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Measurements of air-water flow properties in hydraulic jumps in a sloping channel Laura Montano1, Stefan Felder2 1

PhD candidate, Water Research Laboratory, School of Civil and Environmental Engineering, UNSW Sydney, Australia E-mail: [email protected] 2

Lecturer, Water Research Laboratory, School of Civil and Environmental Engineering, UNSW Sydney, Australia E-mail: [email protected]

Abstract Hydraulic jumps are a complex phenomenon characterised by high turbulence, strong fluctuations and 3D motions which result in high energy dissipation and flow aeration. Past experimental research has been conducted on hydraulic jumps on sloped channels including conjugate depth ratio, roller length and velocity distributions. However, experimental analysis on air-water flow properties in hydraulic jumps on sloped channels remains limited apart from some recent experiments performed on a slope of θ = 2.5°. The present study conducted an experimental analysis of the air entrainment characteristics of hydraulic jumps on a sloped channel of θ = 5°. The air-water flow properties of Classical Hydraulic Jumps, Type B and D jumps were compared. Basic air entrainment characteristics were observed including void fraction, bubble count rate, interfacial velocity and chord times revealing distinctive differences between Type D jump and Classical Hydraulic Jumps.

1. INTRODUCTION A sudden transition from rapid flows to slow flows is known as a hydraulic jump. Extensive research has been conducted on Classical Hydraulic Jumps (CHJ) defined as hydraulic jumps in rectangular horizontal channels. While a CHJ represents the most efficient and desired hydraulic jump for energy dissipation downstream of a steeply sloping channel, an increased downstream tailwater flow depth can shift the hydraulic jump upstream into the sloped section of the channel (Hager, 1989; Ohtsu & Yasuda, 1991). Hydraulic jumps on a positive slope are defined as hydraulic jumps Type B, C, D and E depending upon their position on the slope (Kindsvater, 1944; Bradley & Peterka, 1957; Rajaratnam, 1966; Ohtsu & Yasuda, 1991). Type B jumps start on the slope and end in the horizontal section of the channel. Type C, D and E jumps occur on the slope only. While the end of the roller in a Type C jump occurs at the intersection between the sloped and the horizontal channel sections, Type D and E jumps end in the sloped section. Type E jumps are rare and occur in long flat slopes where the tailwater flow depth is parallel to the sloped channel bed (Kindsvater, 1944; Rajaratnam, 1966). Several investigations have been conducted on hydraulic jumps in sloped channels (e.g. Bakhmeteff & Matzke, 1938; Kindsvater, 1944, Bradley & Peterka, 1957; Rajaratnam & Murahari, 1974). Some of the most important insights into hydraulic jumps on sloped sections have focused on empirical and theoretical equations to estimate the conjugate depth ratio (Bakhmeteff & Matzke, 1938; Kindsvater, 1944; Bradley & Peterka, 1957; Hager, 1989). Other research has focused upon the energy dissipation performances (Hager, 1989; Beirami & Chamani, 2010) and the roller length of hydraulic jumps in slopes (Hager, 1989; Ohtsu & Yasuda, 1991). Velocity distributions have been investigated by Rajaratnam & Murahari (1974), Ohtsu & Yasuda (1991) and Gunal & Narayanan (1996). So far, very limited research has been conducted to evaluate the air entrainment characteristics in hydraulic jumps on sloped channels despite some recent experiments on a slope of θ = 2.5° (Montano & Felder, 2017). Herein, the present contribution expanded the findings of Montano & Felder (2017) to a steeper sloped channel of θ = 5°. The present study compared the air-water flow properties of CHJ with Type

Air-water flow properties in hydraulic jumps in sloping channels

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B and D jumps for comparative Froude and Reynolds numbers expanding the current understanding of the air-water flow properties in hydraulic jumps on sloping channels.

2. EXPERIMENTAL CONFIGURATION The experiments were undertaken at the Water Research Laboratory (WRL) of UNSW Sydney, Australia in a rectangular channel of 0.6 m width, 40 m length and 0.6 m height. The discharge was supplied from Manly dam controlled by an ABB WaterMaster electromagnetic flowmeter with ± 0.4% accuracy. At the upstream end of the flume a false wooden floor with a slope of θ = 5° was installed followed by the horizontal channel (Montano & Felder, 2017). A tail gate was used to generate CHJs as well as jumps on the sloped channel section. Upstream and downstream of the hydraulic jumps, the conjugate flow depths were measured with a pointer gauge within an accuracy of ± 0.5 mm. Conjugate flow depths and flow visualisations were performed for a flow range of 0.01 < Q < 0.070 m3/s for Type B and D jumps and for 0.036 < Q < 0.070 m3/s for CHJs. The boundary layer development at several cross-sections upstream of the hydraulic jump was measured with a Pitot tube. Detailed observations of air entrainment in hydraulic jumps on slopes was conducted in channel centre line with a WRL double-tip conductivity probe with needle tip sensors with an inner diameter of ∅ = 0.125 mm (Felder & Pfister, 2017). Both probe sensors were sampled with 20 kHz for 45 s (Felder & Chanson, 2015). In comparison with the range of flow visualizations, the air-water flow properties were measured only for flows with sufficient flow aeration. Table 1 shows the experimental flow conditions for the air-water flow experiments in the present study including the inflow depth d1, upstream Froude number Fr1 and Reynolds number Re. A total of four experimental configurations were investigated with comparable Froude and Reynolds numbers. The present setup did not allow to control the inflow depth upstream of the hydraulic jumps and it was not possible to observe the same Froude number for the three types of hydraulic jumps. For the CHJ and Type B jump, detailed observations with the Pitot tube confirmed fully developed inflow conditions whereas the inflow conditions for the Type D jump were partially developed. For all experimental flow conditions, detailed air-water flow measurements were conducted at five cross-sections along the hydraulic jump to observe the development of the air-water flow features and to compare the effect of the channel slope on the flow aeration. Table 1. Experimental configuration of air-water flow properties analysis in the present study with same Froude and Reynolds numbers (bold font); θ = 5° Hydraulic Jump Type CHJ Type B Type D X x x X

Q (m3/s) 0.069 0.030 0.069 0.069

d1 (m) 0.040 0.023 0.047 0.058

Fr1 (-) 4.6 4.6 3.6 2.6

Re (-) 1.1x105 8.4x104 1.2x105 1.1x105

Inflow conditions Fully developed inflow Fully developed inflow Fully developed inflow Partially developed inflow

3. FLOW PATTERNS Visual observations were performed for a flow range of 0.01 < Q < 0.070 m3/s for Type B and D jumps and for 0.036 < Q < 0.070 m3/s for the CHJ. These flow conditions corresponded to inflow Froude numbers of 4.4 < Fr1 < 4.8 for the CHJs, to 3.7 < Fr1 < 5.0 for the Type B jumps and to 2.6 < Fr1 < 4 for the Type D jumps. No comparable Froude numbers were achieved between Type D jump and CHJ due to the uncontrolled flow conditions upstream of the hydraulic jumps. Flow visualisations showed an increase in jump toe oscillations and air entrainment with an increase in inflow Froude number. Similar observations have been reported before in CHJ (e.g. Chachereau & Chanson, 2011) and hydraulic jumps on a slope (Montano & Felder, 2017). Figure 1 shows typical photographs of the flow visualisations for the hydraulic jumps in the present study with similar Froude numbers. The CHJs and the Type B jump showed similar flow behaviour with strong air entrainment at the jump toe and freesurface disturbances (Figure 1a & b). The flow features were consistent with observations of hydraulic jumps in previous studies for similar range of Froude and Reynolds numbers (e.g. Hager, 1989; Chachereau & Chanson, 2011). Larger oscillations and a slightly longer region of white water and turbulence was identified for the CHJ compared with the Type B jump (Figure 1a and b). In contrast to the strong similarity between CHJ and Type B jump with similar Froude numbers, Type D jump showed almost no air entrainment at the impingement point of the hydraulic jump and significant lower flow aeration (Figure 1c). The free-surface oscillations and hydraulic jump toe fluctuations were also lower for the Type D jump. Overall, the CHJs and the Type B jumps presented similar flow instabilities

HIWE2017 Montano and Felder

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and oscillations for all flow conditions, while the Type D jumps were less aerated and more stable. These observations were independent of the Froude and Reynolds numbers.

a. CHJ: d1 = 0.040 m, Q = 0.069 m3/s, Fr1 = 4.6, Re = 1x105

b. Type B jump: d1 = 0.023 m, Q = 0.030 m3/s, Fr1 = 4.60, Re = 5x104

c. Type D jump: d1 = 0.012 m, Q = 0.011 m3/s, Fr1 = 4.02, Re = 1.75x104 Figure 1 –Visual observation of hydraulic jumps in sloped and flat channels with similar Froude number. Left figures represent the hydraulic jump profile in side view (Flow from left to right) and right figures show the jump toe behaviour (Flow from bottom to top).

The conjugate depths were measured with a pointer gauge upstream and downstream of the hydraulic jumps. The present data were in agreement with previous experimental observations of CHJs and Type B and D jumps with comparable slopes (Bakhmeteff & Matzke, 1938; Kindsvater, 1944; Bradley & Peterka, 1957; Hager, 1989). The present CHJ was in good agreement with the Bélanger equation. Type B and D jumps were well correlated with the empirical formulas by Kindsvater (1944), Rajaratnam (1966) and Hager (1989).

4. AIR-WATER FLOW PROPERTIES To improve the understanding of the internal air-water flow behaviour and the turbulent characteristics of hydraulic jumps on sloped channels, a detailed analysis of the air-water flow properties was performed for all hydraulic jumps in the present study (Table 1). The analysis was performed with the double-tip conductivity probe and included the measurement of void fraction C, bubble count rate F, interfacial velocity V and average bubble chord time Chtime for the same Froude and Reynolds numbers respectively.

4.1.

Void Fraction

The void fraction distributions in Figure 2 show the vertical and longitudinal air entrainment development in CHJ and jumps in sloped sections for comparative Froude and Reynolds numbers respectively. In Figure 2, the x axis shows the void fraction distribution C. For better illustration of the longitudinal change in C, the dimensionless distance along the jump roller x/d1 is included. Hence, the void fraction distributions are illustrated for the same dimensionless distances x/d1 along the hydraulic jump starting at the hydraulic jump toe for the respective jump type. The distributions are shown in terms of the dimensionless elevation above the channel bed y/d1 (Note that all data were recorded perpendicular to the flat and sloped channel beds respectively). The free-surface of the roller η/d1 is included; it is defined as the elevation where C = 0.9. For x/d1 ≤ 9.4, the shear region (lower region) and the recirculation region (upper region) could be clearly distinguished for all jump types. The shear region was characterised by convective transport and entrapped air bubbles at the impingement point of the hydraulic jump (Chanson, 1995, 2010; Takahashi & Ohtsu, 2017). In the upper region, the freesurface was represented by roller movement with reverse flows and an interchange of air and water


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generating splashes, foam and droplets (e.g. Chanson & Brattberg, 2000). For all experiments, higher data scatter was found for the CHJ as a result of stronger jump toe fluctuations compared with hydraulic jumps on sloped sections as was reported previously by Montano & Felder (2017). Figure 2a shows a comparison between CHJ and Type B jump for the same inflow Froude number (Fr1 = 4.6). The void fraction distributions for both jump types followed typical void fraction distributions for hydraulic jumps with fully developed inflow conditions (Takahashi & Ohtsu, 2017). For x/d1 ≤ 9.4, both hydraulic jump types followed the diffusion equation where the air concentration distribution increased monotonically from the channel bed to a maximum void fraction Cmax followed by a decrease in the air concentration until the flow depth reached the recirculation region (Chanson, 1995; Chanson & Brattberg, 2000; Zhang et al., 2014). In the recirculation region, the void fraction distribution increased until it reached 100% aeration (Chanson & Brattberg, 2000; Zhang et al. 2014). For all cross sections, the CHJ showed a slightly larger maximum void fraction compared with the corresponding Type B jump suggesting larger air entrainment for the CHJ. This finding was in agreement with the observations by Montano & Felder (2017) on a milder slope. The difference between CHJ and Type B jumps increased with increasing distance from the jump toe indicating a larger length of air entrainment for the CHJ. The elevation of the roller surface η/d1 was consistently larger for the Type B jump along the hydraulic jump. Figure 2b presents the void fraction distribution for the three jump types with the same Reynolds number (Re = 1.1x105). Although the shear and recirculation region could be identified for the three hydraulic jump types, the Type D jump did not present a clear maximum peak in the shear region (Figure 2b). In fact, the void fraction distribution for the Type D jump presented a monotonic increase in the shear region for x/d1 ≤ 3.3. This result suggested lower air entrainment at the impingement point of the Type D jump which can be caused by a lower inflow Froude number and lower jump toe fluctuations. It could be also linked with partially developed inflow conditions (Takahashi & Ohtsu, 2017). As a consequence, air bubbles in Type D jump were more affected by buoyancy and gravity effects limiting the generation of the maximum peak in the advective diffusion layer (Chanson, 1995). The maximum void fractions Cmax were similar for the CHJ and Type B jumps for x/d1 ≤ 5.8. For x/d1 > 5.8, the CHJ showed higher void fraction concentrations suggesting a longer air entrainment region compared with Type B and D jumps with the same Reynolds number. For all cross sections, CHJ presented the largest roller surface elevation while the lowest elevation was found in the Type D jump. This finding may be associated with the inflow Froude number (Wang 2014). 8

CHJ (Fr1 = 4.6) Type B (Fr1 = 4.6) CHJ (/d1) Type B (/d1)

7

y/d1 (-)

6 5 4 3 2 1 0 0

1

2

3

4

5 6 C + x/d1 (-)

7

8

9

10

11

a) Void fraction distributions with the same Froude number (Fr1 = 4.6).


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CHJ (Fr1 = 4.6) Type B (Fr1 = 3.6) Type D (Fr1 = 2.6) CHJ (/d1) Type B (/d1) Type D (/d1)

7 6

y/d1 (-)

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5 4 3 2 1 0 0

1

2

3

4

5 6 C + x/d1 (-)

7

8

9

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b) Void fraction distributions with the same Reynolds number (Re = 1.1x105). Figure 2 – Comparison of void fraction distributions for CHJ and Type B and D jumps (θ = 5°).

4.2.

Bubble count rate

In hydraulic jumps, typical bubble count rate distributions are characterised by two peaks located in the shear and recirculation regions respectively (e.g. Chanson, 2010). Figure 3a presents the dimensionless time-averaged bubble count rate distributions for CHJ and Type B jump with the same Froude number. For the entire jump length, the maximum bubble count rates were larger for the CHJ both in the shear and the recirculation region. This finding was in agreement with the experiment conducted previously on a slope of θ = 2.5° (Montano & Felder, 2017). Although the CHJ presented higher bubble count rate in the recirculation region, the difference was not as significant as it was in the shear region suggesting similar air-water features in the upper part of the roller whereas CHJ presented a significant larger number of bubbles in the shear region. Figure 3b shows the comparison of bubble count rate between CHJ, Type B and Type D jump for the same Reynolds number. Despite similar distribution patterns between the three jump types, differences in the bubble count rate were identified in the shear and recirculation regions. A clear peak in bubble count rate could be identified in the shear region for all jump types for x/d1 ≤ 5.8. However, the peak in bubble count rate decreased faster in downstream direction for the Type D jump. This finding was consistent with the visual observation of lesser flow aeration for the Type D jump (Figure 1c). In contrast to the observations for the same inflow Froude number (Figure 3a), the Type B jump presented slightly larger dimensionless time-averaged bubble count rates in the shear region compared to the CHJ for x/d1 ≤ 9.4. Overall, the shape of the bubble count rate distributions were similar for Type B and CHJ whereas the Type D jump presented a remarkable faster decrease in the bubble count rate with increasing distance from the jump toe which indicated a smaller roller length for the Type D jump. 8

CHJ (Fr1 = 4.6) Type B (Fr1 = 4.6) CHJ (/d1) Type B (/d1)

7

y/d1 (-)

6 5 4 3 2 1 0 0

1

2

3

4

5

6 7 8 9 F×d1/V1 + x/d1 (-)

10

11

12

13

14

15

a) Bubble count rate distributions for the same Froude number (Fr1 = 4.6)


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CHJ (Fr1 = 4.6) Type B (Fr1 = 3.6) Type D (Fr1 = 2.6) CHJ (/d1) Type B (/d1) Type D (/d1)

7 6

y/d1 (-)

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5 4 3 2 1 0 0

1

2

3

4

5

6 7 8 9 F×d1/V1 +x/d1 (-)

10

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12

13

14

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b) Bubble count rate distributions for the same Reynolds number (Re = 1.1x105) Figure 3 – Comparison of dimensionless bubble count rate distributions of CHJ and Type B and D jumps (θ = 5°). Although some distinctive differences were identified in the bubble count rate distributions between the three hydraulic jump types, the illustration in Figure 3 distorted the magnitude of the differences between the three jump types. This was due to the dimensionless distance factor x/d1. To highlight the differences in bubble count rate more clearly, Figure 4 shows the summation of the dimensionless number of bubbles for the CHJ and Type B jump for the same inflow Froude number. The analysis was conducted for the shear region and the recirculation region. In the shear region, the CHJ was characterised by the largest number of bubbles with more than twice the number of detected bubbles for x/d1 ≤ 5.8. In the recirculation region, the CHJ showed about 50% more bubbles compared with the Type B jump for x/d1 ≤ 5.8. Overall, Figure 4shows that the strongest differences in the summation of the number of detected bubbles between CHJ and Type B jump occurred in the shear region. The continuous black line in Figure 4 shows the average of the summation of the dimensionless number of bubbles for CHJ and Type B jump. An increase in the number of bubbles was observed for the CHJ and Type B jump for x/d1 = 3.3. Further downstream, the average bubble count rate decreased with a similar rate for both jump types. The averaged bubble count rate was independent of the hydraulic jump type for the same inflow Froude number (Figure 4). For the comparative analysis with the same Reynolds number, the CHJ and Type B jump presented a similar number of bubbles whereas the Type D jump showed a much stronger decrease in the number of bubbles for x/d1 ≥ 9.4. For x/d1 = 14, the CHJ presented more than 9 times the number of detected bubbles compared with Type D jump.

Figure 4 – Comparison of the time-averaged number of bubbles in CHJ and Type B jumps with the same Froude number (Fr1 = 4.6) for the shear region, the recirculation region and along the complete vertical profile. Black line shows an averaged trend line.


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4.3.

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Interfacial velocity distribution

The local time-averaged interfacial velocity V was calculated as the ratio of the distance of the two probe tips of the conductivity probe and the average travel time of the air-water flows between the two probe tips. Figure 5 illustrates the dimensionless velocity distributions V/Vmax in the present study as a function of the dimensionless flow depth (y-YVmax)/y0.5, where Vmax is the maximum interfacial velocity in the shear region, y is the flow depth, YVmax is the flow depth for Vmax, Vrecirc is the velocity in the recirculation region and y0.5 is the flow depth where V = 0.5 Vmax. Previous studies showed a similarity in velocity distributions between the free mixing region of CHJs and jumps on sloped sections with the classical wall jet velocity distribution (Rajaratnam, 1965; Rajaratnam & Murahari, 1974; Ohtsu & Yasuda, 1991; Chanson & Brattberg, 2000; Chanson, 2010): 𝑉 𝑉𝑚𝑎𝑥 𝑉−𝑉𝑟𝑒𝑐𝑖𝑟𝑐 𝑉𝑚𝑎𝑥 −𝑉𝑟𝑒𝑐𝑖𝑟𝑐

=(

1/𝑁

𝑦

𝑌𝑉𝑚𝑎𝑥

)

for 𝑦/𝑌𝑉𝑚𝑎𝑥 < 1

1

𝑦−𝑌𝑉𝑚𝑎𝑥

2

𝑦0.5

= 𝑒𝑥𝑝 {− [1.765(

)]}

for 1 < 𝑦/𝑌𝑉𝑚𝑎𝑥 < 3 𝑡𝑜 4

(4) (5)

Figure 5a & b present the dimensionless time-averaged interfacial velocity distributions in the present study for the same Froude number (Fr1 = 4.6) for x/d1 ≤ 5.8 and x/d1 > 5.8 respectively as well as the comparison of experimental data with the wall jet theory. Overall, CHJ and Type B jump presented a similar trend in the shear region for all cross-sections and the experimental data were well fitted by the wall jet theory (Equations 4 and 5) despite some data scatter. Similar to the results obtained by Ohtsu & Yasuda (1991), the velocity distribution in Type B jump was not affected by the change from sloped to horizontal section. In the recirculation region, higher data scatter and velocity fluctuations were identified for both hydraulic jump types. Since the conductivity probe was positioned in flow direction, the data scatter was associated with the wake of the probe support, and the negative velocities in this region (e.g. Chanson & Brattberg, 2000; Chanson, 2010; Zhang et al., 2014). The velocity distributions in the recirculation region x/d1 ≤ 5.8 were characterised by negative velocities for both jump types (Figure 5a). For x/d1 > 5.8, a negligible number of negative velocities were identified, and the velocity distributions were in the transition to a more uniform flow velocity profile (Figure 5b). These observations were consistent with previous findings (Wu & Rajaratnam, 1996). Overall for the same Froude number, no significant differences in the interfacial velocity distributions were identified between CHJ and Type B jumps. Figure 5c and d show the dimensionless interfacial velocity distribution for CHJ, Type B and D jumps with same Reynolds number (Re = 1.1x105). Similar to the close agreement in velocity distributions with the same Froude number (Figure 5a & b), no significant differences were observed in the shear region between the three hydraulic jump types (Figure 5c & d). However, significant differences were observed in the recirculation region (Figure 5c & d). For x/d1 ≤ 5.8, the CHJ and Type B jump presented similar velocity distributions in the recirculation region with negative velocity values whereas almost no negative velocities were observed for the Type D jump. In other words, while CHJ and Type B jump followed the wall jet velocity distribution in the region downstream of the jump toe, Type D jump showed a more uniform velocity distribution throughout the roller. This result suggested that the Type D jump presented a faster transition from wall jet velocity distribution to uniform flow velocity compared with Type B and CHJ. This result is in agreement with the lower air entrainment region and the rapid decrease in the number of bubbles in Type D jump. For x/d1 > 5.8, all hydraulic jumps showed more uniform flow velocity distributions with some negligible negative velocities in the recirculation region for the Type B jump and the CHJ.


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a) Velocity distribution for x/d1 = 2.2, 3.3 and 5.8 with the same Froude number (Fr1 = 4.6).

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b) Velocity distribution for x/d1 = 9.4 and 14 with the same Froude number (Fr1 = 4.6).

c) Velocity distribution for x/d1 = 2.2, 3.3 and 5.8 d) Velocity distribution for x/d1 = 9.4 and 14 with with the same Reynolds number (Re = 1.1x105). the same Reynolds number (Re = 1.1x105). Figure 5 – Comparison of dimensionless interfacial velocity distributions of CHJ and Type B and D (θ = 5°). Comparison of the experimental data with the wall jet velocity distribution by Rajaratnam (1965) (Equations 4 and 5).

4.4.

Chord time distributions

The time-averaged bubble chord time chtime = C/F represents the mean time of air bubble in contact with the probe tip of the conductivity probe (Chanson, 2007; Wang, 2014). The analysis of the air chord time was limited to flow depths with void fractions lower than 30% (Chanson, 2007; Wang, 2014). A comparative analysis of the dimensionless chord time distributions was conducted for the CHJ and Type B jump with the same Froude number (Figure 6). In the present study, the bubble chord time increased with increasing flow depth with a steeper rise in the upper shear region as was reported before by Wang (2014). Some comparable patterns were recognized in the chord time distribution for CHJ and Type B jumps. While the overall chord time distributions were similar for the two jump types for x/d1 ≤ 3.3, the bubble chord time in the shear region was smaller in the CHJ for x/d1 > 3.3 and the differences increased with increasing distance from the jump toe. This result was consistent with the larger void fraction and larger bubble count rate in CHJs suggesting smaller bubble sizes. Similar bubble chord times were also observed in the recirculation region for the CHJ and Type B jump. For the entire cross-sections, the largest chord time was identified in the recirculation region for both jump types showing similar bubble coalescence in the upper part of the roller for CHJ and Type B jumps.

a) Chord distributions x/d1 = 3.3.

time for

b) Chord distributions x/d1 = 5.8


time for

c) Chord distributions x/d1 = 9.4.

time for

d) Chord distributions x/d1 = 14.

time for

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Figure 6 – Comparison of the time-averaged air chord time distribution for the same Froude number (Fr1 = 4.6) in CHJ and Type B jumps.

5. CONCLUSIONS New experiments were conducted of air-water flow properties in hydraulic jumps in a sloped channel of θ = 5° comprising classical hydraulic jumps as well as Type B and D jumps. Comparative analyses were conducted for comparable Froude and Reynolds numbers. Flow visualisations suggested lower aeration and lower instabilities for Type D jumps while CHJ and Type B jumps presented larger turbulence and larger air entrainment. Void fraction measurements for the same Froude number suggested larger air concentration for CHJ compared to Type B jumps. For the same Reynolds number, Type D jumps presented the lowest air entrainment in the impingement point of the hydraulic jump with significant less aeration compared with Type B jumps and CHJ. CHJ showed the largest bubble count rates for the same Froude number with double the number of air bubbles in the shear region. For the same Reynolds number, the Type D jump presented the fastest decrease in the bubble count rate suggesting a rapid decrease in entrained air and a shorter roller. For all hydraulic jump types, the velocity distributions followed a close similarity with the wall jet theory. For the same Froude and Reynolds numbers, Type B and CHJ presented similar velocity distributions along the hydraulic jumps. For the same Reynolds number, the Type D jump showed a shorter region of negative velocities. Overall, the Type D jump presented significant less turbulence and air entrainment compared with Type B jumps and CHJ. Further air-water flow experiments are recommended for a larger range of slopes to expand the present findings to a larger range of flow conditions.

6. ACKNOWLEDGMENTS The authors thank Robert Jenkins and Larry Paice (WRL, UNSW) for their technical assistance.

7. REFERENCES Bakhmeteff, B. A. and Matzke, A. E. (1938). The hydraulic jump in sloped channels. Transactions, ASME, 60(HYD-60-1), 111-118. Beirami, M. K. and Chamani, M. R. (2010). Hydraulic Jump in Sloping Channels: Roller length and energy loss. Canadian Journal of Civil Engineering, 37, 535 – 543. Bradley, J. N. and Peterka, A. J. (1957). Hydraulic design of stilling basins: stilling basin with sloping apron (Basin V). Journal of the Hydraulics Division, Proc. ASCE, 83 (HY5). Chachereau, Y. and Chanson, H. (2011). Free-surface fluctuations and turbulence in hydraulic jumps. Experimental Thermal and Fluid Science, 35(6), 896-909. Chanson, H. (1995). Air entrainment in two-dimensional turbulent shear flows with partially developed inflow conditions. International Journal of Multiphase Flow, 21(6), 1107-1121. Chanson, H. (2007). Bubbly flow structure in hydraulic jump. European Journal of MechanicsB/Fluids, 26(3), 367-384. Chanson, H. (2010). Convective transport of air bubbles in strong hydraulic jumps. International Journal of Multiphase Flow, 36(10), 798-814. Chanson, H. and Brattberg, T. (2000). Experimental study of the air–water shear flow in a hydraulic jump. International Journal of Multiphase Flow, 26(4), 583-607. Felder S. and Chanson H. (2015). Phase-detection probe measurements in high-velocity free-surface flows including a discussion of key sampling parameters Experimental Thermal and Fluid Science, Vol. 61, pp. 66 – 78. Felder, S. and Pfister, M. (2017) Comparative analyses of phase-detective intrusive probes in highvelocity air-water flows. International Journal of Multiphase Flow; 90, 88-101.


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Gunal, M. and Narayanan, R. (1996). Hydraulic jump in Sloping Channels. Journal of Hydraulic Engineering, 122(8), 436-442. Kindsvater, C. E. (1944). The hydraulic jump in sloping channels. Trans. American Society of Civil Engineers, 108 (109) 1107 – 1154. Hager, W. H. (1989). B-jump in sloping channel. Journal of Hydraulic Research, 27(1), 539-558. Montano, L. and Felder, S. (2017). Air-water flow properties in hydraulic jumps on a positive slope. Eproceedings of the 37th IAHR World Congress, August 13-18, Kuala Lumpur, Malaysia, 10 pages. Ohtsu, I. and Yasuda, Y. (1991). Hydraulic Jump in Sloping Channels. Journal of Hydraulic Engineering, 117(7), 905-921. Rajaratnam, N. (1965). The Hydraulic Jump as a Well Jet. Journal of the Hydraulics Division, 91(5), 107-132. Rajaratnam, N. (1966). The hydraulic jump in sloping channels. Water and Energy International, 23(2), 137-149. Rajaratnam, N. and Murahari, V. (1974). Flow characteristics of Sloping Channel Jumps. Journal of the Hydraulic Division, 100(6), 731-740. Takahashi, M. and Ohtsu, I. (2017). Effects of inflows on air entrainment in hydraulic jumps below a gate. Journal of Hydraulic Research, 55(2), 259-268. Wu, S., and Rajaratnam, N. (1996). Transition from hydraulic jump to open channel flow. Journal of hydraulic engineering, 122(9), 526-528. Wang, H. (2014). Turbulence and air entrainment in hydraulic jumps. PhD thesis, School of Civil Engineering, The University of Queensland, Brisbane, Australia. Zhang, W., Liu, M., Zhu, D. Z. and Rajaratnam, N. (2014). Mean and turbulent bubble velocities in free hydraulic jumps for small to intermediate Froude numbers. Journal of Hydraulic Engineering, 140(11), 04014055.


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