Analysis of dilute solid–liquid suspensions in turbulent stirred tanks

In this work, dilute suspensions of solid particles in stirred tanks are investigated by Particle Image Velocimetry measurements, which were specifically designed to determine the effects of the dispersed phase on mean velocity and turbulence levels of the continuous phase and the local solid–liquid slip velocity. In order to determine the effect of particle size and concentration, glass particles of narrow size distribution were selected; the particle content was increased stepwise up the maximum of 0.2 vol.%. Overall, moderate dampening of liquid turbulent fluctuations was found with the smaller particles, while turbulence enhancement was observed with the bigger ones. Continuous phase turbulence was found to affect the local map of the particle settling velocity, which was also discussed on the basis of a force balance analysis. The reduction of particle settling velocity due to free stream turbulence under specific conditions is confirmed.     

DEM-LES of coal combustion in a bubbling fluidized bed. Part I: gas-particle turbulent flow structure

The gas and particle motions in a bubbling fluidized bed both with and without chemical reactions are numerically simulated. The solid phase is modelled as Discrete Element Method (DEM) and the gas phase is modelled as 2-D Navier-Stokes equations for 2-phase flow with fluid turbulence calculated by large Eddy simulation (LES), in which the effect of particles on subgrid scale gas flow is taken into account. The gas/particle flow structure, the mean velocities and turbulent intensities can be predicted as a function of several operating parameters (particle size, bed temperature, and inlet gas velocity). The lower the inlet gas velocity, the higher the ratio of particle collision. The distributions of the particle anisotropic velocity show that the particles have no local equilibrium, and the distribution of gas kinetic energy corresponds to the distribution of gas-particle coupling moment in the fluidized bed. An intensive particle turbulent region exists near the wall, and the gas Reynolds stress is always much higher than the particle stress. The presence of the large reactive particles in the fluidized bed may affect significantly the gas and particle velocities and turbulent intensities. The effects of the bed temperature and inlet gas velocity on the gas particle flow structure, velocity, and turbulent intensity are also studied.     

PARTICLE CONCENTRATION AND SIZE MEASUREMENTS IN TWO-PHASE TURBULENT COAXIAL JETS

Particle concentration and particle size distributions have been measured for two-phase (solid/air) turbulent coaxial jets using the Laser Diffraction Method (LDM) and a tomography data transform technique. Effects of velocity ratio, particle loading ratio, and particle size on the dispersions of gas and particles were determined. Experimental results show that the gas disperses much more rapidly than the particles and particle dispersion decreases with increasing in particle size. Increasing velocity ratio significantly increases gas dispersion, while effects of other variables are less significant. The mean particle size at the jet edge is about 15-20% smaller than that at the jet centerline. The turbulent Schmidt number Sc_p for two-phase turbulent coaxial jets ranges from 1.4 to 1.5.     

PDF method for population balance in turbulent reactive flow

Turbulent reactive flows with particle formation, such as soot formation and precipitation, are characterized by complex interactions between turbulence, scalar transport, particle formation and particle transport and inter-particle events such as coagulation. The effect of formation, growth and coagulation on the particle size distribution (PSD) must be modelled by the population balance equation (PBE). While the PBE has been studied extensively in homogeneous systems and, recently, in simple flows, its coupling with turbulent reactive flows poses a wealth of new questions. Processes such as nucleation, growth and coagulation are described by kinetic laws that link them to the local concentrations of the reactive scalars, which are random in a turbulent flow. This accounts for additional mechanisms that induce randomness and fluctuations to the particle concentration and PSD. Furthermore, conventional RANS closure of the coagulation term PDE (which describes the evolution of the PSD) leads to unknown correlations. In this work a new pdf approach is developed, based on the transport of the joint pdf of reactive scalars and particle number densities at different sizes, which overcomes the additional closure problems. It is also shown how the pdf method can be solved numerically via Monte-Carlo methods, and this is demonstrated via two applications in a partially stirred reactor: precipitation via nucleation-growth and coagulation. In each case the pdf method is compared with models that neglect correlations at various levels, and it is demonstrated that the interaction of turbulence with particle formation mechanisms accounts for significant deviations in the PSD.     

Experimental investigation on flow structures and mixing mechanisms of a gas–solid burner jet

The objective of this study was to investigate the flow structures and mixing mechanisms of a gas–solid two-phase jet from a burner employed in the utility boiler. Laboratory experiments were conducted in a 0.15 m internal diameter test facility. Gas–solid jet flow downstream of the burner exit was measured by a fiber optic probe. Local solid concentration and particle size distribution were obtained using the probe that was traversed over the cross-section of the jet. The effects of the side flow on the primary air gas–solid flow characteristics were also studied. The measurements showed the availability of fiber optic probe to investigate the gas–solid jet flow downstream the industrial burner nozzle with high solid concentration. Obvious slip between the gas phase and the solid phase in the gas–solid jet flow was found in the experiments. The side flow disturbed the solid concentration distribution in the jet, a more smooth solid concentration profile across the jet can be achieved after the side flow was introduced. The particle size distributions in the jet were similar with the distributions of the solid concentration, the particles with large diameters always appeared in the zones where the solid concentrations were high.     

Wall Loss Rate of Polydispersed Aerosols

Wall loss rates of polydispersed aerosols in a stirred vessel were studied theoretically and experimentally. A formula for the poly- dispersity factor of the wall loss rate was derived using the moment method of log-normal size distribution and compared with numerical calculations. The representative theory of Crump and Seinfeld (1981) was used as the wall loss rate of monodispersed aerosols in which the Brownian diffusion, the turbulent eddy diffusion, and the gravitational settling are included as wall loss mechanisms. The results of the analysis show that the wall loss rate of a polydispersed aerosol is substantially higher than that based on a monodispersed size distribution model if the particle size distribution can be represented reasonably well by a log-normal function. The existing diagram showing the loss rate as a function only of the particle size was expanded to include the polydispersity effects. Experimental measurements of particle wall loss rate were performed by observing the time-dependent changes in particle number concentration for various stirring intensities in a cylindrical stirred chamber. It was shown that by correcting for the polydispersity effect, the dependence of the wall loss rate on particle size and stirring intensity agreed with the theory of Crump and Seinfeld (1981).     

PREDICTION OF A GAS-PARTICLE TURBULENT JET WITH THE FLUCTUATION-SPECTRUM-RANDOM-TRAJECTORY MODEL

A numerical treatment for determining the particle velocity and the trajectories in a two-phase flow is described herein and this new fluctuation-spectrum-random-trajectory (FSRT) model is proposed to account for the turbulent diffusion of particles. It is predicted for the flow of a turbulent axisymmetric gaseous jet laden with spherical solid particles of nonuniform size. The particle velocity and the concentration field are obtained by the revised volume average method. The predictions are compared with experiment.     

Validation of the Lagrangian Approach for Predicting Turbulent Dispersion and Evaporation of Droplets within a Spray

The accuracy of the Lagrangian approach for predicting droplet trajectories and evaporation rates within a simple spray has been addressed. The turbulent dispersion and overall evaporation rates of droplets are modeled reasonably well, although the downstream velocity decay of the larger droplets is underpredicted, which is attributed to a poor estimate of the radial fluctuating velocity of these droplets at the inlet boundary. Qualitative agreement is found between the predicted and experimental evolution of the droplet size distribution downstream of the nozzle. These results show that smaller droplets evaporate preferentially to larger droplets, because they disperse more quickly toward the edge of the jet, where the entrainment of fresh air from the surroundings produces a significant evaporative driving force. Droplet dispersion and evaporation rates are highly influenced by the rate of turbulence generation within the shear layer. This work demonstrates the potential of the Lagrangian approach for analyzing particle trajectories and drying within the more complex spray dryer system.     

Validation of the Lagrangian Approach for Predicting Turbulent Dispersion and Evaporation of Droplets within a Spray

The accuracy of the Lagrangian approach for predicting droplet trajectories and evaporation rates within a simple spray has been addressed. The turbulent dispersion and overall evaporation rates of droplets are modeled reasonably well, although the downstream velocity decay of the larger droplets is underpredicted, which is attributed to a poor estimate of the radial fluctuating velocity of these droplets at the inlet boundary. Qualitative agreement is found between the predicted and experimental evolution of the droplet size distribution downstream of the nozzle. These results show that smaller droplets evaporate preferentially to larger droplets, because they disperse more quickly toward the edge of the jet, where the entrainment of fresh air from the surroundings produces a significant evaporative driving force. Droplet dispersion and evaporation rates are highly influenced by the rate of turbulence generation within the shear layer. This work demonstrates the potential of the Lagrangian approach for analyzing particle trajectories and drying within the more complex spray dryer system.     

Presumed joint probability density function model for turbulent combustion

A presumed joint probability density function (pdf) model of turbulent combustion is proposed in this paper. The turbulent fluctuations of reactant concentrations and temperature are described using a presumed joint pdf of three-dimensional Gaussian distribution based on first and second-order moments of reactant concentration and temperature. Mean reaction rates in both premixed and diffusion combustion are obtained by mean of integration under the presumed joint pdf. This model is applied to predict turbulent premixed combustion of sudden-expansion flow and turbulent jet diffusion methane/air flame. For turbulent premixed combustion, the predicted results of temperature distribution and maximum temperature using the proposed model agree better with the experiment than that using the conventional eddy-breakup (EBU)-Arrhenius model. For the turbulent jet diffusion methane/air flame, the predicted results of velocity, temperature and species concentrations using the proposed model, the Arrhenius, EBU-Arrhenius, and laminar flamelet models are compared with experiment data. Results obtained with the presumed pdf model and that obtained by the laminar flamelet model both agree well with experiments, while results using the other models have a significant difference. The presumed joint pdf model is used to predict the NO formation process, which also agrees well with the experiment data. A unified turbulent combustion model, in which both effects of turbulent diffusion and chemical dynamics are considered, is established for both premixed and diffusion combustion, especially for the process of NO formation.     

Validation of the Langevin particle dispersion model against experiments on turbulent mixing in a T-junction

The fluctuating fluid velocities seen by particles entrained in a turbulent fluid have recently been modeled using a stochastic model based normalized Langevin Continuous Random Walk (CRW). This model has been quite successful in predicting particle dispersion in mildly complex flows. In the present study, we aim at validating the CRW model further against data collected in a challenging 3D geometry. We consider turbulent fluid mixing downstream of a T-junction using a hybrid Euler-Lagrange approach whereby tracer particle trajectories are computed and mixing of the streams deduced from the relative concentration of particles originating from the two inlet branches of the Tee. In a first simulation, RANS Reynolds Stress Model (RSM) is used to obtain the mean flow field, whereas the fluid fluctuations are specified from a CRW. Simulation results are compared to experimental data on mixing of two isothermal streams consisting of tap and de-ionized water, respectively. It is found that RSM-CRW yields strong under-prediction of the mixing. Closer look at the results shows that the Reynolds stresses, which are required inputs to the CRW, are poorly predicted with RSM. Detached Eddy Simulations (DES) are subsequently performed to provide the mean flow field, and the DES-CRW model predictions are found to compare quite well with the experimental data.     

Extended log-normal method of moments for solving the population balance equation for Brownian coagulation

An extended log-normal method of moments (ELNMOM) is presented in this study for solving the population balance equation (PBE) for Brownian coagulation. The method is an extension of the log-normal method of moments (LNMOM) proposed by Lee in 1983. The ELNMOM uses the superposition of log-normal subdistributions to represent the size distribution. Unlike previous modal studies, the subdistributions are not independent modes but flexible components in this study and the closure of this method is achieved by introducing additional higher-order moment equations. Based on some simplifying assumptions, the ELNMOM is implemented with only four adjustable parameters for a preliminary exploration. The method is then validated by comparing the size distribution parameters predicted by this method with those predicted by the LNMOM and other numerical methods for Brownian coagulation in the continuum regime and the free-molecular regime. The results show that the ELNMOM more accurately predicts the total particle number concentration, the geometric standard deviation and the geometric mean particle volume than the LNMOM while not taking much more computation time.

Copyright © 2019 American Association for Aerosol Research     

Modeling of Mixing and Precipitation Using CFD and Population Balances

Simulations of particle size distributions in technical precipitation reactors require the consideration of turbulent mixing and precipitation kinetics. For that, spatially resolved population balances have to be evaluated. In turbulent flows these balances cannot be solved directly, instead either Reynolds averaging or Large Eddy Simulations have to be applied, while unresolved fluctuations need to be modeled. Reynolds averaging of the population balance leads to a turbulent growth dispersion term which has to be modeled. As no theoretically founded approach is available, an assumption was made in analogy to the turbulent diffusion, which improves the prediction of the size distribution shape compared to experiments.     

Numerical simulation of fiber orientation distribution in round turbulent jet of fiber suspension

The Reynolds averaged Navier–Stokes equation was solved numerically with the Reynolds stress model to get the mean fluid velocity and the turbulent kinetic energy in a round turbulent jet of fiber suspension. The fluctuating fluid velocity was described as a Fourier series with random coefficients. Then the slender-body theory was used to calculate the fiber orientation distribution and orientation tensor. Numerical results of mean axial velocity and turbulent shear stress along the lateral direction were validated by comparing with the experimental ones. The results show that most fibers are aligned with the flow direction as they go downstream, and fibers are more aligned with the flow direction within the region near the jet core. The fibers with high aspect ratio tend much easier to align with the flow direction, and the fiber orientation distribution is not sensitive to fiber aspect ratio when fiber aspect ratio is larger than 5. Fiber density has no obvious influence on the fiber orientation distribution and fiber orientation tensor. The randomizing effect of turbulence is insignificant in the regions near outside and jet core, and becomes significant in the region between outside and jet core. The randomizing effect increases with the increasing of the distance from the jet exit. Different components of fiber orientation tensor show a similar distribution pattern.     

Analytic solutions for filtration of polydisperse aerosols in fibrous filter

In this study, analytical solutions for penetration efficiency of a polydisperse aerosol in fibrous filter were derived employing Brownian diffusion and inertial impaction as removal mechanisms. Size distribution of aerosol particles was assumed to be represented by a log-normal function during the filtration. Derived solutions were compared with the exact solution, which is not based on the log-normal assumption, showing good agreement. Error resulting from the log-normal assumption was shown to be greater in the impaction-dominant regime than in the diffusion-dominant regime due to higher size dependency of collision kernel which destructed log-normal shape of size distribution. The penetration efficiency of the analytic solution initially decreases faster and then decreases slower than that of the exact solution in the diffusion-and intermediate dominant size regimes due to its polydispersity of particle distribution, while it overpredicted the particle removal in the impaction size range because of neglect of polidispersity effect. A new solution for the most penetrating particle diameter was also provided showing the dependence on filtration velocity, fiber volume fraction, and fiber size.     

Some characteristics of concentration fluctuations in free turbulent jets

Becker, Hottel and Williams have employed marker nephelometry to determine many characteristics of the nozzle fluid concentration field of the round turbulent free jet: the mean concentration, concentration fluctuations, intermittency factor, spectrum and correlation functions, and integral scales. In the present work a much larger jet nozzle was employed, 7.14 cm throat diameter compared to 0.635 cm in the reference, and the Reynolds number was correspondingly greater, around 270,000 compared to 54,000. The results support Becker et al's findings and extend the range of the data. In particular, the spectrum of the concentration fluctuations has been measured into the viscous convective subrange where a (-1) power mode dependency on wave number is indicated, as expected for the slow diffusing smoke marker. Other new measurements include the skewness, kurtosis, and probability density function of the concentration fluctuations.     

Wet scrubbing of polydisperse aerosols by freely falling droplets

In this study, analytical solutions for removal of a polydisperse aerosol by wet scrubbing were derived employing Brownian diffusion and inertial impaction as removal mechanisms. Size distribution of aerosol particles were assumed to be represented by a time-evolving log-normal function during the scrubbing process. Derived solutions were compared with the direct integration solution, which is not based on the log-normal assumption, showing good agreement. Error resulting from the log-normal assumption was shown to be greater in the impaction-dominant regime than in the diffusion-dominant regime due to higher size dependency of collision kernel which destructed log-normal shape of size distribution. The monodisperse model significantly overpredicted particle removal in the diffusion- and impaction-dominant size regimes due to its incapability of tracing average particle size change, while it underpredicted particle removal in the intermediate size range because of neglect of polydispersity effect. A new solution for the minimum collection efficiency particle diameter was also provided. The minimum efficiency diameter was shown not to be very sensitive to the scrubbing condition and to lie around for wide range of size and concentration of water drops.     

Prediction for particle removal efficiency of a reverse jet scrubber

Numerical computation was conducted to predict the collection performance of a reverse jet scrubber for polydisperse particles. The particle size distribution of polydisperse particles was represented by a lognormal function, and the continuous evolution of the particle size distribution in a reverse jet scrubber is taken into account with the first three moment equations. Numerical results were compared with the analytic results using average relative velocity in all zones and experimental results.

In a reverse jet scrubber, the impaction is the main particle collection mechanism because of high relative velocity and short collection time. The particle collection by impaction increases with an increase in particle size, and geometric mean diameter and geometric standard deviation decrease as time goes on. High droplet velocity and gas velocity increase the particle collection efficiency, and the small droplet size also increases the collection efficiency because smaller droplet size provides broader surface area. The packing density is a factor affecting particle collection efficiency in a scrubbing process. The dense packing density also provides large surface area and leads to high collection efficiency.     

CFD Modelling of Mixing Effects on the Course of Parallel Chemical Reactions Carried out in a Stirred Tank

Effects of turbulent mixing on the course of two fast parallel chemical reactions (neutralization of sodium hydroxide and hydrolysis of ethyl chloroacetate) carried out in a semibatch stirred tank reactor are experimentally investigated and numerically simulated. The flow pattern in the stirred tank is predicted using CFD and experimentally validated using Laser Doppler Anemometry. Mixing effects are modelled using three CFD based models. In the first and the second model the Beta probability distribution and the spiked distribution are used respectively; in the third model concentration fluctuations are neglected.     

Scalar mixing in turbulent concentric round jets

The scalar mixing field of a free, turbulent concentric round jet has been examined using marker nephelometry. The flow conditions included velocity ratios between the centre and annular jet of 0.188, 0.519 and 0.911. The correlation function between the concentration fluctuations in the two jet streams increased from –1.0 near the nozzle to + 1.0 further downstream indicating a tendency to complete mixing between the jets. The initial mixing behaviour between the jets was better for the lower velocity ratio between the jets (U_i/U_o = 0.188) although further downstream there was better transverse mixing between the jets with the higher velocity ratio (U_i/U_o = 0.911).