Numerical modelling of horizontal sediment-laden jets

Sediment-laden turbulent flows are commonly encountered in natural and engineered environments. It is well known that turbulence generates fluctuations to the particle motion, resulting in modulation of the particle settling velocity. A novel stochastic particle tracking model is developed to predict the particle settling out and deposition from a sediment-laden jet. Particle velocity fluctuations in the jet flow are modelled from a Lagrangian velocity autocorrelation function that incorporates the physical mechanism leading to a reduction of settling velocity. The model is first applied to study the settling velocity modulation in a homogeneous turbulence field. Consistent with basic experiments using grid-generated turbulence and computational fluid dynamics (CFD) calculations, the model predicts that the apparent settling velocity can be reduced by as much as 30 % of the stillwater settling velocity. Using analytical solution for the jet mean flow and semi-empirical RMS turbulent velocity fluctuation and dissipation rate profiles derived from CFD predictions, model predictions of the sediment deposition and cross-sectional concentration profiles of horizontal sediment-laden jets are in excellent agreement with data. Unlike CFD calculations of sediment fall out and deposition from a jet flow, the present method does not require any a priori adjustment of particle settling velocity.     

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.     

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).     

Design and Testing of a Turbulence Probe for Harsh Flows

The force of wind on the ground created by turbulent eddies is commonly used to describe the horizontal flux of material during wind erosion. Here we present the Murdoch Turbulence Probe, an instrument for use in both clean and eroding flows which uses pressure differences to measure the three components of wind velocity. Correlation techniques calculate the forces near the ground and turbulence statistics in nearly real time, including turbulent velocity fluctuations from less than 0.1 Hz to 200 Hz, mean flow velocities, Reynolds stresses as well as the integral length and time scales. In the portable wind-tunnel used by Agriculture Western Australia, turbulence statistics were recorded over stable surfaces and in blowing sand from the initiation of erosion up to the time the sand supply was exhausted. Estimates of the friction velocity derived from the turbulence probe were compared with estimates obtained from the wind speed profile measured with a rake of pitot and static tubes. The Murdoch Turbulence Probe appears to work well in sandblasting conditions. Relative turbulence intensities ranged from 0.11 to 0.2 and are in close agreement with values in the literature. The ratio of the turbulence to the friction velocity (3 to 3.2) is at the high end of the reported range. The Reynolds stress measurements agree closely with predictions of the threshold friction velocities of the sand and estimates from the wind speed profile with a von Kármán constant of about 0.3, lower than the commonly accepted value of 0.4. We suggest that the wind-tunnel profile represents the `outer layer' of the boundary-layer that may best be described by a `Wake Law' or `Defect Law'. At about 54 mm above the surface, the friction velocity decreases from 0.64 m/s to 0.39 m/s and the mean velocity increases from 9.6 m/s to 11.6 m/s as the supply of sand is depleted. In addition to the friction velocity, other scales may be necessary to characterise the overriding effect of the wind and in extending wind-tunnel results to the field.     

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.     

Some effects of langmuir circulation on the quality of water resource systems

The quantitative extent to which the large-scale organized water motion in the surface waters of lakes and reservoirs, known as Langmuir circulation, affects the distribution and settling of algae and other suspended particles is not known and has thus been ignored in conventionally used water-quality models. Since the distribution and settling of these particles is important in determining water quality, this study set out to investigate these effects. Current literature which discusses this problem is reviewed and a mathematical model is developed based on the two-dimensional advection-diffusion mass transport describing the temporal and spatial distribution of suspended particles in a typical Langmuir cell; the Langmuir circulation flow field and turbulent diffusion coefficients are empirically modelled by relating them to environmental parameters.The results show that Langmuir circulation does affect particle distribution and settling. For particles with small sinking speeds, such as the lighter algae, the circulation causes intense mixing, resulting in essentially uniform distribution of particles over the cell (as assumed in the ‘well-mixed compartment model’). For particles with high sinking velocities, however, aggregation can occur, giving rise to significant reduction in sinking loss when compared with that predicted by conventional models. For diatoms, reductions of 6% and higher can occur depending on which conventionally used model is being considered, while for silt and sand particles in a cell of large width-to-depth ratio a reduction of more than 60% is possible.     

Near-boundary velocity and turbulence in depth-varying stream flows

This research examined the temporal distribution of turbulent structure near a streambank toe through the progression of a flood wave in West Run (Morgantown, WV, USA). Three-dimensional velocities and water depths were measured through a 17-h flood event. Turbulence characteristics were examined: Reynolds stresses, turbulent kinetic energy, and turbulence intensities. On average, near-boundary velocity during the rising stage was less than the falling stage, likely due to the measurement location and local roughness. The velocity vectors shifted from towards bed before the flood wave to toward the streambank during progression of the flood wave. Turbulent kinetic energy increased with increasing water depth during the rising stage. Reynolds stress, τ_xz, increased with increasing water depth during the rising stage, but the majority of the stresses were negative through the storm event. Reynolds stress, τ_xy, was positive throughout the event and did not vary with depth. This work is among the first to evaluate turbulence during depth-varying flows in the field.     

Characterization of bedload intermittency near the threshold of motion using a Lagrangian sediment transport model

At the smallest scales of sediment transport in rivers, the coherent structures of the turbulent boundary layer constitute the fundamental mechanisms of bedload transport, locally increasing the instantaneous hydrodynamic forces acting on sediment particles, and mobilizing them downstream. Near the critical threshold for initiating sediment motion, the interactions of the particles with these unsteady coherent structures and with other sediment grains, produce localized transport events with brief episodes of collective motion occurring due to the near-bed velocity fluctuations. Simulations of these flows pose a significant challenge for numerical models aimed at capturing the physical processes and complex non-linear interactions that generate highly intermittent and self-similar bedload transport fluxes. In this investigation we carry out direct numerical simulations of the flow in a rectangular flat-bed channel, at a Reynolds number equal to Re = 3632, coupled with the discrete element method to simulate the dynamics of spherical particles near the bed. We perform two-way coupled Lagrangian simulations of 48,510 sediment particles, with 4851 fixed particles to account for bed roughness. Our simulations consider a total of eight different values of the non-dimensional Shields parameter to study the evolution of transport statistics. From the trajectory and velocity of each sediment particle, we compute the changes in the probability distribution functions of velocities, bed activity, and jump lengths as the Shields number increases. For the lower shear stresses, the intermittency of the global bedload transport flux is described by computing the singularity or multifr actal spectrum of transport, which also characterizes the widespread range of transport event magnitudes. These findings can help to identify the mechanisms of sediment transport at the particle scale. The statistical analysis can also be used as an ingredient to develop larger, upscaled models for predicting mean transport rates, considering the variability of entrainment and deposition that characterizes the transport near the threshold of motion.     

Spatial–temporal structure of mixing interface turbulence at two large river confluences

Converging flows at stream confluences often produce highly turbulent conditions. The shear layer/mixing interface that develops within the confluence hydrodynamic zone (CHZ) is characterized by complex patterns of three-dimensional flow that vary both spatially and temporally. Previous research has examined in detail characteristics of mean flow and turbulence along mixing interfaces at small stream confluences and laboratory junctions; however few, if any, studies have examined these characteristics within mixing interfaces at large river confluences. This study investigates the structure of mean velocity profiles as well as spatial and temporal variations in velocity, backscatter intensity, and temperature within the mixing interfaces of two large river confluences. Velocity, temperature, and backscatter intensity data were obtained at stationary locations within the mixing interfaces and at several cross sections within the CHZ using acoustic Doppler current profilers. Results show that mean flow within the mixing interfaces accelerates over distance from the junction apex. Turbulent kinetic energy initially increases rapidly over distance, but the rate of increase diminishes downstream. Hilbert–Huang transform analysis of time series data at the stationary locations shows that multiple dominant modes of fluctuations exist within the original signals of velocity, backscatter intensity, and temperature. Frequencies of the largest dominant modes correspond well with predicted frequencies for shallow wake flows, suggesting that mixing-interface dynamics include wake vortex shedding—a finding consistent with spatial patterns of depth-averaged velocities at measured cross sections. Spatial patterns of temperature and backscatter intensity show that the converging flows at both confluences do not mix substantially, indicating that turbulent structures within the mixing interfaces are relatively ineffective at producing mixing of the flows in the CHZ.     

Turbulent velocity profile in fully-developed open channel flows

The determination of velocity profile in turbulent narrow open channels is a difficult task due to the significant effects of the anisotropic turbulence that involve the Prandtl’s second type of secondary flow occurring in the cross section. With these currents the maximum velocity appears below the free surface that is called dip phenomenon. The well-known logarithmic law describes the velocity distribution in the inner region of the turbulent boundary layer but it is not adapted to define the velocity profile in the outer region of narrow channels. This paper relies on an analysis of the Navier–Stokes equations and yields a new formulation of the vertical velocity profile in the center region of steady, fully developed turbulent flows in open channels. This formulation is able to predict time averaged primary velocity in the outer region of the turbulent boundary layer for both narrow and wide open channels. The proposed law is based on the knowledge of the aspect ratio and involves a parameter C_Ar depending on the position of the maximum velocity (ξ_dip). ξ_dip may be derived, either from measurements or from an empirical equation given in this paper. A wide range of longitudinal velocity profile data for narrow open channels has been used for validating the model. The agreement between the measured and the computed velocities is rather good, despite the simplification used.     

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 investigation in the roughness sub-layer of a near wall flow

The turbulence behaviour along a wall roughened by pyramidal elements was analysed in the region extending from the apex of the roughness elements up to the external limit of the roughness sub-layer. The data used for the analysis were obtained by particle image velocimetry technique. The rough wall turbulent boundary layer flow is characterized by a relatively low Reynolds number. All the results on the rough wall were compared with data referring to the canonical flow on a smooth wall turbulent boundary layer. Mean values and turbulence quantities for the two flows collapse when approaching the external limit of the roughness sublayer. The quadrant analysis of the Reynolds shear stress, in the region near the surface, shows that the contribution of the sweep motions is about equivalent for the two flows (except for wall distances lower than 40 viscous units). The contribution of the ejection motions appears to be more important over the smooth wall than over the rough wall with increasing differences approaching the wall. The probability density functions of the streamwise fluctuating velocity field for the rough wall case appear to be positively skewed in the zone very close to the pyramid apex, in contrast with the behavior observed for the smooth wall case at corresponding distances from the wall. The integral and Taylor scales for the rough wall case appear to be strongly reduced by the presence of the roughness, while the Kolmogorov microscale shows higher values.     

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.     

Simulation of exchange flow between open water and floating vegetation using a modified RNG <Emphasis Type="Italic">k</Emphasis>-<Emphasis Type="Italic">ε</Emphasis> turbulence model

The paper focuses on the numerical simulation of the exchange flow between open water and floating vegetation, which plays an important role in maintaining the ecological balance by transporting nutrient matter. The simulation was conducted using a new solver developed upon OpenFOAM. A modified RNG k-ε turbulence model, which is expected to model both the high- and low-Reynolds number flows correctly, was used to determine the eddy viscosity. Several particular terms were added into the momentum equations and turbulence model equations to model the effects of vegetation and buoyancy. Among these terms, the term for the effect of vegetation in the ε-equation was re-modelled. The model was validated by properly predicting the profiles of mean velocity and turbulent kinetic energy for flows through suspended canopies. The density flow between open and vegetated water was simulated with the same conditions as those of the experiment conducted by Zhang and Nepf. The predicted results agreed well with the experimental data and provided more detailed information of such exchange flow. The convection between the root layer and the layer beneath the roots, which was not observed in the experiment, was observed in the numerical simulation.     

Clustering of aerosols in atmospheric turbulent flow

A mechanism of formation of small-scale inhomogeneities in spatial distributions of aerosols and droplets associated with clustering instability in the atmospheric turbulent flow is discussed. The particle clustering is a consequence of a spontaneous breakdown of their homogeneous space distribution due to the clustering instability, and is caused by a combined effect of the particle inertia and a finite correlation time of the turbulent velocity field. In this paper a theoretical approach proposed in Elperin et al. (2002) Phys Rev E 66:036302 is further developed and applied to investigate the mechanisms of formation of small-scale aerosol inhomogeneities in the atmospheric turbulent flow. The theory of the particle clustering instability is extended to the case when the particle Stokes time is larger than the Kolmogorov time scale, but is much smaller than the correlation time at the integral scale of turbulence. We determined the criterion of the clustering instability for the Stokes number larger than 1. We discussed applications of the analyzed effects to the dynamics of aerosols and droplets in the atmospheric turbulent flow.     

Transport of Sewage Sludge in a Mixed Water Column

Abstract

Sewage sludge from four publicly-owned treatment works was sampled and characterized in terms of parameters affecting transport at the 106-mile deep ocean disposal site as part of the US Environmental Protection Agency's site monitoring programme. Samples from treatment plants in Passaic Valley, Rahway, and Elizabeth, New Jersey and New York City were characterized in terms of dynamic size distribution, suspended solids and density. the transport characteristics of sludge particles were measured using a 2 metre computer-interfaced laboratory settling column. Experiments were conducted at constant salinity (35 ppt) while varying hydrodynamic mixing, sludge type and concentration using a modified factorial experimental design. Hydrodynamic power dissipation was varied so that the vertical dispersion and rms fluid shear rate ranged between 0-6 cm²S^?1 and 0-30s^?1 respectively. Results indicate that at least 80% of suspended sludge particles will eventually settle under mixed conditions. the average settling velocities ranged between 0.05-4.05 × 10^-3 cm ^s-1. Shear rates above 15 s^?1 inhibited sludge settling due to aggregate breakup and boundary effects, but at a lower shear rate, differential settling and fluid shear were the dominant transport mechanisms. Sludge dilution (1/500-1/5000) had a limited effect on the settling rate. Results from this study can be used to calibrate particle transport models to determine the fate of sludge disposed at an ocean disposal site.     

LE of shallow mixing interfaces: A review

Eddy-resolving techniques have become a powerful tool to investigate shallow flows at both laboratory and field scale. In this paper several examples are given where high-resolution 3D numerical simulation are used to investigate the spatial development of mixing interfaces (MIs) forming in shallow environments like open channels with idealized and natural bathymetry where the bed friction plays a major role in the spatial development of the MI and associated large-scale turbulence. The focus is on the coherent structures forming within the MI and in its vicinity that control the momentum and mass exchange and heat transfer between the two sides of the MI. Examples include: (1) a MI developing in a flat-bed open channel downstream of a splitter wall separating two parallel fully-turbulent streams of different velocities, (2) a MI developing in a flat-bed open channel downstream of a 60 \(^{\circ }\) wedge separating two non-parallel fully turbulent streams of different velocities, (3) a MI developing downstream of a river confluence for cases with a large and, respectively, a small difference between the mean velocities of the two streams. Stratification effects due to unequal densities of the two incoming streams are also discussed, (4) a MI developing between a main rectangular straight channel and a series of shallow embayments present at one of the channel banks. Besides using available experimental data to demonstrate that eddy resolving techniques can accurately predict the structure of the MI and its development, the paper discusses new insights into the physics of these flows obtained based on the simulations. The paper also provides an overview of the main numerical approaches that can be used to simulate the unsteady dynamics of the large scale turbulence in flows containing shallow MIs.