Two-Phase Flow Characteristics of Stepped Spillways
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VIEW THE REPLYPublication: Journal of Hydraulic Engineering
Volume 129, Issue 9
Abstract
An experimental study on a large model flume with fiber-optical instrumentation indicated that minimum Reynolds and Weber numbers of about and 100, respectively, are required for viscosity and surface tension effects to become negligible compared to gravitational and inertial forces expressed by Froude similitude. Both the location of and the flow depth at the inception point of air entrainment can be expressed as functions of a so-called roughness Froude number containing the unit discharge, step height and chute angle. The depth-averaged air concentration is found to depend only on a normalized vertical distance from the spillway crest and the chute angle for chute slopes ranging from embankment to gravity dam spillways. Air concentration profiles can be expressed by an air bubble diffusion model. The pseudobottom air concentration allows the assessment of the cavitation risk of stepped chutes and is approximated by a regression function. Finally, a new velocity distribution function is presented consisting of a power law up to 80% of the characteristic nondimensional mixture depth, and a constant value above.
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References
BaCaRa. (1991). “Etude de la dissipation d’énergie sur les évacuateurs à marches.” (‘Study of the energy dissipation on stepped spillways’). Rapport d’Essais, Projet National BaCaRa, CEMAGREF-SCP, Aix-en-Provence, France (in French).
Boes, R. M. (2000). “Zweiphasenströmung und Energieumsetzung auf Grosskaskaden.” PhD thesis, VAW, ETH Zurich, Switzerland (in German).
Boes, R. M., and Hager, W. H. (1998). “Fiber-optical experimentation in two-phase cascade flow.” Proc., Int. RCC Dams Seminar, K. Hansen, ed., Denver.
Boes, R. M., and Minor, H.-E. (2000). “Guidelines for the hydraulic design of stepped spillways.” Proc., Int. Workshop on Hydraulics of Stepped Spillways, VAW, ETH Zurich, H.-E. Minor and W. H. Hager, eds., Balkema, Rotterdam, The Netherlands, 163–170.
Cain, P. (1978). “Measurements within self-aerated flow on a large spillway.” PhD thesis, Univ. of Canterbury, Christchurch, New Zealand.
Chamani, M. R. (2000). “Air inception in skimming flow regime over stepped spillways.” Proc., Int. Workshop on Hydraulics of SteppedSpillways, VAW, ETH Zurich, H.-E. Minor and W. H. Hager, eds., Balkema, Rotterdam, The Netherlands, 61–67.
Chamani, M. R., and Rajaratnam, N.(1999). “Characteristics of skimming flow over stepped spillways.” J. Hydraul. Eng., 125(4), 361–368.
Chanson, H.(1989). “Flow downstream of an aerator–Aerator spacing.” J. Hydraul. Res., 27(4), 519–536.
Chanson, H. (1994). Hydraulic design of stepped cascades, channels, weirs and spillways, Pergamon, Oxford, U.K.
Chanson, H. (1996). Air bubble entrainment in free-surface turbulent shear flows, Academic, London.
Chanson, H.(1997). “Air bubble entrainment in open channels: Flow structure and bubble size distributions.” Int. J. Multiphase Flow, 23(1), 193–203.
Chanson, H.(2000). “Discussion of ‘Characteristics of skimming flow over stepped spillways’ by M. R. Chamani and N. Rajaratnam.” J. Hydraul. Eng., 126(11), 862–865.
Cubizolles, G. (1996). “Etude stéréologique de la topographie des écoulements diphasiques à haute pression.” PhD thesis, Ecole Centrale, Lyon, France (in French).
Eccher, L., and Siegenthaler, A.(1982). “Spillway aeration of the San Roque project.” Int. Water Power Dam Constr., 34(9), 37–41.
Ervine, D. A., and Falvey, H. T.(1987). “Behaviour of turbulent water jets in the atmosphere and in plunge pools.” Proc., Inst. Civ. Eng., Part 2, 83(3), 295–314.
Frizell, K. H. (1992). “Hydraulics of stepped spillways for RCC dams and dam rehabilitations.” Proc., 3rd ASCE Specialty Conf. on RCC, San Diego, 423–439.
Frizell, K. H., and Mefford, B. W.(1991). “Designing spillways to prevent cavitation damage.” Concr. Int.: Des. Constr., 13(5), 58–64.
Hager, W. H.(1991). “Uniform aerated chute flow.” J. Hydraul. Eng., 117(4), 528–533.
Hager, W. H. (1992). “Spillways-Shockwaves and air entrainment.” ICOLD Bull. 81, Paris.
Hager, W. H., and Blaser, F.(1998). “Drawdown curve and incipient aeration for chute flow.” Can. J. Civ. Eng., 25(3), 467–473.
Hager, W. H., and Boes, R. M. (2000). “Backwater and drawdown curves in stepped spillway flow.” Proc., Int. Workshop on Hydraulics of Stepped Spillways, VAW, ETH Zurich, H.-E. Minor and W. H. Hager, eds., Balkema, Rotterdam, The Netherlands, 129–136.
Kobus, H. (1984). “Local air entrainment and detrainment.” Proc., Symp. on Scale Effects in Modelling Hydraulic Structures, H. Kobus, ed., Esslingen, Germany, Vol. 4.10, 1–10.
Mateos, I. C., and Elviro, G. V. (1992). “The use of stepped spillways in energy dissipation.” Proc., Int. Symp. on Dams and Extreme Floods, ICOLD, Granada, Spain, 241–250.
Mateos, I. C., and Elviro, G. V. (1997). “Initiation of aeration in stepped spillways.” Proc., 27th IAHR Congress, F. M. Holly and A. Alsaffar, eds., ASCE, San Francisco, 589–594.
Matos, J. (1999). “Emulsionamento de ar e dissipação de energia do escoamento em descarregadores em degraus.” Research Rep., IST, Lisbon, Portugal (in Portuguese).
Matos, J.(2000). “Discussion of ‘Characteristics of skimming flow over stepped spillway’ by M. R. Chamani and N. Rajaratnam.” J. Hydraul. Eng., 126(11), 865–869.
Matos, J., and Frizell, K. H. (1997). “Air concentration measurements in highly turbulent aerated flow.” Proc., 27th IAHR Congress, S. S. Y. Wang and T. Carstens, eds., ASCE, San Francisco, 149–154.
Matos, J., and Frizell, K. H. (2000). “Air concentration and velocity measurements on self-aerated flow down stepped chutes.” Proc., ASCE 2000 Conf. (CD-ROM), ASCE, Reston, Va.
Matos, J., Sánchez, M., Quintela, A., and Dolz, J. (2000). “Air entrainment and safety against cavitation damage in stepped spillways over RCC dams.” Proc., Int. Workshop on Hydraulics of Stepped Spillways, VAW, ETH Zurich, H.-E. Minor and W. H. Hager, eds., Balkema, Rotterdam, The Netherlands, 69–76.
Minor, H.-E. (2000). “Spillways for high velocities.” Proc., Int. Workshop on Hydraulics of Stepped Spillways, VAW, ETH Zurich, H.-E. Minor and W. H. Hager, eds., Balkema, Rotterdam, The Netherlands, 3–10.
Minor, H.-E., and Boes, R. M. (2001). “Hydraulic design of stepped spillways.” Proc., 29th IAHR Congress, Beijing, Vol. I, 754–759.
Ohtsu, I., and Yasuda, Y. (1997). “Characteristics of flow conditions on stepped channels.” Proc., 27th IAHR Congress, F. M. Holly and A. Alsaffar, eds., San Francisco, 583–588.
Pegram, G. G. S., Officer, A. K., and Mottram, S. R.(1999). “Hydraulics of skimming flow on modeled stepped spillways.” J. Hydraul. Eng., 125(5), 500–510.
Peterka, A. J. (1953). “The effect of entrained air on cavitation pitting.” Proc., 5th IAHR Congress, Minneapolis, 507–518.
Pinto, N. L. de S. (1984). “Model evaluation of aerators in shooting flow.” Proc., Symp. on Scale Effects in Modelling Hydraulic Structures, H. Kobus, ed., Esslingen, Germany, Vol. 4.2, 1–6.
Rajaratnam, N.(1990). “Skimming flow in stepped spillways.” J. Hydraul. Eng., 116(4), 587–591.
Ruff, J. F., and Frizell, K. H. (1994). “Air concentration measurements in highly-turbulent flow on a steeply-sloping chute.” Proc., ASCE National Conf. on Hydraulic Engineering, N.Y., Buffalo, G. V. Cotroneo and R. R. Rumer, eds., Vol. 2, 999–1003.
Rutschmann, P. (1988). “Belüftungseinbauten in Schussrinnen.” PhD thesis, VAW, ETH Zurich, Switzerland (in German).
Schläpfer, D. (2000). “Treppenschussrinnen.” MSc thesis, VAW, ETH, Zurich, Switzerland (in German).
Schwalt, M., and Hager, W. H.(1992). “Die Strahlbox.” Schweiz. Ing. Archit. 110(27–28), 547–549 (in German).
Speerli, J. (1999). “Strömungsprozesse in Grundablassstollen.” PhD thesis, VAW, ETH Zurich, Switzerland (in German).
Tozzi, M. J. (1992). “Caracterização/Comportamento de escoamentos em vertedouros com paramento em degraus.” PhD thesis, Univ. of São Paulo, São Paulo, Brazil (in Portuguese).
Tozzi, M. J.(1994). “Residual energy in stepped spillways.” Int. Water Power Dam Constr., 46(5), 32–34.
Vischer, D. L. and Hager, W. H. (1998). Dam hydraulics, Wiley, Chichester, U.K.
Vischer, D., Volkart, P., and Siegenthaler, A. (1982). “Hydraulic modelling of air slots in open chute spillways.” Proc., Hydraulic Modelling of Civil Engineering Structures, Coventry, U.K., 239–252.
Wahrheit-Lensing, A. (1996). “Selbstbelüftung und Energieumwandlung beim Abfluss über treppenförmige Entlastungsanlagen.” PhD thesis, Univ. of Karlsruhe, Karlsruhe, Germany (in German).
Wood, I. R. (1984). “Air entrainment in high speed flows.” Proc., Int. Symp. on Scale Effects in Modelling Hydraulic Structures, H. Kobus, ed., Esslingen, Germany, 4.1, 1–7.
Yasuda, Y., and Ohtsu, I. (1999). “Flow resistance of skimming flows in stepped channels.” Proc., 28th IAHR Congress, H. Bergmann, R. Krainer, and H. Breinhälter, eds. (CD-ROM), Graz, Austria, B14.
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Copyright © 2003 American Society of Civil Engineers.
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Received: Mar 15, 2001
Accepted: Mar 28, 2003
Published online: Aug 15, 2003
Published in print: Sep 2003
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