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A: Based on Criterion A (Equation 7.2) B: Based on Criterion B (Equation 7.3)

Figure 140 A: Based on Criterion A (Equation 7.2) B: Based on Criterion B (Equation 7.3)

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Figure 1.1 Hydraulic jump in the stilling basin of the Paradise dam in Burnett River, Bundaberg QLD. Australia. Flow from left to right. Discharge estimated to be in excess of 6300 m?/s with the Reynolds number of 1.9x10’ (Courtesy of Hubert Chanson) projections above the breaking surface are visible in Figure1.1.
Figure 1.1 Hydraulic jump in the stilling basin of the Paradise dam in Burnett River, Bundaberg QLD. Australia. Flow from left to right. Discharge estimated to be in excess of 6300 m?/s with the Reynolds number of 1.9x10’ (Courtesy of Hubert Chanson) projections above the breaking surface are visible in Figure1.1.
Figure 1.2 Hydraulic jump stilling basin in operation at the Hinze dam (Australia) on 29 January 2013; qu=16.6 m’/s, Re=1.6E7 (Felder and Chanson 2016) spillway during a flood (Chanson 2004a).
Figure 1.2 Hydraulic jump stilling basin in operation at the Hinze dam (Australia) on 29 January 2013; qu=16.6 m’/s, Re=1.6E7 (Felder and Chanson 2016) spillway during a flood (Chanson 2004a).
in contact with the structure for only a short time (Raikar and Kamatagi 2015).
in contact with the structure for only a short time (Raikar and Kamatagi 2015).
Figure 1.4 The process of mixing and aeration
Figure 1.4 The process of mixing and aeration
Figure 1.5 Hydraulic jump in laboratory flume (F7r;=6.5) (A) Hydraulic jump in the small flume (inflow conditions: Fr;=6.5, Re;=2.7E+4, Vi=2.2m/s, d;=0.012m, W=0.25m) flow from left to right. (B) Hydraulic jump in the large flume (inflow conditions: Fri=6.5, Re=7.1E+4, Vi=3.1m/s, d;=0.023m, W=0.5m) flow from left to right (Gualtieri and Chanson 2007)
Figure 1.5 Hydraulic jump in laboratory flume (F7r;=6.5) (A) Hydraulic jump in the small flume (inflow conditions: Fr;=6.5, Re;=2.7E+4, Vi=2.2m/s, d;=0.012m, W=0.25m) flow from left to right. (B) Hydraulic jump in the large flume (inflow conditions: Fri=6.5, Re=7.1E+4, Vi=3.1m/s, d;=0.023m, W=0.5m) flow from left to right (Gualtieri and Chanson 2007)
Figure 2.1 Sketches of typical void fraction and bubble count rate distributions in hydraulic jump rolle: jumps with partially-developed inflow conditions together with the relevant characteristi
Figure 2.1 Sketches of typical void fraction and bubble count rate distributions in hydraulic jump rolle: jumps with partially-developed inflow conditions together with the relevant characteristi
where D* is a dimensionless diffusivity in the upper free-surface region, and the Gaussian error
where D* is a dimensionless diffusivity in the upper free-surface region, and the Gaussian error
Table 2.1 Summary of literature review of air entrainment in hydraulic jump on smooth bed
Table 2.1 Summary of literature review of air entrainment in hydraulic jump on smooth bed
FL: Flume Length, FW: Flume Width, FH: Flume Height, FS: Flume Slope
FL: Flume Length, FW: Flume Width, FH: Flume Height, FS: Flume Slope
FL: Flume Length, FW: Flume Width, FH: Flume Height, FS: Flume Slope
FL: Flume Length, FW: Flume Width, FH: Flume Height, FS: Flume Slope
probe systems for measuring air entrainment properties. and to Reynolds numbers of 6.3 x 10*< Re; < 2.1 x 10°. They used two double-tip conductivity
probe systems for measuring air entrainment properties. and to Reynolds numbers of 6.3 x 10*< Re; < 2.1 x 10°. They used two double-tip conductivity
Table 2.3 Summary of literature review of hydraulic jump on rough bed
Table 2.3 Summary of literature review of hydraulic jump on rough bed
Table 2.4 Effect of bed roughness on flow properties
Table 2.4 Effect of bed roughness on flow properties
Table 2.5 Summary of literature review on numerical study of hydraulic jump
Table 2.5 Summary of literature review on numerical study of hydraulic jump
Now, Equation (3.1) may be rewritten as:
Now, Equation (3.1) may be rewritten as:
Figure 3.1 Side view of channel. Upstream head tank on the right. Flow from right to left — Flow conditions: Q = 0.07 m*/s, Fr; = 1.93, d; = 0.084 m, x; = 1.0m
Figure 3.1 Side view of channel. Upstream head tank on the right. Flow from right to left — Flow conditions: Q = 0.07 m*/s, Fr; = 1.93, d; = 0.084 m, x; = 1.0m
Where: /; is the upstream gate opening and x is the position of cross section where air bubbles were measured Table 3-1 Experimental flow conditions (x = x; = 1 m)
Where: /; is the upstream gate opening and x is the position of cross section where air bubbles were measured Table 3-1 Experimental flow conditions (x = x; = 1 m)
Table 3.2 Properties of gravels 3.3 Instrumentation and signal processing pebbles sieved between 9.5 mm and 13.2 mm with dso = 0.011 m and ps = 2530 kg/m’.
Table 3.2 Properties of gravels 3.3 Instrumentation and signal processing pebbles sieved between 9.5 mm and 13.2 mm with dso = 0.011 m and ps = 2530 kg/m’.
Figure 3.3 Preparing bed roughness, a: installing gravels, b: attaching plates, c: sticking plates and putting on channel d: black and white walls on two sides
Figure 3.3 Preparing bed roughness, a: installing gravels, b: attaching plates, c: sticking plates and putting on channel d: black and white walls on two sides
Figure 3.4 Measuring gate opening using ruler based on the average height of gravels as done for the gate opening.
Figure 3.4 Measuring gate opening using ruler based on the average height of gravels as done for the gate opening.
Figure 3.5 Conductivity probe a: dimension (4x = 6.5 mm, 4z = 2.1 mm), b: zero level for rough bed and c: with supporter against flow direction during measurement dimension and position of conductivity probe. MitutoyoTM digimatic scale unit with an accuracy of 0.01 mm. Figure 3.5 shows in detail the
Figure 3.5 Conductivity probe a: dimension (4x = 6.5 mm, 4z = 2.1 mm), b: zero level for rough bed and c: with supporter against flow direction during measurement dimension and position of conductivity probe. MitutoyoTM digimatic scale unit with an accuracy of 0.01 mm. Figure 3.5 shows in detail the
bubble count rate as well as air-flow properties (Chanson 2007a, Felder and Chanson 2015). ‘aw signal segments of 9 s each to minimize any bias. Note that sampling frequency higher
bubble count rate as well as air-flow properties (Chanson 2007a, Felder and Chanson 2015). ‘aw signal segments of 9 s each to minimize any bias. Note that sampling frequency higher
Table 3.3 Experiments for the basic parameters and free surface measurements (Group A)
Table 3.3 Experiments for the basic parameters and free surface measurements (Group A)
Table 3.4 Experiments for the air-flow parameters (Group B)
Table 3.4 Experiments for the air-flow parameters (Group B)
Figure 4.1 Hydraulic jump on rough bed, flow condition: Run AR1, Q = 0.043 m*/s, Fr; = 1.31, flow from right to left
Figure 4.1 Hydraulic jump on rough bed, flow condition: Run AR1, Q = 0.043 m*/s, Fr; = 1.31, flow from right to left
A: Smooth bed, flow condition: Run AS8, Q = 0.036 m*/s, Fr; = 1.54, flow from right to left
A: Smooth bed, flow condition: Run AS8, Q = 0.036 m*/s, Fr; = 1.54, flow from right to left
B: Rough bed, flow condition: Run AR2, Q = 0.051 m*/s, Fr; = 1.57, flow from right to left Figure 4.2 Comparison between hydraulic jump type and free surface pattern between rough and smooth bed (same gate opening h = 0.06 m)
B: Rough bed, flow condition: Run AR2, Q = 0.051 m*/s, Fr; = 1.57, flow from right to left Figure 4.2 Comparison between hydraulic jump type and free surface pattern between rough and smooth bed (same gate opening h = 0.06 m)
A: Smooth bed, flow condition: Run AS9, Q = 0.044 m°/s, Fr; = 1.92, flow from right to left following wave crests (Figures 4.2B and 4.3B).
A: Smooth bed, flow condition: Run AS9, Q = 0.044 m°/s, Fr; = 1.92, flow from right to left following wave crests (Figures 4.2B and 4.3B).
B: Rough bed, flow condition: Run AR4, Q = 0.07 m*/s, Fr; = 1.93, flow from right to left Figure 4.3 Comparison between hydraulic jump type and free surface pattern between rough and smooth bed (for the same gate opening h = 0.06 m)
B: Rough bed, flow condition: Run AR4, Q = 0.07 m*/s, Fr; = 1.93, flow from right to left Figure 4.3 Comparison between hydraulic jump type and free surface pattern between rough and smooth bed (for the same gate opening h = 0.06 m)
A: Flow condition: Run AR5, Q = 0.076 m*/s, Fr; = 2.07 flow from right to left that were advected downstream. These structures were visible in the aerated roller region.
A: Flow condition: Run AR5, Q = 0.076 m*/s, Fr; = 2.07 flow from right to left that were advected downstream. These structures were visible in the aerated roller region.
B: Flow condition: Run AR6, Q = 0.085 m°*/s, Fr; = 2.4, flow from right to left Figure 4.4 Hydraulic jump on rough bed, undular jump with unstable roller (4 = 0.06 m). Red circles show the formation of vortex, red line show the negative flow
B: Flow condition: Run AR6, Q = 0.085 m°*/s, Fr; = 2.4, flow from right to left Figure 4.4 Hydraulic jump on rough bed, undular jump with unstable roller (4 = 0.06 m). Red circles show the formation of vortex, red line show the negative flow
A: Rough bed, flow condition: Run AR7, Q = 0.085 m*/s, Fr; = 2.4, flow from right to left
A: Rough bed, flow condition: Run AR7, Q = 0.085 m*/s, Fr; = 2.4, flow from right to left
B: Rough bed, flow condition: Run AR8 Q = 0.1 m*/s, Fr; = 2.87, up: from right to left, down: flow
B: Rough bed, flow condition: Run AR8 Q = 0.1 m*/s, Fr; = 2.87, up: from right to left, down: flow
C: Smooth bed, flow condition: Run AS12 Q = 0.073 m’/s, Fr; = 3.1, up: from right to left, down:
C: Smooth bed, flow condition: Run AS12 Q = 0.073 m’/s, Fr; = 3.1, up: from right to left, down:
A: Comparison between the present study (smooth bed) and previous studies on smooth bed
A: Comparison between the present study (smooth bed) and previous studies on smooth bed
The pointer gauge measurements were performed for several seconds, and the mean free-
The pointer gauge measurements were performed for several seconds, and the mean free-
A: Comparison between pointer gauge measurements and the characteristic water flow depth
A: Comparison between pointer gauge measurements and the characteristic water flow depth
B: Comparison between pointer gauge measurements, conductivity probe data and equivalent clear water.
B: Comparison between pointer gauge measurements, conductivity probe data and equivalent clear water.
A: Comparison between the present study (smooth bed) and previous studies on smooth bed
A: Comparison between the present study (smooth bed) and previous studies on smooth bed
B: Comparison between the present and previous studies on rough bed Figure 4.8 Jump roller length
B: Comparison between the present and previous studies on rough bed Figure 4.8 Jump roller length
Figure 4.9 Air flow length Lai, for both smooth and rough beds, comparison with Chanson (2011) on
Figure 4.9 Air flow length Lai, for both smooth and rough beds, comparison with Chanson (2011) on
Figure 4.10 Relationship between dimensionless air flow length and jump roller length
Figure 4.10 Relationship between dimensionless air flow length and jump roller length
the jump toe.
the jump toe.
Figure 4.11 Dimensionless boundary friction force and dimensionless shear stress
Figure 4.11 Dimensionless boundary friction force and dimensionless shear stress
rough and smooth bed. * Wang (2014) based on experimental data correlation extracted dimensionless characteristic frequencies of longitudinal jump toe oscillations and large vortex ejections, respectively, as follow: decreasing with increasing inflow Froude number, albeit with almost no difference between
rough and smooth bed. * Wang (2014) based on experimental data correlation extracted dimensionless characteristic frequencies of longitudinal jump toe oscillations and large vortex ejections, respectively, as follow: decreasing with increasing inflow Froude number, albeit with almost no difference between
Figure 4.12 Dimensionless characteristic frequency of longitudinal jump toe oscillations
Figure 4.12 Dimensionless characteristic frequency of longitudinal jump toe oscillations
Figure 4.13 Dimensionless characteristic frequencies of large vortex ejections as a function of the
Figure 4.13 Dimensionless characteristic frequencies of large vortex ejections as a function of the
Figure 4.14 Sketch of advection of large vortices in the shear layer on rough bed (based on Wang et
Figure 4.14 Sketch of advection of large vortices in the shear layer on rough bed (based on Wang et
\: Dimensionless advection velocity of large vortices in the jump roller based on inflow Froude when the vortices were advected within the turbulent shear layer. surface. The flow bulking was associated to free surface fluctuations and wave propagation,
\: Dimensionless advection velocity of large vortices in the jump roller based on inflow Froude when the vortices were advected within the turbulent shear layer. surface. The flow bulking was associated to free surface fluctuations and wave propagation,
B: Dimensionless advection velocity of large vortices in the jump roller based on inflow Reynolds Figure 4.15 Dimensionless advection velocity of large vortices in the jump roller
B: Dimensionless advection velocity of large vortices in the jump roller based on inflow Reynolds Figure 4.15 Dimensionless advection velocity of large vortices in the jump roller
Table 4.1 Flow conditions for observations of transverse impingement perimeter and water surface variation, x; = 1m 4.8.1 Impingement perimeter
Table 4.1 Flow conditions for observations of transverse impingement perimeter and water surface variation, x; = 1m 4.8.1 Impingement perimeter
A: Jump toe perimeter, smooth bed, Run AS13 B: Jump toe perimeter, rough bed Run AR8
A: Jump toe perimeter, smooth bed, Run AS13 B: Jump toe perimeter, rough bed Run AR8
Run AS13: Q = 0.078 m°*/s, Fr; = 3.25 for smooth bed with the same gate opening h = 0.06 m
Run AS13: Q = 0.078 m°*/s, Fr; = 3.25 for smooth bed with the same gate opening h = 0.06 m
Figure 4.18 Probability density functions of instantaneous jump toe position; Fr; = 2.87, 2.56, 2.4 with d; = 0.082, 0.84, 0.083 m, respectively, on rough bed, Fr; = 3.25, d; = 0.062 m on smooth bed the data followed a normal distribution.
Figure 4.18 Probability density functions of instantaneous jump toe position; Fr; = 2.87, 2.56, 2.4 with d; = 0.082, 0.84, 0.083 m, respectively, on rough bed, Fr; = 3.25, d; = 0.062 m on smooth bed the data followed a normal distribution.
A: Longitudinal water profile, smooth bed, Run AS13 2.56 on rough bed, respectively.
A: Longitudinal water profile, smooth bed, Run AS13 2.56 on rough bed, respectively.
B: Longitudinal water profile, rough bed, Run AR8
B: Longitudinal water profile, rough bed, Run AR8
C: Longitudinal water profile, rough bed, Run AR7
C: Longitudinal water profile, rough bed, Run AR7
Figure 4.19 Continuous frames with time step of 0.5s for jump toe perimeter and longitudinal water
Figure 4.19 Continuous frames with time step of 0.5s for jump toe perimeter and longitudinal water
A: Median water surface profiles
A: Median water surface profiles
Figure 4.20 Median and standard deviations of the instantaneous water surface profile on both bed m/s, Fr; = 2.56 and Run AR6: O = 0.085 m*/s, Fr: = 2.4 for rough bed and Run AS13 Q = 0.078
Figure 4.20 Median and standard deviations of the instantaneous water surface profile on both bed m/s, Fr; = 2.56 and Run AR6: O = 0.085 m*/s, Fr: = 2.4 for rough bed and Run AS13 Q = 0.078
Figure 4.21 Three regions along the jump roller length m?/s, Fr; = 3.25 on smooth bed for the same gate opening h = 0.06 m
Figure 4.21 Three regions along the jump roller length m?/s, Fr; = 3.25 on smooth bed for the same gate opening h = 0.06 m
A: First region 0.0<(x -x,)/ L, <0.27
A: First region 0.0<(x -x,)/ L, <0.27
Figure 4.22 Probability density functions of instantaneous water surface profile; Fr; = 2.87, 2.56, 2.4
Figure 4.22 Probability density functions of instantaneous water surface profile; Fr; = 2.87, 2.56, 2.4
Figure 5.1 Air entrainment in classical hydraulic jumps with partially-developed inflow conditions were compared with those on smooth bed as well as with those of previous literature studies.
Figure 5.1 Air entrainment in classical hydraulic jumps with partially-developed inflow conditions were compared with those on smooth bed as well as with those of previous literature studies.
Table 5.1 Summary of flow conditions for basic air-water flow measurements 5.2 Air-flow properties in supercritical flow
Table 5.1 Summary of flow conditions for basic air-water flow measurements 5.2 Air-flow properties in supercritical flow
Figure 5.2 Void fraction distributions upstream of hydraulic jump on both rough and smooth beds gate opening h = 0.06 m, comparison with the advection-diffusion equation (Equation 5.1) profiles (Toombes and Chanson 2007). vertical elevation y/d;. The data showed the strong pre-aeration of the flow on rough bed witk
Figure 5.2 Void fraction distributions upstream of hydraulic jump on both rough and smooth beds gate opening h = 0.06 m, comparison with the advection-diffusion equation (Equation 5.1) profiles (Toombes and Chanson 2007). vertical elevation y/d;. The data showed the strong pre-aeration of the flow on rough bed witk
Figure 5.3 Mean void fractions upstream of hydraulic jump, gate opening h = 0.06 m for present study or both rough and smooth beds, compared with the data with Felder and Chanson (2016)
Figure 5.3 Mean void fractions upstream of hydraulic jump, gate opening h = 0.06 m for present study or both rough and smooth beds, compared with the data with Felder and Chanson (2016)
Figure 5.4 Bubble count rate distributions upstream of the hydraulic jump roughness.
Figure 5.4 Bubble count rate distributions upstream of the hydraulic jump roughness.
Figure 5.5 Maximum bubble count rate distributions upstream of the hydraulic jump
Figure 5.5 Maximum bubble count rate distributions upstream of the hydraulic jump
and Chanson (2016, 2018) indicated a higher bubble count rate on pebbled rough bed.
and Chanson (2016, 2018) indicated a higher bubble count rate on pebbled rough bed.
Figure 5.7 Interfacial velocity distributions upstream of hydraulic jump on both rough and smooth beds momentum transfer in the boundary layer and hence the boundary layer growth.
Figure 5.7 Interfacial velocity distributions upstream of hydraulic jump on both rough and smooth beds momentum transfer in the boundary layer and hence the boundary layer growth.
Table 5.2 Characteristic velocities upstream of hydraulic jump 5.3 Air-flow properties in the hydraulic jump flov equivalent clear-water flow depth.
Table 5.2 Characteristic velocities upstream of hydraulic jump 5.3 Air-flow properties in the hydraulic jump flov equivalent clear-water flow depth.
A: Rough bed, Run BR3, Q = 0.1 m?/s, d; = 0.0825 m, Fr; = 2.84, Re; = 2.2E+5
A: Rough bed, Run BR3, Q = 0.1 m?/s, d; = 0.0825 m, Fr; = 2.84, Re; = 2.2E+5
B: Rough bed, Run BR2, Q = 0.07 m*/s, d; = 0.0835 m, Fr) = 1.96, Re: = 1.6E+5
B: Rough bed, Run BR2, Q = 0.07 m*/s, d; = 0.0835 m, Fr) = 1.96, Re: = 1.6E+5
C: Rough bed, Run BR1, Q = 0.061 m*/s, d; = 0.0835 m, Fr; = 1.7, Re; = 1.4E+5
C: Rough bed, Run BR1, Q = 0.061 m*/s, d; = 0.0835 m, Fr; = 1.7, Re; = 1.4E+5
D: Smooth bed, Run BS1, Q = 0.078 m?/s, d; = 0.0675 m, Fri = 2.84, Re: = 1.7E+5
D: Smooth bed, Run BS1, Q = 0.078 m?/s, d; = 0.0675 m, Fri = 2.84, Re: = 1.7E+5
A: Rough bed, Run BR3, Q = 0.1 m*/s, d; = 0.0825 m, Fr; = 2.84, Re; = 2.2E+5
A: Rough bed, Run BR3, Q = 0.1 m*/s, d; = 0.0825 m, Fr; = 2.84, Re; = 2.2E+5
B: Smooth bed, Run BS1, Q = 0.078 m°*/s, di = 0.0675 m, Fr; = 2.84, Re; = 1.7E+5 Figure 5.9 Void fraction distributions in hydraulic jump, comparison with the characteristic flow
B: Smooth bed, Run BS1, Q = 0.078 m°*/s, di = 0.0675 m, Fr; = 2.84, Re; = 1.7E+5 Figure 5.9 Void fraction distributions in hydraulic jump, comparison with the characteristic flow
A: Dimensionless longitudinal distribution
A: Dimensionless longitudinal distribution
averaged void fraction, smooth bed
averaged void fraction, smooth bed
B: Dimensionless longitudinal distribution related of the maximum void fraction, smooth bed to the dimensionless roller length of the maximum
B: Dimensionless longitudinal distribution related of the maximum void fraction, smooth bed to the dimensionless roller length of the maximum
void fraction, smooth bed
void fraction, smooth bed
Figure 5.12 Local void fraction minimum at boundary of shear and recirculation regions in the
Figure 5.12 Local void fraction minimum at boundary of shear and recirculation regions in the
A: As functions of relative longitudinal position in jump roller, smooth bed B: As functions of the dimensionless longitudinal position, smooth bed rough bed, respectively.
A: As functions of relative longitudinal position in jump roller, smooth bed B: As functions of the dimensionless longitudinal position, smooth bed rough bed, respectively.
In the shear region, the diffusion of air bubbles was observed with the broadening of the bell- shaped void fraction vertical profile with longitudinal distance as shown in Figure (5.8A and
In the shear region, the diffusion of air bubbles was observed with the broadening of the bell- shaped void fraction vertical profile with longitudinal distance as shown in Figure (5.8A and
d, = 0.0825 m, Fr; = 2.84, Re; = 2.2E+5 d; = 0.0835 m, Fr; = 1.96, Re: = 1.6E+5
d, = 0.0825 m, Fr; = 2.84, Re; = 2.2E+5 d; = 0.0835 m, Fr; = 1.96, Re: = 1.6E+5
[The comparison between rough and smooth bed showed higher bubble flux on rough bed
[The comparison between rough and smooth bed showed higher bubble flux on rough bed
A: Rough bed, Run BR3, Q = 0.1 m?/s, d; = 0.0825 m, Fr; = 2.84, Re; = 2.2E+5 similar inflow Froude and Reynolds numbers.
A: Rough bed, Run BR3, Q = 0.1 m?/s, d; = 0.0825 m, Fr; = 2.84, Re; = 2.2E+5 similar inflow Froude and Reynolds numbers.
B: Smooth bed, Run BS1, Q = 0.078 m*/s, di = 0.0675 m, Fr; = 2.84, Re, = 1.7E+5
B: Smooth bed, Run BS1, Q = 0.078 m*/s, di = 0.0675 m, Fr; = 2.84, Re, = 1.7E+5
A: Present study, comparison between rough and smooth bed of inflow Froude number and roughness for 2.8 < Fri < 4.3: Felder and Chanson (2018) on rough bed, an empirical relationship was developed in terms
A: Present study, comparison between rough and smooth bed of inflow Froude number and roughness for 2.8 < Fri < 4.3: Felder and Chanson (2018) on rough bed, an empirical relationship was developed in terms
Figure 5.17 Bubble count rate distribution in hydraulic jumps with different bed roughness
Figure 5.17 Bubble count rate distribution in hydraulic jumps with different bed roughness
A: Dimensionless longitudinal distribution of the
A: Dimensionless longitudinal distribution of the
C: Dimensionless longitudinal distribution of the maximum dimensionless bubble count rate, rough
C: Dimensionless longitudinal distribution of the maximum dimensionless bubble count rate, rough
Figure 5.19 Local maximum bubble count rate in the recirculation region on both rough and smooth
Figure 5.19 Local maximum bubble count rate in the recirculation region on both rough and smooth
smooth channel bed data from previous study (Felder and Chanson 2016, Chachereau and Chanson
smooth channel bed data from previous study (Felder and Chanson 2016, Chachereau and Chanson
A: Rough bed, Run BR3, Q = 0.1 m*/s, d= 0.0825 m, Fri = 2.84, Re; = 2.2E+5
A: Rough bed, Run BR3, Q = 0.1 m*/s, d= 0.0825 m, Fri = 2.84, Re; = 2.2E+5
B: Smooth bed, Run BS1, Q = 0.078 m*/s, di = 0.0675 m, Fr; = 2.84, Re; = 1.7E+5 Figure 5.22 Dimensionless interfacial velocity distributions upstream and in the hydraulic jump,
B: Smooth bed, Run BS1, Q = 0.078 m*/s, di = 0.0675 m, Fr; = 2.84, Re; = 1.7E+5 Figure 5.22 Dimensionless interfacial velocity distributions upstream and in the hydraulic jump,
Figure 5.23 Comparison of interfacial velocity in hydraulic jumps with different bed roughness comparison showed the larger interfacial velocities on rough bed, slightly shifted upwards.
Figure 5.23 Comparison of interfacial velocity in hydraulic jumps with different bed roughness comparison showed the larger interfacial velocities on rough bed, slightly shifted upwards.
Figure 5.24 Dimensionless velocity distributions in hydraulic jump, comparison between were derived for Vinax/V: based on data on smooth bed, as an example Chanson and Brattberg
Figure 5.24 Dimensionless velocity distributions in hydraulic jump, comparison between were derived for Vinax/V: based on data on smooth bed, as an example Chanson and Brattberg
A: As functions of dimensionless longitudinal
A: As functions of dimensionless longitudinal
C: As functions of dimensionless longitudinal position, rough bed position in jump roller, smooth bed position, smooth bed
C: As functions of dimensionless longitudinal position, rough bed position in jump roller, smooth bed position, smooth bed
Figure 5.25 Maximum interfacial velocity in the shear region, comparison with previous studies and
Figure 5.25 Maximum interfacial velocity in the shear region, comparison with previous studies and
Figure 5.26 Interfacial velocity in recirculation region, comparison with previous studies, colored
Figure 5.26 Interfacial velocity in recirculation region, comparison with previous studies, colored
yielded R = 0.80 and 0.99 and SE =0.065 and 0.044. fraction, smooth bed
yielded R = 0.80 and 0.99 and SE =0.065 and 0.044. fraction, smooth bed
yielded R = 0.67 and 0.99 and SE = 0.2 and 0.08. bubble count rate, smooth bed Figure 5.28 Characteristic flow depth at location with maximum bubble count rate in the shear region. comparison with previous studies, colored symbols present data
yielded R = 0.67 and 0.99 and SE = 0.2 and 0.08. bubble count rate, smooth bed Figure 5.28 Characteristic flow depth at location with maximum bubble count rate in the shear region. comparison with previous studies, colored symbols present data
Chanson (2016) on rough and smooth bed configurations for 2.8 < Fri < 4.3: An empirical relationship was extracted from the present data and those from Felder and
Chanson (2016) on rough and smooth bed configurations for 2.8 < Fri < 4.3: An empirical relationship was extracted from the present data and those from Felder and
A: As functions of dimensionless longitudinal position, smooth bed Chanson (2010), Wang (2014).
A: As functions of dimensionless longitudinal position, smooth bed Chanson (2010), Wang (2014).
The average value of Yvimax/d1 was 0.85 and 0.8 for rough and smooth bed configurations, section of jump roller, so that:
The average value of Yvimax/d1 was 0.85 and 0.8 for rough and smooth bed configurations, section of jump roller, so that:
Figure 5.31 Characteristic flow depths Yymax as functions of dimensionless longitudinal position,
Figure 5.31 Characteristic flow depths Yymax as functions of dimensionless longitudinal position,
Figure 6.1 Turbulence intensity distributions upstream of hydraulic jump with bed roughness rates as observed in the study by Felder and Chanson (2016). argest bubble count rate. Overall, vertical Tu profiles were relatively similar to bubble cou 6.2.2 Turbulence intensity downstream of jump toe
Figure 6.1 Turbulence intensity distributions upstream of hydraulic jump with bed roughness rates as observed in the study by Felder and Chanson (2016). argest bubble count rate. Overall, vertical Tu profiles were relatively similar to bubble cou 6.2.2 Turbulence intensity downstream of jump toe
B: Rough bed, Run BR2, Q = 0.07 m/s, A: Rough bed, Run BR3, Q = 0.1 m/s, d; = 0.0825 m, Fri = 2.84, Re; = 2.2E+5 d, = 0.0835 m, Fr: = 1.96, Re; = 1.6E+5
B: Rough bed, Run BR2, Q = 0.07 m/s, A: Rough bed, Run BR3, Q = 0.1 m/s, d; = 0.0825 m, Fri = 2.84, Re; = 2.2E+5 d, = 0.0835 m, Fr: = 1.96, Re; = 1.6E+5
A: Rough bed, Run BR3, Q = 0.1 m*/s, d; = 0.0825 m, Fr; = 2.84, Re; = 2.2E+5
A: Rough bed, Run BR3, Q = 0.1 m*/s, d; = 0.0825 m, Fr; = 2.84, Re; = 2.2E+5
B: Smooth bed, Run BS1, Q = 0.078 m°*/s, di = 0.0675 m, Fr: = 2.84, Re: = 1.7E+5
B: Smooth bed, Run BS1, Q = 0.078 m°*/s, di = 0.0675 m, Fr: = 2.84, Re: = 1.7E+5
bed, resulting in a shorter length of roller on rough bed (Section 4.4). bed (Figure 6.4B). This could be associated with a higher rate of energy dissipation on rough and R2 roughness types 1 and 2 by Felder and Chanson (2016)
bed, resulting in a shorter length of roller on rough bed (Section 4.4). bed (Figure 6.4B). This could be associated with a higher rate of energy dissipation on rough and R2 roughness types 1 and 2 by Felder and Chanson (2016)
the jump toe. Figure 6.5 The turbulence intensity at the characteristic elevations of maximum interfacial velocity.
the jump toe. Figure 6.5 The turbulence intensity at the characteristic elevations of maximum interfacial velocity.
Figure 6.6 Relationship between turbulent intensity and dimensionless bubble count rate Toombes 2002) and in a hydraulic jump on rubber mat rough bed (Felder and Chanson 2016)
Figure 6.6 Relationship between turbulent intensity and dimensionless bubble count rate Toombes 2002) and in a hydraulic jump on rubber mat rough bed (Felder and Chanson 2016)
A: Rough bed, Run BR3, Q = 0.1 m*/s, d= 0.0825 m, Fr; = 2.84, Re; = 2.2E+5
A: Rough bed, Run BR3, Q = 0.1 m*/s, d= 0.0825 m, Fr; = 2.84, Re; = 2.2E+5
Figure 6.7 Auto-correlation time scale (filled symbols), longitudinal cross-correlation time scale
Figure 6.7 Auto-correlation time scale (filled symbols), longitudinal cross-correlation time scale
A: Dimensionless auto-correlation time scales velocity data; comparison with characteristic flow depth Yoo/d
A: Dimensionless auto-correlation time scales velocity data; comparison with characteristic flow depth Yoo/d
Figure 6.9 Dimensionless advective length scale measured on the channel centreline, filled symbols
Figure 6.9 Dimensionless advective length scale measured on the channel centreline, filled symbols
A: Rough bed, Run BR3, Q = 0.1 m?/s, d; = 0.0825 m, Fr = 2.84, Re; = 2.2E+5 advection and diffusion of bubbles further downstream. rapidly, i.e. over a shorter distance in the horizontal direction, indicating a well-separated
A: Rough bed, Run BR3, Q = 0.1 m?/s, d; = 0.0825 m, Fr = 2.84, Re; = 2.2E+5 advection and diffusion of bubbles further downstream. rapidly, i.e. over a shorter distance in the horizontal direction, indicating a well-separated
B: Smooth bed, Run BS1, Q = 0.078 m°*/s, di = 0.0675 m, Fr; = 2.84, Re: = 1.7E+5
B: Smooth bed, Run BS1, Q = 0.078 m°*/s, di = 0.0675 m, Fr; = 2.84, Re: = 1.7E+5
time increased with the dimensionless elevation.
time increased with the dimensionless elevation.
A: Rough bed, Fr; = 2.84, d; = 0.0825m
A: Rough bed, Fr; = 2.84, d; = 0.0825m
figure, the legend included the location (x-x1, y/d1) and the local air-water flow properties (C,
figure, the legend included the location (x-x1, y/d1) and the local air-water flow properties (C,
Table 7.1 Percentage of the bubble chord time at y= Y,,,,,
Table 7.1 Percentage of the bubble chord time at y= Y,,,,,
7.2.2 Particle chord length
7.2.2 Particle chord length
signal segment received by leading probe tip, some bubble groups can be observed in the distribution. An investigation of clustering events may provide some information to conclude soncentration of air bubbles in a short interval of time rather than a uniform bubble In the bubbly flow region, the phase-detection probe signal consistently suggested a 7.3 Clustering characterisation 7.3.1. Introduction
signal segment received by leading probe tip, some bubble groups can be observed in the distribution. An investigation of clustering events may provide some information to conclude soncentration of air bubbles in a short interval of time rather than a uniform bubble In the bubbly flow region, the phase-detection probe signal consistently suggested a 7.3 Clustering characterisation 7.3.1. Introduction
Figure 7.6 Definition sketch of the detection of 1D bubble cluster the free surface region above the jump roller.
Figure 7.6 Definition sketch of the detection of 1D bubble cluster the free surface region above the jump roller.
Figure 7.7 Phase-detection probe signal indicating longitudinal bubble grouping, rough bed, Run BR3, Q = 0.1 m*/s, di = 0.0825 m, Fr) = 2.84, Re; = 2.2E+5, x-x1 = 0.6m, y = 0.3m
Figure 7.7 Phase-detection probe signal indicating longitudinal bubble grouping, rough bed, Run BR3, Q = 0.1 m*/s, di = 0.0825 m, Fr) = 2.84, Re; = 2.2E+5, x-x1 = 0.6m, y = 0.3m
that might be associated with the undular behaviour of hydraulic jump. and Fimax, 1.e. Y(Fcluymax © YFmax. Only the data of Fr; = 1.96 exhibited some scattet
that might be associated with the undular behaviour of hydraulic jump. and Fimax, 1.e. Y(Fcluymax © YFmax. Only the data of Fr; = 1.96 exhibited some scattet
toe (Figure 7.14C).
toe (Figure 7.14C).
A: Based on Criterion A (Equation 7.2)
A: Based on Criterion A (Equation 7.2)
A1: Rough bed, based on Criterion A A2: Corresponding void fraction distribution
A1: Rough bed, based on Criterion A A2: Corresponding void fraction distribution
B2: Corresponding void fraction distribution B1: Rough bed, based on Criterion B
B2: Corresponding void fraction distribution B1: Rough bed, based on Criterion B
C2: Corresponding void fraction distribution C1: Smooth bed, based on Criterion A
C2: Corresponding void fraction distribution C1: Smooth bed, based on Criterion A
A1: Rough bed, based on Criterion A A2: Corresponding void fraction distribution 1ydraulic jump on smooth bed, which showed 0.14 < Ave. Pew <0.34 for 3.8 < Fri < 14.3
A1: Rough bed, based on Criterion A A2: Corresponding void fraction distribution 1ydraulic jump on smooth bed, which showed 0.14 < Ave. Pew <0.34 for 3.8 < Fri < 14.3
B1: Rough bed, based on Criterion B
B1: Rough bed, based on Criterion B
C2: Corresponding void fraction distribution C1: Smooth bed, based on Criterion A
C2: Corresponding void fraction distribution C1: Smooth bed, based on Criterion A
Table 7.2 Classes of bubbles for the IAT analysis Table 7.3 Measurement points chosen for the IAT analysis in the hydraulic jump
Table 7.2 Classes of bubbles for the IAT analysis Table 7.3 Measurement points chosen for the IAT analysis in the hydraulic jump
class of bubble chord time.
class of bubble chord time.
Table 7.4 Details of IAT analysis for each flow condition deviation from Poisson law decreased with increasing the size of bubble chord time (Table
Table 7.4 Details of IAT analysis for each flow condition deviation from Poisson law decreased with increasing the size of bubble chord time (Table
B: (x-x1)/di = 1.48, ten-ap: 3.0-5.0 ms A: (x-x1)/d) = 1.48, ten-ap: 0.0-0.5 ms
B: (x-x1)/di = 1.48, ten-ap: 3.0-5.0 ms A: (x-x1)/d) = 1.48, ten-ap: 0.0-0.5 ms
rough and smooth bed configurations, the effects of the distance from the jump toe upon the
rough and smooth bed configurations, the effects of the distance from the jump toe upon the
A: Bubbles with t;4 from 0 to 0.5 ms B: Bubbles with 74 from 1.0 to 1.5 ms ‘igure 7.24 Distribution with the distance of the PDF for bubbles in the hydraulic jump on rough and smooth bed configurations. Comparison with drop shaft and hydraulic jump on smooth bed by Gualtieri and Chanson (2013), HJ stands for hydraulic jump
A: Bubbles with t;4 from 0 to 0.5 ms B: Bubbles with 74 from 1.0 to 1.5 ms ‘igure 7.24 Distribution with the distance of the PDF for bubbles in the hydraulic jump on rough and smooth bed configurations. Comparison with drop shaft and hydraulic jump on smooth bed by Gualtieri and Chanson (2013), HJ stands for hydraulic jump
a. Small undular hydraulic jump, run AS9, Q = 0.044 m?/s, d; = 0.06 m, Fr; =1.92, Re; = 9.5E+4
a. Small undular hydraulic jump, run AS9, Q = 0.044 m?/s, d; = 0.06 m, Fr; =1.92, Re; = 9.5E+4
b. Small undular hydraulic jump with air entrainment, run AS10, Q = 0.048 m°/s, d;=0.06 m, Fr; =
b. Small undular hydraulic jump with air entrainment, run AS10, Q = 0.048 m°/s, d;=0.06 m, Fr; =
c. Undular hydraulic jump with air entrainment, run AS11, Q = 0.054 m*/s, d= 0.06 m, Fr) = 2.47.
c. Undular hydraulic jump with air entrainment, run AS11, Q = 0.054 m*/s, d= 0.06 m, Fr) = 2.47.
d. Hydraulic jump with roller and fluctuations of jump toe, run AS12, Q = 0.073 m*/s, di = 0.061 m,
d. Hydraulic jump with roller and fluctuations of jump toe, run AS12, Q = 0.073 m*/s, di = 0.061 m,
>. Hydraulic jump floating on top of clear water flow region, run AS13, Q = 0.078 m°*/s, d; = 0.062 m,
>. Hydraulic jump floating on top of clear water flow region, run AS13, Q = 0.078 m°*/s, d; = 0.062 m,
f. Hydraulic jump with strong vortex shedding and free-surface fluctuations, run AS14, Q = 0.089
f. Hydraulic jump with strong vortex shedding and free-surface fluctuations, run AS14, Q = 0.089
a. Small undular hydraulic jump, run AR1, QO = 0.043 m?/s, d; = 0.078 m, Fr; = 1.31, Re; = 9.6E+4
a. Small undular hydraulic jump, run AR1, QO = 0.043 m?/s, d; = 0.078 m, Fr; = 1.31, Re; = 9.6E+4
b. Undular hydraulic jump, run AR2, Q = 0.051m?/s, d; = 0.0785 m, Fr; = 1.57, Re; = 1.1E+5
b. Undular hydraulic jump, run AR2, Q = 0.051m?/s, d; = 0.0785 m, Fr; = 1.57, Re; = 1.1E+5
c. Undular hydraulic jump with air entrainment, run AR4, Q = 0.07m*/s, di = 0.084m, Fri = 1.93, Re:
c. Undular hydraulic jump with air entrainment, run AR4, Q = 0.07m*/s, di = 0.084m, Fri = 1.93, Re:
d. Hydraulic jump with roller and vortex street on clear water, run AR5, Q = 0.076 m*/s, di = 0.085 m,
d. Hydraulic jump with roller and vortex street on clear water, run AR5, Q = 0.076 m*/s, di = 0.085 m,
Hydraulic jump with strong vortex shedding, run AR7, Q = 0.092 m*/s, d= 0.084 m, Fr; = 2.56, Re
Hydraulic jump with strong vortex shedding, run AR7, Q = 0.092 m*/s, d= 0.084 m, Fr; = 2.56, Re
f. Hydraulic jump with strong vortex shedding and splashing, run AR8, Q = 0.1 m*/s, d; = 0.085 m,
f. Hydraulic jump with strong vortex shedding and splashing, run AR8, Q = 0.1 m*/s, d; = 0.085 m,
Fr, = 1.7, Q = 0.061 m?*/s, Re\=1.4x10°, h = 0.06 m; d\=0.083 m: x-x = -0.3 m
Fr, = 1.7, Q = 0.061 m?*/s, Re\=1.4x10°, h = 0.06 m; d\=0.083 m: x-x = -0.3 m
Fr, = 1.96, Q= 0.07 m*/s, Re\=1.6x10°, h = 0.06 m; d\=0.083 m: x-x; = 0.3
Fr, = 1.96, Q= 0.07 m*/s, Re\=1.6x10°, h = 0.06 m; d\=0.083 m: x-x; = 0.3
Fr = 1.96, Q = 0.07 m*/s, Rei=1.6x10°, h = 0.06 m; d\=0.083 m: x-x; = 0.6 m
Fr = 1.96, Q = 0.07 m*/s, Rei=1.6x10°, h = 0.06 m; d\=0.083 m: x-x; = 0.6 m
Fr, = 1.96, Q= 0.07 m*/s, Rei=1.6x10°, h = 0.06 m; d\=0.083 m: x-x1 = 1.1 m
Fr, = 1.96, Q= 0.07 m*/s, Rei=1.6x10°, h = 0.06 m; d\=0.083 m: x-x1 = 1.1 m
Fr, = 2.84, Q = 0.1 m?/s, Rei=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = -0.3 m
Fr, = 2.84, Q = 0.1 m?/s, Rei=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = -0.3 m
Fr, = 2.84, Q = 0.1 m*/s, Rei=2.2x10°, h = 0.06 m; di=0.082 m: x-x; = 0.1 n
Fr, = 2.84, Q = 0.1 m*/s, Rei=2.2x10°, h = 0.06 m; di=0.082 m: x-x; = 0.1 n
Fr, = 2.84, Q=0.1 m’/s, Re:=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 0.15 m
Fr, = 2.84, Q=0.1 m’/s, Re:=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 0.15 m
Fr, = 2.84, 0 =0.1 m*/s, Re:=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 0.3 m
Fr, = 2.84, 0 =0.1 m*/s, Re:=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 0.3 m
Fr = 2.84, Q=0.1 m’/s, Re:=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 0.45 m
Fr = 2.84, Q=0.1 m’/s, Re:=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 0.45 m
Fr = 2.84, 0 =0.1 m*/s, Re:=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 0.6 m
Fr = 2.84, 0 =0.1 m*/s, Re:=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 0.6 m
Fr, = 2.84, Q = 0.1 m?/s, Rei=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 0.8 m
Fr, = 2.84, Q = 0.1 m?/s, Rei=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 0.8 m
Fr, = 2.84, Q = 0.1 m?/s, Rei=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 1.1 m
Fr, = 2.84, Q = 0.1 m?/s, Rei=2.2x10°, h = 0.06 m; d\=0.082 m: x-x; = 1.1 m
Fr, = 2.84, Q = 0.078 m?/s, Rei=1.7x10°, h = 0.06 m; di=0.067 m: x-x; = 0.1 m
Fr, = 2.84, Q = 0.078 m?/s, Rei=1.7x10°, h = 0.06 m; di=0.067 m: x-x; = 0.1 m
Fr) = 2.84, Q = 0.078 m*/s, Rei=1.7x10°, h = 0.06 m; d:=0.067 m: x-x; = 0.15 m
Fr) = 2.84, Q = 0.078 m*/s, Rei=1.7x10°, h = 0.06 m; d:=0.067 m: x-x; = 0.15 m
Fr; = 2.84, Q = 0.078 m?/s, Rei=1.7x10°, h = 0.06 m; di=0.067 m: x-x; = 0.3 m
Fr; = 2.84, Q = 0.078 m?/s, Rei=1.7x10°, h = 0.06 m; di=0.067 m: x-x; = 0.3 m
Fr; = 2.84, O = 0.078 m?/s, Rei=1.7x10°, h = 0.06 m; d\=0.067 m: x-x; = 0.45 m
Fr; = 2.84, O = 0.078 m?/s, Rei=1.7x10°, h = 0.06 m; d\=0.067 m: x-x; = 0.45 m
Fr; = 2.84, Q = 0.078 m?/s, Rei=1.7x10°, h = 0.06 m; di=0.067 m: x-x; = 0.8 m
Fr; = 2.84, Q = 0.078 m?/s, Rei=1.7x10°, h = 0.06 m; di=0.067 m: x-x; = 0.8 m
Fr; = 2.84, O = 0.078 m/s, Re:=1.7x10°, h = 0.06 m; d\=0.067 m: x-x; = 1.1m
Fr; = 2.84, O = 0.078 m/s, Re:=1.7x10°, h = 0.06 m; d\=0.067 m: x-x; = 1.1m
Related topics:
MechanicsHydraulic RoughnessAir EntrainmentSupercritical FlowFroude number
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