phase using dpm coupled calculations. Applied Mathematical Modelling, 37(5), 3478–3494. doi: 10.1016/j.apm.2012.08.011
Tsavdaris, A., Mitchell, S., & Williams, J. B., (2015). Computational fluid dynamics modelling of different detention pond configurations in the interest of sustainable flow regimes and gravity sedimentation potential. Water and Environment Journal, 29(1), 129–139. doi: 10.1111/wej.12086
Zehe, E., Ehret, U., Blume, T., Kleidon, A., Scherer, U., & Westhoff, M., (2013). A thermodynamic approach to link self-organization, preferential flow and rainfall–runoff behaviour. Hydrology and Earth System Sciences, 17(11), 4297–4322. doi: 10.5194/hess-17-4297-2013
Zhou, J. G., Liu, H., Shafiai, S., Peng, Y., & Burrows, R., (2010). Lattice boltzmann method for open-channel flows. Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics, 163(4), 243–249.
