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Experimental Study Of The Energy Dissipation In The Stepped Channels: Comparison With The Empirical Model
Congress:
2015
Author(s):
Mostefa Gafsi (Laghouat, Algeria), Kettab Ahmed, Djehiche Abdelkader, Benmamar Saadia, BENNAi‡AR Naoual
Ecole Nationale Polytechnique Alger (ENP),
^{1}
, Research Laboratory of Civil Engineering: RLCE, ResearchTeam
^{2}
, Centre dÂ’Ă‰tude et de recherches sur le Droit des ActivitĂ©s Maritimes et de lÂ’Environnement
^{3}
Keyword(s):
Subtheme 10: Management of water resources,
Abstract
Abstract We made an experimental approach in the laboratory of civil engineering at the University of Laghouat (Algeria), in three (03) models: model A (4cm x 7.5cm 4cmx) and model B (8cm x 7.5cm 8cmx), and the third model C size (12cm x 12 cm x 7.5 cm) developed "Plexiglas." In what follows, we set the rate of flow and vary the slope of the channel. Three slopes were studied in this experiment: a = 15, 30 Â° and a = 45 Â° for the model A, and a = 20 Â°, 30 Â° and 45 Â° for the models B and C. The simulated flows range from 0.072 l/s to 2.569 l/s. As result, the effect of the rate flow allowed us to see that: For low flows, the energy dissipation (nappe flow) is maximum is around 95% for the three models. For a large flow, the energy dissipation (nappe flow) is minimal and in the order of 82%, 80% and 77% for models A, B and C respectively, The energy dissipation relative maximum and minimum flows in skimming flow are of the order of 73% and 70% respectively. 1. Introduction: Several research models have distinguished themselves in the field of flow in channels stairs, among the most recent works are Benmamar (2006), Kerbache and Benmamar (2008a, 2008b, 2010, 2012), Gafsi and Benmamar (1999, 2012, 2013a, 2013b), and the most popular are those of Chanson (1994 , 1996, 1997, 2000) and Chanson et al (2000, 2002). We made an experimental approach in the laboratory of civil engineering at the University of Laghouat (Algeria), in three reduced stepped channels models: model A (4cm x 7.5cm 4cmx) and model B (8cm x 7.5cm 8cmx), and the third model C size (12cm x 12 cm x 7.5 cm) developed "Plexiglas." In what follows, we set the rate of flow and vary the slope of the channel to show the effect of the slope on the energy dissipation. Three slopes were studied in this experiment: = 15, 30 Â° and = 45 Â° for the the model A, and = 20 Â°, 30 Â° and 45 Â° for the the models B and C. The simulated flows range from 0.072 l/s to 2.569 l/s. As result, the effect of the rate flow allowed us to see that: For low flows, the energy dissipation (nappe flow) is maximum is around 95% for the three models. For a large flow, the energy dissipation (nappe flow) is minimal and in the order of 82%, 80% and 77% for models A, B and C respectively; The energy dissipation relative maximum and minimum flows in skimming flow are of the order of 73% and 70% respectively. 2. Physical model The experimental device consists of: A flume made of Plexiglas length 5m, width 0.075 m, and height of the walls is 0.175 m (see photo 1); A metal catchment connected to the glass by pipe carrying water pumped by a pump channel. This pipe has a valve for controlling the flow (see photo 1); A channel model stairs made "Plexiglas." This pattern is connected to the glass channel seals, and mastic sealing installation; A sump plastic for recycling the water to the supply conduit by PVC (gravity flow) basin, our system thus making a closed circuit. Experimental studies were conducted on three (03) models stairs developed "Plexiglas." The geometrical characteristics of the three models are shown in Table 1 The simulated flows range from 0.072 l/s to 2.569 l/s. 3. Analysis of results Comment In Figures 2 at 5, the experimental and analytical curves show the same profiles, that is, decreasing trends, of low (low value of the Froude number) at high flow rate (high value of the Froude number). Energy dissipation in model A is greater than B and C models, and values as e.g. for α = 30 Â° and Fr = 0.2: ∆H/H = 93.48 % (model A), ∆H/H = 86.79 % (mode B), ∆H/H = 81.41 % (model C); For a given (Figures 2, 3 and 4) rate flow, the energy dissipation increases to a relative increase in the slope. This is explained by the increase in slope of the first channel which influences the increase in the height of the weir (Hchan= Lsinα), and therefore the increase of the kinetic energy for example model for C , for Fr = 0.1: ∆H/H=73.31 % for α=15Â°, ∆H/H=84.96 % for α=30Â° and ∆H/H = 89.66 % for α=45Â°; For a given (Figures 2, 3 and 4) slope, the energy dissipation decreases with increased flow. This is explained by the effect of the increase of macroroughness with increasing speed. Therefore the energy dissipation is reduced. For example for r model B (α = 45Â°) : Q = 0.167 l/s: ∆H/H = 93.726 %; Q = 0.586 l/s: ∆H/H = 90.630 %; Q = 0.820 l/s: ∆H/H = 89.544 %; Q = 1.995 l/s: ∆H/H = 85.224 %: 4. General conclusion For steep slopes and lowflow steps, the flows in stepped channels, cause significant dissipation of energy in the nappe flow and skimming flow. The flows with average to high flow rates, favor rather skimming flows on the steps of small dimensions than those large, which verifies the assumption made by H.CHANSON 1995. The influence of the slope of large energy dissipation is more visible on the nappe, those on skimming flows. The larger values of energy dissipation are obtained on the nappe flows, those on the skimming flows. This is explained by the effect of the macroroughness which is less on the small steps. References 1. Benmamar, S. Â« Etude des Ă©coulements dans les conduits Ă motifs pĂ©riodiques Â– Application aux Ă©vacuateurs de crues Â». ThĂ¨se de doctorat, Ecole Nationale Polytechnique dÂ’Alger, AlgĂ©rie, 197 pages, 2006. 2. Chanson, H. Â‘Â’Comparison of Energy Dissipation between Nappe and Skimming Flow Regimes on Stepped Chutes.Â’Â’ Jour. of Hyd. Res., IAHR, Vol. 32, NÂ° 2, pp 213218. Errata:Vol. 33, No. 1, p. 13. Discussion: Vol. 33, No. 1, pp. 114143, 1994. 3 .Chanson, H.. Â‘Â’ Hydraulic Design of Stepped cascades, Channels, Weirs and Spillways.Â’Â’ Pergamon, Oxford, Uk, Jan., 292 pages (ISBN 0080419186), 1995. 4. Chanson, H. Â‘Â’ Prediction of the Transition Nappe/ Skimming Flow on a Stepped Channel.Â’Â’ Jour. of Hyd. Res., MIAHR, Vol. 34, NÂ°3, pp. 421429, 1996. 5. Chanson, H. Â«Forum article. Hydraulics of Stepped Spillways: Current StatusÂ». Journal of Engineering, ASCE, Volume 126, No. 9, pp. 636637, 2000. 6. Chanson, H. Â« The hydraulics of stepped chutes and spillways Â». Balkema, Lisse, the Netherlands, 2001. 7. Chanson, H. & Toombes, L. Â« Air Water Flows down Stepped chutes: Turbulence and Flow Structures ObservationÂ». International of Multiphase Flow, volume 27, NÂ°11, pp. 17371761, 2002. 8. Chanson, H., "The Hydraulics of Stepped Chutes and Spillways", Balkema, Lisse, 2010. 9. Chen, C.L. Â‘Â’Unified Theory on Power Laws for Flow Resistance.Â’Â’ Jour. of Hyd. Eng., ASCE, Vol. 117, N 3, pp. 371389, 1990. 10. Ditchey, E.J., and Campbell, D.B. "Roller compacted concrete and stepped spillways." Intl Workshop on Hydraulics of Stepped Spillways, ZĂĽrich, Switzerland, Balkema Publ., pp. 171178, 2000. 12. Essery, I.T.S., and Horner, M.W. Â« The Hydraulic Design of stepped Spillways Â». CIRIA Report N. 33, 2nd edition, Jan., London, UK, 1978. 13. Hanson, K.D., and Reinhardt, K.D.. "Rollercompacted concrete dams" McGrawHill, New York, USA, 298 pages, 1991. 14. Gafsi Mostefa, Benmamar Saadia. Etude ExpĂ©rimentale des Ecoulements dans les Canaux Ă Motifs PĂ©riodiques. ThĂ¨se de Magister, Ecole Nationale Polytechnique dÂ’Alger (ENP), soutenu le 20 Novembre, 1999 Ă lÂ’ENP, 1999. 15. Gafsi Mostefa, Benmamar Saadia, Djehiche Abdelkader, and Kerbache Khadidja . Influence of the Flow Rates and the Channel Slope in the Energy Dissipation on Flows in the Stepped Channel. Wulfenia Journal (ISSN: 1561882X), Vol 19, No. 11;Nov 2012, pp 385393, 2012. 16.Gafsi, M., Benmamar, S.. 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Kherbache K. & Benmamar S. Â« Simulation numĂ©rique de lÂ’Ă©coulement graduellement variĂ© aĂ©rĂ© sur les coursiers dÂ’Ă©vacuateur de crues en marches dÂ’escaliers Â». 5Ă¨me confĂ©rence internationale sur : les Ressources en Eau dans le Bassin MĂ©diterranĂ©en. Lille, France, 2010.. 22. Kherbache K. & Benmamar S. Â« ModĂ©lisation de lÂ’Ă©coulement turbulent dans un canal a ciel ouvert Â». Communication acceptĂ©e pour publication Ă la 6 Ă¨me confĂ©rence internationale sur : les Ressources en Eau dans le Bassin MĂ©diterranĂ©en ; Octobre ; 1012 ; Tunis, Tunisie, Septembre 2012, 2012. 23. Moore W.L. Â« Energy Loss at the Base of a Free Overfall Â».. Transactions, ASCE, Vol. 108, 13431360. Discussion : Vol.108, 13611392, 1943. 23. Peyras. L., Royet. P., and Degoutte. G. Â« Ecoulement et Dissipation sur les DĂ©versoirs en Gradins de Gabions Â». ('Flows and Dissipation of Energy on Gabion Weirs.') Journal La Houille Blanche, No, I, pp. 37.47, 1991. 24. Rajaratnam, N. Â« Skimming flow in stepped spillways Â». Journal of Hydraulic Engineering, ASCE, volume 116, NÂ°4, pp. 587591. Discussion : volume 118, NÂ°1, pp. 111114, 1990. 25. Rand, W. Â« Flow geometry at straight drop spillwaysÂ». Proceeding ASCE, volume 81, Paper 791, pp. 113, 1955. 26. Sarfaraz, M., Attari, J., Roshan, R. and Khorasanizadeh, A. "Comparison of Empirical Relationships for Energy Dissipation with Physical Model Data of Stepped Spillways in Iran", 9th IranÂ’s Hydraulic Conference, Tehran, (in Persian), 2010. 27. Sarfaraz, M. "Hydraulic Design and Modelling of Stepped Spillways Located on Body of RCC Dams, Case Study: Javeh Stepped Spillway", A thesis submitted in partial fulfillment of the requirement for the degree of Bachelor of Science, Power and Water University of Technology (Shahid Abbaspoor), Tehran, (in Persian), 2010. 28. SimĂµes, A.L.A.; Schulz, H.E. & Porto, R.M. "Transition length between water and airwater flows on stepped chutes. 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