Abstract
Intense turbulence develops in the two-phase flow region of hydraulic jump, with a broad range of turbulent length and time scales. Detailed air–water flow measurements using intrusive phase-detection probes enabled turbulence characterisation of the bubbly flow, although the phenomenon is not a truly random process because of the existence of low-frequency, pseudo-periodic fluctuating motion in the jump roller. This paper presents new measurements of turbulent properties in hydraulic jumps, including turbulence intensity, longitudinal and transverse integral length and time scales. The results characterised very high turbulent levels and reflected a combination of both fast and slow turbulent components. The respective contributions of the fast and slow motions were quantified using a triple decomposition technique. The decomposition of air–water detection signal revealed “true” turbulent characteristics linked with the fast, microscopic velocity turbulence of hydraulic jumps. The high-frequency turbulence intensities were between 0.5 and 1.5 close to the jump toe, and maximum integral turbulent length scales were found next to the bottom. Both decreased in the flow direction with longitudinal turbulence dissipation. The results highlighted the considerable influence of hydrodynamic instabilities of the flow on the turbulence characterisation. The successful application of triple decomposition technique provided the means for the true turbulence properties of hydraulic jumps.
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Abbreviations
- C :
-
Time-averaged void fraction
- \(\overline{C}\) :
-
Decomposed time-averaged void fraction of average signal component
- C′:
-
Decomposed time-averaged void fraction of low-frequency signal component
- C″:
-
Decomposed time-averaged void fraction of high-frequency signal component
- C max :
-
Local maximum time-averaged void fraction in the shear flow region
- c :
-
Instantaneous void fraction
- \(\overline{c}\) :
-
Decomposed instantaneous void fraction of average signal component
- c′:
-
Decomposed instantaneous void fraction of low-frequency signal component
- c″:
-
Decomposed instantaneous void fraction of high-frequency signal component
- d 1 :
-
Inflow water depth immediately upstream of the jump toe (m)
- d 2 :
-
Downstream water depth (m)
- F :
-
Bubble count rate (Hz)
- \(\overline{F}\) :
-
Decomposed bubble count rate of average signal component (Hz)
- F′:
-
Decomposed bubble count rate of low-frequency signal component (Hz)
- F″:
-
Decomposed bubble count rate of high-frequency signal component (Hz)
- F max :
-
Maximum bubble count rate in the shear flow region (Hz)
- Fr 1 :
-
Inflow Froude number, \({Fr}_{ 1} {\, =\, }{{V_{ 1} } \mathord{\left/ {\vphantom {{V_{ 1} } {\sqrt {g \times d_{ 1} } }}} \right. \kern-0pt} {\sqrt {g \times d_{ 1} } }}\)
- g :
-
Gravity acceleration (m/s2)
- h :
-
Upstream gate opening (m)
- L r :
-
Length of jump roller (m), defined as the distance over which the free-surface level increased monotonically
- L X :
-
Longitudinal integral turbulent length scale (m)
- L X′:
-
Decomposed longitudinal integral turbulent length scale of low-frequency signal component (m)
- L X″:
-
Decomposed longitudinal integral turbulent length scale of high-frequency signal component (m)
- (L X″)max :
-
Maximum decomposed longitudinal integral turbulent length scale of high-frequency signal component (m)
- L xx :
-
Advection length scale (m)
- L xx′:
-
Decomposed advection length scale of low-frequency signal component (m)
- L xx″:
-
Decomposed advection length scale of high-frequency signal component (m)
- L Z :
-
Transverse integral turbulent length scale (m)
- Q :
-
Flow rate (m3/s)
- R xx :
-
Normalised auto-correlation function
- R xx′ :
-
Normalised cross-correlation function between leading and trailing phase-detection probe signals
- R xx′″:
-
Decomposed cross-correlation function between high-frequency signal component
- R xz :
-
Normalised cross-correlation function between side-by-side phase-detection probe signals
- Re :
-
Reynolds number, \(Re{ = }{{\rho \times V_{ 1} \times d_{ 1} } \mathord{\left/ {\vphantom {{\rho \times V_{ 1} \times d_{ 1} } \mu }} \right. \kern-0pt} \mu }\)
- T :
-
Time lag for maximum cross-correlation coefficient (s)
- T′:
-
Time lag for maximum decomposed cross-correlation function of low-frequency signal component (s)
- T″:
-
Time lag for maximum decomposed cross-correlation function of high-frequency signal component (s)
- T X :
-
Longitudinal integral turbulent time scale (s)
- T X′:
-
Decomposed longitudinal integral turbulent time scale of low-frequency signal component (s)
- T X″:
-
Decomposed longitudinal integral turbulent time scale of high-frequency signal component (s)
- (T X″)max :
-
Maximum longitudinal integral turbulent time scale of high-frequency signal component (s)
- (T X″)mean :
-
Depth-averaged longitudinal integral turbulent time scale of high-frequency signal component (s)
- T xx :
-
Auto-correlation time scale (s)
- T xx′:
-
Decomposed auto-correlation time scale of low-frequency signal component (s)
- T xx″:
-
Decomposed auto-correlation time scale of high-frequency signal component (s)
- T xx′ :
-
Longitudinal cross-correlation time scale (s)
- T xx′′:
-
Decomposed longitudinal cross-correlation time scale of low-frequency signal component (s)
- T xx′″:
-
Decomposed longitudinal cross-correlation time scale of high-frequency signal component (s)
- T xz :
-
Transverse cross-correlation time scale (s)
- T Z :
-
Transverse integral turbulent time scale (s)
- T 0.5 :
-
Time lag for maximum auto-correlation coefficient (s)
- Tu :
-
Turbulence intensity
- Tu′:
-
Decomposed turbulence intensity of low-frequency signal component
- Tu″:
-
Decomposed turbulence intensity of high-frequency signal component
- V :
-
Average air–water interfacial velocity (m/s)
- V′:
-
Decomposed interfacial velocity of low-frequency signal component (m/s)
- V″:
-
Decomposed interfacial velocity of high-frequency signal component (m/s)
- V 1 :
-
Average inflow velocity (m/s)
- v′:
-
Standard deviation of interfacial velocity (m/s)
- W :
-
Channel width (m)
- x :
-
(1) Longitudinal distance from the upstream gate (m)
(2) Signal of leading sensor of phase-detection probe
- x′:
-
Signal of trailing sensor of phase-detection probe
- x 1 :
-
Longitudinal position of jump toe (m)
- Y 90 :
-
Characteristic elevation where C = 0.9 (m)
- y :
-
Vertical distance from the channel bed (m)
- Δx :
-
Longitudinal separation distance between two phase-detection probe sensors (m)
- Δz :
-
Transverse separation distance between two phase-detection probe sensors (m)
- μ:
-
Dynamic viscosity (Pa × s)
- ρ:
-
Density (kg/m3)
- τ:
-
Time lag (s)
- τ0.5 :
-
Time lag between maximum and half maximum cross-correlation coefficient (s)
References
Chachereau Y, Chanson H (2011) Free-surface fluctuations and turbulence in hydraulic jumps. Exp Thermal Fluid Sci 35(6):896–909. doi:10.1016/j.expthermflusci.2011.01.009
Chanson H (1995) Air entrainment in two-dimensional turbulent shear flows with partially developed inflow conditions. J Multiphase Flow 21(6):1107–1121
Chanson H (2006) Air bubble entrainment in hydraulic jumps. Similitude and scale effects. Academic Report No. CH57/05, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia
Chanson H (2007) Bubbly flow structure in hydraulic jump. Eur J Mech B/Fluids 26(3):367–384. doi:10.1016/j.euromechflu.2006.08.001
Chanson H (2010) Convective transport of air bubbles in strong hydraulic jumps. Int J Multiph Flow 36(10):798–814. doi:10.1016/j.ijmultiphaseflow.2010.05.006
Chanson H, Carosi G (2007) Turbulent time and length scale measurements in high-velocity open channel flows. Exp Fluids 42(3):385–401. doi:10.1007/s00348-006-0246-2
Chanson H, Toombes L (2002) Air-water flows down stepped chutes: turbulence and flow structure observations. Int J Multiph Flow 28(11):1737–1761
Cox D, Shin S (2003) Laboratory measurements of void fraction and turbulence in the bore region of surf zone waves. J Eng Mech 129:1197–1205
Felder S (2013) Air-water flow properties on stepped spillways for embankment dams: aeration, energy dissipation and turbulence on uniform, non-uniform and pooled stepped chutes. PhD thesis, School of Civil Engineering, The University of Queensland, Brisbane, Australia
Felder S, Chanson H (2014) Triple decomposition technique in air–water flows: application to instationary flows on a stepped spillway. Int J Multiph Flow 58:139–153. doi:10.1016/j.ijmultiphaseflow.2013.09.006
Hager WH (1992) Energy dissipators and hydraulic jump. Kluwer Academic Publ, Water Science and Technology Library 8, Dordrecht, The Netherlands
Hoyt JW, Sellin RHJ (1989) Hydraulic Jump as ‘Mixing Layer’. J Hydrolic Eng ASCE 115(12):1607–1614
Leandro J, Carvalho R, Chachereau Y, Chanson H (2012) Estimating void fraction in a hydraulic jump by measurements of pixel intensity. Exp Fluids 52(5):1307–1318
Lennon JM, Hill DF (2006) Particle image velocity measurements of undular and hydraulic jumps. J Hydraulic Eng ASCE 132(12):1283–1294
Leutheusser HJ, Kartha VC (1972) Effects of inflow condition on hydraulic jump. J Hyd Div, ASCE 98(HY8):1367–1385
Lighthill J (1978) Waves in fluids. Cambridge University Press, Cambridge
Liu M, Rajaratnam N, Zhu D (2004) Turbulence structure of hydraulic jumps of low Froude numbers. J Hydraulic Eng 130(6):511–520. doi:10.1061/(ASCE)0733-9429(2004)130:6(511
Long D, Rajaratnam N, Steffler PM, Smy PR (1991) Structure of flow in hydraulic jumps. J Hydraulic Res, IAHR 29(2):207–218
Longo S (2010) Experiments on turbulence beneath a free surface in a stationary field generated by a Crump weir: free-surface characteristics and the relevant scales. Exp Fluids 49:1325–1338
Longo S (2011) Experiments on turbulence beneath a free surface in a stationary field generated by a Crump weir: turbulence structure and correlation with the free surface. Exp Fluids 50:201–215
Lopardo RA (2013) Extreme velocity fluctuations below free hydraulic jumps. J Eng, Hindawi Publishing Corporation, Article ID 678065
Lopardo RA, Romagnoli M (2009) Pressure and velocity fluctuations in stilling basins. Advances in Water Resources and Hydraulic Engineering, Proceedings of 16th IAHR-APD Congress and 3rd IAHR International Symposium on Hydraulic Structures ISHS, Nanjing, China
Lubin P, Glockner S (2013) Detailed numerical investigation of the three-dimensional flow structures under breaking waves. In: 7th conference on coastal dynamics, Arcachon, France, 24-28 June 2013, pp 1127–1136
Mignot E, Cienfuegos R (2010) Energy dissipation and turbulent production in weak hydraulic jumps. J Hydraulic Eng, ASCE 136(2):116–121
Montes JS (1998) Hydraulics of open channel flow. ASCE Press, New York
Mossa M (1999) On the oscillating characteristics of hydraulic jumps. J Hydraulic Res, IAHR 37(4):541–558
Mossa M, Tolve U (1998) Flow visualization in bubbly two-phase hydraulic jump. J Fluids Eng, ASME 120:160–165
Mouaze D, Murzyn F, Chaplin JR (2005) Free surface length scale estimation in hydraulic jumps. J Fluids Eng, Trans ASME 127:1191–1193. doi:10.1115/1.2060736
Murzyn F, Chanson H (2009) Experimental investigation of bubbly flow and turbulence in hydraulic jumps. Environ Fluid Mech 9(2):143–159. doi:10.1016/j.expthermflusci.2009.06.003
Murzyn F, Mouaze D, Chaplin JR (2007) Air-water interface dynamic and free surface features in hydraulic jumps. J Hydraulic Res, IAHR 45(5):679–685
Peregrine DH, Svendsen IA (1978) Spilling breakers, bores and hydraulic jumps. Proceedings of 16th international conference coastal Eng., Hamburg, Germany
Prosperetti A, Tryggvason G (2009) Computational methods for multiphase flow. Cambridge University Press, London
Rajaratnam N (1962) An experimental study of air entrainment characteristics of the hydraulic jump. J Instr Eng India 42(7):247–273
Rajaratnam N (1967) Hydraulic jumps. In: Chow VT (ed) Advances in hydroscience. Academic Press, New York, vol 4, pp 197–280
Resch FJ, Leutheusser HJ (1972) Le ressaut hydraulique: mesure de turbulence dans la région diphasique. Journal La Houille Blanche 4:279–293 (in French)
Richard GL (2013) Élaboration d’un modèle d’écoulements turbulents en faible profondeur: application au ressaut hydraulique et aux trains de rouleaux. PhD thesis, Institut Universitaire des Systèmes Thermiques Industriels, Univerité d’Aix-Marseille, Marseille, France (in French)
Richard GL, Gavrilyuk SL (2013) The classical hydraulic jump in a model of shear shallow-water flows. J Fluid Mech 725:492–521. doi:10.1017/jfm.2013.174
Svendsen IA, Veeramony J, Bakunin J, Kirby JT (2000) The flow in weak turbulent hydraulic jumps. J Fluid Mech 418:25–57
Wang H, Chanson H (2014) Air entrainment and turbulent fluctuations in hydraulic jumps. Urban Water J. doi:10.1080/1573062X.2013.847464
Yan Z, Zhou C (2006) Pressure fluctuations beneath spatial hydraulic jumps. J Hydrodynam 18(6):723–726
Zhang G, Wang H, Chanson H (2013) Turbulence and aeration in hydraulic jumps: free-surface fluctuation and integral turbulent scale measurements. Environ Fluid Mech 13(2):189–204. doi:10.1007/s10652-012-9254-3
Acknowledgments
The authors thank Jason Van Der Gevel (The University of Queensland) for manufacturing the phase-detection probes. The financial support of the Australian Research Council is acknowledged.
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Wang, H., Felder, S. & Chanson, H. An experimental study of turbulent two-phase flow in hydraulic jumps and application of a triple decomposition technique. Exp Fluids 55, 1775 (2014). https://doi.org/10.1007/s00348-014-1775-8
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DOI: https://doi.org/10.1007/s00348-014-1775-8