Cylindrical Mixing Research Articles

Modeling Erosion Wear Rates in Slurry Flotation Cells

In processes using slurry as the working fluid, wear due to solid particles impinging on elements of the process units is a serious reliability issue. This study considers modeling wear damage in flotation cells, which are widely used in mineral processing. Flotation cells are typically cylindrical vessels where an impeller is used to agitate the fluid, enabling the liberation of the minerals from the slurry. Some solids, particularly those entrained in the impeller stream, can impact on the wall of the cell, leading to material loss and eventually to loss of structural integrity. The problem of predicting the remaining life of the unit due to erosion requires understanding of various sub-processes: flow modeling, particle–fluid interaction, energy interactions at the surface, and the mechanism of erosion itself. In this study, empirically developed equations for the flow field of cylindrical mixing vessel with a Rushton turbine are used in formulating a model relating and the damage accumulation rate to a simple set of measurable variables. To validate a model, a PIV technique was used to measure velocities in the flow field and near the wall on a physical model of the cell with transparent walls and particles that match the refractive index of the fluid. An Eulerian–Langrangian approach has been used to determine the particle trajectories and the effect of a squeeze film is incorporated into the model to modify the velocity distribution of particles prior to impacts. An analytical model based on equations of impulse and momentum for a particle of any shape striking a flat massive surface has been used to describe the energy lost at the walls. Finally, a damage model is developed that takes into account impact velocity, attack angle, properties of the impinging particles and the surface. This model is verified against a second physical model that measures material loss rate at different locations within the cell.

Gas ejector with isobaric mixing chamber

A method is proposed for calculating a gas ejector with a tapering isobaric mixing chamber. The efficiency of ejectors with isobaric and cylindrical mixing chambers is compared.

Effect of Blade Speed on Granular Flow and Mixing in a Cylindrical Mixer

The discrete element method (DEM) offers the possibility of understanding mixing processes at a microscopic, particle level. In connection with previous studies, DEM is used in this work to investigate the mixing of monosized spherical particles with blade speeds in the range 2−100 rpm. Recirculating flows are observed in both horizontal and cylindrical sections of the bed, providing a mixing mechanism. The recirculating flows formed in front of the blade in cylindrical sections seem to disappear, bringing a reduction of mixing rate at high blade speeds. Viewed at the particle scale, a zone of large interparticle forces is present in front of the blade, and this zone moves toward the vessel walls at high speeds. These are the regions where particle breakage or fracture can happen. Interparticle forces in the bed as a whole increase with the blade speed. Moreover, particle mixing has been studied at both macroscopic and particle scales using conventional mixing index and coordination or contact numbers. One conventional mixing index shows a slight reduction in mixing rate in the transition mixing region up to a certain blade speed and a slight improvement thereafter. This improvement is probably caused by the toroidal motion of particles induced at high blade speeds. Coordination number is successful in capturing the mixing process, and indicates a new way of studying particle-scale mixing.

Numerical simulation of the hydrodynamic instability experiments and flow mixing

Based on the numerical methods of volume of fluid (VOF) and piecewise parabolic method (PPM) and parallel circumstance of Message Passing Interface (MPI), a parallel multi-viscosity-fluid hydrodynamic code MVPPM (Multi-Viscosity-Fluid Piecewise Parabolic Method) is developed and performed to study the hydrodynamic instability and flow mixing. Firstly, the MVPPM code is verified and validated by simulating three instability cases: The first one is a Riemann problem of viscous flow on the shock tube; the second one is the hydrodynamic instability and mixing of gaseous flows under re-shocks; the third one is a half height experiment of interfacial instability, which is conducted on the AWE’s shock tube. By comparing the numerical results with experimental data, good agreement is achieved. Then the MVPPM code is applied to simulate the two cases of the interfacial instabilities of jelly models accelerated by explosion products of a gaseous explosive mixture (GEM), which are adopted in our experiments. The first is implosive dynamic interfacial instability of cylindrical symmetry and mixing. The evolving process of inner and outer interfaces, and the late distribution of mixing mass caused by Rayleigh-Taylor (RT) instability in the center of different radius are given. The second is jelly layer experiment which is initialized with one periodic perturbation with different amplitude and wave length. It reveals the complex processes of evolution of interface, and presents the displacement of front face of jelly layer, bubble head and top of spike relative to initial equilibrium position vs. time. The numerical results are in excellent agreement with that experimental images, and show that the amplitude of initial perturbations affects the evolvement of fluid mixing zone (FMZ) growth rate extremely, especially at late times.

A procedure for calculating gas ejectors

Results obtained from an analysis of the most widespread and commonly used procedure for calculating gas ejectors equipped with a cylindrical mixing chamber are presented. Boundaries of the application field of this procedure are revealed. A new approach for determining the main parameters of an ejector is proposed, and a sequence for calculating it is given.

Large eddy simulation and PIV experiments of air–water mixing tanks

The simulations and experiments of a turbulent bubbly flow are carried out in a cylindrical mixing vessel. Dynamics of the turbulent bubbly flow is visualized using a novel two-phase particle image velocimetry (PIV) with a combination of back lighting, digital masking and fluorescent tracer particles. Using an advanced technique, Mie’s scattering at surfaces of bubbles is totally filtered out and, henceforth, images of tracer particles and of bubbles are obtained with high quality. In parallel to the comprehensive experimental studies, numerical results are obtained from large eddy simulations (LES) of the two-phase air–water mixer. The impeller-induced flow at the blade tip radius is modeled by using sliding mesh method. The results demonstrate the existence of large structures such as tip-vortex tips, and also some finer details. In addition, the stability of the jet is found to be connected with the fluctuations of the tip vortices whose dynamics are affected by the presence of bubbles. Numerical results are used to interpret the measurement data and to guide the refinement of consistent theoretical analyses. Such information is invaluable in the development of advanced theories capable of describing bubbly flows in the presence of complex liquid flow. This detailed information is of real significance in facilitating the design and scale-up of practical stirred tanks.

Effects of blade rake angle and gap on particle mixing in a cylindrical mixer

Performance optimization of a mixer is an issue of great significance in many industrial technologies dealing with particulate materials. By means of Discrete Element Method (DEM), this work examines how the mixing performance of a cylindrical mixer is affected by the two design parameters: blade rake angle and blade gap at the vessel bottom, extending our previous work on particulate mixing. The flow and mixing performance are quantified using the following: velocity fields in vertical cylindrical sections, Lacey’s mixing index, inter-particle forces in vertical cylindrical sections through the particle bed and the applied torque on the blade. Simulation results show that the mixing rate is the fastest for a blade of 90° rake angle, but inter-particle forces are large. Conversely, the inter-particle forces are small for a blade of 135° rake angle, but the mixing rate is slow. The simulation results also indicate that the force applied on particles, velocity field and mixing are interrelated in that order.

Measuring Mixing Time in the Agitation of Non‐Newtonian Fluids through Electrical Resistance Tomography

AbstractElectrical resistance tomography (ERT), which is a non‐invasive and robust measurement technique, was employed to visualize, in three dimensions, the concentration field inside a cylindrical mixing vessel equipped with a radial‐flow Scaba 6SRGT impeller. The ability of ERT to work in opaque fluids makes this technique very attractive from an industrial perspective. An ERT system with a 4‐plane assembly of peripheral sensing rings, each containing 16 electrodes, was used to measure the mixing time in agitation of xanthan gum solution which is a pseudoplastic fluid with yield stress. An image reconstruction algorithm was used to generate images of the tracer distribution within the sensing zone. In this study, the effect of impeller speed, fluid rheology, power consumption, and Reynolds number on the mixing time was investigated.

Melt compounding of various polymers with organoclay by shear flow

AbstractWe studied melt compounding of polymer/organoclay composites by shear flow in a rotating cylindrical mixer to investigate an effect of shear stress on the dispersion state of clay. The commercial organoclay, which is intercalated by dimethyl benzyl stearyl ammonium ion between clay platelets, and four kinds of commercial polymer (polystyrene (PS), poly(lactic acid) (PLA), polyamide(PA6), and poly(butylene succinate) (PBS)) were used in this study. According to the TEM photographs, there is exfoliated clay in PA6/organoclay composite, but the exfoliated clay cannot be seen in other polymer/organoclay composites. We calculated the value of clay dispersion from the low magnification TEM photograph, called the dispersion coefficient to consider the micro level dispersion of the clay in a polymer matrix. Generally, the dispersion coefficient increases with shear stress. However, the dispersion coefficients in case using PA6 and PBS as the matrix, whose melts have low viscosity, are larger than those in case using PS and PLA, whose melts have high viscosity. According to XRD results, d001 peak originated from organoclay mostly shifted to the low value of angle for PA6/organoclay composite and began shifting to the low value of angle for PBS/organoclay composite. However, there is a peak for PS and PLA based organoclay composites. From the cases of PA6 and PBS in the DMA results, the storage modulus increases with an addition of organoclay. These results imply that low viscosity polymer is typical easy to get the composites with intercalated clay by melt compounding. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers

Experimental determination of the optimum performance of ejector refrigeration system depending on ejector area ratio

The performance of the ejector refrigeration system using ejectors with cylindrical mixing chamber is studied at operating conditions with choking in the mixing chamber. The condenser pressure is chosen so that the secondary flow choking can occur even in the ejector with the smallest area ratio. In the present study, the performance of the constructed system is determined by using six configurations of ejector and R-123 as working fluid in the system. The study is performed over a range of the ejector area ratio from 6.5 to 11.5 at the compression ratio 2.47. In the studied range, the experimental coefficient of performance of the system rises from 0.29 to 0.41, as the optimum generator temperature increases from 83 to 103 °C. Similar results were also found in the parametric study when the efficiencies of the nozzle and diffuser are taken as 0.90.

Experimental and numerical investigation of circularly lobed ejector with bend mixers

AbstractThe vent pipe for a turbo shaft engine may be required to have a lobed nozzle installed and to bend for the purpose of infrared stealth. The experimental setup was a circular 12‐lobed nozzle with bend mixers to study the effects on the pumping performance of the lobed bend mixer parameters. The experimental results show that the pumping ratio of the secondary mass flow to the primary mass flow for a mixer bend angle equal to 40° is the same as that for the same lobed nozzle with the same diameter cylindrical mixer that was used in the author's previous papers. There is a great decrease of the pumping ratio for a mixer bend angle larger than 40°. The higher the bend angles, the lower the pumping ratios. The pumping ratios initially increase and then decrease with the increasing of the cross‐area ratio of mixer to lobe. The optimal cross‐area ratio that corresponds to the maximum pumping ratio is strangely nearly equal to the optimal cross‐area ratio of a cylindrical mixer, although the maximum pumping ratio is less than that for a cylindrical mixer. The pumping ratios increase approximately linearly with the cross‐area ratio of the secondary inlet to the lobed nozzle. To investigate the flow characteristics and the pumping ratio changing mechanism, the flow field inside the ejector is numerically simulated. The numerical results show that the main reason for the great decrease of the pumping ratio when the mixer bend angle is larger than 40° is due to the great static pressure around the bend part, which is caused by the primary flow jet. The great static pressure around the bend section chokes back the exhausted secondary fluid flow. There is a good agreement between the calculated and the measured wall static pressure coefficients in the mixer wall along the lobe crest symmetry plane of the lobed ejector. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(7): 387–397, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20175

Macro-instability: a chaotic flow component in stirred tanks

Chaotic features of the macro-instability (MI) of flow patterns in stirred tanks are studied in this paper. Datasets obtained by measuring the axial component of the fluid velocity and the tangential force affecting the baffles are used. Two geometrically identical, flat-bottomed cylindrical mixing tanks (diameter of 0.3m) stirred with either pitched blade turbine impellers or Rushton turbine impeller are used in the experiments, and water and aqueous glycerol solutions are used as the working liquids. First, the presence of the MI component in the data is examined by spectral analysis. Then, the MI components are identified in the data using the proper orthogonal decomposition (POD) technique. The attractors of the macro-instability are reconstructed using either the POD eigenmodes or a method of delays and finally the attractor invariants are evaluated. The dependence of the correlation dimension and maximum Lyapunov exponent on the vessel operational conditions is determined together with their distribution within the tank. No significant spatial variability of the correlation dimension value is observed. Its value is strongly influenced by impeller speed and by the vessel-impeller geometry. More profound spatial distribution is displayed by the maximum Lyapunov exponent taking distinctly positive values. These two invariants, therefore, can be used to locate distinctive regions with qualitatively different MI dynamics within the stirred tank.

Analysis of Combustion Induced Vortex Breakdown Driven Flame Flashback in a Premix Burner With Cylindrical Mixing Zone

In earlier experimental studies of the authors a previously unknown mechanism leading to flame flashback—combustion induced vortex breakdown (CIVB)—was discovered in premixed swirl burners. It exhibits the sudden formation of a recirculation bubble in vortical flows, which propagates upstream into the mixing zone after the equivalence ratio has exceeded a critical value. This bubble then stabilizes the chemical reaction and causes overheat with subsequent damage to the combustion system. Although it was shown earlier that the sudden change of the macroscopic character of the vortex flow leading to flashback can be qualitatively computed with three-dimensional as well as axisymmetric two-dimensional URANS-codes, the proper prediction of the flashback limits could not be achieved with this approach. For the first time, the paper shows quantitative predictions using a modified code with a combustion model, which covers the interaction of chemistry with vortex dynamics properly. Since the root cause for the macroscopic breakdown of the flow could not be explained on the basis of experiments or CFD results in the past, the vorticity transport equation is employed in the paper for the analysis of the source terms of the azimuthal component using the data delivered by the URANS-model. The analysis reveals that CIVB is initiated by the baroclinic torque in the flame and it is shown that CIVB is essentially a two-dimensional effect. As the most critical zone, the upstream part of the bubble was identified. The location and distribution of the heat release in this zone governs whether or not a flow field is prone to CIVB.

Vapor condensation on nanoparticles in the mixer of a particle size magnifier

The vapor condensation on nanoparticles in a supersaturated gaseous mixture is considered. Supersaturation was created by mixing two flows with different temperatures in a cylindrical mixer at atmospheric pressure. The conditions for mixing were chosen such that the homogeneous nucleation of vapor did not mask the growth of heterogeneous droplets with nanoparticles inside. A mathematical model of the growth of heterogeneous droplets was developed at one-dimensional description of the mixer. Five parameters that affect the performance of the particles size magnifier were identified: temperature of the saturator and the flow with nanoparticles, the number density and initial radius of the nanoparticles, and ratio of flow rates. The results of the simulation are compared with our experimental data.

Experimental and numerical research on high pumping performance mechanism of lobed exhauster-ejector mixer

The lobed nozzle exhauster-ejector mixer has a lot of potential applications in industry. The experimental setup is established to explore its high pumping performance mechanism. Experimental results show that the pumping performance is dominantly dependent on the primary flowing fluid “attachment” on the inner wall of the mixer. If the primary flowing fluid attaches the inner wall of the mixer in the exit section, the pumping ratio of the entrained secondary mass flow rate to the primary mass flow rate is definitely high. In order to find the high pumping performance mechanism from flow field, the N–S equations are solved. The numerical results show that the flow field to give high or the highest pumping ratio is that there is a distinct thin layer (tear layer) of the secondary flowing fluid with less velocity on the inner wall of the mixer. The distinct thin layer much decreases the friction loss between the primary high-speed flow and the solid wall. The necessary conditions for establishing the distinct thin layer are that the cross-area ratio is not too high or too low and the expand angle of the conical mixer is slightly less than the initial diffusion angle of the primary eject flow. According to the experimental and numerical results, the conical mixer with the cross-area ratio of 2.5 and the expand angle of 14.4° gives the highest pumping ratio of 0.528. The highest pumping ratio 0.598 for cylindrical mixers is experimentally in the case of the cross-area ratio of 3.8. The reason for the highest pumping ratio difference between the conical mixer and the cylindrical mixer is that in the cylindrical mixer the primary flowing fluid properly attaches the inner wall of the mixer in the outlet section and there is a larger space with negative pressure downstream of the lobed nozzle for entraining the secondary flowing fluid.

Large Eddy Simulations of a Brine-Mixing Tank

Abstract Traditionally, solid–liquid mixing has always been regarded as an empirical technology with many aspects of mixing, dispersing, and contacting related to power draw. One important application of solid–liquid mixing is the preparation of brine from sodium formate. This material has been widely used as a drilling and completion fluid in challenging environments such as in the Barents Sea. In this paper large-eddy simulations, of a turbulent flow in a solid–liquid, baffled, cylindrical mixing vessel with a large number of solid particles, are performed to obtain insight into the fundamental aspects of a mixing tank. The impeller-induced flow at the blade tip radius is modeled by using the sliding mesh. The simulations are four-way coupled, which implies that both solid–liquid and solid–solid interactions are taken into account. By employing a soft particle approach the normal and tangential forces are calculated acting on a particle due to viscoelastic contacts with other neighboring particles. The results show that the granulated form of sodium formate may provide a mixture that allows faster and easier preparation of formate brine in a mixing tank. In addition it is found that exceeding a critical size for grains phenomena, such as caking, can be prevented. The obtained numerical results suggest that by choosing appropriate parameters a mixture can be produced that remains free-flowing no matter how long it is stored before use.

Computer simulations of sodium formate solution in a mixing tank

Traditionally, solid–liquid mixing has always been regarded as an empirical technology with many aspects of mixing, dispersing and contacting were related to power draw. One important application of solid–liquid mixing is the preparation of brine from sodium formate. This material has been widely used as a drilling and completion fluid in challenging environments such as the Barents Sea. In this paper, large-eddy simulations of a turbulent flow in a solid–liquid baffled cylindrical mixing vessel with large number of solid particles are performed to obtain insight into the fundamental aspects of a mixing tank. The impeller-induced flow at the blade tip radius is modeled by using the dynamic-mesh Lagrangian method. The simulations are four-way coupled, which implies that both solid–liquid and solid–solid interactions are taken into account. By employing a soft particle approach the normal and tangential forces are calculated acting on a particle due to viscoelastic contacts with other neighboring particles. The results show that the granulated form of sodium formate may provide a mixture that allows faster and easier preparation of formate brine in a mixing tank. In addition it is found that exceeding a critical size for grains phenomena, such as caking, can be prevented. The obtained numerical results suggest that by choosing appropriate parameters a mixture can be produced that remains free-flowing no matter how long it is stored before use.

Characterization of granular flow of wet solids in a bladed mixer

AbstractIn this study, we measure instantaneous, average, and fluctuating velocity fields at exposed surfaces for dry and wet grains in a vertical cylindrical mixer, agitated by four pitched blades. When the material is dry, the free surface of the granular bed deforms, rising where the blades are present, and falling between blade passes. Although average velocities are predominantly azimuthal, instantaneous velocities tracked in time reveal three‐dimensional particle circulations, including significant periods of particle motion in the opposite direction to that of the blades, indicative of bed penetration. When moisture is added to the solid particles, the flow dynamics change from a regime dominated by the motion of individual grains to a regime controlled by the motion of small clumps that form as a result of the cohesive forces. This transition is characterized by a reduced particle–particle collision frequency and exhibits a sharp decrease in the granular temperature at the free surface. This transition is also characterized by an increase in bed porosity, which is attributed to increased cohesiveness arising from liquid bridges. A Fourier transform analysis conducted on the tangential component of the velocities (dominant flow) shows that a group of high frequencies exceeding the blade rotation frequency become significant with added moisture. These are characteristics of the large number of wet agglomerates flowing between successive blade passes. © 2006 American Institute of Chemical Engineers AIChE J, 2006

PERFORMANCE ANALYSIS OF CYLINDRICAL TYPE AIR EJECTOR

Performance tests were conducted for an air ejector entraining two secondary jets whose axes are coaxia l of that of primary stream. A unique ejector housing was constructed to receive both the convergent or convergent-divergent primary nozzle a nd the cylindrical mixing chamber. The air ejector under investigation has nozzle throat -to- cylindrical section area ratio of 0.12. The investi gation is conducted for ejector having cylindrical length-to-diameter ratio , which varies from 2.31 to 23.08. It covers a range of spacing from -1 to 0.5 of cylindrical lengths and of secondary to ambient pressure ratio of 1.0. The recorded axial distributions of the static wall pressure are plotted in non- dimensional forms and the extent of consistency of the profiles is shown. The induced air flow rate ratio is plotted for the measured primary to secondary stagnation pressure ratio range. Results offered a valuable appreciation of the effect of the cylindrical length and nozzle spacing-to- diameter ratios on both wall pressure distribution and jet entrainment capacity. The occurrence of flow choking in both th e convergent or convergent-divergent primary nozzle was ensured.

Granular flow and segregation in a four-bladed mixer

In this study, we experimentally examine flow and segregation of granular material in a cylindrical mixer geometry agitated by four 45 ∘ pitched blades, which is representative of equipment such as high-shear granulators and filter-dryers. We observe that the free surface of the granular bed deforms, rising where the blades are present and falling between blades passes. Using particle image velocimetry (PIV), we measure the instantaneous, average, and fluctuating velocity fields at exposed surfaces (top surface and near the wall), for both near-monodisperse and polydisperse granular materials. The radial and axial point-velocity profiles indicate three-dimensional recirculation patterns indicative of avalanching and bed penetration. For polydisperse mixtures, we find that depending on the shear rate, different segregation mechanisms can take place. Under low shear, complex lobe and striation segregation patterns occur through stretching and folding due to surface avalanching. This leads to enhanced initial mixing rates in a manner consistent with spontaneous chaotic granular mixing. At high-shear rates, segregation is controlled by the rotation of the blades. As a result, coarse particles have a tendency to migrate both to the free surface and the outer wall independently of initial bed loading conditions.