Singular air entrapment at vertical and horizontal supported jets: plunging jets versus hydraulic jumps

Environmental Fluid Mechanics - In plunging jets and at hydraulic jumps, large amounts of air bubbles are entrained at the impingement of the liquid jet into the receiving body. Air is entrapped...     

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.     

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.     

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.     

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.     

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.     

A new model for the CBL growth based on the turbulent kinetic energy equation

Starting from the evolution equation for the turbulent energy density spectrum (EDS), we develop a new model for the growth of the Convective boundary layer (CBL). We apply dimensional analysis to parameterize the unknown inertial transport and convective source term in the dynamic equation for the three-dimensional (3-D) spectrum and solve the 3-D EDS equation. The one-dimensional vertical spectrum is derived from the 3-D spectrum, employing a weight function. This allows us to select the magnitude of the vertical spectral component for the construction of the growing 3-D EDS. Furthermore, we employ the vertical component of the energy spectrum to calculate the eddy diffusivity (required in dispersion models). Currently there are no available experimental data to directly verify our EDS model.     

Energy dissipation estimates in oscillating grid setup: LDV and PIV measurements

The dissipation of turbulent kinetic energy has been increasingly used as a scaling parameter to integrate microbiological accrual and metabolic rates with fluid-flow motion in natural and engineered aquatic ecosystems. The estimation of turbulent kinetic energy under field conditions and the generation of energy dissipation rates under controlled laboratory conditions with microbiological organisms are necessities required to integrate environmental/ecological laboratory protocols with a moving fluid in the environment. Turbulent fluid-flow conditions were generated in an oscillating grid setup, and turbulence variables were quantified using laser-Doppler velocimetry (LDV) and particle image velocimetry (PIV) measuring techniques. The rate of dissipation of the turbulent kinetic energy in the setup ranged from 10⁻⁹ to 10⁻⁴ m²/s³ and was similar to the levels of energy dissipation commonly reported in engineered and natural aquatic ecosystems. Time-averaged velocities were close to zero with the root-mean-square velocity ratios about 1, indicating nearly isotropic fluid-flow conditions in the setup. The velocity spectra, obtained by stationary LDV measurements for the vertical and horizontal velocity components across the setup revealed the existence of inertial subrange with the frequency power scaling law of “ω ^−5/3.” The estimated Eulerian frequency spectrum followed the theoretical functional relation and confirmed the applicability of inertial dissipation method for the estimation of turbulent kinetic energy dissipation rates. PIV was used for a direct estimation of dissipation by evaluating spatially distributed velocity gradients. The direct dissipation estimate in conjunction with the estimated Eulerian frequency spectrum provided evaluation of a “universal” constant, α, commonly used for the estimation of an energy dissipation rate over the inertial subrange of the Eulerian spectrum. The results demonstrated a range of values, rather than a universal constant, of α with a lognormal probability distribution for vertical and horizontal velocity components. In order to encompass a 0.955 probability range under the lognormal distribution the universal constant, α, should be in the range 2.91 ≥ α _u ≥ 0.43 and 4.44 ≥ α _w ≥ 0.42 for horizontal and vertical velocity components, respectively.     

On Disturbances Introduced by Impulse Source into Stratified Two-Component Media

The paper considers the problem concerning the response of a stably stratified two-component medium (salt water, moist air) in the presence of a stationary source of vertical impulse. For a homogeneous vertical distribution of the impulse source (i.e., the applied vertical force), due to the symmetry of the problem, one succeeded in finding the explicit analytical solution of the stationary problem for arbitrary source amplitude. The solution is expressed through Kelvin’s cylindrical functions and represents the stationary vertical jet. The two-component character of the medium can influence substantially the quality of the properties of the solution. In particular, the jet parameters are not defined uniquely by the buoyancy frequency (density stratification). In the solution, the stratifications of the two hydrodynamic components have the distinctive influences that are defined by values of corresponding exchange coefficients. For example, in salt water the solution dependence on salinity stratification may be much more than on temperature stratification.     

Applications of Venturi Principle to Water Aeration Systems

The concentration of dissolved oxygen is an important indicator of water quality because aquatic life lives on the dissolved oxygen in the water. Aeration can increase dissolved oxygen when levels become deficient. Hydraulic structures can significantly improve dissolved oxygen levels by creating turbulent conditions where small air bubbles are carried into the bulk of the flow. Recent researches have focused on developing measurement and predictive techniques for oxygen transfer at hydraulic structures to maintain and enhance water quality. However, reviewing existing studies on aeration performance of hydraulic structures, it seems that there are not too many studies on venturi aeration. The present paper shows applications of venturi principle to water aeration systems. The aeration characteristics of venturi nozzle, venturi conduit and venturi weir are analyzed. The results indicate that venturi aeration might contribute significantly to air entrainment and aeration efficiency. Therefore, venturi device can be used as highly effective aerator in aeration processes.     

Circular economy strategies for combating climate change and other environmental issues

Global industrialization and excessive dependence on nonrenewable energy sources have led to an increase in solid waste and climate change, calling for strategies to implement a circular economy in all sectors to reduce carbon emissions by 45% by 2030, and to achieve carbon neutrality by 2050. Here we review circular economy strategies with focus on waste management, climate change, energy, air and water quality, land use, industry, food production, life cycle assessment, and cost-effective routes. We observed that increasing the use of bio-based materials is a challenge in terms of land use and land cover. Carbon removal technologies are actually prohibitively expensive, ranging from 100 to 1200 dollars per ton of carbon dioxide. Politically, only few companies worldwide have set climate change goals. While circular economy strategies can be implemented in various sectors such as industry, waste, energy, buildings, and transportation, life cycle assessment is required to optimize new systems. Overall, we provide a theoretical foundation for a sustainable industrial, agricultural, and commercial future by constructing cost-effective routes to a circular economy.

     

Observation of bioturbation and hyporheic flux in streambeds

In the Elkhorn River, burrows, tubes, and sediment mounds created by invertebrate bioturbation were observed in the exposed streambed and commonly concentrated on the fine-sediment patches, which consist of silt, clay, and organic matter. These invertebrate activities could loosen the thin layer of clogging sediments and result in an increase of pore size in the sediments, leading to greater vertical hydraulic conductivity of the streambed (K _v ). The measurements of the vertical hydraulic gradient across the submerged streambed show that vertical flux in the hyporheic zone can alter directions (upward versus downward) for two locations only a few meters apart. In situ permeameter tests show that streambed K _v in the upper sediment layer is much higher than that in the lower sediment layer, and the calculated K _v in the submerged streambed is consistently greater than that in the clogged sediments around the shorelines of the sand bars. Moreover, a phenomenon of gas bubble release at the water-sediment interface from the subsurface sediments was observed in the groundwater seepage zone where flow velocity is extremely small. The bursting of gas bubbles can potentially break the thin clogging layer of sediments and enhance the vertical hydraulic conductivity of the streambed.     

太原市空气的SO2污染及树木的吸收净化

研究了太原市空气中SO2浓度的年际、月份和垂直变化规律．实验结果表明，夏季和秋季SO2浓度低，污染较轻，春季和冬季的SO2浓度大，污染重，沿垂直方向在1m高处的SO2浓度最大，7m高的位置SO2浓度明显降低，20m处更低．测试了银杏、白蜡和国槐3种绿化树种的枝条韧皮部和叶片的含硫量，其逐月变化规律说明这些树种对城市空气中的SO2具有很强的吸收能力，是城市绿化和净化污染的优良树种．结合树木的叶片容量和含硫量的关系，评价了它们净化污染的效益，结合SO2垂直变化规律提出立体绿化配置．图2表3参7     

Steady open channel flows with curved streamlines: the Fawer approach revised

Rapidly varied open channel flows are characterized by curvilinear streamlines, thereby resulting in a pressure field different from the hydrostatic approach proposed in the standard gradually varied flow theory. This problem is related to environmental hydraulic problems such as the undular hydraulic jump and flow over round-crested weirs, for which streamline curvature effects are significant. The inclusion of the curvilinear streamline effect in an extended energy equation was firstly by Fawer. Most of the extended energy equations currently employed are therefore modified forms of the original Fawer approach. The aim of the present study is to highlight and remind engineers of the outstanding theory presented by Fawer. Herein, his approach for steady open channel flow with curved streamlines is revised and compared with experimental observations. Computational methods are presented in detail and based on present results, it can be observed that more recent and complex models for these problems are similar to the original proposal of Fawer, and hardly more accurate in some instances. Based on the proposed study an useful framework for theoretical models for steady open channel flows with curved streamlines is proposed.     

Flow aeration, cavity processes and energy dissipation on flat and pooled stepped spillways for embankments

The design floods of several reservoirs were recently re-evaluated and the revised spillway outflow could result in dam overtopping with catastrophic consequences for some embankment structures. Herein a physical study was performed on flat and pooled stepped spillways with a slope typical of embankments $(\uptheta = 26.6^{\circ })$ and four stepped configurations were tested: a stepped spillway with flat horizontal steps, a pooled stepped spillway, and two stepped spillways with in-line and staggered configurations of flat and pooled steps. The focus of the study was on the flow aeration, air–water flow properties, cavity flow processes, and energy dissipation performances. The results demonstrated the strong aeration of the flow for all configurations. On the in-line and staggered configurations of flat and pooled steps, the flow was highly three-dimensional. The residual head and energy dissipation rates at the stepped chute downstream end were calculated based upon the detailed air–water flow properties. The results showed that the residual energy was the lowest for the flat stepped weir. The data for the stepped spillway configuration with in-line and staggered configurations of flat and pooled steps showed large differences in terms of residual head in the transverse direction. Altogether the present results showed that, on a $26.6^{\circ }$ slope stepped chute, the designs with in-line and staggered configurations of flat and pooled steps did not provide any advantageous performances in terms of energy dissipation and flow aeration, but they were affected by three-dimensional patterns leading to some flow concentration.     

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.     

Verification of the geographical origin of modeled air-mass trajectories by means of the isotope composition of rainwater during the SALLJEX experiment

The SALLJEX experiment was held during the summer 2002–2003. It consisted of three-dimensional observation of the atmosphere to study the structure of the low level jet along the eastern slopes of the Andes. Daily precipitation water samples were collected at two stations (Resistencia and Salta) in northern Argentina and isotope content was analyzed. The isotope data were used in conjunction with air parcel trajectories obtained from a 3-D kinematic model (3D-MTC) developed by the University of Sao Paulo, Brazil. Values of deuterium excess were related with air masses of continental origin, whilst low values were associated with air masses with longer oceanic trajectories. Furthermore, although data are scarce, results show that oxygen-18 and deuterium excess in rainwater are related with the occurrence of the low level jet.     

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.     

Are breaking waves,bores, surges and jumps the same flow?

The flow structure in the aerated region of the roller generated by breaking waves remains a great challenge to study, with large quantities of entrained air and turbulence interactions making it very difficult to investigate in details. A number of analogies were proposed between breaking waves in deep or shallow water, tidal bores and hydraulic jumps. Many numerical models used to simulate waves in the surf zone do not implicitly simulate the breaking process of the waves, but are required to parameterise the wave-breaking effects, thus relying on experimental data. Analogies are also assumed to quantify the roller dynamics and the energy dissipation. The scope of this paper is to review the different analogies proposed in the literature and to discuss current practices. A thorough survey is offered and a discussion is developed an aimed at improving the use of possible breaking proxies. The most recent data are revisited and scrutinised for the use of most advanced numerical models to educe the surf zone hydrodynamics. In particular, the roller dynamics and geometrical characteristics are discussed. An open discussion is proposed to explore the actual practices and propose perspectives based on the most appropriate analogy, namely the tidal bore.     

Self-organization of tropical seasonal rain forest in southwest China

How to measure development of ecosystems is both a theoretical and practical question in ecology. Species richness and biomass accumulation are familiar figures of merit, but they cannot be instant watched. Self-organization is a tacit character. However, methods to measure the degree of self-organization of ecosystem are problematic. To this end Lin et al. (2009) have devised indicators of energy capture and dissipation so that self-organization defined via maximum energy dissipation can be quantified easily. Here the method is used to analyze long-term data (2004-2006) of a tropical seasonal rain forest included in the ChinaFLUX program. Three years of average self-organization values were clearly separated by seasonal variation. Reflection and long wave radiation are the main two pathways of energy loss. For tropical seasonal rain forest studied, long wave radiation contributed most to energy loss, and was negatively correlated with energy capture ability (Rn/DR). The nocturnal difference between canopy and air temperatures had a strong negative correlation with the long wave radiation loss ratio. However, the long wave radiation loss ratio was slightly lower than the reflection loss ratio in rainy season, when values were very low. Precipitation and wind had significant impact on energy dissipation ability in the hot dry season, but the correlation coefficients between precipitation and wind with thermal response numbers (TRNs) were very low. The results indicated that the self-organization estimation system based on “maximum energy dissipation theory” is applicable for tropical forest.