(A) Hydraulic jump on Mattervispa stream, Zermatt (Switzerland) on 14 December 2013, lookin downstream (B) Drop structures along Daiya River below Mount Nantai, Nikko City (Japan) close to the railway station on 8 October 2012 1.2 THEORETICAL CONSIDERATIONS irregular prismatic channel (CHANSON 2012): Equation (1.9) gives a theoretical solution with the upstream Froude number being a function of the atio of conjugate cross-sectional areas A,/A, and the flow resistance force. For a given upstream “roude number, Equation (1.9) implies a smaller ratio of conjugate depths d2/d; with increasing (A) General view of channel with HDPE bed and glass sidewalls - Flow direction from right to left herein. Some photographs of the experimental facility are shown in Figure 2-1. from upstream with flow direction from right to left [he air-water flow properties were recorded using a dual-tip phase-detection probe (Fig. 2-3). The Fig 2-3 - Dual-tip conductivity phase-detection probe and pressure probe mounted together (view in Fig 2-3 - Dual-tip conductivity phase-detection probe and pressure probe mounted together (view in elevation) - Flow from right to left - Longitudinal distance (1) between tips Axtip = 7.25 mm; transverse distance (2) between tips Az;,, = 2.2 mm. The pressure sensor was mounted at the tip of a Pitot tube-like holder (Fig. 2-4). The probe sensor with the phase-detection probe. During the experiments, the sensor was mounted close to the phase- Table 2-2 - Experimental free-surface measurements using the acoustic displacement meters properties and pressure outputs at the same location Table 2-1 - Experimental conditions for simultaneous acquisitions of free surface, two-phase flov limensionless distance to the jump toe (x-x1)/d; Fig 3-4 - Maximum turbulent fluctuations of the free surface elevation as a function of the Froude number - Comparison with experimental data (MADSEN 1981, MOUAZE et al. 2005, KUCUKALI and CHANSON 2007, MURZYN et al. 2007, MURZYN and CHANSON 2009, CHACHEREAU and CHANSON 2011b, WANG and CHANSON 2013), computational data (RICHARD and GAVRILYUK 2013) and Equation (3.2) local peaks were too ambiguous. numbers up to 1.6x10°. Fig 3-6 - Free surface fluctuation frequencies in hydraulic jumps Fig 3-7 - Dimensionless frequencies of longitudinal jump toe oscillations Fioexdj/V1 as a function of the Froude number - Comparison with experimental data (CHANSON 2007, MURZYN and CHANSON 2009, CHANSON 2010, CHACHEREAU and CHANSON 2011b, ZHANG et al. 2013, WANG and CHANSON 2013) and computational data (RICHARD 2013), and physical observations of formation rates of large-size vortices in the roller shear layer F.jxd1/V; (CHANSON 8 as functions of the relative position (x-x;)/L, within the roller (>. and vertical roller free-surface motions quation (3.3) (solid line) in the shear region and Equation (3.4) (dashed line) in the upper free- Figure 3-13, showing the dimensionless data presented a linear trend independently of the Froude estimated as y = y» where a local void fraction minimum was observed. The data are plotted in ee MMA ME EN, REE ENTE De YN SRD ONE ee ee ee A ES SERRE PS OM el Me See Me Me two probe sensors. The theoretical considerations were developed by CHANSON and TOOMBES (2002) (also FELDER and CHANSON (2014)). Figure 3-18 presents the turbulence intensity data, including those in the recirculation region. They were found to increase monotonically from the channel bed to the upper boundary of shear layer. High consistency was shown between different longitudinal positions, suggesting that the dissipation of relative turbulence level was limited within Fig. 3-18 - Vertical distributions of turbulence intensity Tu in hydraulic jumps ' that the fluctuating nature of the flow, of much larger time scales, might also generate som were seen for the flows with relatively small Froude and Reynolds numbers. density functions. Assuming a positive flow direction parallel to the channel bed, the bubble chord length could be bubbles being broken up into finer ones in the regions of high shear stresses. percentage of small bubbles in the downstream direction. It suggested a dominant process of Equation (3.8) implied that the magnitude of dimensionless bubble rate was related to the Reynolds characteristic elevation YFmax Of maximum bubble count rate in hydraulic jumps Equation (3.9) is plotted in Figure 3-26 for some experimental results. 3.2.5 Comparison with previous studies Figure 3-26 - Longitudinal distributions of cluster proportion - Comparison with best fit correlations and data of CHANSON (2010) lower elevation than the maximum bubble count rate and maximum void fraction. That is: marked roller: best fit relationship Table 3-1 - Characteristic elevations Yomax/d1, y*/di, Yemax/d; and Yvmax/d; in hydraulic jumps with a The instantaneous total pressure was recorded at several elevations above the channel bed up to the he piezometric pressure was a function of the flow depth and relative probe elevation, while the kinetic pressure was a function of the local velocity four statistical moments of the total pressure data sets. was maximum. Further total pressure PDF data are presented in Appendix A, together with the first The total pressure fluctuations are discussed herein in terms of the standard deviation p' of pressure data were recorded in the shear layer at the elevation ypmax where the time-averaged total pressure Fig 4-5 - Vertical profiles of standard deviation of total pressure in hydraulic jumps Different amplitudes of fluctuations were clearly shown between Froude numbers The corresponding elevation of maximum pressure fluctuation Ypmax/d is shown in Figure 4-3B. A scattered; neither data were reliable in the recirculation region. motion (i.e. instantaneous negative velocity) were regularly detected. rate and bubble cluster count rate Fig 4-10 - Longitudinal variations of dimensionless low characteristic frequencies of total pressure fluctuations in the shear layer of hydraulic jumps - Data at y = Yrmax - Comparison with the characteristic frequencies of free surface fluctuations (Present study, WANG and CHANSON 2013) ‘ig 4-10 - Longitudinal variations of dimensionless low characteristic frequencies of total pressure characteristic frequencies of free surface fluctuations (Present study, WANG and CHANSON 2013) of measurements could be improved by the application of a total pressure probe with narrower the pressure and void fraction signals, the results are presented below as functions of the vertical displacement meter; PDP: phase-detection probe; TPP: total pressure probe surface motions were independent of the elevation of total pressure and phase-detection probes. Fc invert, suggesting different characteristic shapes between the shear layer and recirculation region. In the shear region, both correlation functions exhibited a positive maximum as illustrated in Figure observed more frequently (see Fig. 3.9). deformation and instantaneous void fraction - Comparison with vertical distribution of void fraction displacement meter signals suggested that the free-surface descent with downstream toe motion was the invert. The same results were obtained for different Froude numbers. In the second half roller, (Ryp)max presented a similar distribution as in the first half roller, whereas ig 5-6 - Correlation function R,, between instantaneous total pressure and void fraction in and the void fraction is small. Fig 5-9 - Self-similar flow structures in jump roller: characteristic thickness of main and lower latter investigation was limited to photographic observations in a small size facility Fr, = 3.8, (x-x,)/d; = 8.35: Fr, = 3.8, (x-x;)/d, = 12.5: Fr; = 5.1, (x-x;)/d; = 4.15: Fr, = 5.1, (x-x1)/d1 = 8.35: Fr, = 5.1, (x-x;)/d; = 12.5: Fr, = 5.1, (x-x)/d; = 18.75: Fr, = 7.5, (x-x;)/d; = 4.15: Fr, = 7.5, (x-x1)/d, = 8.35: Fr, = 75, (x-x1)/d; = 12.5: Fr, = 75, (x-x1)/d; = 18.75: Fr, = 8.5, (x-x;)/d; = 4.15: Fr, = 8.5, (x-x;)/d; = 8.35: Fr = 8.5, (x-x1)/d; = 12.5: Fr, = 8.5, (x-x1)/d1 = 18.75: Fig B-1 - Sketch of characteristic air-water flow properties in a hydraulic jump roller. rate Fiyax at an elevation Ypmax in the air-water shear layer. 7 = 3.8 r Fig D-1 - Sketch of instrumental setup and correlation coefficients - Flow direction from bottom left Q = 0.0179 m?/s, d, = 0.02 m, x; = 0.83 m, Fr; = 3.8, Re = 3.5x10° Q = 0.0239 m°/s, d; = 0.02 m, x; = 0.83 m, Fr; = 5.1, Re = 4.8x10* Q = 0.0347 m°/s, d; = 0.02 m, x; = 0.83 m, Fr) = 7.5, Re = 6.8x10° Q = 0.0397 m*/s, d, = 0.02 m, x; = 0.83 m, Fr, = 8.5, Re = 8.0x10° APPENDIX F. PHOTOGRAPHIC OBSERVATIONS OF EXPERIMENTS Fig. F-1 - Hydraulic jump experiment - Flow conditions: Q = 0.0241 m°’/s, dj = 0.020 m, x; = 0. m, Fr; = 5.1, Re = A.8x10", flow direction from left to right (A) General view (A) Side view, flow direction from left to right (B) Three-quarter view highlighting large air-water projection, flow direction from left to right (A) Side view, flow direction from left to right (B) Details of acoustic displacement meters and probes (shutter speed: 1/100 s) Url: http://www.eng.uq.edu.au/civil/ Email: enquiries @civil.ug.edu.au Brisbane 4072, Australia - Tel.: (61 7) 3365 3619 - Fax : (61 7) 3365 4599 Note: Prices include postages and processing. Url: http://www.eng.uq.edu.au/civil/ Email: hodciveng @uq.edu.au School Secretary, School of Civil Engineering, The University of Queensland 2- Cheque/remittance payable to: THE UNIVERSITY OF QUEENSLAND and crossed "Not
