Axial Mixing Research Articles

Spatially Resolved Tomographic Assessment of Axial Mixing in Structured and Random Packings

AbstractThe liquid axial dispersion inside modern structured packings (Sulzer Mellapak™ 500.Y, Raschig Super‐Pak 350Y) and one random packing of the 4th generation (Raschig Super‐Ring 0.3) was measured by means of computed tomography. As the gas velocity is known to have little effect on the liquid axial dispersion at low hydraulic load, all experiments were conducted without countercurrent gas flow at liquid loads of B = 10, 15, and 20 m3m−2h−1 in a column with an inner diameter of 100 mm. Injection of the X‐ray‐active tracer potassium iodide allows the identification of active and passive liquid accumulations inside the structured packing. Good agreement was found between the active liquid holdup from tomographic images and the total holdup calculated from the mean residence time for the structured packings.

Influence of Bionic Waveform Leading Edge Blade on Drag Reduction Characteristics of Mixed Pump

Because the helical axial flow gas-liquid mixing pump has the great advantage of conveying gas-liquid two-phase mixed medium, it has become the main core equipment for deep-sea oil and natural gas exploitation. The gas phase aggregation and bubble movement trajectory in the impeller channel have been widely studied, but the increase of medium flow resistance caused by flow separation has not been deeply discussed. Combined with the Euler multiphase flow model and the SST k-ω turbulence model, the numerical calculation of the helical axial flow gas-liquid mixed pump is carried out. Under design flow conditions Q = 100 m3/h, head H = 30 m, speed n = 4500 r/min, specific speed ns =213.6 r/min, and under different inlet gas content conditions, the influence of the bionic waveform leading edge blade on drag reduction characteristics of the helical axial flow gas-liquid mixed pump was investigated. By designing the blade with a leading-edge structure with different heights and pitches, the separation of the mixed medium and the suction surface is effectively suppressed, and the flow resistance of the medium in the 1/10 area of the inlet end of the blade is reduced. The results show that when the height A is 0.25%L and the pitch λ is 12.5%h, the maximum drag reduction rate in this region is 52.6%, the maximum increase in efficiency of the mixed pump is 2.2%, and the maximum increase in head is 4.8%. This study can provide technical support for flow drag reduction in gas-liquid mixed pump.

Effect of inter-particle forces on solids mixing in fluidized beds

Mixing of particles is important in fluidized beds. For a more accurate and realistic investigation of this process, it is necessary to consider the inter-particle forces. The effect of four inter-particle forces (van der Waals, liquid bridge, electrostatic, and hydrogen bond) on the particles mixing in a fluidized bed is investigated in this work. A pseudo-2D fluidized bed was simulated in two cases; particles of the same size with different densities, and particles of the same density with different diameters. The effect of each force alone on the axial mixing of particles was investigated, and results were compared with a bed in the absence of inter-particle force. The combined technique of computational fluid dynamics and discrete element method was adopted for simulations. For better comparison, each force was normalized with respect to the weight of particles. It was observed that the hydrogen bond force has the most significant impact on the size of bubbles, thus the mixing of particles. The porosity distribution in the bed was examined, and it was observed that the bubble phase fraction increases in the presence of inter-particle force. It was found that diffusivity increases with increasing the gas velocity in the presence of inter-particle forces due to the formation of larger bubbles. Finally, the Ashton mixing index was evaluated for the two simulation cases in the presence of each inter-particle force, and the results showed that although diffusivity is greater in the presence of inter-particle force due to the formation of larger bubbles, the mixing time is higher due to slower mixing in the particle scale. • The effect of four principal inter-particle forces in a fluidized bed was studied. • The pseudo-2D fluidized bed was simulated by the CFD-DEM method. • The bubbles' size, porosity distribution, and diffusivity were studied. • The Ashton mixing index was evaluated in the presence of each inter-particle force. • It was observed that the hydrogen bond force had the most impact on the mixing.

Insight into hydrodynamics and heat transfer characteristics in a gas–solid spout fluidized bed from a multiple zone view

In this work, the hydrodynamics and heat transfer characteristics within a gas–solid spout fluidized bed were investigated from a multiple-zone view by employing the coupled computational fluid dynamic and discrete element method. Results show that both the axial and radial particle mixing rates are accelerated with the axial particle mixing rate much faster than the radial one when increasing the spouting gas velocity. Besides, the particle-scale and the multiple-zone heat transfer analyses show that the annulus zone makes the major contribution to inter-particle conduction with the particle–particle conduction and the particle–fluid-particle conduction heat fluxes taking up about 64 % and 73 %, followed by the fountain zone taking up about 28 % and 22 %, respectively. As for the particle–fluid convective heat transfer, the spouting and annulus zones make almost the comparative contributions being about 38 %, followed by the fountain zone being less than 24 %. Moreover, the full-bed time-averaged heat transfer analysis shows that the particle–fluid convective heat transfer plays a dominant role in the heat transfer process in the spout fluidized bed with the particle–particle conductive and the particle–fluid-particle conductive heat fluxes being about 0.1 % and 1 % of the particle–fluid convective heat flux. The results of this study can provide an efficient theoretical reference for the gas–solid flow-mixing-heat transfer processes optimization and intensification of spout fluidized beds.

CFD-DEM study on mixing characteristics of ZrO2 particles using the fluidized bed-chemical vapor deposition method

Fluidized bed-chemical vapor deposition (FB-CVD) is the key method to prepare low-temperature isotropic pyrolytic carbon (LTIC) for artificial heart valve. In the process of FB-CVD of pyrolytic carbon, ZrO 2 hollow particles are not only the bed particles forming the fluidized bed, but also play the role of heat carrier in the pyrolysis reaction of carbon source gas. The mixing degree of particles directly affects the coating quality of pyrolytic carbon. In this paper, a coarse-grained CFD-DEM model is used to conduct 3D numerical simulation of fluidized bed to investigate the effect of fluidization wind speed on the mixing characteristics (particle distribution, particle motion and Lacey index) of ZrO 2 hollow particles from the particle perspective. The results show that the mixing process can be accelerated by increasing the fluidization wind speed within a reasonable range, and radial mixing is more sensitive to fluidization wind speed than axial mixing. In addition, due to the different densities of particles in the furnace along the radial direction, the number of particle collisions and the influence of traction also differ greatly, resulting in more significant changes of particle velocity in the fountain area, while the velocity distribution in the annular gap area near the wall is relatively smooth.

Effect of the rotational speeds of the screw conveyor and milling roller on the behaviour of grain flows in the connected chamber of a vertical “conveying-milling” rice mill

The continuous feeding rice into a rice mill is one of the main factors affecting milling quality. Understanding the conveying mechanism of rice in the connected chamber is the key to control the feeding, however the internal mechanisms involved remain poorly understood. In this work, the discrete element method was used to simulate rice movement in a rice mill and the validity of the simulation verified by experiments. The influence of rotational speed ratio i on rice conveying effect in connected chamber was analysed. A mathematical model involving the relationship between mill parameters and conveying uniformity was established. The simulations showed that particle groups will enter continuous limited state when particles enter the entrance of milling chamber. In particular, when i was 0.5 and 0.75, the flux near the shaft is even <0. With the increase of i , the rice conveying efficiency increased, but the milling time decreased. When i was <1.25, the amount fed into the milling chamber gradually increased but then suddenly decreased when i was >1.25. The ability of the particle group breaking through the restriction of convex rib increased with i . Thus, the phenomenon of uneven conveying can occur in the conveying process and the mechanism involved is convection. The degree of axial mixing is closely related to the sweep volume difference between screw conveyor and convex rib. This study helped clarify the rice conveying mechanism and provided guidance for the design of rice mills and similar equipment. • Rice will enter a continuous limited state when they enter milling chamber entrance. • Conveying efficiency increases but milling time decreases with the increase of i. • The axial movement of rice particles is mainly inhibited by convex ribs. • Rice axial mixing is decided by swept volume difference between screw and rib.

Numerical analysis of the rice transport uniformity in vertical friction rice mill based on discrete element method

Rice milling is a crucial step to determine the final rice quality in rice processing. The uniformity of rice transportation in milling chamber is the key factor affecting the milling uniformity. Unfortunately, the cause of the uneven transport of rice in milling chamber is still poorly understood, which constrains the development of rice milling industry. In this study, the movement process of rice in vertical friction rice mill was numerically simulated by discrete element method. The macroscopic motion law of rice was obtained first and then quantified by residence time distribution (RTD). Then, the transport mechanism of rice in the milling chamber was analyzed from the kinematic perspective. Finally, a mathematical model involving the relationship between the mill parameters and the rice transport uniformity was established. The results showed that the axial dispersion of rice occurs during the transport process in milling chamber. The RTD curve indicates that the residence time of most particles in the milling chamber is short while that of a few particles is long. Besides, with the increase of rotational speed, the axial motion consistency of the particles becomes worse. The particle bulk density distribution shows that particle flow is affected by both axial backflow and radial centrifugation. There are complex convection and local vortices flow in particle vector field. In addition, the trough value and peak value of the axial velocity of the particle flow layer decrease and increase respectively with rotational speed. The swept volume method containing the structural and operating parameters of the rice mill is established. There is a strong corresponding relationship between swept volume and the uniformity of flow layer. Specifically, the larger the swept volume, the stronger the axial convective mixing, the more uneven the rice transportation. Finally, it is verified by experiments that the milling uniformity of rice mainly depends on the swept volume. The research result is of guiding significance for the design of relevant parameters of similar equipment.

Investigation of the mixing characteristics of industrial flotation columns using computational fluid dynamics

The mixing characteristics of industrial flotation columns were investigated using computational fluid dynamics (CFD). Particular emphasis was placed on the clarification of the relationship between the liquid and solids mixing parameters such as the mean residence time and axial dispersion coefficients. The effects of particle size and bubble size on liquid dispersion in the column were also studied. An Eulerian-Eulerian method was applied to simulate the multiphase flow, while additional scalar transport equations were introduced to predict the liquid residence time distribution (RTD) and particle age distribution inside the column. The results obtained show that particle residence time decreases with increasing particle size. The residence time of the coarser particles (112.5 pm) was found to be at least 60% of the liquid residence time, while the finer particles (19 pm) had a residence time similar to the liquid. The results also show that an increase in the particle size of the solids results in a decrease in the liquid vessel dispersion number, while a decrease in the bubble size increases liquid axial mixing. Finally, the simulated axial velocity profiles confirm the similarity between the liquid and solids axial dispersion coefficients in column flotation.

Particle mixing and segregation behaviors in the rotating drums with adjacent axial segmentations in different speed directions

The axial mixing and segregation behavior of particles with different properties is a complicated movement process, whose mechanism is still indistinct. Consequently, it is very important to explore dynamic repose angle and flow characteristics of the particles along the axial direction during the mixing and segregation process. Focusing on the mixing and segregation phenomenon in the rotary drum, this paper studies the particle mixing and segregation behavior by changing the speed direction of adjacent axial segmentations. The results show that alternating axial segregation band characteristics can be formed in adjacent axial segmentations with same velocity direction, while the overall mixing degree is better under the condition of the opposite velocity direction. Although the different rotational speed directions of adjacent axial segmentations will cause opposite axial mixing and segregation phenomenon, the general rules of the dynamic angle of repose and axial flow velocity are similar in the rotary drum. In addition, the axial flow structure of the binary particles varies with rotational speed direction of the adjacent axial segments, but not with the drum length to diameter (L / D) ratio and particle filling rate.

Hydrodynamic and axial mixing studies in asymmetric rotating impeller column at high dispersed to continuous phase ratios

In the present work, hydrodynamics characteristics such as dispersed phase holdup (εD), Sauter mean diameter (d32), drop size distribution (DSD), and continuous phase axial mixing was investigated in an asymmetric rotating impeller column (ARIC). Water – heavy normal paraffin (HNP) liquid system was used in ARIC to carry out the experiments. The effect of operating parameters such as impeller speed (N), superficial velocity of the continuous phase (Vc) was investigated. Experiments were performed at several dispersed to continuous phase (O/A) ratios. Volume displacement method and an image analysis technique were utilized to investigate the εD and d32, respectively. The pulse tracer technique was used to study the axial mixing in the continuous phase. The εD and d32 were strongly influenced by the impeller speed. More than 50% increase in εD was noticed when impeller speed increases from 100 to 350 rpm. The increase in dispersion coefficients (Dc) is observed with impeller speed. Whereas, it was noticed that O/A has a significant impact on Dc. About 80% decrease in Dc was observed when O/A increases from 5 to 25. The generalize equations have been developed for the prediction εD, d32, and Pec.

Prediction of particle mixing time in a rotary drum by 2D DEM simulations and cross-correlation

A new concept for the prediction of the mixing time of a large particle system from the mixing time of a small particle system and a scale-spanning cross-correlation are presented. By way of example, the considered large system is a 3D rotary drum, and the used small system is a 2D rotary drum. At both levels, data for the change in mixing degree with time are created by DEM simulation. The cross-correlation is developed from a learning set which consists of 17 sets of simulation data and represents a variation of revolution frequency. The prediction of mixing time through the cross-correlation is excellent within the parametric range of the learning set (R2 = 0.92). Beyond the parametric range of the learning set, good predictions are obtained for binary mixtures of particles with different density (R2 = 0.86), but not in case of different size. Whether the additional parameter will affect the axial mixing in the rotary drum is considered to be the key for such parameter expansion. Advantages of interpretability, expandability and relatively high accuracy for the limited data size compared to machine learning approaches are seen in the cross-correlation method, which may promote its application for the fast and cheap prediction of industrial mixers.

Solids lateral mixing and compartmentalization in dynamically structured gas–solid fluidized beds

An adequate use of gas pulsation can create an ordered, dynamically structured bubble flow in a bed of Geldart B particles. A structured bed is more homogeneous, responds to external control and is scalable. While earlier studies have focused on describing the self-organization of the gas bubbles, the solid mixing and gas–solid contact patterns have remained unclear. In this work, the solids circulation and mixing behavior in structured and unstructured beds at various pulsation frequencies are compared with a traditional fluidized bed operation. The degree of lateral mixing is hereby quantified through an effective lateral dispersion coefficient extracted from CFD-DEM (discrete element modelling) simulations in a thin fluidized bed system. Mixing shows major quantitative and qualitative differences amongst the investigated cases. The coordinated motion of the gas bubbles wraps the solid flow into a series of compartments with minimal interaction, whereby effective lateral dispersion coefficients are an order of magnitude lower than in an unstructured operation. More importantly, unlike a traditional bed, dispersion in a structured bed is driven by advection and is no longer a diffusive process. Compartmentalization decouples the time scales of micro- and macromixing. Every pulse, the compartments rearrange dynamically, causing a level of local axial mixing that is scale-independent. While further work is necessary to fully understand the compartmentalization at a larger scale, the circulation described here indicates that a dynamically structured bed can provide a tight control of mixing at low gas velocities and a narrower distribution of stresses in the solid phase compared to traditional devices.

A cell-based PBM for continuous open-circuit dry milling: Impact of axial mixing, nonlinear breakage, and screen size

This theoretical study examined the impact of the degree of mixing, nonlinear particle breakage, and screen opening size on the particle size distribution (PSD) and mass hold-up in continuous dry mills with internal classification. A cell-based population balance model (PBM) incorporating a non-ideal screen model was formulated, wherein the back-mixing ratio and number of cells modulated the extent of axial mixing. The set of differential–algebraic equations (DAEs) was solved for the spatio-temporal evolution of the PSD in the mill and the product stream. The simulation results suggest that a smaller screen opening delayed the attainment of the steady state, increased the hold-up, and yielded a finer product PSD. The cushioning action of fines resulted in a coarser product PSD; however, a screen with a smaller opening mitigated this effect. The cell-based PBM predicted various features of experimental milling observations while providing insights into the mixing–nonlinear breakage–classification interplay.

Numerical Simulation of Low-Pressure Drop Static Mixers for Mixing Enhancement

Static mixers (SM), also generally known as inline mixers, form a newly developing industry trend. They have no moving parts, hence have lower energy consumption, lower installation cost, and very low maintenance cost, and are thus an attractive alternative to the conventional agitators. Modifications were made in the design to reduce pressure drop and increase the mixing intensity across the mixer and increase the application of inline mixers in the industries. Three hybrid geometries (different combinations of Kenics and LPD) of static mixers were constructed and simulated using computational fluid dynamics (CFD) tools. Kenics is an excellent radial mixing device, and low-pressure drop (LPD) an excellent axial mixing device. The key design parameter to modify LPD was the slope angle of elliptical plates which affects the mixer performance. Different slope angles from 90o to 120o were simulated. Kenics was modified for different aspect ratios, and the edge of Kenics was curved. Pressure drop, thermal, and Discrete Phase Model (DPM) analysis were performed on these three different classifications of hybrid geometries. The most promising geometry to emerge based on the low-pressure drop and good mixing efficiency both was the curved edge Kenics. Keen-sighted these results, further analysis was performed on curved edge Kenics after the modification of blend radius. It was concluded that for a lower Reynold number, the curved edge with a higher blend radius dominates all other mixers. Result validation was done by comparing the trends and sensitivity of process variables with the established results and standards.

Numerical Simulation of Fluid Flow and Mixing Dynamics inside Planetary Roller Extruders

Abstract In this contribution, the fluid flow and mixing dynamics inside planetary roller extruders are simulated using the finite element method (FEM) and the mesh superposition technique (MST). Three-dimensional configurations with planetary spindles of varying number and geometry of planetary spindles were created to analyse the influence of the spindle configuration and the rotational speed on the process behavior. Therefore, pressure gradients, flow velocities and directions, shear rates, the mixing index and residence time distributions were evaluated. The distributive and dispersive mixing efficiencies varied depending on the planetary spindle configuration, and these configurations thus suit different processing tasks. In comparison to the standard planetary spindles, the TT3 spindles, with their incomplete toothing, and the knob spindles, with their double transversal helical toothing, showed intense axial and radial mixing. In general, the mixing performance of the planetary roller extruder is explained by a high rate of extensional flow and frequent changes in flow type. The reported numerical approach allows, for the first time, a comprehensive observation of the process behavior of planetary roller extruders.

DEM study on identification of mixing mechanisms in a pot blender

A pot blender with both blending and storage capabilities offers an advantage over a conventional rotating drum. However, the mixing mechanism of the pot blender is extremely complicated because the pot blender rotates and swings simultaneously. Owing to the lack of systematic investigations, the mixing mechanism of the pot blender has not been fully elucidated. In this study, we clarify the mixing mechanism of the pot blender by using the discrete element method. Simulation results reveal that the main mixing mechanism is convective mixing in the rotational direction and shear mixing in the axial direction. Moreover, the mixing performance is unaffected by particle density, whereas the velocity gradient in the axial direction, which mainly determines the axial mixing performance, is affected by the particle filling ratio. Considering the relationship between the variance of axial particle velocity and granular temperature, the filling ratio is shown to significantly influence the mixing efficiency in the pot blender. In addition, the dependency of shear and diffusive mixing on Lacey’s mixing index in the pot blender is newly clarified. Consequently, this study demonstrates essential insights into the mixing mechanism of the pot blender and the pot blender as an effective industrial mixer.

Influence of Buoyancy Effects on the Mixing Process and RTD in a Side-Injection Reactor Equipped with Static Mixers

The mixing process and the residence time distribution (RTD) of molecules inside reactors are well-known topics in chemical engineering; good radial mixing and poor axial mixing of chemical species...

Estimation of Rate Constants and Mixing Characteristics in Flotation Columns

The effect of mixing in a flotation column has long been recognized as an important factor in determining the performance of flotation. The paper presents the effects of mixing on the rate constant in a flotation column, and the establishment of relationships based on vessel dispersion numbers (Nd) that can describe axial dispersion. The rate constants were evaluated using models of plug flow, fully mixed tanks, and axial mixing for a coal cleaning operation. Results showed that fine particles are similar between each model; however, for coarse particles, the deviation is large in the case of perfect mixing, while axial mixing is suitable. It reveals the suitability of using an axial dispersion model for estimating the rate constants, particularly for coarser particles. A regression equation to determine the flotation rate constant was also developed with Nd values between 0.2 to 0.5. The ratio of particles to liquid the residence times time (τp/τL) decreases with particle size from small sizes to coarser sizes. Axial dispersion is increased by the superficial gas velocity while is suppressed by the wash water. The relationship between calculated and observed Nd can be used with a 94% accuracy for the coal cleaning application within the range of operating conditions of superficial gas velocity (0.7–1.6 cm/s), superficial wash water velocity (0.1–0.4 cm/s), and Hc/dc (26.8–32.7). The empirical relationship of Nd with significant variables along with the aspect ratio of the column was found to be applicable for coal beneficiation. It may be useful in terms of design and scale up of the columns.

The influence of longitudinal dispersion on the capacity and stability of UASB operation with substrate inhibition

A volumetric dispersion model (VDM) with inhibitory kinetics was proposed to describe the biogas production from the acetolastic methanogenesis of the acetate medium process in modeling aspects of the operating capacity and stability. The influence of axial mixing promoted by ultrasonic disruption had been investigated during the methane conversion under a progressive inhibition of substrate in the up-flow anaerobic sludge blanket (UASB) reactor. Increasing the organic loading rates was conducted for the model calibration and prediction to indicate when the process instability occurs due to a potent inhibition and suggest a proper axial mixing. For this simplified substrate characteristics investigation with controlled hydraulic retention time, the results showed that the flow and transfer system with a Peclet number of 1.254 could prevent the system failure. The process instability due to a potent inhibition could be manipulated by using suitable axial mixing to eliminate the inhibitory effect within the reactor.

Dry Powder Mixing Is Feasible in Continuous Twin Screw Extruder: Towards Lean Extrusion Process for Oral Solid Dosage Manufacturing.

Using discrete element method (DEM) modeling and near-infrared (NIR) spectroscopy, the feasibility of powder mixing in the initial pre-melting zones of a twin screw extruder using two independent feeders was studied. Previous work in the pharmaceutical and food industry has focused on mixing when materials are melted or on material homogeneity at the extruder's output. Depending on the formulation, ensuring a fully blended formulation prior to melting may be desired. Experiments were conducted using a Coperion ZSK-18 extruder to evaluate if blend uniformity can be achieved by exploring screw configuration, screw speed, and powder feed rate. As powder exited the extruder and deposited on a conveyor belt, an in-line NIR spectrophotometer measured spectra of material. Chemometric-based models predicted unknown concentrations to evaluate if blend uniformity was achieved. Using the EDEM software, Hertz-Mindlin contact model, and dimensions of the extruder, DEM simulations complemented the experimental work. The DEM computational models provided understanding of mixing patterns inside the extruder at particle scale and helped select the screw configuration before doing experimentation. The simulations showed good axial mixing for all the screw configurations studied, while good cross (radial) mixing was only observed for the screw configuration with 90-degree kneading elements. Therefore, the screw configuration with two 90-degree kneading elements was chosen for the experimental study. The RTD profiles when using a screw configuration with only conveying screw elements are comparable to a plug flow reactor (PFR), while the profiles when using kneading elements are more comparable to an ideal continuous stirred tank reactor (CSTR). For the screw configuration with 90 degrees kneading elements, the mean residence time (MRT) decreases with an increase in the screw speed. Experimental NIR spectra showed that concentrations can be predicted with an error of 2%. It was demonstrated that the twin screw extruder can provide proper dry powder mixing of two powder feed streams based on a unit dose scale, enabling continuous powder mixing prior to the melting zone in the extruder for the formulation studied with a cohesive API. This setup may also work for other types of formulations. These studies can help in developing lean hot melt as well as wet extrusion/granulation processes using twin screw extruders for the continuous manufacturing of oral solid dosage products.