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.     

Surface waves and roughness in self-aerated supercritical flow

In high-velocity open channel flows, free-surface aeration is commonly observed. The effects of surface waves on the air–water flow properties are tested herein. The study simulates the air–water flow past a fixed-location phase-detection probe by introducing random fluctuations of the flow depth. The present model yields results that are close to experimental observations in terms of void fraction, bubble count rate and bubble/droplet chord size distributions. The results show that the surface waves have relatively little impact on the void fraction profiles, but that the bubble count rate profiles and the distributions of bubble and chord sizes are affected by the presence of surface waves.     

Turbulence and aeration in hydraulic jumps: free-surface fluctuation and integral turbulent scale measurements

In an open channel, a change from a supercritical to subcritical flow is a strong dissipative process called a hydraulic jump. Herein some new measurements of free-surface fluctuations of the impingement perimeter and integral turbulent time and length scales in the roller are presented with a focus on turbulence in hydraulic jumps with a marked roller. The observations highlighted the fluctuating nature of the impingement perimeter in terms of both longitudinal and transverse locations. The results showed further the close link between the production and detachment of large eddies in jump shear layer, and the longitudinal fluctuations of the jump toe. They highlighted the importance of the impingement perimeter as the origin of the developing shear layer and a source of vorticity. The air–water flow measurements emphasised the intense flow aeration. The turbulent velocity distributions presented a shape similar to a wall jet solution with a marked shear layer downstream of the impingement point. The integral turbulent length scale distributions exhibited a monotonic increase with increasing vertical elevation within 0.2 < L_z/d₁ < 0.8 in the shear layer, where L_z is the integral turbulent length scale and d₁ the inflow depth, while the integral turbulent time scales were about two orders of magnitude smaller than the period of impingement position longitudinal oscillations.     

Experimental assessment of characteristic turbulent scales in two-phase flow of hydraulic jump: from bottom to free surface

A hydraulic jump is a turbulent shear flow with a free-surface roller. The turbulent flow pattern is characterised by the development of instantaneous three-dimensional turbulent structures throughout the air–water column up to the free surface. The length and time scales of the turbulent structures are key information to describe the turbulent processes, which is of significant importance for the improvement of numerical models and physical measurement techniques. However, few physical data are available so far due to the complexity of the measurement. This paper presents an investigation of a series of characteristic turbulent scales for hydraulic jumps, covering the length and time scales of turbulent flow structures in bubbly flow, on free surface and at the impingement point. The bubbly-flow turbulent scales are obtained for Fr = 7.5 with 3.4 × 10⁴ < Re < 1.4 × 10⁵ in both longitudinal and transverse directions, and are compared with the free-surface scales. The results highlight three-dimensional flow patterns with anisotropic turbulence field. The turbulent structures are observed with different length and time scales respectively in the shear flow region and free-surface recirculation region. The bubbly structures next to the roller surface and the free-surface fluctuation structures show comparable length and time scales, both larger than the scales of vortical structures in the shear flow and smaller than the scales of impingement perimeter at the jump toe. A decomposition of physical signals indicates that the large turbulent scales are related to the unsteady motion of the flow in the upper part of the roller, while the high-frequency velocity turbulence dominates in the lower part of the roller. Scale effects cannot be ignored for Reynolds number smaller than 4 × 10⁴, mainly linked to the formation of large eddies in the shear layer. The present study provides a comprehensive assessment of turbulent scales in hydraulic jump, including the analyses of first data set of longitudinal bubbly-flow integral scales and transverse jump toe perimeter integral scales.     

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.     

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.     

Modelling hydraulic jump using the bubbly two-phase flow method

Hydraulic jumps have complex flow structures, characterised by strong turbulence and large air contents. It is difficult to numerically predict the flows. It is necessary to bolster the existing computer models to emphasise the gas phase in hydraulic jumps, and avoid the pitfall of treating the phenomenon as a single-phase water flow. This paper aims to improve predictions of hydraulic jumps as bubbly two-phase flow. We allow for airflow above the free surface and air mass entrained across it. We use the Reynolds-averaged Navier–Stokes equations to describe fluid motion, the volume of fluid method to track the interface, and the k–ε model for turbulence closure. A shear layer is shown to form between the bottom jet flow and the upper recirculation flow. The key to success in predicting the jet flow lies in formulating appropriate bottom boundary conditions. The majority of entrained air bubbles are advected downstream through the shear layer. Predictions of the recirculation region’s length and air volume fraction within the layer are validated by available measurements. The predictions show a linear growth of the shear layer. There is strong turbulence at the impingement, and the bulk of the turbulence kinetic energy is advected to the recirculation region via the shear layer. The predicted bottom-shear-stress distribution, with a peak value upstream of the toe of the jump and a decaying trend downstream, is realistic. This paper reveals a significant transient bottom shear stress associated with temporal fluctuations of mainly flow velocity in the jump. The prediction method discussed is useful for modelling hydraulic jumps and advancing the understanding of the complex flow phenomenon.     

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.     

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.     

Two-phase flow insights into open-channel flows with suspended particles of different densities

The effect of particle density on the turbulent open-channel flow carrying dilute particle suspensions is investigated using two specific gravities and three concentrations of solid particles. The particles, identical in size and similar in shape, were natural sand and a neutrally buoyant plastic. The particles were fully suspended, and formed no particle streaks on the channel’s bed. Accordingly, the changes in the flow are attributed to the interactions between suspended particles and flow turbulence structures. Measurements were obtained by means of image velocimetry enabling simultaneous, but distinct, measurement of liquid and particle velocities. The experimental results show that, irrespective of particle specific gravity, particle suspension influences bulk velocity of flow and the Kármán coefficient, while friction velocity essentially remains constant. The results also show that particles in suspension modify local water turbulence over the flow depth, but in ways not accurately predicted using the customary parameters for characterizing turbulence modification.     

Stratified flow interactions with a suspended canopy

Field observations of the interactions between a stratified flow and a canopy suspended from the free surface above a solid boundary are described and analysed. Data were recorded in and around the canopy formed by a large long-line mussel farm. The canopy causes a partial blockage of the water flow, reducing velocities in the upper water column. Deceleration of the approaching flow results in a deepening of isopycnals upstream of the canopy. Energy considerations show that the potential for an approaching stratified flow to be diverted beneath a porous canopy is indicated by a densimetric Froude number. Strong stratification or low-velocities inhibit vertical diversion beneath the canopy, instead favouring a horizontal diversion around the sides. The effect on vertical mixing is also considered with a shear layer generated beneath the canopy and turbulence generated from drag within the canopy. In the observations, stratification is shown to be of sufficient strength to limit the effectiveness of the first mixing process, while the turbulence within the canopy is likely to enhance vertical exchange. Velocity and temperature microstructure measurements are used to investigate the effect of the canopy on turbulent dissipation and show that dissipation is enhanced within the canopy.     

Analysis of the velocity field in a large rectangular channel with lateral shockwave

In this work the authors describe the main characteristics of the velocity field of hydraulic jumps in a very large channel where lateral shockwaves occur. Experiments were carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). Extensive flow velocity measurements were investigated in order to have a clearer understanding of both hydraulic jump development and lateral shockwave formation in a very large channel. Eight experiments were performed in a 4m wide rectangular channel; the experiments differed in the inlet Froude number F ₀ and the jump type. Seven tests were carried out with undular jumps and one with a roller jump. The flow velocity and the flow free surface measurements were taken using a two-dimensional Acoustic Doppler Velocimeter (ADV) and an ultrasonic profiler, respectively. The experimental results can be summarized as follow: (i) the formation of well developed lateral shockwaves similar to those of oblique jumps were observed; (ii) the comparison of the experimental and theoretical data shows that the classic shockwave theory is sufficiently confirmed in the analyzed range of Reynolds number, taking into account the experimental errors and the difference between the theoretical and experimental assumptions; (iii) the transversal flow velocity profiles in the recirculating zone show a good agreement with the numerical simulations presented in literature in the case of a separated turbulent boundary layer over a flat plate. This conclusion enables us to confirm the hypothesis that the lateral shockwaves in the channel are the result of a boundary layer which, as observed, forms on the channel sidewalls.     

Coupling between free-surface fluctuations,velocity fluctuations and turbulent Reynolds stresses during the upstream propagation of positive surges,bores and compression waves

In open channel, canals and rivers, a rapid increase in flow depth will induce a positive surge, also called bore or compression wave. The positive surge is a translating hydraulic jump. Herein new experiments were conducted in a large-size rectangular channel to characterise the unsteady turbulent properties, including the coupling between free-surface and velocity fluctuations. Experiments were repeated 25 times and the data analyses yielded the instantaneous median and instantaneous fluctuations of free-surface elevation, velocities and turbulent Reynolds stresses. The passage of the surge front was associated with large free-surface fluctuations, comparable to those observed in stationary hydraulic jumps, coupled with large instantaneous velocity fluctuations. The bore propagation was associated with large turbulent Reynolds stresses and instantaneous shear stress fluctuations, during the passage of the surge. A broad range of shear stress levels was observed underneath the bore front, with the probability density of the tangential stresses distributed normally and the normal stresses distributed in a skewed single-mode fashion. Maxima in normal and tangential stresses were observed shortly after the passage of a breaking bore roller toe. The maximum Reynolds stresses occurred after the occurrence of the maximum free-surface fluctuations, and this time lag implied some interaction between the free-surface fluctuations and shear stress fluctuations beneath the surge front, and possibly some causal effect.     

Quantifying vertical mixing in estuaries

Estuarine turbulence is notable in that both the dissipation rate and the buoyancy frequency extend to much higher values than in other natural environments. The high dissipation rates lead to a distinct inertial subrange in the velocity and scalar spectra, which can be exploited for quantifying the turbulence quantities. However, high buoyancy frequencies lead to small Ozmidov scales, which require high sampling rates and small spatial aperture to resolve the turbulent fluxes. A set of observations in a highly stratified estuary demonstrate the effectiveness of a vessel-mounted turbulence array for resolving turbulent processes, and for relating the turbulence to the forcing by the Reynolds-averaged flow. The observations focus on the ebb, when most of the buoyancy flux occurs. Three stages of mixing are observed: (1) intermittent and localized but intense shear instability during the early ebb; (2) continuous and relatively homogeneous shear-induced mixing during the mid-ebb, and weakly stratified, boundary-layer mixing during the late ebb. The mixing efficiency as quantified by the flux Richardson number Rf was frequently observed to be higher than the canonical value of 0.15 from Osborn (J Phys Oceanogr 10:83–89, 1980). The high efficiency may be linked to the temporal–spatial evolution of shear instabilities.     

Turbulence suppression by suspended sediment within a geophysical flow

Experiments are performed in a mixing box to evaluate the effect of suspended sediment on turbulence generated by an oscillating grid. Quartz-density sand of varying sizes and concentrations is used, and particle image velocimetry is employed to quantify only the fluid phase. Results show that (1) while a relatively large secondary flow field is present in the box, turbulence is a maximum near the grid and it decreases systematically toward the water surface; (2) relatively high concentrations of fine sediment can markedly alter this secondary flow field and significantly decrease both the time-mean and turbulent kinetic energy within the flow, yet these same sediment concentrations have little effect on the integral time and length scales derived for each velocity component; and (3) the overall turbulence suppression observed can be related to the transfer of energy from the fluid to the sediment and the maintenance of a suspended sediment load rather than commonly employed turbulence modulation criteria. These experimental data demonstrate unequivocally that the presence of a suspended sediment load can significantly reduce overall turbulent kinetic energy, and these results should be applicable to a range of sediment-laden geophysical flows.     

水动力条件对藻类影响的研究进展

水动力过程是影响水体富营养化状态和水华爆发的重要因素,水动力因素对藻类影响的研究对于富营养化水体藻类控制具有重要意义。归纳分析近年来关于流速、流态对藻类生长和种类变化的研究报道;就水动力条件对藻类的影响及其作用机理等详细地进行了文献综述。水动力条件对藻类生长的影响分为流速和流态两个方面,不论是单一藻种还是混合藻类,低流速、小扰动有利于藻类的生长和聚集,流速增大则导致Chla浓度先递增后递减,不同藻类的临界流速并不相同;藻类生长随着湍流程度的增加而逐渐受到抑制,抑制作用与水流流态（层流、过渡流、湍流）无明显相关关系,水体流态的变化造成水流剪应力的变化,藻类种类的差异导致其对水流剪应力的响应变化。水动力条件变化引起的藻类种群结构变化,主要表现为水体混合加剧导致优势种群的转换。水动力条件对藻类影响的作用原理主要是引起了光强的改变、细胞长度的变化、营养盐运送及捕食行为变化等。综观当前的研究成果,水动力能否真正阻止藻类细胞的生长或聚集,影响藻类生长或种类变化的扰动的最低水平以及水动力对藻类影响的作用机理是这一领域未来研究的重点所在。     

A Computational Fluid Dynamics Approach for Urban Area Transport and Dispersion Modeling

A simulation tool has been developed to model the wind fields, turbulence fields, and the dispersion of Chemical, Biological, Radiological and Nuclear (CBRN) substances in urban areas on the building to city blocks scale. A Computational Fluid Dynamics (CFD) approach has been taken that naturally accounts for critical flow and dispersion processes in urban areas, such as channeling, lofting, vertical mixing and turbulence, by solving the steady-state, Reynolds-Averaged Navier–Stokes (RANS) equations. Rapid generation of high quality cityscape volume meshes is attained by a unique voxel-based model generator that directly interfaces with common Geographic Information Systems (GIS) file formats. The flow and turbulence fields are obtained by solving the steady-state RANS equations using a collocated, pressure-based approach formulated for unstructured and polyhedral mesh elements. Turbulence modeling is based upon the Renormalization Group variant of the k–ε model (k–ε RNG). Neutrally buoyant simulations are made by prescribing velocity boundary condition profiles found by a power–law relationship, while turbulence quantities boundary conditions are defined by a prescribed mixing length in conjunction with the assumption of turbulence equilibrium. Dispersion fields are computed by solving an unsteady transport equation of a dilute gas, formulated in a Eulerian framework, using the velocity and turbulence fields found from the steady-state RANS solution. In this paper the model is explained and detailed comparisons of predicted to experimentally obtained velocity, turbulence and dispersion fields are made to neutrally stable wind tunnel and hydraulic flume experiments.     

Experimental study of recirculating flows generated by lateral shock waves in very large channels

Due to the lack of data on hydraulic-jump dynamics in very large channels, the present paper describes the main characteristics of the velocity field and turbulence in a large rectangular channel with a width of 4 m. Although a hydraulic jump is always treated as a wave that is transversal to the channel wall, in the case of this study it has a trapezoidal front shape, first starting from a point at the sidewalls and then developing downstream in an oblique manner, finally giving rise to a trapezoidal shape. The oblique wave front may be regarded as a lateral shockwave that arises from a perturbation at a certain point of the lateral wall and travels obliquely toward the centreline of the channel. The experimental work was carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). In addition to the hydraulic jump formation, a large recirculating flow zone starts to develop from the separating point of the lateral shock wave and a separate boundary layer occurs. Intensive measurements of the streamwise and spanwise flow velocity components along one-half width of the channel were taken using a bidimensional Acoustic Doppler Velocimeter (ADV). The water surface elevation was obtained by means of an ultrasonic profiler. Velocity vectors, transversal velocity profiles, turbulence intensities and Reynolds shear stresses were all investigated. The experimental results of the separated boundary layer were compared with numerical predictions and related work presented in literature and showed good agreement. The transversal velocity profiles indicated the presence of adverse pressure gradient zones and the law of the wall appears to govern the region around the separated boundary layer.