Solids Concentration Distribution Research Articles

Floating particles mixing characteristics in an eccentric stirred tank coupled with dislocated fractal impellers

Abstract The mixing characteristics of floating particle dispersion process in an eccentric stirred tank with dislocated fractal impellers were investigated using computational fluid dynamics (CFD) and experimental analyses. Solid concentration distribution, axial solid concentration profile, cloud height, solid integrated velocity, power consumption and just drawdown speed were investigated. Results showed that dislocated fractal impeller can enhance solid integrated velocity and fluid turbulent fluctuation intensity compared with dislocated pitched blade impeller, and eccentric agitation coupled with dislocated fractal impeller could destroy the typical circulation loops and symmetric flow field and improve the axial circulation efficiency of floating particles on the basis of dislocated fractal impeller. Eccentric agitation coupled with dislocated fractal impeller could further enhance the floating particle dispersion homogeneity (MI) and decrease the just drawdown speed (N jd) on the basis of dislocated fractal impeller and dislocated pitched blade impeller at the specific power consumption. Meanwhile, eccentric ratio of 0.3 or 0.4 was optimal for the floating particle mixing process in this work.

On the concentration models in electrical capacitance tomography for gas-fluidized bed measurements

Electrical capacitance tomography (ECT) has been widely applied in gas-fluidized bed measurements, which however is constrained by the sensor designs, image reconstruction algorithms and concentration models owing to the “soft-field” nature. Among the three factors, the concentration models that map the permittivity to solid concentration distribution are less understood. In this paper we present an experimental investigation on the effects of concentration models for the ECT measurements of gas-fluidized beds containing Geldart’s group A particles. The results show that the bubble velocity, bubbling frequency and fluidization regime transition velocity are intrinsic whatever the concentration model employed. However, the time-averaged solid concentrations measured by ECT with the conventional concentration models are usually higher than the corresponding results obtained by the bed expansion experiments in homogeneous fluidization. It has been further found that the concentration models can significantly influence the threshold selection in identifying the bubbles and surrounding emulsion phase in gas-fluidized beds. Thus, a new concentration model given in the formula of a power function (ϕ=Gα) has been proposed, with the optimal exponent α obtained via the least-square fitting of solid concentration in bed expansion during homogeneous fluidization. The model is robust and the sensitivity analysis shows that the variation of time-averaged solid concentration is negligible (≤ 3%) suppose that α changes by ± 20%.

The Impact of Swirls on Slurry Flows in Horizontal Pipelines

In deep ocean transportation pipeline, the swirling internal flow has a significant impact on the marine minerals transportation efficiency and safety. Therefore, the present work investigates various swirl flow motions for the slurry transport characteristics of the multi-sized particulate flow in a horizontal pipeline. Since the internal flow is a liquid-solid-solid mixture, a steady-state three-dimensional Eulerian-Eulerian multiphase approach in conjunction with the k-ω SST turbulence model is implemented for numerical simulation in the commercial CFD software ANSYS FLUENT 17.0. Numerical predictions of the mixture solid concentration distributions are generally in good conformance with experimental measurements. It is clearly revealed the transition of flow regime from heterogeneous to pseudo-homogeneous with the increasing level of swirl intensity at inlet. Compared to non-swirling flow, the swirling flow is of benefit to the multi-sized solid suspension capacity and the transportation efficiency. Moreover, the intense swirling vortex results in a strong influence on the characteristics of the lubrication layer formed by fine solid particles near the bottom of the pipe. These results provide valuable insights regarding the influence of swirl flow on the transport process for deep ocean mining.

Numerical modeling of multifrequency complex dielectric permittivity dispersion of clay-rich rocks

Dielectric permittivity measurements in sedimentary rocks are dominated by mineralogy, the volumetric concentration and spatial distribution of solids and fluids, and interfacial polarization. Conventional interpretation models oversimplify these factors, leading to uncertainties in estimates of formation properties such as hydrocarbon reserves. Interpretation challenges are magnified in clay-rich rocks, such as shaly sands and organic-rich mudrocks, due to convoluted rock fabric and mineralogical composition. However, the impact of fabric features and mineralogy on broadband permittivity is not well understood. Therefore, the main objective of this work is to develop a numerical framework to quantify the impact of different minerals and corresponding spatial distribution on the multifrequency complex permittivity of clay-rich rocks. We have solved the quasielectrostatic approximation to Maxwell’s equations in the frequency domain through the finite-volume method. We also introduce a workflow to calculate the effective admittance of the clay network. Furthermore, we derive an equation to incorporate the induced polarization effect into the effective admittance of pyrite particles. Finally, we perform a sensitivity analysis of the complex permittivity of clay-rich rocks in the frequency range from 100 Hz to 1 GHz to the volumetric concentration and spatial distribution of clays, cation exchange capacity (CEC), volumetric concentration of pyrite, and the orientation of the electric field. The simulation results confirm that the presence of clay minerals affects the permittivity and conductivity of the rocks. However, clays can enhance or diminish electrical conductivity values at different frequencies depending on their intrinsic properties and spatial distribution. For instance, laminations significantly enhance permittivity in the sub-MHz frequency range, but their effect is imperceptible at 1 GHz. The CEC variation affects conductivity in the entire frequency range from 100 Hz to 1 GHz and the permittivity at sub-MHz frequencies. A volumetric concentration of pyrite of 5% can enhance permittivity and conductivity at 100 Hz by approximately 50% and 30%, respectively.

Experimental and simulation study on mixing time and suspension quality of liquid-solid flow field in stirred reactor with draft tube

Abstract The solid-liquid flow field is established in the stirred reactor with baffles and draft tube. Mixing time and suspension quality of the flow field are studied. Based on the Eulerian multiphase flow model and RNG k−ε turbulence model, the CFD model is established for the simulation research. By comparing the experimental data of solid concentration distribution and mixing time with the simulated values, it is proved that the CFD model established can be used to study the flow field in the stirred reactor. The effects of stirring speed, liquid viscosity and solid particle size on mixing time and suspension quality are considered. With the increase of stirring speed, mixing time decreases, mixing uniformity is improved. Mixing time decreases first, then increases slightly with the increase of liquid viscosity, and the suspension quality is improved. When the solid particle size increases, mixing time increases rapidly, but the mixing uniformity becomes worse.

CFD simulation of tailings slurry thickening in a gravity thickener

In the present study, the thickening process of tailings slurry in a gravity thickener is modelled using Computational Fluid Dynamics (CFD), with a focus on the effects of particle size and feed velocity. A Two-Fluid Model (TFM) is employed to describe the particle-fluid and particle-particle interactions while turbulence is described by the ω-based Reynolds Stress Model (RSM). The validity of the model is demonstrated by close agreement between experimental measurement and simulation predictions of total solid mass of underflow, and particle cumulative mass distribution as a function of particle size in the underflow. The feedwell performance is evaluated in terms of kinetic energy dissipation and mixing performance. Particle size has a significant influence on the distribution of solid concentration. The increase of particle size leads to a higher critical settling height. For a given underflow discharging rate, solid concentration in the underflow increases with feed velocity only in a certain range, whereas increases continuously in the overflow. Large particle size corresponds to a higher critical feed velocity. Modelling the granular flow with a wide particle size distribution in a thickener helps explore the particle dynamic behaviors, thereby improving the thickening process.

Nonequilibrium characteristics and spatiotemporal long-range correlations in dense gas-solid suspensions

The nonequilibrium properties and strong spatiotemporal long-range correlations in gas-solid suspensions were analyzed systematically by discrete particle simulation in periodic domains. The effective interphase slip velocity is significantly larger than the particle terminal velocity, the particle velocity distribution function is non-Maxwellian with a high-energy tail and the solid concentration distribution function is far from the discrete Poisson distribution, all of which manifest strong deviation from the equilibrium or homogeneous state in gas-solid flow. The solid concentration, gas and solid velocities are spatiotemporally correlated and show a clear scale-dependence. More importantly, all characteristic correlation lengths scale linearly with the size of simulation domain, although the correlation length of solid concentration is much smaller than those of gas and solid velocities. On the other hand, the characteristic correlation times at first increase with increasing domain size and then seem to approach to asymptotic values. Those results indicate that the heterogeneity and spatiotemporal long-range correlations should be considered properly in continuum theory of heterogeneous gas-solid flow.

Improved scatter correction model for high attenuation gamma-ray tomography measurements

In this study a state-of-the-art gamma-ray tomography (GRT) unit was used to measure the solids concentration distributions of high density, high attenuation clay/water/sand slurries in a 4 in. (100 mm) diameter recirculating pipe loop. The presence of neighbouring radiation sources on the GRT results in a scattered radiation contribution to the total intensity measured at each detector. The scattered radiation decreases the signal-to-noise ratio of the measured radiation intensity and introduces error in the measured tomography data and the reconstructed tomograms (Maad et al 2008 Meas. Sci. Technol. 19 6). Because of the high attenuation of the materials being measured, the scatter contribution was a significant fraction of the total radiation measured at each detector. To correct for the scattered radiation contribution in the measurements, a test campaign was undertaken to characterize and model the scattering behaviour of the GRT at the Saskatchewan Research Council. The scattered radiation was measured experimentally from empty pipe, water filled pipe and a number of flowing clay/water/sand slurries at densities ranging from 1206 kg m−3 to 1580 kg m−3. A semi-empirical scatter correction model has been developed which allows the scattered contribution at each detector to be calculated iteratively based on the measured uncorrected attenuated radiation intensity. This article is an extension of the work presented at the 9th World Congress for Industrial Process Tomography (Spelay et al 2018 Proc. 9th World Congress Industrial Process Tomography p 14).

Calibration of solids concentration optical fibre probes with solids‐polymer blocks

AbstractOwing to the determinant effects of the local distribution of solids concentration on transport phenomena, particularly in gas‐solids flows in such processing units as gas‐solid fluidized beds and pneumatic conveying lines, its accurate measurement has received considerable attention. Despite the widespread applications of optical fibre probes for the measurement of local solids concentration, these instruments may create measurement uncertainties due to their structural designs and challenges in their accurate calibrations. Several calibration methods have been proposed in the literature, while they need to be further improved. In the present study, we calibrated in‐house, fabricated, solids concentration mixed parallel optical fibre probes by two sets of solids‐polymer blocks covering solids volume fractions in the range of 0‐0.30. The uniform blocks were produced by a twin‐screw extruder and an injection moulding machine. FCC particles, 86 μm in diameter, formed the dispersed solids in the blocks, while poly styrene and poly methyl methacrylate were separately acting as the transparent medium. They helped us investigate the effects of the refractive index of the medium and the probe tip design on the calibration curve. The blind distance (zone) in front of the adopted probes was determined, at about 0.70 mm, upon measuring their reflective curves. Two glass windows with 1.00 and 1.60 mm thicknesses were separately installed at the tip of a probe to study their effects on the calibration curve. Experimental results indicated that in the absence of a glass window, the probes' voltage readings varied nonlinearly with solids concentration, the voltage readings were higher for blocks with a higher refractive index of the transparent medium, while the normalized calibration curves were similar for both sets of solids‐polymer blocks. In addition, the extent of the uniform distribution of illuminating and reflecting fibre strands at the tip of a mixed parallel optical fibre probe can change the degree of nonlinearity of its calibration curve. The application of glass windows thicker than the blind distance decreased the degree of nonlinearity of the calibration curve, yet did not completely eliminate it.

On the reversibility of membrane fouling by deposits produced during crossflow ultrafiltration of casein micelle suspensions

The formation of a deposit layer on membrane surfaces is an important problem, particularly in milk filtration. Properties of the deposit and efficiency of deposit removal can be studied using various indirect methods based mainly on average membrane resistance in deposit formation–deposit removal cycles, but their conclusions on deposit reversibility depend on conditions surrounding deposit analysis.Here we present a method for direct characterization of the reversibility of deposit compression via analysis of local solid concentration distribution during deposit formation at constant pressure and cross-flow velocity and deposit removal after pressure relaxation. Two models are proposed for deposit characterization: a model of crossflow filtration with deposit formation to characterize deposit compressibility-permeability from the data on concentration distribution at steady-state of deposit formation, and a model for evaluating deposit swelling kinetics from the data on steady-state compressibility-permeability.The method was applied here for analysis of the deposit formed on the surface of a polymeric ultrafiltration membrane during crossflow filtration of casein micelle suspensions at 25°C. Local solid concentration distribution in the deposit and concentration polarization layer was probed in situ using small-angle X-ray scattering (SAXS). Experiments were performed in a special-purpose SAXS–filtration cell. It was demonstrated that casein micelle deposits obtained at 1.1 bar transmembrane pressure swell after pressure relaxation. However, swelling rate was significantly lower than that obtained by modeling using deposit compressibility–permeability obtained from the analysis of steady-state concentration distribution. We thus find evidence that casein micelle deposits produced during crossflow membrane filtration undergo compression that is partially irreversible.

Dynamics Of Total Suspended Solid (TSS) Around Coral Reef Beach Damas, Trenggalek

Total suspended solids (TSS) are sediment material that floats in the water column that moves without touching the water bed, influenced by input from land, river flow, and water oceanography factors. TSS is closely related to sedimentation, which can harm aquatic ecosystems, especially coral reefs. This research was conducted using TSS data as well as flow data for each season (May, June, October 2019, February and March 2020) to know the distribution of suspended solids concentration, knowing the dynamics of changes in TSS concentrations on Damas Beach by season, and to determine the relationship TSS with the growth of coral reefs at Damas Beach. TSS levels in Damas waters are quite high, which can be indicated by the turbid waters. TSS levels in March 2020 showed dominating results with a range of 37.8–72.6 mg/L and an increase in the range of 72.7-145 mg/L. The highest distribution of TSS on Damas Beach is found in the Rainy season.

Flow development and prediction of solids concentration in a large gas‐solids turbulent fluidized bed

AbstractIn a 5 m high turbulent fluidized bed with a 0.3 m inner diameter, local solids concentration in the dense region and axial pressure difference along the column were measured using an optical fibre probe (PC6M) and differential pressure sensors (PX653), respectively. The time‐series signals of the solids concentration fluctuations are analyzed via statistical methods. The axial and radial profiles of solids concentration are non‐uniform. In the developing dense region, the radial profiles of solids concentration are significantly influenced by operating conditions, and the fluctuation of solid concentration is considerably enhanced with the development of flow. In the fully developed dense region, the axial solids concentration decreases monotonously with height, and the radial profiles of solids concentration are exponential. The flow development in the dense region could be accelerated by the superficial gas velocity. Based on the analysis of the characteristics of the radial solids concentration distribution in the dense region, an empirical correlation of this distribution is proposed. The formulated correlation is found to be consistent with the experimental data reported in the literature.

Analysis of Total Suspended Solid Distribution and Its Effect To The Fertility of Marine Waters Around Fish Auction Place (TPI) Dumai

This study aims to determine the distribution of total suspended solid concentration (TSS) in the waters around TPI Dumai. Water samples were taken from 12 sampling point from the waters during high and low tides to determine TSS concentration. The concentration of total suspended solids ranges from 60-130 mg/l. The concentration is relatively higher (>80 mg/l) in the area that is close to residential areas and TPI. The highest concentration of total suspended solids was 117 mg/l found in waters with a depth of 1-3 m, while the lowest was 81 mg/l found at the sampling point of 5,9. The distribution of chlorophyll-a concentration is relatively higher around the coast which is around 0.476-0.178 mg/l, and it's lower off the shore which is around 0.080-0.090 mg/l. The chlorophyll-a concentration is lower in waters far from the coast because there is no direct nutrient supply from the land. The regression analysis indicate that Tss and chlorophyll-a has a weak relationship between the two variables relatively weak but they are still affecting each other.

Numerical Analysis of Solidification Behavior during Laser Welding Nickel-Based Single-Crystal Superalloy Part I: Crystallography-Dependent Solid Aluminum Distribution

The thermal metallurgical modeling of alloying aluminum redistribution was further developed through couple of heat transfer model, dendrite selection model, multicomponent dendrtie grwoth model and nonequilibrium solidification model during three-dimensional nickel-based single-crystal superalloy weld pool solidification over a wide range of welding conditions (laser power, welding speed and welding configuration) to facilitate understanding of solidification cracking phenomena. It is indicated that the welding configuration plays more important role than heat input in aluminum redistribution. The bimodal distribution of solid aluminum concentration along the solid/liquid interface is crystallographically symmetrical about the weld pool centerline for (001) and [100] welding configuration, while the distribution of solid aluminum concentration along the solid/liquid interface is crystallographically asymmetrical throughout the weld pool for (001) and [110] welding configuration. The size of vulnerable [100] dendrite growth region is beneficially suppressed in favor of epitaxial [001] dendrite growth region through optimum low heat input (low laser power and high welding speed) to facilitate single-crystal dendrite growth for successful crack-free weld at the expense of shallow weld pool geometry. The overall aluminum concentration in (001) and [100] welding configuration is significantly smaller than that of (001) and [110] welding configuration regardless of heat input. Severe aluminum enrichment is confined to [100] dendrite growth region where is more susceptible to solidification cracking. Heat input and welding configuration are optimized in order to minimize the solidification cracking susceptibility and improve microstructure stability. The relationship between welding conditions and alloying aluminum redistribution are established for solidification cracking susceptibility evaluation. The higher heat input is used, the more aluminum enrichment is monotonically incurred by diffusion with considerable increase of metallurgical driving forces for morphology instability and microstructure anomalies to deteriorate weldability and vice versa. The mechanism of asymmetrical solidification cracking because of crystallography-dependent alloying redistribution is proposed. The theoretical predictions agree well with the experiment results. Moreover, the useful modeling is also applicable to other single-crystal superalloys with similar metallurgical properties during laser welding or laser cladding.

How to evaluate the mass transfer resistances in dense solid–liquid suspensions

The dissolution of solids in slurry stirred tanks is affected from the solid concentration distribution to different extend, depending on the agitation conditions. In this work, the relationship between solid–liquid mixing and mass transfer is investigated by estimating the characteristic times of different phenomena: liquid mixing, solid dissolution, diffusion of the dissolved species in the vessel volume. The analysis is based on Electrical Resistance Tomography data collected during the simultaneous operations of dissolution and mixing. For dilute solid–liquid systems, the relative importance of the solid dissolution and the liquid mixing depends on the particle size and the impeller speed, while the diffusion in stagnant zones is often negligible. Instead, the diffusion mechanism has an important effect on mass transfer for dense systems, where strong axial gradients of solid concentration are established and the stirred tank volume can be divided into a lower zone containing a cloud of dense mixture and an almost stagnant clear liquid layer on top. Based on original and literature experimental data, a method for the main mass transfer resistance identification depending on the agitation condition, the solid volume fraction distribution and the soluble particle size is suggested.

Numerical investigation of zinc tailings slurry flow field in a horizontal pipeline

Thispaperreportsthefindingsofnumericalinvestigationofdenseparticulateslurryflowfieldinaslurrypipelinewith an objective of examining erosive wear. Parametric study with velocities 2 m/s, 2.75 m/s and 3.5 m/s, and volumetric concentration of 4% and 26% were carried out on a pipeline of nominal inside diameter 105 mm. The range of volumetric concentration was chosen to ascertain the flow field characteristics for low to high particle loading. All the simulations have been computationally performed using ANSYS-FLUENT. The dense particulate slurry is modelled using Eulerian-Eulerian approach while finite volume method (FVM) is employed as the numerical method. Mesh refinement study and validation with experimental results for pressure drop have been reported. Solids concentration and velocity profiles show dependence on flow velocity and inlet average concentration. The distribution of solids concentration and its dependence on the bulk flow velocity qualitatively indicates the regions of relatively higher erosion wear.

Experimental investigation of axial Solid concentration distribution in fluidized bed

The axial solid concentration distributions were measured by using pressure inspection instrument in a glass bead fluidized bed. Set 1-3 belong to single size distribution and Set 4-5 have wide size distribution, respectively. The change trend of axial solid concentration distributions were investigated under different superficial gas velocities, particle size and particle density. The results showed that, with increasing superficial gas velocity, the solid concentrations in dense region decreased, but increased in dilute region. The glass bead particles whose particle size and particle density were smaller had good fluidization quality. It was also found that the joining of fine particles can significantly change the flow characteristics of the fluidized solid particles.

Study on the Flow Field Characteristics of a Liquid–Solid–Solid Three-Phase System and the Influence of a Draft Tube in a Stirred Reactor

The liquid–solid–solid three-phase flow field was established in a stirred reactor with a draft tube and baffles. The solid concentration distribution, mixing time, velocity distribution, flow patt...

Numerical investigation on mixing characteristics of floating and sinking particles in a stirred tank with fractal impellers

The hydrodynamics of floating and sinking particles mixing process in a stirred tank with four pitched-blade impellers and fractal impellers were investigated employing computational fluid dynamics (CFD) simulation. Axial solid concentration profile, solid concentration distribution, power consumption, trailing vortex, cloud height, water integrated velocity, just suspension speed (Njs) and just drawdown speed (Njd) in the stirred tank were predicted. Results showed that the mixing quality of floating and sinking particles increased with the increase of impeller speed. Smaller density difference between solid-liquid two phases and smaller particle diameter resulted in higher suspension degree. Fractal impeller can enhance water integrated velocity and improve suspension quality compared with four pitched-blade impeller under the constant power consumption, and increasingly so with fractal iteration number. Meanwhile, fractal impeller can reduce the size of trailing vortex and decrease the power consumption based on four pitched-blade impeller at the same impeller speed. In addition, the just suspension speed (Njs), just drawdown speed (Njd) and correlation equation for Njs and Njd in the three different impeller systems were obtained. Fractal impeller could decrease the Njs and Njd on the basis of four pitched-blade impeller, and decreasingly so with the fractal iteration number.

Study on the length of pipe inlet section of pulp fluid based on CFD

In the paper industry, to determine the installation positions of concentration sensor and flow sensor of pulp pipe transportation system, the length of pipe inlet section of pulp fluid must be determined. In order to solve the problem that it is difficult to determine the length of pipe inlet section of pulp fluid, the paper presents a method to determine the length of pipe inlet section of pulp fluid, and the relationship between the length of inlet section and pulp fluid parameters is studied by this method. Firstly, CFD (Computational Fluid Dynamics) method is applied to obtain flow velocity and solid phase concentration distribution data of pulp fluid at different axial positions in the pipe. Then, Pearson correlation coefficient method is applied to analyze these data. Finally, the length of pipe inlet section of pulp fluid is determined according to the obtained correlation coefficient, and the relationship between the length of pipe inlet section of pulp fluid and initial average flow velocity and solid phase concentration is obtained. The conclusion shows that the method can well obtain the length of pipe inlet section of pulp fluid, which provide some theoretical basis for the design of pulp pipe transportation system.