Mixing at a sediment concentration interface in turbulent open channel flow

In this work we address the role of turbulence on mixing of clear layer of fluid with sediment-laden layer of fluid at a sediment concentration interface. This process can be conceived as the entrainment of sediment-free fluid into the sediment-laden layer, or alternatively, as the transport of sediment into the top sediment-free flow. This process is governed by four parameters—Reynolds number of the flow \(Re_\tau\), non-dimensional settling velocity of the sediment (proxy for sediment size) \(\tilde{V}\), Richardson number \(Ri_\tau\) and Schmidt number Sc. For this work we have performed direct numerical simulations for fixed Reynolds and Schmidt numbers while varying the values of Richardson number and particle settling velocity. In the simple model considered here, the flow’s momentum and turbulence pre-exists over the entire layer of fluid, while the sediment is initially confined to a layer close to the bed. Mixing of sediment-free fluid with the sediment-laden layer is associated primarily with upward transport of sediment and buoyancy. There is no simultaneous upward transport of fluid momentum and turbulence into the sediment-free fluid layer, which is already in motion and turbulent. The analysis performed shows that the ability of the flow to transport a given sediment size decreases with the distance from the bottom, and thus only fine enough sediment particles are transported across the sediment concentration interface. For these cases, the concentration profiles evolve to a final steady state in good agreement with the well-known Rouse profile. The approach towards the Rouse profile happens through a transient self-similar state. This behavior of the flow is not seen for larger particles. Detailed analysis of the three dimensional structure of the sediment concentration interface shows the mechanisms by which sediment particles are lifted up by tongues of sediment-laden fluid with positive correlation between vertical velocity and sediment concentration. Finally, the mixing ability of the flow is addressed by monitoring the time evolution of the center of mass of the sediment-laden layer and the vertical location of the sediment-free/sediment-laden interface.     

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.     

Hierarchical modeling of the dilute transport of suspended sediment in open channels

We propose, discuss and validate a theoretical and numerical framework for sediment-laden, open-channel flows which is based on the two-fluid-model (TFM) equations of motion. The framework models involve mass and momentum equations for both phases (sediment and water) including the interactive forces of drag, lift, virtual mass and turbulent dispersion. The developed framework is composed by the complete two-fluid model (CTFM), a partial two-fluid model (PTFM), and a standard sediment-transport model (SSTM). Within the umbrella of the Reynolds-Averaged Navier-Stokes (RANS) equations, we apply K–ε type closures (standard and extended) to account for the turbulence in the carrier phase (water). We present the results of numerical computations undertaken by integrating the differential equations over control volumes. We address several issues of the theoretical models, especially those related to coupling between the two phases, interaction forces, turbulence closure and turbulent diffusivities. We compare simulation results with various recent experimental datasets for mean flow variables of the carrier as well as, for the first time, mean flow of the disperse phase and turbulence statistics. We show that most models analyzed in this paper predict the velocity of the carrier phase and that of the disperse phase within 10% of error. We also show that the PTFM provides better predictions of the distribution of sediment in the wall-normal direction as opposed to the standard Rousean profile, and that the CTFM is by no means superior to the PTFM for dilute mixtures. We additionally report and discuss the values of the Schmidt number found to improve the agreement between predictions of the distribution of suspended sediment and the experimental data.     

Analytical expression for predicting the reduced settling velocity of small particles in turbulence

The influence of turbulence on the settling velocity of small particles remains an inconclusive research subject. Both enhanced and retarded particle settling compared to quiescent settling have been reported in previous literature, and several theories have been proposed. Among the mechanisms that account for reduced settling velocities in turbulence, the loitering effect is an important one that generally exists in various conditions. This study focuses on an analytical prediction of reduced particle settling velocities due to the loitering effect. By considering the velocity autocorrelation function as a step function analogous to the free path theory, and using a modified integral time scale to capture the essence of the loitering effect, an analytical expression is derived for predicting the reduction in particle settling velocities in turbulent flows. Calculation results of the expression are then examined by comparing with the results of a random walk model, direct numerical simulations that conditionally captured the reduction of particle settling velocities due to the loitering effect, and several representative experiments. Major possible influencing factors on the prediction of the analytical expression and applicable conditions of the expression are then further discussed. The proposed analytical expression is shown to be suitable for predicting the reduced settling velocities of small particles with relatively weak inertia in turbulent flows and could provide a reasonable explanation for reported cases in which small to moderate reductions in particle settling velocities were observed.

     

A simplified approach to address turbulence modulation in turbidity currents as a response to slope breaks and loss of lateral confinement

Turbidity currents traversing canyon-fan systems flow over bed slopes that decrease in the downstream direction. This slope decrease eventually causes turbidity currents to decelerate and enter a net-depositional mode. When the slope decrease is relatively rapid in the downstream direction, the turbidity current undergoes a concomitantly rapid and substantial transition. Similar conditions are found when turbidity currents debouch to fan systems with loss of lateral confinement. In this work a simplified approach to perform direct numerical simulation of continuous turbidity currents undergoing slope breaks and loss of lateral confinement is presented and applied to study turbulence modulation in the flow. The presence of settling sediment particles breaks the top–bottom symmetry of the flow, with a tendency to self-stratify. This self-stratification damps turbulence, particularly near the bottom wall, affecting substantially the flow’s ability to transport sediment in suspension. This work reports results on two different situations: turbidity currents driven by fine and coarser sediment flowing through a decreasing slope. In the case of fine sediment, after the reduction in the slope of the channel, the flow remains turbulent with only a modest influence on turbulence statistics. In the case of coarse sediments, after the change in slope, turbulence is totally suppressed.     

Markovian–Octant analysis based stable turbulent shear stresses in near-bed bursting phenomena of vortex settling chamber

The coherent structure in near-bed turbulent boundary layer of vortex chamber, particularly the bursting events and their associated shear stresses play the main role in sediment flushing process and consequently the trap efficiency of the vortex settling chamber. Hence, three-dimensional velocity measurements were made at 48 points near the bed of physical model of vortex chamber by using Micro-ADV. The pattern of sediment deposition at the bed of vortex settling chamber reveals three separate regions formed by three predominant currents of inlet flow, flushing flow and outlet over flow. Additionally, due to the instability and three-dimensional nature of the bursting events near the bed of chamber, the new method of Markovian–Octant analysis was applied to study the different classes of near-bed stable shear stresses of vortex chamber in three dimensions. Moreover, the role of each class of stable shear stresses on Sediment transport mechanism at the bed of vortex chamber is investigated.     

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.     

Surface signatures of submerged heated jet

The flow induced at the surface of a water body by a submerged heated horizontal turbulent jet was investigated experimentally with the aim of developing parameterizations for surface mean temperature/velocity fields. The jet nozzle diameter was fixed, the depth of the jet beneath the free surface was varied, and two jet Reynolds numbers (5020, 11300) were considered. The surface temperature was measured using a highly sensitive infrared camera, and the near-surface horizontal velocity field was measured using particle image velocimetry. The experimental results were explained using a model based on similarity solutions with variable turbulent viscosity. While classical Schlichting’s solution with constant turbulent viscosity predicts complete similarity for transverse velocity/temperature distributions only in a plane that coincides with the flow axis, the present solution predicts similarity in an arbitrary plane parallel to the flow axis, which was confirmed using data collected at the surface. Comparisons of present data with available previous results also showed general agreement.     

A model of vertical distribution of suspended matter in an open channel flow

A quasi-stationary model of vertical distribution of concentration of suspended particular matter in the bottom layer of 1D open channel with a sloped bottom and varying free surface slope is discussed. The model proceeds from the balance between the turbulent diffusion and settling with the buoyancy flux effects on the medium turbulence neglected. The model outcome is formulated in the form of an analytic formula for the vertical distribution of concentration. It is shown that the derived formula embraces two basic types of vertical distribution of concentration, one with a monotonic decrease of concentration gradient and the other with a gradient maximum (lutocline) located at some distance from the bottom. The first distribution type realizes for a relatively large settling velocity or low intensity of turbulence and the second type for a small settling velocity or high intensity of turbulence. The skill of the model to mimic realistic situations is demonstrated on data measured in the Jiaojiang Estuary (China).     

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.     

Theoretical modeling of suspended grain-size distribution in fluvial environment by stratification and secondary current approaches

Here we propose a theoretical model to compute the suspended grain-size distribution in fluvial environment. We derive the model based on the Reynolds averaged Navier–Stokes equation and the continuity equation of sediment phase. The model includes the effects of secondary current and stratification which are the cause of complex interaction between turbulence and grain-size distribution in the sediment-laden flow. Due to an immense importance of particle–particle and particle-turbulence interactions near the channel bed, we include their impacts in the boundary condition of the model. The present model has noteworthy contribution to demonstrate the phenomena of suspended grain-size distribution in the real world. Reported experimental data in literature shows well agreement with the numerical solution computed from the suggested model. The better computational accuracy of the present model is ascertained when the upper bound of calculated error between observed experimental data and computed values is found to be lowest for our model in comparison to a large number of existing models developed from different mathematical viewpoints.     

Hydrodynamics and turbulence in emergent and sparsely vegetated open channel flow

This present study reports the results of an experimental study characterizing thorough variation of turbulent hydrodynamics and flow distribution in emergent and sparsely vegetated open channel flow. An emergent and rigid sparse vegetation patch with regular spacing between stems along the flow and transverse directions was fixed in the central region of the cross-section of open channel. Experiments were conducted in subcritical flow conditions and velocity measurements were obtained with an acoustic Doppler Velocimetry system. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and vortical motions are found in and around the vegetation patch. At any cross-section through the interior of the vegetation patch, streamwise velocity decreases with increase in streamwise length and the velocity profiles converge from the log-law to a linear profile with increasing slope. Time-averaged lateral and vertical velocities inside the vegetation patch increase with increasing streamwise distance and converge from negative values to positive values. Turbulence intensities interior of the sparse vegetation patch are more than those of without the vegetation patch. Similar to the trend of streamwise velocity profiles inside the vegetation, turbulence intensities and longitudinal-normal Reynolds shear stress profile decreases with streamwise direction. In the interior of the vegetation patch and downstream of the trailing edge, turbulent kinetic energy profiles are exhibiting irregular fluctuations and the maximum values are occurring in the outer layer. Analysis of flow distribution confirms sparse vegetation patch is inducing a serpentine flow pattern in its vicinity. At the leading edge, flow is rushing towards the right hand sidewall, and at the trailing edge, flow is turning to the left hand sidewall. In between the leading and trailing edges, the streamlines are following a zig-zag fashion at varied degree along the streamwise and lateral directions. Immediate upstream of the leading edge and in the interior of the vegetation patch, vortex motion is clearly visible and the vortices are stretched along the width of the channel with streamwise direction.     

A simplified computational analysis of turbulent plumes and jets

The application of computational fluid dynamics (CFD), particularly Large Eddy Simulation, for the modelling of buoyant turbulent plumes, has been demonstrated to be very accurate, but computationally expensive. Here a more basic, and therefore more generally practicable, approach is presented. Commercial CFD software is used to model such plumes using Reynolds-Averaged Navier-Stokes (RANS) turbulence models. A careful comparison is made between the numerical predictions and well-established results regarding the bulk properties of plumes. During this process, we are able to observe the well-known approximate Gaussian nature of the plume and achieve quantitative agreement with empirical plume spread coefficients. The use of numerical modelling allows for the investigation of the flow field and turbulence in those regions of the plume of most interest—the plume edge and near source regions. A comprehensive sensitivity study is conducted to identify the limits of applicability of this modelling approach. It is shown that the standard modelling approach of Morton, Taylor and Turner, which introduced the well-known entrainment assumption, pertains in a region well above the source region. At the plume edge, the levels of turbulence are contrasted with the value of the entrainment parameter. Finally, the effects of forcing the plumes with additional momentum at the source are considered, including the case of a pure jet. We show how these forced plumes eventually lose their momentum excess and tend to the behaviour of a pure, buoyant plume.     

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.     

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.     

Model of turbulence penetration into a suspension layer on a sediment bed and effect on vertical solute transfer

The vertical diffusional mass (solute) transfer through a suspended sediment layer, e.g. at the bottom of a lake, reservoir or estuary, by the propagation of velocity fluctuations from above was investigated. The attenuation of the velocity fluctuations in the suspension layer and the associated effect on solute transfer through the suspension layer was simulated. To represent large eddies traveling downstream in water over a high-concentration suspended sediment layer, a streamwise velocity fluctuation moving in downstream direction was imposed along the upper boundary of the suspension layer. Velocity fluctuations and downstream velocity were normalized by the shearvelocity (U_*) at the top of the suspension layer. Streamwise and vertical velocity components inside the suspension layer, were obtained from the 2-D continuity and the Navier–Stokes equations. The persistence of turbulence with depth—as it penetrates from the overlying water into the suspension layer—was found to depend on its amplitude, its period, and on the apparent viscosity of the suspension. The turbulence was found to propagate efficiently into the suspension layer when its frequency is low, and the apparent viscosity of the suspension is high. Effects on vertical mass transfer were parameterized by penetration depth and effective diffusion coefficient, and related to apparent viscosity of the suspension, Schmidt number and shear velocity on top of the suspension layer. The enhancement of turbulence penetration by viscosity is similar to the flow near an oscillating flat plate (Stokes’ second problem), but is opposite to turbulence penetration into a stationary porous and permeable sediment bed. The information is applicable to water quality modeling mear the sediment/water interface of lakes, river impoundments and estuaries.     

The Modelling of Turbulence from Traffic in Urban Dispersion Models — Part I: Theoretical Considerations

The modelling of pollutant dispersion at the street scale in an urban environment requires the knowledge of turbulence generated by the traffic motion in streets. In this paper, a theoretical framework to estimate mechanical turbulence induced by traffic in street canyons at low wind speed conditions is established. The standard deviation of the velocity fluctuations is adopted as a measure of traffic-produced turbulence (TPT). Based on the balance between turbulent kinetic energy production and dissipation, three different parameterisations for TPT suitable for different traffic flow conditions are derived and discussed. These formulae rely on the calculations of constants that need to be estimated on the basis of experimental data. One such estimate has been made with the help of a wind tunnel data set corresponding to intermediate traffic densities, which is the most common regime, with interacting vehicle wakes.     

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.