Turbulent Dispersion Coefficients Research Articles

Computational fluid dynamics of rectangular external loop airlift reactor

AbstractThe novel design of a rectangular external loop airlift reactor is at present the most used large-scale reactor for microalgae culture. It has a unique future for a large surface to volume ratio for exposure of light radiation for photosynthesis reaction. The 3D simulations have been performed in rectangular EL-ALR. The Eulerian–Eulerian approach has been used with a dispersed gas phase for different turbulent models. The performance and applicability of different turbulent model’s i.e., K-epsilon standard, K-epsilon realizable, K-omega, and Reynolds stress model are used and compared with experimental results. All drag forces and non-drag forces (turbulent dispersion, virtual mass, and lift coefficient) are included in the model. The experimental values of overall gas hold-up and average liquid circulation velocity have been compared with simulation and literature results. It is seemed to give good agreements. For the different elevations in the downcomer section, liquid axial velocity, turbulent kinetic energy, and turbulent eddy dissipation experimental have been compared with different turbulent models. The K-epsilon Realizable model gives better prediction with experimental results.

Turbulent mixing and dispersion mechanisms over flexible and dense vegetation

The present study investigates flow turbulence and dispersion processes in the presence of flexible and dense vegetation on the bed. The turbulent dispersion coefficients and the terms of the turbulent kinetic energy equation are determined by using data collected in a straight laboratory channel with living vegetation on the bed. Results show that the turbulent integral lengths assume an order of magnitude comparable to the stems’ characteristic dimension independently by the direction and the turbulence assumes an isotropic behavior. The coefficients of dispersion have a trend similar to that of the turbulent lengths and assume low values in the longitudinal, transversal and vertical directions. Results also show that, in the mixing layer, the shear and wake turbulence production terms balance the dissipation; the turbulent diffusion term also assumes low values and its sign varies along the vertical indicating a transport of turbulent energy both from the vegetation to the free surface and from the free surface to vegetation.

CFD dispersion study based on a variable Schmidt formulation for flows around different configurations of ground-mounted buildings

Computational fluid dynamics (CFD) has become a reference tool for the investigation of pollutant emission and dispersion in urban areas, and for the assessment of the associated risk. In this framework, specific focus is given to the estimation of the downwind and ground level concentration of air pollutants coming from emission sources such as vehicular traffic, industrial plants or accidental events. Pollutant dispersion in the Atmospheric Boundary Layer (ABL) is strongly impacted by the turbulence. This leads to a complex coupled problem, considering the reciprocal influence of the two phenomena. A key role in pollutant dispersion is played by the turbulent Schmidt number Sct which directly affects the turbulent dispersion coefficient and, consequently, the concentration field. No universally-accepted formulation for the turbulent Schmidt number exists in the literature, although its impact on the prediction of pollutant dispersion is recognised. Stemming from a brief review of the existing literature and knowledge on the topic, this paper aims to propose a novel approach for the optimal determination of Sct, also through the use of uncertainty quantification. The proposed Sct is based on the local turbulece level, and is validated on different idealized test cases, representative of typical urban configurations.

Molecular dispersion in pre-turbulent and sustained turbulent flow of carbon dioxide

The average dispersion coefficients, Da¯, of two small molecules (acetonitrile and coronene) were measured under laminar, transient, and sustained turbulent flow regimes along fused silica open tubular capillary (OTC) columns (180 μm inner diameter by 20 m length). Carbon dioxide was used as the mobile phase at room temperature (296 K) and at average pressures in the range from 1500 to 2700 psi. The Reynolds number (Re) was increased from 600 to 5000. The measurement of Da¯ is based on the observed plate height of the non-retained analytes as a function of the applied Reynolds number. Da¯ values are directly estimated from the best fit of the general Golay HETP equation to the experimental plate height curves.The experimental data revealed that under a pre-turbulent flow regime (Re < 2000), Da¯ is 2–6 times larger (3.5 × 10−4 cm2/s) than the bulk diffusion coefficients Dm of the analyte (1.6 × 10−4 and 5.8 × 10−5 cm2/s for acetonitrile and coronene, respectively). This result was explained by the random formation of decaying or vanishing turbulent puffs under pre-turbulent flow regime. Yet, the peak width remains controlled exclusively by the slow mass transfer in the mobile phase across the inner diameter (i.d.) of the OTC. Under sustained turbulent flow regime (Re > 2500), Da¯ is about four to five orders of magnitude larger than Dm. The experimental data slightly overestimated the turbulent dispersion coefficients predicted by Flint-Eisenklam model (Da¯=4 cm2/s). The discrepancy is explained by the approximate nature of the general Golay equation, which assumes that Da¯ is strictly uniform across the entire i.d. of the OTC. In fact, both the viscous and buffer wall layers, in which viscous effects dominate inertial effects, cannot be considered as fully developed turbulent regions. Remarkably, the mass transfer mechanism in OTC under sustained turbulent flow regime is not only controlled by longitudinal dispersion but also by a slow mass transfer in the mobile phase across the thick buffer layer and the thin viscous layer. Altogether, these layers occupy as much as 35% of the OTC volume at Re = 4000. From a theoretical viewpoint, the general Golay HETP equation is only an approximate model which should be refined based on the actual profile of the analyte dispersion coefficient across the OTC i.d. In practice, the measured plate height of non-retained analytes under sustained turbulent flow of carbon dioxide are two orders of magnitude smaller than those expected under hypothetical laminar flow regime.

CFD MODELING OF BINARY MIXTURE HYDRODYNAMICS IN GAS-SOLID PARTICLE FLUIDIZED BED REACTOR SYSTEM

The objective of this research was to compare the effect of a binary mixture between coal, including 500, 700 and 1000-micron size, and sand, 180-micron size, on the mixing behavior in a fluidized bed system. In addition, suitable computational fluid dynamics drag models were explored, including an EMMS model, Gidaspow model and Wen &amp; Yu model. The simulation results were compared for correctness with real plant information. The EMMS model matched well with the obtained data, This is because the employed model considers the particle cluster effect. The EMMS drag model was then used for further computational fluid dynamics simulation. The levels of mixing between sand and coal were predicted by turbulent dispersion coefficient. These coefficients of coal particle were exhibited in axial and radial direction. The highest turbulent dispersion coefficients were found in the mixture with 500 and 1000 micron coal size for radial and axial directions, respectively. The low axial turbulent dispersion coefficient and high radial turbulent dispersion coefficient were preferred for good hydrodynamics behavior.

Flow and turbulence in an industrial/suburban roughness canopy

A field study conducted to investigate the flow and turbulence structure of the urban boundary layer (UBL) over an industrial/suburban area is described. The emphasis was on morning and evening transition periods, but some measurements covered the entire diurnal cycle. The data analysis incorporated the dependence of wind direction on morphometric parameters of the urban canopy. The measurements of heat and momentum fluxes showed the possibility of a constant flux layer above the height $$z\approx 2{H}$$ , wherein the Monin-Obukhov Similarity Theory (MOST) is valid; here $$H$$ is the averaged building height. For the nocturnal boundary layer, the mean velocity and temperature profiles obeyed classical MOST scaling up to $$\sim 0.5\Lambda \left( {\sim 6{H}}\right) $$ , where $$\Lambda $$ is the Obukhov length scale, beyond which stronger stratification may disrupt the occurrence of constant fluxes. For unstable and neutral cases, MOST scaling described the mean data well up to the maximum measured height $$(\sim 6{H})$$ . Available MOST functions, however, could not describe the measured turbulence structure, indicating the influence of additional governing parameters. Alternative turbulence parameterizations were tested, and some were found to perform well. Calculation of integral length scales for convective and neutral cases allowed a phenomenological description of eddy characteristics within and above the urban canopy layer. The development of a significant nocturnal surface inversion occurred only on certain days, for which a criterion was proposed. The nocturnal UBL exhibited length scale relationships consistent with the evening collapse of the convective boundary layer and maintenance of buoyancy-affected turbulence overnight. The length and velocity scales so identified are useful in parameterizing turbulent dispersion coefficients in different diurnal phases of the UBL.

Computation of system turbulences and dispersion coefficients in circulating fluidized bed downer using CFD simulation

In this study, the Eulerian computational fluid dynamics model with the kinetic theory of granular flow model was effectively used to compute the system turbulences and dispersion coefficients in a circulating fluidized bed (CFB) downer. In addition, the obtained model was used to simulate all the system velocities.The system turbulences, which were the granular temperatures and turbulent kinetic energies, and dispersion coefficients were investigated and employed as an explanation for the system hydrodynamics. The laminar granular temperatures were higher than the turbulent ones, which implies that an individual gas/solid particle oscillation dominates the flow structure in the CFB downer. There was a good agreement between the total granular temperature values in this study and those in the literature. The obtained turbulent kinetic energies varied within two orders of magnitude, but their values remained low. At increasing depths in the CFB downer, the turbulent kinetic energies were directly increased due to the formation of more gas bubble/solid particle clusters. The laminar and turbulent dispersion coefficients were significantly higher and lower, respectively, when compared to the previously reported ones. This shows the improper mixing of the gas bubble/solid particle cluster inside the CFB downer when compared to the individual movement ones.

Measuring turbulence in a circulating fluidized bed using PIV techniques

This study utilized the particle image velocimetry (PIV) technique, non-invasively near the wall, in the developing region, for the measurements of laminar and turbulent properties during circulation of Geldart B type particles in the U.S. Department of Energy (DOE) National Energy Technology Laboratory (NETL) riser. A novel method was used to measure axial and radial laminar and turbulent solids dispersion coefficients using autocorrelation technique. The instantaneous and hydrodynamic velocities for the solid phase were measured simultaneously in the axial and radial directions using a CCD camera, with the help of a colored rotating transparency. The measured properties, such as laminar and Reynolds stresses, laminar and turbulent granular temperatures, laminar and turbulent dispersion coefficients and energy spectra exhibited anisotropy. The mixing in the riser was on the level of clusters. The total granular temperatures were in reasonable agreement with the literature values. However, the axial and radial solids dispersion coefficients measured near the wall were slightly lower than the radially averaged values in the literature.

On the Numerical Study of Bubbly Wakes Generated by Ventilated Cavity Using Population Balance Approach

In this study, an Eulerian–Eulerian two-fluid model integrated with the population balance approach based on Multiple-Size-Group (MUSIG) model was proposed to simulate on the gas leakage bubbly wake of a ventilated cavitation problem. Three selected flow conditions with Froude number ranging from 20 to 29 have been selected for investigation. Predicted void fraction and bubble velocity profiles were validated against the experimental measurements in the high-speed water tunnel of Schauer (2003) and Wosnik (2005). Sensitivity studies on the mesh resolution and three different turbulence closures were first carried out. In comparison with experimental data, the shear stress transport (SST) turbulence model was found to be the best candidate in modelling the re-circulation motions within the cavity wake region. To consider the neighbouring effect of closely packed bubbles, an empirical equation was proposed to correlate the turbulent dispersion coefficient to the local gas void fraction. Based on the proposed empirical equation, the turbulent dispersion coefficient reduces to 0.1 when local gas void fraction is higher than 60%. In general, numerical predictions were in satisfactory agreement with the experimental data. Some discrepancies have nonetheless been found between the numerical and experimental results. The lack of exact gas leakage mechanism remains an outstanding challenge in determining the actual gas leakage rate and initial bubble size from the continuous cavity. Further effort should be also focused on combing free-surface tracking model with the present population balance approach to investigate the complex vortex structure and interaction between ventilated cavity and discrete leakage bubbles.

Plume dispersion on a fringing coral reef system

A field program was implemented on a fringing reef located on Oahu, Hawaii, to investigate the dispersion characteristics of near‐bed dye plumes, tracked using an autonomous underwater vehicle (AUV) with an onboard fluorometer. The combination of moored and AUV‐based measurements collected synchronously in this study allowed us not only to observe the dispersion characteristics of individual plumes, but importantly to isolate the flow structures directly responsible for dispersion under a variety of forcing conditions. The evolution of several plumes was observed, each influenced by different wave (surface and internal), current, and stratification conditions. The observed dispersion was caused by both turbulent dispersion and plume meandering. Lateral turbulent dispersion coefficients were roughly an order of magnitude greater than previous observations on sandy beach sites, which is likely attributable to the enhanced surface wave‐induced mixing and the large physical roughness of the reef. For a large portion of the 2‐week experiment the effects of meandering dominated over turbulent dispersion (on average 1.5 times greater). The meandering was the result of large‐scale cross‐reef current variability. Moored thermistor chain data on the forereef suggest that the source of this cross‐reef flow variability were packets of solitary waves that accompanied the propagation of baroclinic bores up the reef slope. Baroclinic bores dissipated before they reached the inner reef when surface wave conditions were large, resulting in the reduction of plume meandering during this period.

DISPERSED OIL TRANSPORT MODELING CALIBRATED BY FIELD-COLLECTED DATA MEASURING FLUORESCEIN DYE DISPERSION

ABSTRACT Oil-spill fate and transport modeling may be used to evaluate water column hydrocarbon concentrations, potential exposure to organisms, and impacts of oil spills with and without dispersant use. Important inputs to transport modeling for such analyses are current velocities and turbulent dispersion coefficients. Fluorescein dye studies off San Diego, California, were used to calibrate an oil transport model by hindcasting movement and dispersion of dye. The oil spill model was then used to predict subsurface hydrocarbon concentrations and potential water column impacts if oil were to be dispersed into the water column under similar conditions. Field-collected data included surface currents calculated from high-frequency radar data (HF-Radar), near-surface currents from drifter measurements drogued at several depths (1m, 2m, 4m or 5m), dye concentrations measured by fluorescence, spreading and dye intensity measurements based on aerial photography, and water density profiles from CTD casts. As the dye plume quickly extended throughout an upper mixed layer (7–15m), the horizontal dye movements were better indicated by the drifters drogued to a depth near the middle of that layer than the HF-Radar, which measured surface (∼top 50 cm) currents (including wind drift). Diffusion rates were estimated based on dye spreading measured by aerial photography and fluorescence-depth profiles. The model used these data as inputs, modeling of wind-forced surface water turbulence and drift as a function of wind speed and direction (based on published results of fluid dynamics studies), and Stokes law for droplet rise/sinking rates, to predict oil transport and dispersion rates within the water column. Use of such diffusion rate data in an oil fate model can provide estimates of likely dispersed oil concentrations under similar conditions, which may be used to evaluate potential impacts on water column biota. However, other conditions with different patterns of current shear (due to background currents, tidal currents, and wind stress) should be examined before these results can be generalized.

Effects of subgrid-scale modeling on Lagrangian statistics in large-eddy simulation

The application of large-eddy simulation (LES) to turbulent transport processes requires accurate prediction of the Lagrangian statistics of flow fields. However, in most existing SGS models, no explicit consideration is given to Lagrangian statistics. In this paper, we focus on the effects of SGS modeling on Lagrangian statistics in LES ranging from statistics determining single-particle dispersion to those of pair dispersion and multiparticle dispersion. Lagrangian statistics in homogeneous isotropic turbulence are extracted from direct numerical simulation (DNS) and the LES with a spectral eddy-viscosity model. For the case of longtime single-particle dispersion, it is shown that, compared to DNS, LES overpredicts the time scale of the Lagrangian velocity correlation but underpredicts the Lagrangian velocity fluctuation. These two effects tend to cancel one another leading to an accurate prediction of the longtime turbulent dispersion coefficient. Unlike the single-particle dispersion, LES tends to underestimate significantly the rate of relative dispersion of particle pairs and multiple-particles, when initial separation distances are less than the minimum resolved scale due to the lack of subgrid fluctuations. The overprediction of LES on the time scale of the Lagrangian velocity correlation is further confirmed by a theoretical analysis using a turbulence closure theory.

Comparative Fractional Efficiency Predictions by Selected Cyclone Simulation Models

The recently introduced ambient air quality standards for fine particulates expand the use of available control system simu- lation models, from the prediction of total particulate matter removal efficiencies, to the prediction of PM2.5 and PM10 particulate matter with diameters less than 2.5 and 10 m ones. In order to assess the suitability of cyclone simulation models for this task, the fractional efficiency predictions of six prominent models Lapple, Leith and Licht, Dietz, Mothes and Loffler, Iozia and Leith, and Mothes and Loffler with the turbulent dispersion coefficient of Salcedo and Coelho are compared for a number of standard cyclone design configurations under a wide range of cyclone diameters and pressure drops. The results reveal a significant discrepancy among model predictions, suggesting that at least some of the models considered are unsuitable for predicting size-specific e.g., PM2.5 and PM10 cyclone efficiencies. They also show that the sensitivity of fractional efficiencies to changes in the configuration ratios, diameter, and gas pressure drop varies widely, and in some cases even in opposite directions, among models. The above-noted results demonstrate the need for a systematic model validation against credible and sufficiently extensive experimental data sets.

Theoretical and numerical investigation of flow stability in porous materials applied as volumetric solar receivers

This article reports results of a theoretical analysis as well as a numerical study investigating the occurrence of flow instabilities in porous materials applied as volumetric solar receivers. After a short introduction into the technology of volumetric solar receivers, which are aimed to supply heat for a steam turbine process to generate electricity, the general requirements of materials applied as solar volumetric receivers are reviewed. Finally, the main methods and results of the two studies are reported. In the theoretical analysis it is shown that heat conductivity as well as permeability properties of the porous materials have significant influence on the probability of the occurrence of flow instabilities. The numerical study has been performed to investigate the occurrence of unstable flow in heated ceramic foam materials. In the simulations a constant heat flow of radiation, that is absorbed in a defined volume, and constant permeability coefficients are assumed. Boundary conditions similar to those of the 10 MW Solucar Solar project have been chosen. In a three dimensional, heterogeneous two phase heat transfer model it was possible to simulate local overheating of the porous structure. The parameters heat conductivity, turbulent permeability coefficient and radial dispersion coefficient have been varied systematically. Consequently, for a heat flux density of 1 MW/m 2 a parameter chart could be generated, showing the possible occurrence of “unstable” or “stable” thermal and fluid mechanical behaviour. These numerical results are beneficial for the design of optimized materials for volumetric receivers.

Turbulent dispersion of droplets for air flow in a pipe

An optical technique was used to study the dispersion of 50 μm, 90 μm and 150 μm droplets downstream of a source located in the center of a vertical pipe through which turbulent air is flowing. A turbulent dispersion coefficient, ɛ P, and a mean-square of the fluctuations in the turbulent velocity, v p 2 , are determined from the change of the measured mean-square displacement of the droplets over the pipe cross section with time. The interesting aspect of the experiments is that they explored conditions where the inertia of the particles is believed to be a much more important effect than that of the “crossing of trajectories” associated with the inequality of the average velocities of the particles and the fluid.

On the modelling of the particle dynamics in electro-hydrodynamic flow-fields: I. Comparison of Eulerian and Lagrangian modelling approach

Electro-hydrodynamic two-phase flows are encountered in various applications, e.g. electrically enhanced coating, electrostatic precipitation or toner application. In all cases there is a complex interaction between a turbulent flow field, a strong electric field, a corona discharge and the particle motion. This paper starts with an overview and classification of possible modelling approaches for all major phenomena. Afterwards the manuscript focuses on the modelling of particle dynamics: A Lagrangian, continuous random walk model is compared with an Eulerian approach for a number of test cases. The study is mostly focused on fine particles, i.e. roughly smaller than 100 μm in diameter for the Lagrangian approach and smaller than about 10 μm in the case of Eulerian modelling. It is shown that a local turbulent dispersion coefficient may be derived based on flow field calculations with a constant of proportionality identical to the Lagrangian random walk model. In this case the turbulent dispersion is equally described by both models even for inhomogeneous turbulence. For a superimposed particle drift velocity a model equation introduced by Csanady gives a reasonable agreement. Finally it is shown that modelling of the charging kinetics is a very crucial point in Eulerian modelling. This is demonstrated for the example of electrostatic precipitation where good agreement between Lagrangian and Eulerian modelling is achieved only if local particle charging kinetics is accounted for. Even though Lagrangian particle tracking is still superior in terms of physical modelling of electro-hydrodynamic particulate flows, it is shown that an Eulerian approach may lead to reasonable results with substantially reduced numerical effort.

Cost-Efficiency Analysis of a Model Wire-Plate Electrostatic Precipitator via DNS Based Eulerian Particle Transport Approach

The object of this work is to outline a methodology that can improve the current procedures used to size cost-optimized, efficient electrostatic precipitators (ESP). Focusing on a model wire-plate ESP initially, we develop a two-dimensional Eulerian, advection-diffusion type model for particle transport with distributed parameters. The Eulerian model is assessed against the accurate Lagrangian particle tracking database obtained for a model ESP using the parameter-free, highly accurate direct numerical simulation database obtained in previous work (Soldati 2000; Soldati and Banerjee 1998). Results show that the simplified Eulerian model can have good performances, provided that the functional form of the required transport parameters (i.e., turbulent dispersion coefficient, electromigration velocity, and convection velocity) are properly defined. Next, the cost function for a model ESP is defined and the influence of several design parameters on cost and collection efficiency is examined to identify guidelines to increase the collection efficiency at the lowest cost. Considering the cost associated with variation of precipitator length and width, wire-to-plate distance, and voltage applied to the wires, results show that the most cost-effective way to increase the collection efficiency of a wire-plate ESP is to decrease the wire-to-wire distance. Furthermore, the reasons for cost effectiveness of wider-spacing ESPs are demonstrated from a theoretical viewpoint, thus confirming the experimental observations of Navarrete et al. (1997).

An improved modelling for prediction of grade efficiency of electrostatic precipitators with negative corona

Generally, an increase of turbulent dispersion coefficient due to negative corona has been thought to be detrimental to the performance of electrostatic precipitators. However, in recent years, the experimental investigations performed with negative corona have repeatedly reported about significantly higher collection efficiencies, particularly, for fine particles than predicted by any known models. In this study, the transport of charged particles in an electrostatic precipitator is investigated by numerical solution of the convection/diffusion equation, which takes into account the effects of a fully developed turbulent flow profile, a simple profile for turbulent dispersion coefficient, and a zero-concentration boundary condition at the collecting wall. It is found that the increase of turbulent dispersion coefficient leads to the increase of collection efficiencies of fine particles with small migration velocities in the early stages of collection process. The collection efficiencies of fine particles predicted by the present model are in good agreement with the experimental data of Riehle and Löffler (Powder Technol. 77 (1993) 201) at a turbulent core dispersion coefficient of 50 cm 2/ s .

DETERMINATION OF THE MIXING RATE OF A HIGH VELOCITY FEED STREAM IN AGITATED VESSELS

In semi-batch or continuously stirred reactors, often a feed containing one or more reactants has to be mixed with the contents of the vessel. For fast competitive or consecutive reactions the mixing rate of the feed stream with the vessel contents has a large influence on the product quality. The mixing rate is often controlled by the turbulent dispersion process. Therefore, it has been suggested in the literature to keep the turbulent dispersion time constant upon scale-up to obtain a constant product quality. In this study, based on a combination of a theoretical model, Planar Laser Induced Fluorescence experiments and Laser Doppler Velocimetry experiments, the turbulent dispersion coefficient is determined. This has been done for the case that a feed stream is mixed in a stirred vessel by a combination of feed stream and stirrer generated turbulence. The turbulent dispersion coefficient is used to derive an equation for the turbulent dispersion time as function of several design and process variables.

GLOBAL OPTIMIZATION OF REVERSE-FLOW GAS CYCLONES: APPLICATION TO SMALL-SCALE CYCLONE DESIGN

This paper addresses the optimum design of reverse-flow gas cyclones through the solution of 2 numerical nonlinear optimization problems that respectively maximize cyclone collection and an efficiency/cost ratio. The simulation model was based on the predictive properties of the 1998 finite diffusivity model of Mothes and Löffler, in which the particle turbulent dispersion coefficient is estimated through an empirical correlation between the radial Peclet and Reynolds numbers. The optimizations were formulated with constraints on pressure drop, saltation velocity, and geometrical considerations such that feasible cyclones could always be obtained. The two geometries, named RS_VHE and RS_K, are different from available high-efficiency designs and represent reverse-flow cyclones with a predicted, significantly improved performance. The geometry RS_VHE was built and tested on a laboratory scale, providing experimental evidence of a significantly improved design.