Experimental investigation of bubbly flow and turbulence in hydraulic jumps

Many environmental problems are linked to multiphase flows encompassing ecological issues, chemical processes and mixing or diffusion, with applications in different engineering fields. The transition from a supercritical flow to a subcritical motion constitutes a hydraulic jump. This flow regime is characterised by strong interactions between turbulence, free surface and air–water mixing. Although a hydraulic jump contributes to some dissipation of the flow kinetic energy, it is also associated with increases of turbulent shear stresses and the development of turbulent eddies with implications in terms of scour, erosion and sediment transport. Despite a number of experimental, theoretical and numerical studies, there is a lack of knowledge concerning the physical mechanisms involved in the diffusion and air–water mixing processes within hydraulic jumps, as well as on the interaction between the free-surface and turbulence. New experimental investigations were undertaken in hydraulic jumps with Froude numbers up to Fr = 8.3. Two-phase flow measurements were performed with phase-detection conductivity probes. Basic results related to the distributions of void fraction, bubble frequency and mean bubble chord length are presented. New developments are discussed for the interfacial bubble velocities and their fluctuations, characterizing the turbulence level and integral time scales of turbulence representing a “lifetime” of the longitudinal bubbly flow structures. The analyses show good agreement with previous studies in terms of the vertical profiles of void fraction, bubble frequency and mean bubble chord length. The dimensionless distributions of interfacial velocities compared favourably with wall-jet equations. Measurements showed high turbulence levels. Turbulence time scales were found to be dependent on the distance downstream of the toe as well as on the distance to the bottom showing the importance of the lower (channel bed) and upper (free surface) boundary conditions on the turbulence structure.     

Advanced post-processing and correlation analyses in high-velocity air–water flows

The interest in air–water flows has not diminished in recent years, but it is accompanied by frequent citations of early, sometimes outdated articles. A basic issue is the inadequate, incomplete interpretation of air–water flow instrumentation by hydraulic engineers and researchers. This article comments on high-velocity air–water flow measurements by means of intrusive phase detection probes. This article focus on the bubbly flow structure of high-velocity air–water flow based upon measurements by means of intrusive phase detection probes. It is shown that some advanced post-processing techniques may yield expanded information on the air–water turbulent flow properties and bubbly flow structures. The outcomes demonstrate simple techniques in high-velocity air–water flow analysis.     

Turbulent air–water flows in hydraulic structures: dynamic similarity and scale effects

In hydraulic structures, free-surface aeration is commonly observed: i.e., the white waters. The air bubble entrainment may be localised (hydraulic jumps, plunging jets) or continuous along an interface (water jets, chutes). Despite recent advances, there are some basic concerns about the extrapolation of laboratory results to large size prototype structures. Herein the basic air bubble entrainment processes are reviewed and the relevant dynamic similarities are discussed. Traditionally, physical studies are conducted using a Froude similitude which implies drastically smaller laboratory Reynolds numbers than in the corresponding prototype flows. Basic dimensional analyses are developed for both singular and interfacial aeration processes. The results are discussed in the light of systematic investigations and they show that the notion of scale effects is closely linked with the selection of relevant characteristic air–water flow properties. Recent studies of local air–water flow properties highlight that turbulence levels, entrained bubble sizes and interfacial areas are improperly scaled based upon a Froude similitude even in large-size models operating with the so defined Reynolds numbers ρ _w × q _w/μ _w up to 5 E+5. In laboratory models, the dimensionless turbulence levels, air–water interfacial areas and mass transfer rates are drastically underestimated.     

Energy dissipation, flow resistance and gas-liquid interfacial area in skimming flows on moderate-slope stepped spillways

With the re-evaluation and revision of a number of design floods, several embankment overtopping protection systems have been developed and a common technique is the construction of a stepped spillway on the downstream slope. For such moderate slope stepped channels, detailed air–water flow measurements were performed in a large facility with a focus on the rate of energy dissipation, flow resistance, air–water interfacial areas and re-aeration rates. Past and present experimental results showed a significant aeration of the flow. The median dimensionless residual head was about 3 × d_c for the 21.8° sloping chute and smaller than that for flatter slopes (θ = 3.4° and 15.9°). The flow resistance results yielded an equivalent Darcy friction factor of about 0.25 implying a larger flow resistance for the 21.8° slope angle than for smaller slope angles. The re-aeration rate was deduced from the integration of the mass transfer equation using measured air–water interfacial areas and air–water flow velocities. The results suggested an increasing re-aeration rate with increasing rate of energy dissipation. The stepped invert contributed to intense turbulence production, free-surface aeration and large interfacial areas. The experimental data showed however some distinctive seesaw pattern in the longitudinal distribution of air–water flow properties with a wave length of about two step cavities. While these may be caused by the interactions between successive adjacent step cavities and their interference with the free-surface, the existence of such “instabilities” implies that the traditional concept of normal flow might not exist in skimming flows above moderate-slope stepped spillways.     

Experimental analysis of Froude number effect on air entrainment in the hydraulic jump

A hydraulic jump is characterized by strong energy dissipation and mixing, large-scale turbulence, air entrainment, waves, and spray. Despite recent pertinent studies, the interaction between air bubbles diffusion and momentum transfer is not completely understood. The objective of this paper is to present experimental results from new measurements performed in a rectangular horizontal flume with partially developed inflow conditions. The vertical distributions of the void fraction and the air bubbles count rate were recorded for inflow Froude number Fr ₁ in the range from 5.2 to 14.3. Rapid detrainment process was observed near the jump toe, whereas the structure of the air diffusion layer was clearly observed over longer distances. These new data were compared with previous data generally collected at lower Froude numbers. The comparison demonstrated that, at a fixed distance from the jump toe, the maximum void fraction C _max increases with the increasing Fr ₁. The vertical locations of the maximum void fraction and bubble count rate were consistent with previous studies. Finally, an empirical correlation between the upper boundary of the air diffusion layer and the distance from the impingement point was derived.     

Turbulence structure and coherent vortices in open-channel flows with wind-induced water waves

When wind-induced water waves appear over the free-surface flows such as natural rivers and artificial channels, large amounts of oxygen gas and heat are transported toward the river bed through the interface between water and wind layers. In contrast, a bed region is a kind of turbulent boundary layer, in which turbulence generation and its transport is promoted by the production of bed shear stress. In particular, coherent hairpin vortices, together with strong ejection events toward the outer part of the layer, promote mass and momentum exchanges between the inner and outer layers. It is inferred that such a near-bed turbulence may be influenced significantly by these air–water interfacial fluctuations accompanied with free-surface velocity shear and wind-induced water waves. However, these wind effects on the wall-turbulence structure are less understood. To address these exciting and challenging topics, we conducted particle imagery velocimetry (PIV) measurements in open-channel flows combined with air flows, and furthermore the present measured data allows us to investigate the effects of air–water interactions on turbulence structure through the whole depth region.     

Self-aeration in the rapidly- and gradually-varying flow regions of steep smooth and stepped spillways

In high-velocity chute flows, free-surface aeration is often observed. The phenomenon is called self-aeration or white waters. When the turbulent shear stresses next to the free-surface are large enough, air bubbles are entrained throughout the entire air–water column. A rapidly-varied flow region is observed immediately downstream of the inception point of free-surface aeration. An analytical solution of the air diffusion equation is proposed and the results compare well with new experimental data. Both experiments and theory indicate that the flow bulking spans over approximately 3–4 step cavities downstream of the inception point of free-surface aeration on a stepped chute. Further downstream the void fraction distributions follow closely earlier solutions of the air diffusion equation. The application of the diffusion equation solution to prototype and laboratory data shows air bubble diffusivities typically larger than the momentum transfer coefficient. The result highlights however a marked decrease in the ratio of air bubble diffusivity to eddy viscosity with increasing Reynolds number. The finding might indicate some limitation of laboratory investigations of air bubble diffusion process in self-aerated flows and of their extrapolation to full-scale prototype applications.     

Verification of Wind-Driven Volatilization Models

Mass-transfer processes of paramount importance, such as reaeration and volatilization, occur at the air–water interface. Particularly, volatilization is intensively studied because it can be a relevant removal process for toxic contaminants from flowing and standing surface waters. The paper provides a comparison among predictive equations available from literature for standing waters for the case of MTBE contamination. Most of the considered equations tend to overestimate the volatilization rate, while three equations offer a good fit with the observed data. Finally, these equations are applied to a larger amount of field data.     

Large-scale turbulent structure of uniform shallow free-surface flows

The hydrodynamics of super- and sub-critical shallow uniform free-surface flows are assessed using laboratory experiments aimed at identifying and quantifying flow structure at scales larger than the flow depth. In particular, we provide information on probability distributions of horizontal velocity components, their correlation functions, velocity spectra, and structure functions for the near-water-surface flow region. The data suggest that for the high Froude number flows the structure of the near-surface layer resembles that of two-dimensional turbulence with an inverse energy cascade. In contrast, although large-scale velocity fluctuations were also present in low Froude number flow its behaviour was different, with a direct energy cascade. Based on our results and some published data we suggest a physical explanation for the observed behaviours. The experiments support Jirka’s [Jirka GH (2001) J Hydraul Res 39(6):567–573] hypothesis that secondary instabilities of the base flow may generate large-scale two-dimensional eddies, even in the absence of transverse gradients in the time-averaged flow properties.     

An improved activated carbon method to quantify dichlorodiphenyltrichloroethane (DDT) in surface water

Currently, South Africa is designing a strategy for surface water protection involving organic contaminants such as dichlorodiphenyltrichloroethane (DDT), which is currently used for malaria control in mosquito-infested areas. Here, we demonstrate the successful use of an improved activated carbon technique using dichloromethane instead of chloroform, and slower leaching rate of 15 mL/min to quantify DDT and its metabolites in surface water. The recovery tests for 2,4′DDT, 2,4′DDD, 2,4′DDE, and 4,4′DDT, 4,4′DDD, 4,4′DDE ranged from 75 to 84% and 87 to 96%, respectively (DDE: dichlorodiphenyldichloroethylene, DDD: dichlorodiphenyldichloroethane). The main advantages of this technique over conventional liquid–liquid extractions are reduced amount of organic solvent, little sample preparation, and larger sample throughput. Because activated charcoal is fairly cheap, the technique can be routinely used to quantify and monitor DDT and its metabolites in surface water samples.     

Modification of light utilization for skeletal growth by water flow in the scleractinian coral <Emphasis Type="Italic">Galaxea fascicularis</Emphasis>

In this study, we tested the hypothesis that the importance of water flow for skeletal growth (rate) becomes higher with increasing irradiance levels (i.e. a synergistic effect) and that such effect is mediated by a water flow modulated effect on net photosynthesis. Four series of nine nubbins of G. fascicularis were grown at either high (600 μE m⁻² s⁻¹) or intermediate (300 μE m⁻² s⁻¹) irradiance in combination with either high (15–25 cm s⁻¹) or low (5–10 cm s⁻¹) flow. Growth was measured as buoyant weight and surface area. Photosynthetic rates were measured at each coral’s specific experimental irradiance and flow speed. Additionally, the instantaneous effect of water flow on net photosynthetic rate was determined in short-term incubations in a respirometric flowcell. A significant interaction was found between irradiance and water flow for the increase in buoyant weight, the increase in surface area, and specific skeletal growth rate, indicating that flow velocity becomes more important for coral growth with increasing irradiance levels. Enhancement of coral growth with increasing water flow can be explained by increased net photosynthetic rates. Additionally, the need for costly photo-protective mechanisms at low flow regimes could explain the differences in growth with flow.     

Surface characteristics of shales and implication on metal sorption

Differences in surface characteristics between alkaline and acidic shales are demonstrated in the present study. The alkaline shales are characterized by convex surface titration profiles, while the acidic shale exhibits a concave titration profile. Analysis of surface functional groups reveal that carboxylic acids predominate in alkaline shales and the acidic shale is characterized by C=S, C=N (pyridine derivative) and urea (C=O) functional groups, while it lacks –COOH group. The close proximity between pH and point of zero charge for the most acidic and alkaline shales indicate that surface complexation may not play a dominant role in sorption when the system pH is controlled by these sediments.     

A Numerical Study for Turbulent Flow and Thermal Influence over Inhomogenous Canopy of Roughness Elements

A large-eddy simulation with transitional structure function(TSF) subgrid model we previously proposed was performed to investigate the turbulent flow with thermal influence over an inhomogeneous canopy, which was represented as alternative large and small roughness elements. The aerodynamic and thermodynamic effects of the presence of a layer of large roughness elements were modelled by adding a drag term to the three-dimensional Navier–Stokes equations and a heat source/sink term to the scalar equation, respectively. The layer of small roughness elements was simply treated using the method as described in paper (Moeng 1984, J. Atmos Sci. 41, 2052–2062) for homogeneous rough surface. The horizontally averaged statistics such as mean vertical profiles of wind velocity, air temperature, et al., are in reasonable agreement with Gao et al.(1989, Boundary layer meteorol. 47, 349–377) field observation (homogeneous canopy). Not surprisingly, the calculated instantaneous velocity and temperature fields show that the roughness elements considerably changed the turbulent structure within the canopy. The adjustment of the mean vertical profiles of velocity and temperature was studied, which was found qualitatively comparable with Belcher et al. (2003, J Fluid Mech. 488, 369–398)’s theoretical results. The urban heat island(UHI) was investigated imposing heat source in the region of large roughness elements. An elevated inversion layer, a phenomenon often observed in the urban area (Sang et al., J Wind Eng. Ind. Aesodyn. 87, 243–258)’s was successfully simulated above the canopy. The cool island(CI) was also investigated imposing heat sink to simply model the evaporation of plant canopy. An inversion layer was found very stable and robust within the canopy.     

Effects of ultraviolet radiation and water motion on the reef coral Porites compressa Dana: a flume experiment

The effects of water flow and ultraviolet radiation (UVR, 280–400 nm) on the reef coral Porites compressa Dana were explored in a manipulative flume experiment. The aim of this study was to determine whether this coral responds to changes in the UVR environment by adjusting the tissue concentration of UV-absorbing compounds (mycosporine-like amino acids, MAAs), and to see whether such an acclimation is affected by water flow. Also, calcification rate and chlorophyll-a concentration were measured during the experiment to estimate the potential costs (in the form of slowed growth and/or reduced photosynthetic capacity) to the coral–alga symbiosis of being exposed to UVR and producing MAAs. Branches of P. compressa from a single male colony were exposed to high or low flow (15 cm s⁻¹ and 3 cm s⁻¹, respectively) and ambient or no UVR in an outdoor, continuous-flow seawater system. Chlorophyll-a and MAA concentrations were determined after zero, 3 and 6 weeks of exposure to the experimental conditions. Increase in buoyant weight during the two 3-week periods was used to calculate calcification rate. The presence of UVR had a significant positive effect on total MAA concentration in the P. compressa colonies; however, there were significant interactions present. In colonies exposed to UVR, MAA concentration increased and then decreased to initial levels in high water flow, and increased steadily in low water flow. In colonies receiving no UVR, MAA concentration decreased steadily, declining 23% in 6 weeks. The absence of UVR did not result in higher chlorophyll-a concentrations, but the calcification rate was slightly affected by UVR. This study supports the putative photoprotective role of MAAs in P. compressa, and suggests that the costs of mitigating the effects of ambient UVR are detectable, but they are very small. Received: 29 February 2000 / Accepted: 20 September 2000     

Fast Ferry Traffic as a Qualitatively New Forcing Factor of Environmental Processes in Non-Tidal Sea Areas: A Case Study in Tallinn Bay,Baltic Sea

The impact of wake wash from high-speed ferries on the coastal environment in non-tidal seas is analysed in terms of wave energy and power, and properties of the largest waves. Shown is that hydrodynamic loads caused by heavy high-speed traffic may play a decisive role not only in low-energy coasts but also in certain areas with high wind wave activity. For example, ship-generated waves form, at least, about 5–8% from the total wave energy and about 18–35% from the wave power in the coastal areas of Tallinn Bay exposed to dominating winds. The periods of wake waves from high-speed ships frequently are much larger than dominating periods of wind waves. The leading waves typically have a height of about 1 m and a period of 10–15 s. Such waves extremely seldom occur in natural conditions in many regions of semi-enclosed seas. They cause unusually high hydrodynamic loads in the deeper part of the nearshore. The fast ferry traffic thus is a qualitatively new forcing component of vital impact on the local ecosystem. It is demonstrated that wakes from high-speed ferries may trigger considerable changes of the existing balance of coastal processes. Owing to their low decay rates combined with their exceptional compactness after crossing many kilometres of the sea surface, such wakes may cause considerable remote impact of the ship traffic. This feature has to be addressed in the analysis of the impact of harbours and associated ship traffic in the neighbourhood of vulnerable areas.     

Numerical Simulation of Interaction of the Heavy Gas Cloud with the Atmospheric Surface Layer

The numerical time-dependent three-dimensional model [Kovalets, I.V. and Maderich, V.S.: 2001, Int. J. Fluid Mech. Res. 30, 410–429] of the heavy gas dispersion in the atmospheric boundary layer has been improved by parameterizing momentum and heat fluxes on the surface of Earth using Monin–Obukhov similarity theory. Three parameterizations of heat exchange with the surface of Earth were considered: (A) formula of Yaglom A.M. and Kader B.A. [1974, J. Fluid Mech. 62, 601–623] for forced convection, (B) interpolation formula for mixed convection and (C) similarity relationship for mixed convection [Kader, B.A. and Yaglom, A.M.: 1990, J. Fluid Mech. 212, 637–662]. Two case studies were considered. In the first study based on experiment of Zhu et al., J. Hazard Mater 62, 161–186], the interaction of an isothermal heavy gas plume with an atmospheric surface layer was simulated. It was found that stable stratification in the cloud essentially suppresses the turbulence in the plume, reducing the turbulent momentum flux by a factor of down to 1/5 in comparison with the undisturbed value. This reduction essentially influences velocities in the atmospheric boundary layer above the cloud, increasing the mean velocity by a factor of up to 1.3 in comparison with the undisturbed value. A simulation of cold heavy gas dispersion was carried out in the second case based on field experiment BURRO 8. It was shown that both forced and free convections under moderate wind speeds significantly influence the plume. The relative rms and bias errors of prediction the plume’s height were σ_H ≈ 30% and ɛ_H = − 10%, respectively, for parameterization B, while for A and C the errors were σ_H ≈ 80% and ɛ_H ≈ − 65%. It is therefore advised to use the simple parameterization B in dense gas dispersion models.     

Population structure of two deep-sea hydrothermal vent gastropods from the Juan de Fuca Ridge, NE Pacific

The gastropods Lepetodrilus fucensis and Depressigyra globulus are abundant faunal components of animal communities at deep-sea hydrothermal vents along the Juan de Fuca Ridge in the NE Pacific. The population structure and recruitment pattern of both species were studied using modal decomposition of length–frequency distributions. Gastropod populations were collected from Axial Volcano and Endeavour Segment in 2002 and 2003. Polymodal size–frequency distributions, particularly at Axial Volcano vent sites, suggest a discontinuous recruitment pattern for D. globulus. In contrast, there were no distinct peaks visible in the distributions of L. fucensis, suggesting a continuous recruitment pattern for this species. For both species, distributions were positively skewed towards the smaller length–classes, implying post-settlement mortality is high. However, variations in growth, due to short- and long-term variability in environmental conditions in the hydrothermal vent habitat, as well as biological interactions, may also be influencing the distribution and abundance of subsequent life-history stages. Using maximum shell lengths from populations of known ages, the growth rate of L. fucensis was estimated as 9.6 μm day⁻¹, indicating adulthood would be reached in ∼1 year. Our results suggest that, despite occupying the same habitat, abundance and population structure are regulated by different biotic and abiotic processes in L. fucensis and D. globulus.     

Larval mortality during export to the sea in the fiddler crab Uca minax

Dense populations of the fiddler crab Uca minax (Le Conte 1855) are common along tidally influenced freshwater rivers and streams >50 km from the sea. Adults do not migrate from inland sites to release larvae, but instead release them directly into an environment where the zoeae cannot survive. Laboratory salinity tolerance experiments were used to determine how long larvae from the inland-most population of U. minax along the Pee Dee River, South Carolina, USA can survive zero salinity compared to larvae from a brackish water population (salinity 5) near the mouth of Winyah Bay in the same estuary. Larvae from the brackish water population were also exposed to a salinity of 5 and their survival tracked. These experiments were conducted from May to August 2004 and 2005. To determine if inland larvae suffered significant mortality in transit due to salinity stress, current profiles were measured in the field and used to model the time taken by a larva using ebb-tide transport to travel to permissive salinities. The laboratory tolerance experiments showed that larvae from the inland freshwater population had LT50’s of 4–5 days at 0 salinity, which were significantly longer than those of the brackish water zoeae (2–3 days). Zoeae from the brackish water population survived for at least one larval molt at a salinity of 5 with LT 50’s of ∼12 days. Estimated travel times to reach permissive salinities from the inland-most population based on current profiles were 3–5 days for larvae using night-time only ebb-tide transport and 1.5–2.5 days for those using ebb-tide transport both day and night. Previously published field data indicate that U. minax larvae do use both day- and night-time ebb-tide transport, and are found in high densities in the water column during the day. These results lead to the conclusion that U. minax stage I zoeae do not undergo significant salinity-induced mortality during their 50+ km trip to the sea.     

Stability and Mixing of a Vertical Axisymmetric Buoyant Jet in Shallow Water

The stability, mixing and effect of downstream control on axisymmetric turbulent buoyant jets discharging vertically into shallow stagnant water is studied using 3D Reynolds-averaged Navier–Stokes equations (RANS) combined with a buoyancy-extended k –ε model. The steady axisymmetric turbulent flow, temperature (or tracer concentration) and turbulence fields are computed using the finite volume method on a high resolution grid. The numerical predictions demonstrate two generic flow patterns for different turbulent heated jet discharges and environmental parameters (i) a stable buoyant discharge with the mixed fluid leaving the vertical jet region in a surface warm water layer; and (ii) an unstable buoyant discharge with flow recirculation and re-entrainment of heated water. A stratified counterflow region always appears in the far-field for both stable and unstable buoyant discharges. Provided that the domain radius L exceeds about 6H, the near field interaction and hence discharge stability is governed chiefly by the jet momentum length scale to depth ratio l_M/H, regardless of downstream control. The near field jet stability criterion is determined to be l_M/H = 3.5. A radial internal hydraulic jump always exists beyond the surface impingement region, with a 3- to 6-fold increase in dilution across the jump compared with vertical buoyant jet mixing. The predicted stability category, velocity and temperature/concentration fields are well-supported by experiments of all previous investigators.