Turbulent Shear Rate Research Articles

On the importance of temporal floc size statistics and yield strength for population balance equation flocculation model

Many aquatic environments contain cohesive sediments that flocculate and create flocs with a wide range of sizes. The Population Balance Equation (PBE) flocculation model is designed to predict the time-dependent floc size distribution and should be more complete than models based on median floc size. However, a PBE flocculation model includes many empirical parameters to represent important physical, chemical, and biological processes. We report a systematic investigation of key model parameters of the open-source PBE-based size class flocculation model FLOCMOD (Verney, Lafite, Claude Brun-Cottan and Le Hir, 2011) using the measured temporal floc size statistics reported by Keyvani and Strom (2014) at a constant turbulent shear rate S. Results show that the median floc size d50, in terms of both the equilibrium floc size and the initial floc growth, is insufficient to constrain the model parameters. A comprehensive error analysis shows that the model is capable of predicting three floc size statistics d16, d50 and d84, which also reveals a clear trend that the best calibrated fragmentation rate (inverse of floc yield strength) is proportional to the floc size statistics considered. Motivated by this finding, the importance of floc yield strength is demonstrated in the predicted temporal evolution of floc size by modeling the floc yield strength as microflocs and macroflocs giving two corresponding fragmentation rates. The model shows a significantly improved agreement in matching the measured floc size statistics.

Effects of Shear Stress and Salinity Stratification on Floc Size Distribution During the Dry Season in the Modaomen Estuary of the Pearl River

The floc size distribution of fine cohesive sediments in estuaries varies spatiotemporally within assorted physical, chemical, and biological factors. However, the distribution of different floc fractions that are affected by shear stress and salinity stratification has not yet been thoroughly investigated. This study intends to clarify the floc size distribution within the influences of turbulent shear rate and salinity stratification, and the implications for the flocculation process during the dry season in the Modaomen Estuary of the Pearl River. The decomposition of multimodal floc size distributions (FSDs) indicates that the floc fractions were composed of macroflocs (Macro), microflocs (Micro), Flocculi, and primary particles (Pp). Macro generally existed among the upper and middle layers, but smaller flocs, i.e., Micro, Flocculi, and Pp, were mostly concentrated in the bottom layer. The results agreed that the flocculation and deflocculation processes were dominant in the upper and bottom layers, respectively. In response to strong turbulent shear rates, FSDs in the bottom layer skewed toward small sizes and had a dual-peak tendency with frequent floc exchanges between Pp and Micro, then being Pp-dominant but converting to Micro when turbulent shear rates decreased. With impeded vertical mixing by salinity stratification, the FSDs in the upper or middle layers skewed toward a larger particle size with single peaks and lack of exchange among different floc fractions, leading to Macro dominance with a larger volume concentration and median size. In addition, turbulence mixing dramatically interfered with the good mixing of floc fractions amidst the vertical water column, with a low-salinity condition greatly affecting the formation of Macro in the bottom layer within proper turbulent shear rates. This study explores the effects of shear stress and salinity stratification on the flocculation process in the Modaomen Estuary, which contributes to a better understanding of sediment movement in a complex estuarine environment.

Modification of turbulence caused by cationic surfactant wormlike micellar structures in two-dimensional turbulent flow

An experimental study is performed to investigate the effects of the extensional rheological properties of drag-reducing wormlike micellar solutions on the vortex deformation and turbulence statistics in two-dimensional (2-D) turbulent flow. A self-standing 2-D turbulent flow was used as the experimental set-up, and the flow was observed through interference pattern monitoring and particle image velocimetry. Vortex shedding and turbulence statistics in the flow were affected by the formation of wormlike micelles and were enhanced by increasing the molar ratio of the counter-ion supplier to the surfactant, ξ, or by applying extensional stresses to the solution. In the 2-D turbulent flow, extensional and shear rates were applied to the fluids around a comb of equally spaced cylinders. This induced the formation of a structure made of wormlike micelles just behind the cylinder. The flow-induced structure influenced the velocity fields around the comb and the turbulence statistics. A characteristic increase in turbulent energy was observed, which decreased slowly downstream. The results implied that the characteristic modification of the 2-D turbulent flow of the drag-reducing surfactant solution was affected by the formation and slow relaxation of the flow-induced structure. The relaxation process of the flow-induced structure made of wormlike micelles was very different from that of the polymers.

Observations of fine sediment flocculation in the turbidity maximum of the Changjiang Estuary

Better understanding of sediment flocculation will better help to predict fine sediment transport. Multiple advanced instruments were employed to get the field observations in the turbidity maximum of the Changjiang Estuary. Floc pictures were taken by a scanning electron microscope in the laboratory. The sediment flocculation dynamics and the floc characteristics are investigated in this paper. The results show that the morphology and size of flocs show obvious tidal variations. There are diverse flocs in each tidal cycle, mainly including loose, porous and dense flocs, which are mainly comprised of silt and clay. They have indistinct or distinct shapes, rough or less rough surfaces, incompact or compact structures. The floc size is highly related to the tidal processes. The average floc size (94.8 μm) during water slacks is larger than that (24.1 μm) during maximum floods and ebbs, owing to the lower flow velocity during water slacks. The average floc size (105.6 μm) during high water slacks is larger than that (83.9 μm) during low water slacks due to the higher salinity during high water slacks. The average floc size (74.7 μm) during neap tide is larger than that (44.3 μm) during spring tide, which can be attributed to the lower flow velocity, the higher salinity and the finer primary particle during neap tides. Additionally, the floc size increases gradually from the surface to the bottom. The turbulent shear stress is the controlling factor for sediment flocculation. The maximum flocs can be formed under the condition of mid-low flow velocity and the optimal flow velocities for the maximum flocs during neap and spring tides are 0.41 and 0.56 m/s, respectively. The floc size decreases significantly with the increase of turbulent shear when the turbulent shear rate parameters during neap and spring tides are higher than about 3 and 4 s−1, respectively. The conclusions can help to extend our understanding of flocculation dynamics and help to predict the fine sediment transport.

Turbulent cylinder-stirred flow heat and momentum transfer research in batch operated single-phase square reactor

Heat transfer and momentum transfer due to water flow in a cylinder-stirred reactor of square cross section were investigated. Important industrial processes like mixing depend on combined effects of heat transfer and fluid flow which can be understood by analyzing the turbulence structure. A reactor of aspect ratio η = 0.21 (diameter of cylinder to tank side wall) was considered. It uses a small-diameter cylinder to stir the water in batch condition with rotating Reynolds number in a range 1.68 × 104 <Re < 10.1 × 104. The cylinder released a constant heat flux rate of 158 W/m2 through its surface. The steady state mean flow was numerically simulated using two models for turbulence, isothermally with a k-ε and thermally with the RSM model. The results revealed a fluid motion like Taylor-Couette vortex which was validated with PIV streamlines for Re = 6.1 × 104 and 10.1 × 104. Turbulent angular momentum and shear rate revealed differences for the corner direction as the Re number increased compared with the wall direction. Temperature fluctuations and thermal gradient in the gap allowed to analyze the turbulent heat diffusivity coefficient and the ratio to predicted diffusivity for momentum. The results revealed that heat and momentum diffusivity increase for higher Re number and show that heat diffusivity is faster than momentum in the gap. The main frequencies of fluid motion showed large-scale structures and secondary cells of fluid motion. The averaged heat transfer as a function of Re number indicate that this reactor is an enhanced mean for mixing process compared to concentric cylinders reactors.

An Extended Entropic Model for Cohesive Sediment Flocculation in a Piecewise Varied Shear Environment.

In this study, an extended model for describing the temporal evolution of a characteristic floc size of cohesive sediment particles when the flocculation system is subject to a piecewise varied turbulent shear rate was derived by the probability methods based on the Shannon entropy theory following Zhu (2018). This model only contained three important parameters: initial and steady-state values of floc size, and a parameter characterizing the maximum capacity for floc size increase (or decay), and it can be adopted to capture well a monotonic pattern in which floc size increases (or decays) with flocculation time. Comparison with 13 literature experimental data sets regarding floc size variation to a varied shear rate showed the validity of the entropic model with a high correlation coefficient and few errors. Furthermore, for the case of tapered shear flocculation, it was found that there was a power decay of the capacity parameter with the shear rate, which is similar to the dependence of the steady-state floc size on the shear rate. The entropic model was further parameterized by introducing these two empirical relations into it, and the finally obtained model was found to be more sensitive to two empirical coefficients that have been incorporated into the capacity parameter than those in the steady-state floc size. The proposed entropic model could have the potential, as an addition to existing flocculation models, to be coupled into present mature hydrodynamic models to model the cohesive sediment transport in estuarine and coastal regions.

Modelling of turbulent shear controllable co-precipitation synthesis of lithium ion battery cathode precursor micro-particles in a Taylor-Couette flow reactor with variable configurations of inner cylinder

Turbulent shear controllable co-precipitation synthesis of lithium ion battery cathode precursor micro-particles, Ni0.6Co0.2Mn0.2(OH)2 (NCM622), in a Taylor-Couette flow (TC) reactor has been investigated using both CFD simulation and experimental validation. The experimental co-precipitation in TC reactor was conducted using two types of inner cylinder, circular and lobed cross-sections (referred to as CTC and LTC), focusing on the effects of processing time and local turbulent shear rate. CFD simulation was employed to reveal the difference of flow field at various operating conditions. Both CFD simulation and experimental results show that the increased shear rate can lead to the decrease of the final synthesised micro-particle size due to the suppression of particle growth by turbulence eddy induced shear. Taylor-Couette flow by using the lobed inner cylinder can achieve an enhanced shear rate in the impinging jet regions formed in the vicinity of the inner cylinder surface due to the occurrence of a large radial velocity gradient. Consequently, the synthesised micro-particle properties such as morphology and specific surface area in the LTC are much more improved than those in the CTC. The mixing was also assessed and characterised by two variables, mean mixture fraction and its variance, predicted by CFD modelling with user-defined scalar (UDS), and correlating with the effect of shear rate for both the CTC and LTC. CFD simulation reveals that effective mixing at both the macro-scale and micro-scale can be quickly achieved in the LTC.

Electrohydrodynamic Flow and Its Impact on Particle Trajectories Inside Wet Electrostatic Precipitator: Experimental and Numerical Analysis

To analyze the flow pattern inside a typical wire-plate wet electrostatic precipitator (WESP) and its impact on particle trajectories, particle image velocimetry, and the finite element method were applied to visualize inner flow pattern. The flow pattern was primarily influenced by inner water flow along with the collector plates and the electrohydrodynamic (EHD) flow. Particle trajectories under various flow patterns were also studied. The results suggest that the EHD flow has a significant influence on the primary flow by creating vortex structures inside the WESP chamber. The water flow causes the inner flow pattern to become more complicated by generating vertical vortices. The particle trajectories were deformed with the inner flow patterns. Therefore, the collection efficiency can be severely hindered under various conditions. In this article, 16 different configurations were studied. The flow patterns of all configurations were given in two-dimensional images. Flow properties, that is, turbulent kinetic energy, turbulent dissipation rate, pressure, velocity magnitude and shear rate, and collection efficiency of each configuration are given in tabled data.

A modified resistance model for simulating baffle arrangement impacts on cross-flow microfiltration performance for oily wastewater

As a principal problem in the microfiltration processes, cake formation and concentration polarization phenomena cause permeate flux reduction. In the industrial scale, baffle as a turbulence promoter is an efficient method to decrease the fouling phenomenon. In the current study, eleven baffle arrangements in the feed channel were considered for an oily wastewater emulsion. The baffles with four general configurations of wall baffle, central baffle, baffles installed near the membrane surface, and a combination of them are used. The effects of baffle arrangements on turbulent kinetic energy, turbulent dissipation rate, pressure drop, and shear rate, and oil concentration on the membrane surface are examined under steady-state conditions. A modified model of total resistance is proposed to predict the baffle impacts on the CP and cake layer thicknesses and decrease the computational time. The predicted values are compared against experimental data and the absolute relative error is decreased from 6.54 % to 0.03 % by applying the modified resistance model. As the main results, the baffles installed near the membrane surface are more efficient to separate oil from oil-in-water emulsion but it may be caused some problems at higher processing times and the central baffles are recommended for the industrial applications.

Ultrafast Preparation of Black Phosphorus Quantum Dots for Efficient Humidity Sensing.

Black phosphorus quantum dots (BPQDs) have been prepared by a high turbulent shear rate generated from a household kitchen blender. A layer-by-layer disintegration mechanism of bulk BP crystals is suggested. As-synthesized BPQDs have shown excellent humidity sensing and photothermal converting properties. Importantly, this work not only explores potential applications for the BPQDs but also provides a successful paradigm for preparing the QDs of other layered materials.

Effect of mixing hydrodynamics on the particle and filtration properties of precipitated lignin

The effects of mixing hydrodynamics on the particle and filtration properties of precipitated lignin from black liquor has been investigated. The hydrodynamics were varied in terms of turbulent shear rate and impeller flow pattern in the stirred tank. The precipitated lignin flocs were characterized in terms of particle size, size distribution, and particle shape. Our findings showed that the effect of hydrodynamics on the size and shape of primary lignin particles were negligible. However, the aggregation of primary particles into lignin flocs were affected by the hydrodynamics of the stirred tank. The size distribution and shape of the final lignin flocs could be controlled mainly through the manipulation of turbulent shear rate. Lignin flocs with higher compactness and size showed better filtration and washing properties. Optimal hydrodynamic conditions led to production of lignin with good filtration and washing properties at 1.83E+09m/kg specific filtration resistance, 243kg/hm2 lignin filtration rate, generating high purity lignin at 0.09% ash content. The reproducibility of the findings was validated using three other black liquor samples.

Turbulence-assisted shear exfoliation of graphene using household detergent and a kitchen blender.

To facilitate progression from the lab to commercial applications, it will be necessary to develop simple, scalable methods to produce high quality graphene. Here we demonstrate the production of large quantities of defect-free graphene using a kitchen blender and household detergent. We have characterised the scaling of both graphene concentration and production rate with the mixing parameters: mixing time, initial graphite concentration, rotor speed and liquid volume. We find the production rate to be invariant with mixing time and to increase strongly with mixing volume, results which are important for scale-up. Even in this simple system, concentrations of up to 1 mg ml(-1) and graphene masses of >500 mg can be achieved after a few hours mixing. The maximum production rate was ∼0.15 g h(-1), much higher than for standard sonication-based exfoliation methods. We demonstrate that graphene production occurs because the mean turbulent shear rate in the blender exceeds the critical shear rate for exfoliation.

Influence of cycles of high and low turbulent shear on the growth rate and equilibrium size of mud flocs

Abstract Effects of repeated exposure to multiple cycles of high and low turbulent shear on mud floc growth pattern and equilibrium size were investigated through a laboratory study. The specific research questions examined were: (1) do repeated cycles of floc growth and breakup change the equilibrium floc size from one cycle to the next?; and (2) do these repeated cycles impact the floc growth rate and path to equilibrium? For the experiments, a 50 mg/l mixture of kaolinite and montmorillonite clay was sonicated and introduced to a mixing chamber to allow for flocculation under a mean turbulent shear rate of G = 35 s− 1. Floc size time series, floc circularity index, and time series of the number of flocs were measured using a camera system and image processing routines. After the flocs reached an equilibrium size, the floc suspension was broken down with vigorous turbulent mixing (G = 400 s− 1) for 15 h. Flocs were then allowed to regrow at a shear rate of G = 35 s− 1. This procedure was repeated seven consecutive times. The data show that the different initial particle size distributions after sonication and after intense shearing had almost no effect on the equilibrium floc size, but that difference in initial size did significantly impact the floc growth pattern before the equilibrium was reached. With each repeated floc breakup and growth cycle, the rate of floc growth decreased. Each of the seven regrowth cycles was modeled with the Winterwerp (1998) equation for the mean floc size by calibrating the collision and breakup efficiency coefficients for each cycle. To obtain a good fit to the data, both the collision and breakup efficiency coefficients had to be reduced with each successive cycle. The observations and modeling results suggest that flocs become slightly stronger and less reactive with each repeated cycle of growth and breakup. The consistency of the equilibrium floc size in the experiment suggest that given enough time, floc settling velocity maybe reasonably modeled as a function of local conditions. However, if the time it takes to reach equilibrium is larger than the time scale of the flow of interest, then the floc settling velocity may be difficult to define without knowledge of the turbulent shear conditions encountered prior to the point of analysis; even when using a size evolving floc modeling approach.

A note on the Krone deposition equation and significance of floc aggregation

For modeling the rate of deposition of cohesive flocs in estuaries the Krone equation is extensively used. It was derived from flume experiments on muddy sediment from the San Francisco Bay, and is applicable to low suspended sediment concentration environments in which shear-induced aggregation – the growth and break up of flocs – has a limited role. It is shown that the use of this equation can lead to erroneous estimates of the mass deposition flux at typically higher estuarine concentrations. Krone's own experimental data permit the development of a more general equation accounting for the effects of concentration and turbulent shear rate on aggregation. These effects are dramatically observed in a deposition test in which a wire mesh was inserted in the flow to change the turbulent shearing rate and increase deposition. Even with the inclusion of aggregation effect in the general equation, field-based observations from San Francisco Bay suggest that typical flumes generally may not meet the space and time scaling requirements for field application of laboratory data. Thus, although the Krone equation should be eschewed in favor of the general equation, interpretations of model-predicted deposition rate must not be accepted without robust field-based verification.

Effects of flow field on the metabolic characteristics of Streptomyces lincolnensis in the industrial fermentation of lincomycin

In this work, the flow field in the existing fermentor with radial-flow impellers (C1) was studied using the computational fluid dynamics (CFD) software package Fluent, then the fermentor with radial-axial flow impellers (C2) was constructed and was compared with the C1 fermentor by CFD and experimental research. The simulation results revealed that the flow field in C2 fermentor had characteristics such as higher turbulent kinetic energy, gas holdup and shear rates. Metabolic variables of Streptomyces lincolnensis in the two fermentors such as carbon and nitrogen source consumption rates, specific growth rates (μ), hyphae morphologies, and lincomycin productivities were further explored. The correlation analysis between the experimental measurements and the simulation results indicated that the hyphae clustering and dry cell weight (DCW) decreasing at production stage were eliminated in C2 fermentor, which had higher gas volumetric mass transfer coefficient (K(L)a), dissolved oxygen (DO) concentration and consumption rates of nutrient materials. When C2 was employed in the fermentor, the specific growth rate of S. lincolnensis at growth stage was higher, and the maintenance metabolism together with secondary metabolism at production stage was kept at higher levels. As a result, the yield of lincomycin was achieved 7039 μg ml(-1) when the 60 m(3) industrial fermentor was equipped with C2, which was increased by 46% compared to that obtained in the C1 fermentor.

Break-Up of Aerosol Agglomerates in Highly Turbulent Gas Flow

Agglomerate aerosols in a turbulent flow may be subjected to very high turbulent shear rates which through the generation of lift and drag can overcome the adhesive forces binding the constituents of an agglomerate together and cause it to break-up. This paper presents an analysis of the experimental measurements of the breakup of agglomerates between 0.1–10 μm in size, in a turbulent pipe flow followed by an expansion zone with a Reynolds numbers in the range 105 to 107. The analysis shows that even in wall bounded turbulence, the high turbulent shear stresses associated with the small scales of turbulence in the core can be the main source of breakup preceding any break-up that may occur by impaction at the wall. More importantly from these results, a computationally fast and efficient solution is obtained for the General Dynamic Equation (GDE) for agglomerate transport and breakup in highly turbulent flow. Furthermore the solution for the evolution of the aerosol size distribution is consistent with the experimental results. In the turbulent pipe flow section, the agglomerates are exposed continuously to turbulent shear stresses and experience more longer term breakup than in the expansion zone (following the pipe flow) where the exposure time is much less and break-up occurs instantaneously under the action of very high local turbulent shear stresses. The validity of certain approximations made in the model is considered. In particular, the inertia of the agglomerates characterised by a Stokes Number from 0.001 for the smallest particles up to 10 for 10 μm particles and the fluctuations of the turbulent shear stresses are important physical phenomena which are not accounted for in the model.

Energy Dissipation and Shear Rate with Geometry of Baffled Surface Aerator

The geometric parameters of surface aeration systems govern the process phenomena. The dissipation rate of turbulent kinetic energy (e) and shear rate (γ) are the key process parameters for mixing in surface aerators. Present work by doing numerical computation by visimix® analyzes the effect of geometric parameters (impeller diameter, cross-sectional area of the tank, liquid height, width of the baffle, rotor blade length and immersion height) on e and γ. Analysis has been done by making the geometric parameters non-dimensionalized through rotor diameter. With an increase in liquid height and baffled width, there is an increase in the case of energy dissipation and shear rate values. In the case of tank area and blade length, it is vice versa. Energy dissipation and shear rate are not affected by the variation in immersion height of the impeller. Keywords: energy dissipation; mixing; shear rate; surface aerator DOI = 10.3329/cerb.v14i2.4910 Chemical Engineering Research Bulletin 14 (2010) 92-96

Floc properties and settling velocity of San Jacinto estuary mud under variable shear and salinity conditions

The flocculation properties of a natural silt–clay mud taken from the San Jacinto estuary near Houston, TX were investigated over a range of suspended sediment concentrations, salinities, and turbulent shear rates. The study was conducted in a laboratory using a paddle mixer to create a turbulent shear field for driving the flocculation process; floc settling velocity and size attributes were measured in a settling column with a camera system and image analysis. In general, maximum floc sizes were observed at turbulent shear rates less than 30 s −1. For turbulent shear rates less than 50 s −1, flocs originating in saline water at 10 and 15 ppt were larger and more loosely packed than those created in freshwater at identical turbulent shear rates and suspended sediment concentrations. At turbulent shear rates of 50 s −1, floc properties of size, submerged specific gravity and fractal dimension were approximately equal for all conditions. Two ranges of behavior were observed in regards to the fractal dimension of flocs at a constant turbulent shear rate. In the first region, for floc sizes less than 200 μ m , a variable fractal dimension was needed to describe the submerged specific gravity as a function of floc size. It is suggested that this variability in fractal dimension may physically be the result of ploysized primary particles. In the second region, for floc sizes greater than 200 μ m , a constant fractal dimension was found to suffice in describing the submerged specific gravity. The constant fractal dimension for this second region was n f =2.3 for freshwater flocs and n f =1.95 for saltwater flocs. Based on the observation of the two-region behavior, a new variable fractal dimension model is presented using a simple exponential decay which asymptotically approaches a constant fractal dimension at a specified floc size. The model itself is based on the uniform-size primary particle formulation of the relationship between floc size and fractal dimension, but the equation was able to model the average shift from variable to constant fractal dimension, which was thought to primarily be due to polysized primary particles.

Variability of Energy Dissipation and Shear Rate with Geometry in Unbaffled Surface Aerator

The dissipation rate of turbulent kinetic energy () and shear rate (γ) are the key process parameters for mixing in surface aerators. At constant dynamic variables (rotational speed), both  and γ are greatly affected by the geometric parameters (impeller diameter, cross-sectional area of the tank, liquid height, rotor blade length and immersion height). By doing numerical computation by VISIMIX ®, present work analyzes the effect of non-dimensional (which is non-dimensionalized through rotor diameter) geometric parameters on e and g. With an increase in liquid height, there is an increase in the case of energy dissipation and shear rate values. In the case of tank area and blade length, it is vice versa. Energy dissipation and shear rate are not affected by the variation in immersion height of the impeller.

Non-equilibrium flocculation characteristics of fine-grained sediments in grid-generated turbulent flow

Results are presented from a series of settling column experiments investigating temporal variations in the flocculation characteristics of purely cohesive (kaolin clay) sediment suspensions and cohesive (kaolin) and non-cohesive (fine sand) sediment fraction mixtures. Experimental runs were conducted under controlled hydrodynamic conditions generated by a rigid array of in-phase oscillating grids. The results indicated that rapid initial floc aggregation occurred under low turbulent shear rates, with peak maximal and root-mean-square (r.m.s.) floc sizes (∼ 400 μm and ∼ 200 μm, respectively) attained after relatively short time periods, before reducing with time. By contrast, lower aggregation rates and smaller floc sizes were observed under higher shear conditions, with flocs retaining suspended in the settling column for longer time scales due to the increased turbulence. The mud input concentration displayed some correlation with maximal and r.m.s. floc sizes at higher shear rates but no correlation was apparent at low shear rates. This observed floc behaviour may be attributed to the differences in concentration gradients at high and low shear rates that affect both floc settling rate and time required for flocs to attain equilibrium size. The addition of the fine sand fraction to the kaolin clay suspension reduced both the initial floc formation (i.e. aggregation) rate and the maximal and r.m.s. floc sizes attained throughout the experiments. The reduction in maximal floc sizes appeared to be enhanced by an increase in the ratio of fine sand to kaolin clay content within the mixture.