Mean and Turbulent Bubble Velocities in Free Hydraulic Jumps for Small to Intermediate Froude Numbers
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 11
Abstract
Bubble characteristics in free hydraulic jumps for inflow Froude numbers ranging from 2.0 to 6.7 were measured using a single-tip optical probe, with a focus on mean and turbulent bubble velocities. It was found that the mean bubble velocity , to a large extent, is able to reflect the water-phase flow structure in a jump. In the boundary layer of the channel bed, follows the th power law in the vertical direction, and it follows a Gaussian distribution beyond that up to the water surface. Dimensionless maximum bubble velocity was found to be smaller than that for the classical wall jet up to a characteristic distance in the longitudinal direction; beyond that, however, they agree well with each other. Turbulence intensity of bubble velocity was found to first increase and then decrease with the vertical distance from the bed. The maximum value of turbulence intensity is 33% of the inflow velocity, which is comparable to that of the water-phase. Exponential relations are proposed to describe the variation of the maximum bubble velocity and maximum turbulence intensity of bubbles, in the longitudinal direction.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors are thankful to Dr. M. Loewen for his help with the optical probe.
References
Cartellier, A. (1992). “Simultaneous void fraction measurement, bubble velocity, and size estimate using a single optical probe in gas–liquid two-phase flows.” Rev. Sci. Instrum., 63(11), 5442–5453.
Cartellier, A. (2001). “Optical probes for multiphase flow characterization: Some recent improvements.” Chem. Eng. Tech., 24(5), 535–538.
Cartellier, A., and Barrau, E. (1998a). “Monofiber optical probes for gas detection and gas velocity measurements: Conical probes.” Int. J. Multiphase Flow, 24(8), 1265–1294.
Cartellier, A., and Barrau, E. (1998b). “Monofiber optical probes for gas detection and gas velocity measurements: Optimised sensing tips.” Int. J. Multiphase Flow, 24(8), 1295–1315.
Chachereau, Y., and Chanson, H. (2011). “Bubbly flow measurements in hydraulic jumps with small inflow Froude numbers.” Int. J. Multiphase Flow, 37(6), 555–564.
Chanson, H. (2002). “Air-water flow measurements with intrusive, phase-detection probes: Can we improve their interpretation?” J. Hydraul. Eng., 252–255.
Chanson, H. (2009a). “Current knowledge in hydraulic jumps and related phenomena. A survey of experimental results.” Eur. J. Mech. B Fluids, 28(2), 191–210.
Chanson, H. (2009b). “Turbulent air-water flows in hydraulic structures: Dynamic similarity and scale effects.” Environ. Fluid Mech., 9(2), 125–142.
Chanson, H. (2010). “Convective transport of air bubbles in strong hydraulic jumps.” Int. J. Multiphase Flow, 36(10), 798–814.
Chanson, H. (2011). “Bubbly two-phase flow in hydraulic jumps at large Froude numbers.” J. Hydraul. Eng., 451–460.
Chanson, H., and Chachereau, Y. (2013). “Scale effects affecting two-phase flow properties in hydraulic jump with small inflow Froude number.” Exp. Therm. Fluid Sci., 45, 234–242.
El-Kamash, M. K., Loewen, M. R., and Rajaratnam, N. (2005a). “An experimental investigation of jet flow on a stepped chute.” J. Hydraul. Res., 43(1), 31–43.
El-Kamash, M. K., Loewen, M. R., and Rajaratnam, N. (2005b). “Measurements of void fraction and bubble properties on a stepped chute using a fiber-optical probe.” Can. J. Civ. Eng., 32(4), 636–643.
Gualtieri, C., and Chanson, H. (2007). “Experimental analysis of Froude number effect on air entrainment in the hydraulic jump.” Environ. Fluid Mech., 7(3), 217–238.
Hager, W. H. (1992). Energy dissipators and hydraulic jump, Vol. 8, Kluwer, Water Science and Technology Library, Dordrecht, Netherlands, 288.
Kucukali, S., and Chanson, H. (2008). “Turbulence measurements in the bubbly flow region of hydraulic jumps.” Exp. Therm. Fluid Sci., 33(1), 41–53.
LabVIEW 7.1 [Computer software]. National Instruments, TX.
Lennon, J. M., and Hill, D. F. (2006). “Particle image velocity measurements of undular and hydraulic jumps.” J. Hydraul. Eng., 1283–1294.
Lin, C., Hsieh, S.-C., Lin, I. J., Chang, K.-A., and Raikar, R. V. (2012). “Flow property and self-similarity in steady hydraulic jumps.” Exp. Fluids, 53(5), 1591–1616.
Liu, M., Rajaratnam, N., and Zhu, D. Z. (2004). “Turbulence structure of hydraulic jumps of low Froude numbers.” J. Hydraul. Eng., 511–520.
Liu, Q., and Uwe, D. (1994). “Turbulence characteristics in free and forced hydraulic jumps.” J. Hydraul. Res., 32(6), 877–898.
Matlab 7.0 [Computer software]. Mathworks, Natick, MA.
McCorquodale, J. A., and Khalifa, A. (1983). “Internal flow in hydraulic jumps.” J. Hydraul. Eng., 684–701.
Murzyn, F., and Chanson, H. (2009). “Experimental investigation of bubbly flow and turbulence in hydraulic jumps.” Environ. Fluid Mech., 9(2), 143–159.
Murzyn, F., Mouaze, D., and Chaplin, J. R. (2005). “Optical fibre probe measurements of bubbly flow in hydraulic jumps.” Int. J. Multiphase Flow, 31(1), 141–154.
Rajaratnam, N. (1962). “An experimental study of air entrainment characteristics of the hydraulic jump.” J. Inst. Eng., 42(7), 247–273.
Rajaratnam, N. (1965). “The hydraulic jump as a wall jet.” J. Hydraul. Div., 91(5), 107–132.
Resch, F. J., Leutheusser, H., and Alemum, S. (1974). “Bubbly two-phase flow in hydraulic jump.” J. Hydraul. Div., 100(1), 137–149.
Resch, F. J., and Leutheusser, H. J. (1972). “The hydraulic jump: Turbulence measurements in the two-phase region.” La Houille Blanche, 4(4), 279–293.
Rojas, G., and Loewen, M. (2007). “Fiber-optical probe measurements of void fraction and bubble size distributions beneath breaking waves.” Exp. Fluids, 43(6), 895–906.
Rouse, H., Siao, T. T., and Nagaratnam, S. (1959). “Turbulence characteristics of the hydraulic jump.” Trans. Am. Soc. Civ. Eng., 124, 926–950.
Schröder, R. (1963). “The turbulent flow in the free hydraulic jump.” Habilitationsschrift, 59, Institute of Hydraulic Engineering and Water Management, TU Berlin, Berlin, Germany.
Sene, K. J. (1984). “Aspects of bubbly two-phase flow.” Ph.D. thesis, Univ. of Cambridge, Cambridge, U.K.
Serdula, C. D., and Loewen, M. R. (1998). “Experiments investigating the use of fiber-optical probes for measuring bubble-size distributions.” IEEE J. Ocean. Eng., 23(4), 385–399.
Svendsen, I. A., Veeramony, J., Bakunin, J., and Kirby, J. T. (2000). “The flow in weak turbulent hydraulic jumps.” J. Fluid Mech., 418, 25–57.
Vejražka, J., Večeř, M., Orvalho, S., Sechet, P., Ruzicka, M. C., and Cartellier, A. (2010). “Measurement accuracy of a mono-fiber optical probe in a bubbly flow.” Int. J. Multiphase Flow, 36(7), 533–548.
Wu, S., and Rajaratnam, N. (1995). “Free jumps, submerged jumps and wall jets.” J. Hydraul. Res., 33(2), 197–212.
Zhang, W. M., and Zhu, D. Z. (2013). “Bubble characteristics of air-water bubbly jets in crossflow.” Int. J. Multiphase Flow, 55, 156–171.
Zobeyer, A. T. M. H., Jahan, N., Islam, Z., Singh, G., and Rajaratnam, N. (2010). “Turbulence characteristics of the transition region from hydraulic jump to open channel flow.” J. Hydraul. Res., 48(3), 395–399.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 11 • November 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 13, 2013
Accepted: Jun 9, 2014
Published online: Jul 21, 2014
Published in print: Nov 1, 2014
Discussion open until: Dec 21, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.