In this article, the Conflict of interest statement “Hubert Chanson has competing interest and conflict of interest with Matthias Kramer.” was removed. The original article has been corrected.

Continuing from the part 1 (Shi et al., 2022) this paper presents an experimental investigation of transient void fraction and bubble statistics in a highly turbulent breaking bore with Fr₁=2.4. The measurements were conducted using a combination of dual-tip phase-detection probes and an ultra-high-speed video camera. The enclosed bubble detection technique (EBDT) used the synchronised probe and camera signals to provide the contour of instantaneous void fraction in the bore roller. The ensemble-averaged void fraction was derived, and compared to analytical solutions of air diffusion models. The bubble statistics were characterised by the bubble clustering properties, pseudo bubble count rate and bubble size spectrum. The clustering data showed the non-random bubble grouping in the shear layer, and the bubble size distributions N(r) followed a commonly adopted bubble break-up model: N(r)∝r^−m, where r was the equivalent bubble radius in the present study. The comparison indicated that, in the breaking bore, its air diffusion process was similar to that in a stationary hydraulic jump, and the bubble break-up process was comparable to that in breaking waves.

This experimental study investigated the air-water flow properties and bubble characteristics in hydraulic jumps with Froude numbers Fr₁ = 2.4 and 6.3, using four dual-tip phase detection probes with sensor sizes from 0.25 mm to 0.64 mm. The hydraulic jumps were characterized by a fully breaking roller with substantial air entrainment and turbulent two-phase flow patterns. The measurements encompassed distributions of void fraction, bubble count rate, interfacial velocity and bubble clustering properties and the data sets were consistent with previous studies. The comparison of the different probes showed a small impact of the tested sensor sizes on the air-water flow properties, in terms of the trends, magnitude and maximum values. Some differences were observed in terms of the bubble count rate, with the larger probes detecting a lesser number of bubbles. The trend was further confirmed through a comparison with the data set of Chanson and Brattberg (2000) [10] with a smaller probe sensor size (Ø₁ = 0.025 mm), in which the maxima of bubble count rates were almost twice that of the present dataset for identical flow conditions. The present results confirm that the traditional signal processing techniques can be used for relatively small probe sizes, although different approaches might be needed for larger probes which cannot detect sub-millimetric bubbles. Overall, the findings should facilitate the development of sturdier phase-detection needle probes and help breaching the gap between laboratory and prototype.

Transient motion, turbulence and bubble dynamics make any velocity quantification extremely difficult in unsteady gas–liquid flows. In the present study, novel Eulerian and Lagrangian techniques of velocimetry were developed, using both intrusive and non-intrusive measurements. The selected unsteady gas–liquid flow was a breaking bore, featured with a transient motion, air entrainment and coherent structures. Intrusively, Eulerian probe measurements resulted to the development of a single bubble event detection (SBED) technique in unsteady air–water flows. Non-intrusively, the motion of air–water pattern was detected using a novel particle tracking velocimetry (PTV). Both velocities obtained using SBED and PTV techniques were validated against the established optical flow (OF) results, achieving consistent velocity data among the three techniques. The filtering criteria of the SBED and PTV techniques were discussed, showing the best options in the breaking bore. It is concluded that the most robust velocity measurements in gas–liquid flow are achieved with consistent velocity data between the SBED, PTV and OF techniques.

Breaking bores are commonly observed in a number of natural processes, often associated with the presence of a transient mixture of air and water, with intense recirculation, air bubble entrainment, and splashing. Two-phase flow measurements in such highly unsteady flows cannot be based on long-duration measurements and require novel ensemble-statistical approaches based on multiple repetitions. Detailed measurements of air-water flow properties were then conducted in a breaking bore with Fr1 = 2.4 using an array of multiple dual-tip phase-detection probes. Based on an extensive experimental program, inclusive of 2000 tests at a single position and 100 tests at multiple elevations, a detailed sensitivity analysis was conducted on the necessary number of repetitions to obtain physically meaningful and statistically reliable air-water flow properties. The results led to a robust methodology to estimate ensemble-statistical values, including confidence intervals and residual error. In addition, these results provided a detailed characterization of the behavior of air-water flow properties in highly unsteady flows, including void fraction, number of interfaces, and bubble chord time/length. Despite the transient nature, all physical processes showed consistent behaviors with theoretical models and other stationary flows, including hydraulic jumps and plunging jets. Overall, this study provided two-phase flow characteristics that go beyond the limitations imposed by the unsteady nature of the flow, proving thoroughly the importance of large datasets for the estimation of air-water flow properties in highly unsteady flows.

Self-aerated free-surface flow studies have a more recent history compared to classical fluid dynamics. Traditional velocimetry techniques are adversely affected by the presence of gas–liquid interfaces. In the present study, detailed air-water flow measurements were performed in a highly turbulent free-surface flow, and three velocimetry approaches were applied: (a) centreline dual-tip phase-detection needle probe measurements at all step edges downstream of the inception location of free-surface aeration; (b) Optical Flow (OF) data based upon ultra-high-speed video movies through the left sidewall; and (c) Optical Flow (OF) data based upon ultra-high-speed video movies overlooking the self-aerated flow, in a direction normal to the pseudo-bottom formed by the staircase profile. The study was conducted in a steep channel and three stepped invert geometries were tested. The results highlighted both advantages and limitations of the three complementary metrologies in free-surface flows with strong turbulence. The dual-tip phase-detection probe delivered reliable interfacial velocity data, but in the form of point measurements. The sideview OF technique provided a great level of details of the cavity recirculation and shear zone between mainstream and cavity, but the data were unreliable for void fractions>0.30 and only limited to the sidewall region. The top view OF technique characterised the surface velocity field across the entire chute width, highlighting the occurrence of three-dimensional air-water surface patterns. One observed limitation of the OF was the requirements of a high frame rate (i.e. 10,000 fps or more) and high-quality light source. Overall, these measurement techniques provided complementary results for a better understanding of the physical behaviour of highly turbulent multiphase flows on stepped channels.

On a stepped spillway, the staircase invert profile generates some intense turbulent dissipation during the spill, associated with a significant reduction of kinetic energy, as well as strong self-aeration. The present study focused on the effects of inclined downward steps on the air-water flow properties, flow resistance, and head losses because these mostly relate to spillway design. Some physical modeling was conducted in a relatively large facility with a 45° stepped chute (1V:1H) operating with Reynolds numbers 2.8×103<Re<1×106. The presence of downward steps induced some elongated asymmetrical cavity shapes, creating a less stable cavity recirculation pattern along the entire chute, leading to different interactions with the main stream. In terms of basic air-water flow properties, the distributions of void fraction and bubble count rate presented very close results for all three stepped geometries, both qualitatively and quantitatively. The interfacial velocities did not reach any uniform equilibrium (i.e., normal flow) condition, and the fastest velocities were recorded with the 1V:2.33H inclined downward stepped chute geometry (δ =23.3° and λ/k=3), and the slowest velocities on the horizontal stepped chute (δ=0 and λ/k=2). The Darcy-Weisbach friction factor f and relative head loss δ H/Hmax were estimated in the self-aerated flow. The comparative analyses suggested that the largest total drag and head losses were observed on the stepped chute with flat horizontal steps. An inclined downward stepped design yielded lesser head losses for all investigated flow conditions, providing an important information for practical engineers designing these hydraulic structures.

At hydraulic structures, some strong interactions may develop between fast flowing waters and the air adjacent to the water in motion that enhance the air-water transfer of atmospheric and volatile gases in the flow. In turn, in-stream structures may contribute to the aeration and re-oxygenation during overflow. The present study aims to characterize the aeration performance of a steep stepped weir, based upon a detailed physical investigation of air-water interfacial properties across a relatively wide range of discharges. The data showed a strong fragmentation of the air-water flows, a very broad range of entrained bubbles and drops, and a large amount of particle clustering. The results implied a monotonic increase in re-aeration with increasing rate of energy dissipation, while the largest aeration efficiency was observed on the horizontal step weir chute, with the smallest on the 1V:2.33H inclined downward steps. Altogether, the study showed that a steep stepped chute can make a sizeable contribution to the re-oxygenation of the waters, although the downward inclined steps reduce the re-aeration performances.

A hydraulic jump is a region of rapidly-varied flow that is extremely turbulent. While the one-dimensional continuity and momentum principles have been successfully applied to express the relationships between upstream and downstream conditions, the three-dimensional equations cannot be resolved without some complicated turbulence closure, often involving two phases, i.e. air and water. Based upon a new dataset, the current investigation has the double objective of presenting a novel experimental investigation of the air-water flow characteristics in hydraulic jumps with a small Froude number (Fr₁ = 2.1) and discussing the potential scale effects involving several Reynolds numbers (0.078 × 10⁵ < Re < 3.05 × 10⁵). Four unique features are the low inflow Froude number Fr₁ = 2.1, the wide range of Reynolds numbers tested systematically, the broad amount of air-water flow properties investigated, and the relatively high Reynolds number (Re = 3.05 × 10⁵) achieved in the largest experiment. More than two dozen of parameters were tested systematically under Froude similar conditions. All the data demonstrated that the selection of relevant (air-water) flow property(ies) used to assess similarity and scale effects is most essential. Further the concept of similarity and scale effects must be linked to specific flow conditions. At low Froude number (Fr₁ = 2.1), the present results showed that many hydraulic jump properties could not be extrapolated from laboratory study to full scale hydraulic structures without substantial scale effects. These findings have profound implications for engineering design applications, often operating with Reynolds numbers in excess of 10⁵.

Abstract: Hydraulic jumps are commonly employed as energy dissipators to guarantee long-term operation of hydraulic structures. A comprehensive and in-depth understanding of their main features is therefore fundamental. In this context, the current study focused on hydraulic jumps with low Froude numbers, i.e. Fr₁ = 2.1 and 2.4, at relatively high Reynolds number: Re ~2 × 10⁵. Experimental tests employed a combination of dual-tip phase-detection probes and ultra-high-speed video camera to provide a comprehensive characterisation of the main air-water flow properties of the hydraulic jump, including surface flow features, void fraction, bubble count rate and interfacial velocities. The current research also focused on the transverse distributions of air-water flow properties, i.e. across the channel width, with the results revealing lower values of void fraction and bubble count rate next to the sidewalls compared to the channel centreline data. Such a spatial variability in the transverse direction questions whether data near the side walls may be truly representative of the behaviour in the bulk of the flow, raising the issue of sidewall effects in image-based techniques. Overall, these findings provide new information to both researchers and practitioners for a better understanding of the physical processes inside the hydraulic jump with low Froude numbers, leading to an optimised design of hydraulic structures. Article Highlights: Experimental investigation of air-water flow properties in hydraulic jumps with low Froude numbersDetailed description of the main air-water surface features on the breaking rollerTransversal distribution of the air-water flow properties across the channel width and comparison between centreline and sidewall.

Highly turbulent free-surface flows are characterised by complex and rapidly varying air-water surface features, leading to enhanced surface roughness, breakup and disintegration processes. Such a strong free-surface turbulence has an impact on a number of environmental flows, and a deeper understanding of its physical nature is fundamental. Unsteady breaking bores are of particular interest because of their recirculating motion, with large air entrainment and splashes, resulting in highly fluctuating and rapidly varying free-surface flows. Herein, new methodologies and innovative approaches are used in support of a deeper understanding of the physical processes within a breaking roller, inclusive of a comprehensive assessment of its free-surface dynamics. Because of the unsteadiness of the flow, multiple repetitions were necessary and all results were based upon an ensemble statistical analysis. Ultra-high-speed videos recorded from both top and side views allowed for a detailed characterisation of the roller's free surface, providing a description and classification of the most recurring air-water surface features. A quantification of their main properties in terms of geometry, duration and frequency of appearance revealed an evolution of these features during their lifespans. In parallel, the use of optical flow techniques provided a characterisation of the surface velocity fields, yielding information on the free-surface kinematic properties and revealing a strong link between air-water surface features, energy dissipation and time/length scales.

Partially-filled pipe flows are commonly observed in urban hydraulics, sewers and road crossings. The occurrence of a compression wave in the confined space may result from flash flooding, transient operation or accidental blockage, inducing explosive conditions. In this study, the propagation of a compression wave was studied in a relatively large-size laboratory flume with a semi-circular cross-section. The unsteady flow properties were recorded to understand how the circular cross-sectional shape impacted onto the surging water propagation. Both free-surface and velocity data indicated a marked impact of the compression wave passage, with large instantaneous fluctuations comparable and sometimes larger than observations of compression waves in rectangular channels.

Breaking surges and bores are observed during flood events, tidal bores and tsunamis propagating in rivers. The sudden increase in water depth generates an aerated and recirculating region, called the roller, whose turbulent behaviour is poorly understood. Based on ensemble-average analyses with multiple repetitions, this experimental work processed high-speed videos from multiple locations to characterise the spatial and temporal dynamics of the bore's roller. The results showed different air entrainment mechanisms for increasing Froude numbers, providing adapted formulae to predict the extension of the shear layer and the air-water boundary. Seen from above, the roller toe perimeter had an indented profile rapidly evolving in time, revealing a certain level of periodicity. A statistical analysis in terms of position of the roller toe, longitudinal fluctuations and instantaneous celerities allowed for a detailed characterisation of the turbulent surface fluctuations and three-dimensional properties of the breaking bore roller, leading to a better understating of the governing process.

Hydraulic jumps are commonly employed as energy dissipators to guarantee long-term operation of hydraulic structures. Thus, a comprehensive and in-depth understanding of its main features is fundamental. In this context, the current study focused on a hydraulic jump with a low Froude number (Fr₁ = 2.4) and a relatively high Reynolds number (Re = 1.83×10⁵). Experimental tests employed dual-tip phase-detection probes to provide a comprehensive characterisation of the main air-water flow properties of the hydraulic jump in terms of void fraction, bubble count rate and interfacial velocities. Importantly, this research focused on the air-water flow property distribution across the channel width, revealing lower values of void fraction and bubble count rate next to the sidewall as compared to the channel centreline. Such a spatial variability in the transverse direction questions whether data near the walls may be representative of the flow behaviour in the centreline, raising the issue of sidewall effects in image-based techniques. These findings provide helpful information to both researchers and practitioners for a better understanding of the physical process, leading to an optimised design of hydraulic structures.

A breaking bore in a translating system of reference is mathematically comparable with a stationary hydraulic jump, whose dissipative nature is used in hydraulic structures to limit damage during floods. Although visually similar, analogies and dissimilarities between hydraulic jumps and bores have been discussed for decades. Recent developments in the investigation of unsteady flows allowed for a direct comparison between stationary and non-stationary flow motions. In this context, the present study provides a preliminary comparative analysis between a hydraulic jump and a breaking bore with the same Froude, Reynolds and Morton numbers in terms of roller toe characteristics and air-water flow properties. The results showed overall a good agreement between the two phenomena, with some differences associated with the non-stationary nature of breaking bores. The comparison between time-averaged void fractions in the hydraulic jump and instantaneous ensemble-averaged void fractions in breaking bore revealed similar patterns, in agreement with existing albeit limited literature. A quantification of analogies and dissimilarities is relevant to the energy dissipation processes, useful to practical engineers and researchers to optimise the design of hydraulic structures.