Shear Entrainment Research Articles

Impact of bubble size on the integral characteristics of bubble plumes in quiescent and unstratified water

We present an experimental study to investigate the impact of bubble size on behavior of bubble plumes from the integral point of view. Two distinct types of bubble plume were generated under the same volumetric gas flow rate: many small bubbles using an air-stone diffuser and a few large bubbles using a single-orifice diffuser. Using Particle Image Velocimetry, we measured the velocity field in the plumes, and derived the integral characteristics for comparison, including the evolution of plume width, centerline velocity, volume flux, momentum flux, momentum amplification factor, and the entrainment coefficient. The measurement data show that the evolution of all the parameters in the plumes are influenced strongly by the different bubble sizes and population. The plumes with many small bubbles behave closer to the single-phase coherent plumes, showing a linear growth of plume width and a decreasing centerline velocity. These characteristics are modified in the plumes with fewer but larger bubbles. With the same total initial buoyancy flux from the source, fewer but larger bubbles give rise to weaker mean flow characteristics, i.e., smaller plume velocity and weaker fluxes of volume and momentum. This modification is attributed to the different mechanisms in fundamental transport of energy and momentum between mean and fluctuating components. In the single-orifice cases, the plumes are influenced by stronger but less frequent bubble wakes, compared to those more coherent bubble plumes in the air-stone cases. Higher momentum amplification factors were found in bubble plumes with fewer but larger bubbles, indicating a stronger ratio of turbulence to mean in these plumes. Despite the modification, all bubble plumes support a typical shear entrainment process within 40 cm height-of-rise. Hence, the integral model and the universal scaling using the plume length scale D and the bubble slip velocity Ws were found to describe the integral behavior of bubble plumes generally well in the range of our experimental parameters, regardless of the different bubble sizes and population.

Formation and erosion of sediment cover in an experimental bedrock‐alluvial channel

AbstractSediment grains in a bedrock‐alluvial river will be deposited within or adjacent to a sediment patch, or as isolated grains on the bedrock surface. Previous analysis of grain geometry has demonstrated that these arrangements produce significant differences in grain entrainment shear stress. However, this analysis neglected potential interactions between the sediment patches, local hydraulics and grain entrainment. We present a series of flume experiments that measure the influence of sediment patches on grain entrainment. The flume had a planar bed with roughness that was much smaller than the diameters of the mobile grains. In each experiment sediment was added either as individual grains or as a single sediment pulse. Flow was then increased until the sediment was entrained. Analysis of the experiments demonstrates that: (1) for individual grains, coarse grains are entrained at a higher discharge than fine grains; (2) once sediment patches are present, the different in entrainment discharge between coarse and fine grains is greatly reduced; (3) the sheltering effect of patches also increases the entrainment discharge of isolated grains; (4) entire sediment patches break‐up and are eroded quickly, rather than through progressive grain‐by‐grain erosion; (5) as discharge increases there is some tendency for patches to become more elongate and flow‐aligned, and more randomly distributed across the bed. One implication of this research is that the critical shear stress in bedrock‐alluvial channels will be a function of the extent of the sediment cover. Another is that the influence of sediment patches equalizes critical shear stresses between different grain sizes and grain locations, meaning that these factors may not need to be accounted for. Further research is needed to quantify interactions between sediment patches, grain entrainment and local hydraulics on rougher bedrock surfaces, and under different types of sediment supply. Copyright © 2016 John Wiley & Sons, Ltd.

Initial mixing of inclined dense jet in perpendicular crossflow

A comprehensive experimental investigation for an inclined (\(60^{\circ }\) to vertical) dense jet in perpendicular crossflow—with a three-dimensional trajectory—is reported. The detailed tracer concentration field in the vertical cross-section of the bent-over jet is measured by the laser-induced fluorescence technique for a wide range of jet densimetric Froude number \(Fr\) and ambient to jet velocity ratios \(U_r\). The jet trajectory and dilution determined from a large number of cross-sectional scalar fields are interpreted by the Lagrangian model over the entire range of jet-dominated to crossflow-dominated regimes. The mixing during the ascent phase of the dense jet resembles that of an advected jet or line puff and changes to a negatively buoyant thermal on descent. It is found that the mixing behavior is governed by a crossflow Froude number \(\mathbf{F} = U_r Fr\). For \(\mathbf{F} < 0.8\), the mixing is jet-dominated and governed by shear entrainment; significant detrainment occurs and the maximum height of rise \(Z_{max}\) is under-predicted as in the case of a dense jet in stagnant fluid. While the jet trajectory in the horizontal momentum plane is well-predicted, the measurements indicate a greater rise and slower descent. For \(\mathbf{F} \ge 0.8\) the dense jet becomes significantly bent-over during its ascent phase; the jet mixing is dominated by vortex entrainment. For \(\mathbf{F} \ge 2\), the detrainment ceases to have any effect on the jet behavior. The jet trajectory in both the horizontal momentum and buoyancy planes are well predicted by the model. Despite the under-prediction of terminal rise, the jet dilution at a large number of cross-sections covering the ascent and descent of the dense jet are well-predicted. Both the terminal rise and the initial dilution for the inclined jet in perpendicular crossflow are smaller than those of a corresponding vertical jet. Both the maximum terminal rise \(Z_{max}\) and horizontal lateral penetration \(Y_{max}\) follow a \(\mathbf{F}^{-1/2}\) dependence in the crossflow-dominated regime. The initial dilution at terminal rise follows a \(S \sim \mathbf{F}^{1/3}\) dependence.

The effect of non-uniform depth on the baroclinic response to wind in elongated basins

We examined the effect of along-thalweg depth variability on the baroclinic response to wind in elongated narrow basins with a sharp thermocline. The effect of depth variability was examined by deriving a modal-based forced model with two density layers and applying the model to a symmetric curved-bottom basin (CB), an asymmetric wedge-shaped basin (with a sloping bottom towards a vertical wall, WB), and a flat-bottom basin (FB). The baroclinic responses of CB, WB, and FB to uniform wind were found to differ in time-scale, number and energy of excited modes, and temporal pattern and along-thalweg structure of baroclinic flow and thermocline deflection. For all bottom profiles that were examined, the fundamental mode was found to dominate the response to spatially-uniform wind. Compared to FB, the asymmetric depth variability in WB increased the number and energy of excited higher modes and localized the interface shear, while the symmetric deviation from flat bottom in CB caused the opposite effects. Linear deviation from uniform wind was found to feed energy into higher baroclinic modes for the symmetric CB, but was found to reduce the energy of higher baroclinic modes for WB when the deviation from uniform wind is comparable to the spatial-average magnitude. Our results can explain the observation of the second baroclinic mode and irregular wave patterns in some lakes and reservoirs. Further, our results suggest that one-dimensional vertical mixed-layer models provide better results for shear entrainment in curved-bottom basins than in wedge-shaped basins.

Spatial variations in surface sediment structure in riffle–pool sequences: a preliminary test of the Differential Sediment Entrainment Hypothesis (DSEH)

ABSTRACTRiffle–pool sequences are maintained through the preferential entrainment of sediment grains from pools rather than riffles. This preferential entrainment has been attributed to a reversal in the magnitude of velocity and shear stress under high flows; however the Differential Sediment Entrainment Hypothesis (DSEH) postulates that differential entrainment can instead result from spatial sedimentological contrasts. Here we use a novel suite of in situ grain‐scale field measurements from a riffle–pool sequence to parameterize a physically‐based model of grain entrainment. Field measurements include pivoting angles, lift forces and high resolution digital elevation models (DEMs) acquired using terrestrial laser scanning, from which particle exposure, protrusion and surface roughness were derived. The entrainment model results show that grains in pools have a lower critical entrainment shear stress than grains in either pool exits or riffles. This is because pool grains have looser packing, hence greater exposure and lower pivoting angles. Conversely, riffle and pool exit grains have denser packing, lower exposure and higher pivoting angles. A cohesive matrix further stabilizes pool exit grains. The resulting predictions of critical entrainment shear stress for grains in different subunits are compared with spatial patterns of bed shear stress derived from a two‐dimensional computational fluid dynamics (CFD) model of the reach. The CFD model predicts that, under bankfull conditions, pools experience lower shear stresses than riffles and pool exits. However, the difference in sediment entrainment shear stress is sufficiently large that sediment in pools is still more likely to be entrained than sediment in pool exits or riffles, resulting in differential entrainment under bankfull flows. Significantly, this differential entrainment does not require a reversal in flow velocities or shear stress, suggesting that sedimentological contrasts alone may be sufficient for the maintenance of riffle–pool sequences. This finding has implications for the prediction of sediment transport and the morphological evolution of gravel‐bed rivers. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Paleotsunami Inundation of a Beach Ridge Plain: Cobble Ridge Overtopping and Interridge Valley Flooding in Seaside, Oregon, USA

The Seaside beach ridge plain was inundated by six paleotsunamis during the last ~2500 years. Large runups (adjusted &gt;10 m in height) overtopped seawardmost cobble beach ridges (7 m elevation) at ~1.3 and ~2.6 ka before present. Smaller paleotsunami (6–8 m in height) likely entered the beach plain interior (4-5 m elevation) through the paleo-Necanicum bay mouth. The AD 1700 Cascadia paleotsunami had a modest runup (6-7 m height), yet it locally inundated to 1.5 km landward distance. Bed shear stresses (100–3,300 dyne cm−2) are estimated for paleotsunami surges (0.5–2 m depths) that flowed down slopes (0.002–0.017 gradient) on the landward side of the cobble beach ridges. Critical entrainment shear stresses of 1,130–1,260 dyne cm−2 were needed to dislodge the largest clasts (26–32 cm diameter) in paleotsunami coulees that were cut (100–200 m width) into the landward side of the cobble ridges.

Probabilistic Modeling of Bed-Load Composition

This paper proposes that the changes which occur in composition of the bed load during the transport of mixed-grain-size sediments are largely controlled by the distributions of critical entrainment shear stress for the various size fractions. This hypothesis is examined for a unimodal sediment mixture by calculating these distributions with a discrete particle model and using them in a probabilistic calculation of bed-load composition. The estimates of bed-load composition compare favorably with observations of fractional transport rates made in a laboratory flume for the same sediment, suggesting that the hypothesis is reasonable. The analysis provides additional insight, in terms of grain mechanics, into the processes that determine bed-load composition. These insights strongly suggest that better prediction methods will result from taking account of the variation of threshold within size fractions, something that most previous studies have neglected.

MODELING THE EFFECTS OF WAVE ON MIXING ENHANCEMENT OF SUBMERGED BUOYANT JETS

A Lagrangian model is developed for predicting a turbulent buoyant jet discharged into wave-induced flow environments. Two entrainment coefficients are involved in the model: one describing the shear entrainment identical with that of traditional models for jets into stagnant ambient fluids while the other describing the forced entrainment due to wave-induced velocity assumed as constant herein. Model predictions are compared with experiments of buoyant jets into ambient water with shallow water wave conditions, and the agreement is very good. The present model is also validated for the limited case of zero ambient velocity. It is revealed that the waves may significantly increase the dilution achieved by the ocean outfalls. Taking into account of the wave effects on the jet mixing would make the outfall design easy to satisfy the environmental standard with lower costs than otherwise.

Flow competence and streambed stability: an evaluation of technique and application

The ability to assess flow hydraulics and the movement of substrata is important to understanding the complexity of habitats and variation in spatial and temporal conditions in stream and river ecosystems. The concept of flow competence (i.e., flow necessary to mobilize the streambed) has been applied to analyses of streambed stability and generally is based on the assumption that measures of rock size composing the substrata can be used to estimate the magnitude of flow that would mobilize the bed material. However, analyses have had limited success owing in part to the expectation that simple linear expressions accurately predict threshold entrainment (i.e., initiation of bed movement) over a broad range of hydraulic conditions from low-gradient sand-bed rivers through high-gradient boulder-bed rivers. Examination of the literature revealed ambiguity of terminology and use of equations without the proper adherence to limitations and assumptions inherent in the derivation of the equations. We present the derivations of the founding equations of flow competence, and discuss their applications, assumptions, and limitations. We also examine the efficacy of a stream stability index based on the ratio of estimated bottom boundary shear stress applied to the bed during bankfull conditions, and the critical entrainment shear stress calculated from the size of the surface bed material. Data from 33 gravel- to boulder-bed river sites were used to evaluate the stream stability index as a predictor of bed movement. The stability index indicated that a bankfull discharge would not generate critical threshold entrainment for 28 of the 33 sites, with most sites requiring a 2-fold increase in bottom boundary shear stress to mobilize the riverbed gravel and cobbles, and nearly an order of magnitude increase in shear stress to mobilize boulders. We conclude that other factors affecting the possible range of variation in flow velocity, particle size distributions, bed packing, and momentum exchange from collisions between saltating particles and those at rest on the bed may lead to departures between predicted and actual streambed movement. Hence, flow-competence approaches to predicting streambed instability should be used only to objectively bracket ranges of variation in disturbance and streambed movement. Moreover, the assumptions and limitations of equations for such indices should be investigated carefully before elaborate statistical analysis of watershed or streambed variables are undertaken to explain deviations from theoretical estimates, or to explain why a particular index does or does not predict bed movement.

Discrete Particle Modeling of Entrainment from Flat Uniformly Sized Sediment Beds

The stability of randomly deposited sediment beds is examined using a discrete particle model in which individual grains are represented by spheres. The results indicate that the threshold shear stress for flat beds consisting of cohesionless uniformly sized grains cannot be adequately described by a single-valued parameter; rather, it is best represented by a distribution of values. Physically, this result stems from the localized heterogeneity in the arrangement of surface grains. For uniformly sized beds, geometric similarity exists such that the critical entrainment shear stress distributions scale directly with grain size. A Shields parameter of 0.06 is commonly used to define “threshold conditions,” and it was found that this corresponds to a point on the distributions where approximately 1.4% by weight of the surface is mobile. Furthermore the analysis includes a comparison of the contributions of sheltering to variation in critical entrainment shear stress. It was found that remote sheltering, ind...

Experimental characterization of non-premixed turbulent jet propane flames

Abstract This paper reports an experimental study conducted on turbulent jet propane flames aiming at further understanding of turbulent structure in non-premixed slow-chemistry combustion systems. Measurements of mean and fluctuating velocity and temperature fields, mean concentration of major chemical species, correlation between velocity and temperature fluctuations, and dissipation of temperature fluctuations are reported in a turbulent round jet non-premixed propane flame, Re =20 400 and 37 600, issuing vertically in still air. The experimental conditions were designed to provide a complete definition of the upstream boundary conditions in the measurement domain for the purpose of validating computational models. The measured data depicts useful flow field information for describing turbulent non-premixed slow-chemistry flames. Velocity–temperature correlation measurements show turbulent heat fluxes tended to be restricted to the mixing layer where large temperature gradients occurred. Observations of non-gradient diffusion of heat at x / D =10 were verified. Temperature fluctuation dissipation, χ , showed the highest values in the shear layer, where the variance of temperature fluctuations was maximum and combustion occurred. The isotropy between the temperature dissipation in the radial and tangential directions was confirmed. By contrast, the observed anisotropy between axial and radial directions of dissipation suggests the influence of large structures in the entrainment shear layer on the production of temperature fluctuations in the flame region. The value of the normalized scalar dissipation at the stoichiometric mixture fraction surface, χ st , was calculated, and ranges between 2 and 4 s −1 . The measured data were used to estimate the budgets in the balance equations for turbulent kinetic energy, Reynolds shear stresses, turbulent heat flux and temperature variance, quantifying the mechanisms involved in the generation of turbulence as well as in the transport of the temperature.

Initial Dilution Equations for Buoyancy-Dominated Jets in Current

Initial dilution of submerged, single, round, buoyancy-dominated jets in a current is considered. Two simple semiempirical equations, one for centerline dilution and the other for minimum surface dilution, are presented. These equations are derived based on the continuity equation for the buoyant jet flow with a hypothesis that shear entrainment and forced entrainment can be added. Available laboratory and field data are used to determine the constants in the equations. Unlike asymptotic equations which apply for the limiting flow regimes, the proposed equations span all flow regimes, from the buoyancy-dominated near field (BDNF), to the transition, and to the buoyancy-dominated far field (BDFF), providing continuous predictions for dilutions.