Macroscopic Flow Structure Research Articles

Eulerian and Lagrangian analyses of entrainment in non-circular orifice impinging jets

In this work, the entrainment characteristics of two different non-circular orifice impinging jets, i.e., elliptical and square orifices, are studied against the circular one. These three orifice jets at the same impinging-distance-to-diameter H/De = 3.0 and the Reynolds number (Re) at 1.6 × 103 were measured by time-resolved tomographic particle image velocimetry. The macroscopic flow structures and local characteristics are discussed in terms of Eulerian and Lagrangian perspectives, respectively. For both the streamwise velocity and the finite-time Lyapunov exponent (FTLE) field, the power spectral density exhibits a significant Strouhal number component St = 0.53 in all three jets, whereas the square orifice jet shows multiple frequency peaks. Observing the large-scale vortical structures of the instantaneous flow field indicates that the up-warping part of the elliptical and square vortex rings as well as the square vortex pairing and merging behavior will substantially enhance the local entrainment. As for the FTLE field, both non-circular orifice impinging jets tend to form the wider entrainment channel as well as more prominent shear along the local turbulent/non-turbulent interface. The entrainment statistics based on the enstrophy supports the above findings. As the fluid flows from the orifice, the entrainment rate of the elliptical orifice jet in the development region first grows slower but overtakes the circular one after H/De > 1.5; the square jet has the lowest entrainment and growth rate upstream, while the largest entrainment growth rate is reached at H/De > 1.5, where the large-scale structures are formed. Near the impingement region, the elliptical orifice jet has the largest entrainment rate and then the square orifice.

Macroscopic flame and flow structures in hydrogen and methane multi-regime combustion

The current experimental investigation focuses on the macroscopic structures of CH4/air and H2/air flames operated on the Darmstadt multi-regime burner adapted for hydrogen operation. Building upon previous research on lean-burn limits, this study utilizes simultaneous PIV and OH-PLIF measurements to examine notable differences in flame and flow structures. Six flame cases are studied, focusing on CH4/air and H2/air jet flames at equivalence ratios of 1.4, 2.2, and 3.5. It is observed that the hydrogen slot 2 flames exhibit unique behavior under ultra-lean conditions, demonstrating thermodiffusive effects that generate finger-like structures. Despite receiving less thermal support from the slot 2 flame, hydrogen jet flames burn faster and resist flame extinction in high-velocity regions. The extensive heat release from fuel-rich H2 jets maintains a stable location compared to CH4 jets at the same equivalence ratio, altering local flow dynamics. Additionally, the study identifies a reshaped primary inner recirculation zone (IRZ) and a secondary IRZ in H2/air flame cases, which is absent in CH4 flames. The interplay between the jet flame and the primary IRZ results in visible flame enhancement in slot 2, indicating preheating and fuel enrichment effects. Overall, this research provides comprehensive insights into the distinct combustion behavior and flow structures of CH4 and H2 flames on a multi-regime burner.

Prediction of Cavitation Evolution and Cavitation Erosion on Centrifugal Pump Blades by the DCM-RNG Method.

Cavitation can reduce the efficiency and service life of the centrifugal pumps, and a long-term operation under cavitation conditions will cause cavitation damage on the surface of material. The external characteristic test of the IS65-50-174 single-stage centrifugal pump was carried out. Moreover, the cavitation mechanism under specific conditions was analyzed by numerical simulation. Considering the macroscopic cavitation flow structure in the centrifugal pump, three different cavitation erosion prediction methods were used to predict the erodible areas. The results show that the calculation results obtained by the density correction method (DCM) can well match the flow characteristics of the centrifugal pump under the rated conditions. When the centrifugal pump head drops by 3%, cavitation mainly occurs on the suction surface, and the cavity on the pressure surface is mainly concentrated near the front cover. The cavitation prediction method based on the time derivation of pressure change is not suitable for centrifugal pumps, while the prediction result of the erosive power method is more reasonable than the others. At time 0.493114 s, the maximum erosive power appears on the blade near the volute tongue, and its value is 1.46e − 04 W.

Novel evaluation method to determine the local mixing time distribution in stirred tank reactors

Stirred tank reactors are frequently used for mixing as well as heat- and mass transfer processes in chemical and biochemical engineering due to their robust operation and extensive experiences in the past. However, for cell culture processes like mammalian cell expression systems, special requirements have to be met to ensure optimal cell growth and product quality. One of the most important requirements to ensure ideal transport processes is a proper mixing performance, characterized typically by the global mixing time tmix,global or the dimensionless global mixing time tmix,global·n. As an evaluation method for mixing time determination, the time is usually determined until a tracer signal (e.g. conductivity) has reached a constant value after a peak has been introduced (e.g. by adding a salt). A disadvantage of this method is, that the position of tracer feeding as well as the position of the probe significantly influences the detected mixing time. Further on, the global mixing time does not provide any information about the spatial and temporal ”history” of the mixing process to identify areas that are mixed poorly or areas that form stable compartments. To overcome this disadvantage, a novel image analysis will be presented in this study for the detailed characterization of mixing processes by taking into account the history of mixing. The method is based on the experimental determination of the local mixing time distribution by using a multi-color change caused by a pH-change in a bromothymol blue solution. A 3L transparent stirred tank reactor is used for the benchmark experiment. To demonstrate the suitability of the new characterization method for the validation of numerical simulations, a calculation with a commercial Lattice-Boltzmann approach (M-Star CFD) has been performed additionally and evaluated regarding mixing time distributions. The exemplary application of image analysis to a numerical mixing time simulation shows good agreement with the corresponding experiment. On the one hand, this shows that the method can also be interesting for numerical work, especially for experimental validation, and on the other hand, this allows much deeper insights into the mixing behavior compared to conventional mixing criteria. For example the new method enables the characterization of mixing on different scales as well as the identification of micro- and macroscopic flow structures. The strong influence of the acid to base ratio on mixing time experiments becomes clearly visible with the new method.

Processing-Structure-Performance Relationships of Microporous Metal-Organic Polymers for Size-Selective Separations.

Small-molecule impurities, such as N-nitrosodimethylamine (NDMA), have infiltrated the generic drug industry, leading to recalls in commonly prescribed blood pressure and stomach drugs in over 43 countries since 2018 and directly affecting tens of millions of patients. One promising strategy to remove small-molecule impurities like NDMA from drug molecules is by size exclusion, in which the contaminant is removed by selective adsorption onto a (micro)porous material due to its smaller size. However, current solution-phase size-exclusion separations are primarily limited by the throughput-selectivity trade-off. Here, we report a bioinspired solution to conquer these critical challenges by leveraging the assembly of atomically precise building blocks into hierarchically porous structures. We introduce a bottom-up approach to form micropores, mesopores, and macroscopic superstructures simultaneously using functionalized oxozirconium clusters as building blocks. Further, we leverage recent advances in photopolymerization to design macroscopic flow structures to mitigate backpressure. Based on these multiscale design principles, we engineer simple, inexpensive devices that are able to separate NDMA from contaminated drugs. Beyond this urgent model system, we expect this design strategy to open up hitherto unexplored avenues of nanomaterial superstructure fabrication for a range of size-exclusion purification strategies.

Global characterization of hydrodynamics and gas-liquid mass transfer in a thin-gap bubble column intended for microalgae cultivation

Global characterization of hydrodynamics and gas-liquid transfer in a 2D column with a 4mm thickness is carried out with water and aqueous glycerol solutions. This new design can be used as a photobioreactor of low thickness to intensify the volumetric productivity by increasing microalgae concentration. To mimic the presence of algae cultures, the liquid viscosity is adjusted with glycerol. Focuses are made on flow regimes and their transitions, mixing, and gas-liquid transfer at the scale of the reactor. In comparison with conventional bubble columns lower terminal velocities are obtained. So, in homogeneous regime, the residence time of bubbles is greater than in conventional bubble columns and the gas holdup is slightly higher. However, regime transitions appear at relatively low superficial gas velocities in the confined bubble column. In addition, two transition regimes are visible and have macroscopic flow structures very similar to the ones observed for conventional columns. For the mixing time, a dependence on the viscosity is observed and whatever the solution tested, this parameter decreases very quickly with the increase of the gas superficial velocity. Finally, global gas-liquid mass transfer coefficients measurements show lower values than in classical bubble columns at the same superficial gas velocity.

Experimental investigations of turbulent fragmenting stresses in a rotor-stator mixer. Part 1. Estimation of turbulent stresses and comparison to breakup visualizations

Despite large industrial relevance, the relation between rotor-stator geometry, hydrodynamics and drop breakup is poorly understood, partly since no methods for measuring the fragmenting stresses acting on drops have been established. This study attempts to bridge this gap by developing, applying and evaluating two approaches for estimating local turbulent stresses based on particle image velocimetry data: namely one traditional but indirect approach based on the dissipation rate of turbulent kinetic energy, and another more direct approach based on the spatial turbulent spectrum that has proven useful in other high-intensity emulsification processing. The approaches are evaluated in terms of validity of underlying assumptions, how they compare to breakup visualizations in the same geometry and with regard to the reliability of primary measurables.Results show three consistent regions of high stress in the rotor-stator region: in a plume extending into the stator-hole from the trailing edge, in the shear layers of the jet exiting the hole and in the macroscopic flow structure formed after the rotor blocks a stator hole. Following a drop travelling along an average velocity flow field, the measurement predict disrupting stresses exceeding the stabilizing stress at the stator hole exit, at approximately the same position where drop breakup is observed in breakup visualizations. Both methods are therefore able to predict the most likely breakup positions. It is also concluded that both methods have limitations, and that average stress alone cannot describe all aspects of the fragmentation process in rotor-stator mixers.

Determination of the entropy radial minimum and the various transition velocities in an air-water bubble column

The bubble column hydrodynamics are complex and the macroscopic flow structure is different in the column core and annulus due to both the bubble coalescence and breakup phenomena as well as the gross liquid circulation. In this work, for the first time the local Kolmogorov entropy (KE) minima at different superficial gas velocities Ug were identified. It was found that there is an agreement between the local KE minima (occurring around r/R=0.63) and the inversion point (dimensionless radius=0.7) for the axial liquid velocity reported by both Chen et al. (1994) and Wu and Al-Dahhan (2001).The KE radial profiles were also used to prove the existence of chaotic similarities between the flow patterns in the bubble bed at three different Ug values (0.089, 0.134 and 0.146m/s) belonging to the heterogeneous regime. This finding implies that the flow patterns and the degrees of turbulence at these Ug values are also identical. The same similarity was also found between the KE profiles at Ug=0.056 and 0.067m/s, which belong to the transition flow regime. These results imply that the flow patterns in the bubble bed repeat (especially at different Ug values falling into the same flow regime).Based on the KE profiles as a function of Ug, the effect of the dimensionless radial position on the various transition velocities was studied. It was found that the end of the gas maldistribution regime is shifted to slightly higher Ug value in column core and annulus. In most of the cases, the onset of the churn-turbulent regime occurs at Ug=0.101m/s.

Effects of Hydrogen Fuel Injection in a Mach 12 Scramjet Inlet

To investigate the potential benefits of hydrogen fuel injection in a three-dimensional scramjet inlet, flow through a Mach 12 rectangular-to-elliptical shape transitioning scramjet inlet was simulated with and without hydrogen fuel injection along its body-side compression surface. The observed flowfields showed that, at an equivalence ratio of 0.33, the fuel cannot escape the body-side boundary layer, having little effect on macroscopic inlet flow structures. Interaction with the surrounding boundary-layer turbulence causes robust mixing of the fuel in the inlet. Fuel radicals are produced immediately following injection, particularly where the fuel plumes interact with thin, hot hypersonic boundary layers sweeping inward from the inlet side walls. Combustion does not proceed until the inlet compression process is nearly complete due to low static pressures in the inlet. Once the well-mixed fuel is processed by the final inlet compression shock, ignition and combustion occurs rapidly in the nearly constant cross-section region just upstream of the throat. The net drag increase observed was less than 5%. This modest increase was primarily due to the fuel-injection process, with almost no additional drag due to fuel combustion. Similar flow structures in other inlets suggest they would benefit from inlet fuel injection.

Embedded Detail Microscopic Models of Rooms within Macroscopic Models of Whole Building Systems

Established methods of computational fluid dynamics (CFD) have been applied to predict the details of airflow, contaminant dispersal and thermal transport within isolated zones, yet zone transport processes do not occur in isolation. They result from and interact with the bulk airflows from the larger whole-building systems in which they are embedded. As multi-zone models can reliably predict these bulk airflows, there is a growing interest in embedding detailed CFD models of specific zones within multi-zone models of the enclosing whole-building system to more faithfully account for these interactions and thus the details within the zone(s) of interest.This paper presents an analysis of an embedded CFD model and outlines some of the associated problems. A formulation is presented using unambiguous mathematical definitions of the coupling relations between the governing CFD and multi-zone equations made possible by using a port-plane approach to the multi-zone model. It is thereby shown that while the micro-to-macro coupling is straightforward, macro-to-micro coupling must remain indeterminate due to the fact that multi-zone models do not account for non-normal airflows to zone port-planes or for turbulent characteristics of the airflow that may be used by the embedded CFD model. The formulation of the embedded detail problem considered herein leads to the direct mathematical coupling of the semi-discrete Finite Element form of the CFD models used in the nonlinear algebraic enclosing multi-zone models. To investigate the limitations of embedded detail analysis the approach taken was applied to a hypothetical test problem configured to be sensitive to one obvious shortcoming of multi-zone models - their inability to account for non-normal inflow velocity components - and one less obvious shortcoming of CFD models - their tendency to model flow resistance differently and thus incompatibly with multi-zone models. The results indicated that these two shortcomings alone may critically limit the value of embedded detail analysis. Specifically, it appears that embedded detail analysis can not, in general, be expected to faithfully model flow detail in the CFD embedded zone nor model the larger macroscopic bulk flow structure correctly - even though these objectives may well be realized in special cases.Additional research is clearly needed to identify the special cases when embedded detailed analysis may be expected to be reliable. As such this paper should be of interest to not only the specialist in this emerging field, but to those seeking to employ or to fund research using these methods.

Hydrodynamics of a liquid–solid circulating fluidized bed: Effect of dynamic leak

Abstract Experiments were conducted in a liquid–solid circulating fluidized bed (LSCFB) of 80 mm i.d. and 2.8 m high to study the macroscopic flow structure over a wide range of liquid velocity and solids inventory in the storage vessel. The results indicate that the valve configuration (i.e. lift pot and the angle made by the solids feed pipe with the riser), solids inventory in the storage vessel and location of the primary liquid distributor were found to play an important role on the macroscopic properties of LSCFB. Dynamic leak, flow of solids from the return leg into the riser in the absence of auxiliary liquid flow, has been noticed at very high liquid velocities when the primary liquid distributor inlet (positioned at the bottom of the riser) is near to the solids feed pipe from the storage vessel. The dynamic leak was prevented by changing the position of the primary distributor inlet and the macroscopic flow behavior with and without dynamic leak was compared. The transitional liquid velocity that demarcates the conventional fluidization from the circulating fluidization was determined by three different methods and was found to be independent of solids inventory and dynamic leak.

Analysis of the chaotic dynamics of a high-flux CFB riser using solids concentration measurements

A high-flux circulating fluidized bed (CFB) riser (0.076-m I.D. and 10-m high) was operated in a wide range of operating conditions to study its chaotic dynamics, using FCC catalyst particles ( d p = 67 μm, ρ p = 1500 kg·m −3). Local solids concentration fluctuations measured using a reflective-type fiber optic probe were processed to determine chaotic invariants (Kolmogorov entropy and correlation dimension). Radial and axial profiles of the chaotic invariants at different operating conditions show that the core region exhibits higher values of the chaotic invariants than the wall region. Both invariants vary strongly with local mean solids concentration. The transition section of the riser exhibits more complex dynamics while the bottom and top sections exhibit a more uniform macroscopic and less-complex microscopic flow structure. Increasing gas velocity leads to more complex and less predictable solids concentration fluctuations, while increasing solids flux generally lowers complexity and increases predictability. Very high solids flux, however, was observed to increase the entropy.

Rheomorphic structures in a high-grade ignimbrite: the Nuraxi tuff, Sulcis volcanic district (SW Sardinia, Italy)

Deposits of the 15.8 Ma Nuraxi explosive eruption crop out in the Sulcis volcanic district, southwestern Sardinia. They consist of a decimeter-thick pumice fallout layer overlain, with no apparent temporal break, by several tens of meters thick, high-grade ignimbrite. The eruption was from a vent probably located ∼20–30 km north of S. Pietro island, and it tapped a compositionally uniform, rhyolite magma reservoir (SiO 2 70–72 wt.%) bearing about 20 vol.% crystals. The ignimbrite consists of: (a) a Lower Ignimbrite (LI), <2-m-thick, fine-grained and glassy grading upward into a partly devitrified lapilli-tuff, and (b) an Upper Ignimbrite (UI) that is an intensely welded to lava-like lapilli-tuff. The deposit has an inferred maximum runout of about 80 km and overall dispersal/thickness characteristic of a low aspect-ratio ignimbrite. Over most of its outcrop the tuff rests on a flat, horizontal paleosurface and forms an ignimbrite plateau with uniform thickness and structural characteristics. However, in some areas it shows extensive folding and over-thickening as a result of rheomorphic flow into topographic depressions. Structural analysis of the ignimbrite reveals the presence of a pervasive foliation and lineation as well as macroscopic and microscopic flow structures. Occurrence of abundant, widely distributed stretched cavities in the tuff indicates that a substantial amount of gas was trapped in the tuff during aggradation. The observed pattern of structures of the ignimbrite plateau accords well with a conceptual model in which syn-depositional structures are formed during non-particulate, basal laminar flow due to agglutination of juvenile particles within the lower part of the pyroclastic density current. The flow was controlled by the substantial transfer of momentum from the high-speed, particulate upper part of the current to the top of the non-particulate part of the current and the onset of a complex relationship between welding, flow and sedimentation processes. It is proposed in particular that elongated gas pockets played a major role in guiding the laminar shear within the non-particulate part of the current in flat, horizontal areas, eventually promoting brittle failure of the deforming tuff mass along shear planes.

Nonlinear Dynamic Analysis of the Local Heat Transfer Rate in Three-Phase Reactors

In this present work, nonlinear dynamic analysis was performed to the fluctuation signals of the local heat transfer rate measured in three-phase reactors of different scales to characterize the dynamics of three-phase reactors. The results of nonlinear test with surrogate data give evidence of nonlinear determinism in heat transfer rates series. The chaotic nature of the local heat transfer rate was further characterized in terms of the correlation dimension and Kolmogorov entropy. It was found that the correlation dimensions were in the range between 2.0 and 4.0 and Kolmogorov entropies were varied with the change of measurement positions and the operating conditions. With the increase of column scale or the addition of solids, Kolmogorov entropies decrease significantly. The dependence of chaotic parameters on the column scale is considered to be closely related to the different macroscopic flow structures observed in three-phase reactors of different scales.

Measurement of Velocity Field in Thermal Turbulence in Mercury by Ultrasonic Doppler Method

With the use of the ultrasonic velocimetry, we measured the velocity profiles in thermal turbulence in mercury. The measurement, which is different from the traditional measurement of time series of the local velocity, has brought about some intriguing results. We observed the inversion of the flow direction near the boundary plate, which seems the appearance of the velocity boundary layer. We also elucidated the nature of the fluctuation in thermal turbulence through the principal component analysis. The macroscopic flow structure and its vertical movement were observed. In addition, the energy spectrum and the velocity structure functions were calculated without employing Taylor’s frozen-flow hypothesis for the first time in thermal turbulence, which appeared to be consistent with the Bolgiano-Obukhov theory.

Local Bubble Dynamics and Macroscopic Flow Structure in Bubble Columns with Different Scales

AbstractLocal bubble behaviours were investigated in three bubble columns with different diameters of 200, 400 and 800 mm. By means of a novel single‐tip optical fibre probe employing laser Doppler technique, the local gas holdup, bubble frequency, bubble size and velocity were measured simultaneously at different locations of the columns. Measurements were performed in air‐water system at superficial gas velocities up to 90 mm/s. The averaged profiles and instantaneous measurements were analyzed and compared for different columns. The presence of a coherent gross circulation structure spanning the entire column diameter in the larger column rather than a pair of symmetrical circulation cells observed in the smaller columns has been confirmed.

Rheology of Granitic Magmas During Ascent and Emplacement

▪ Abstract Considerable progress has been made over the past decade in understanding the static rheological properties of granitic magmas in the continental crust. Changes in H2O content, CO2 content, and oxidation state of the interstitial melt phase have been identified as important compositional factors governing the rheodynamic behavior of the solid/fluid mixture. Although the strengths of granitic magmas over the crystallization interval are still poorly constrained, theoretical investigations suggest that during magma ascent, yield strengths of the order of 9 kPa are required to completely retard the upward flow in meter-wide conduits. In low Bagnold number magma suspensions with moderate crystal contents (solidosities 0.1 ≤ φ ≤ 0.3), viscous fluctuations may lead to flow differentiation by shear-enhanced diffusion. AMS and microstructural studies support the idea that granite plutons are intruded as crystal-poor liquids (φ ≤ 50%), with fabric and foliation development restricted to the final stages of emplacement. If so, then these fabrics contain no information on the ascent (vertical transport) history of the magma. Deformation of a magmatic mush during pluton emplacement can enhance significantly the pressure gradient in the melt, resulting in a range of local macroscopic flow structures, including layering, crystal alignment, and other mechanical instabilities such as shear zones. As the suspension viscosity varies with stress rate, it is not clear how the timing of proposed rheological transitions formulated from simple equations for static magma suspensions applies to mixtures undergoing shear. New theories of magmas as multiphase flows are required if the full complexity of granitic magma rheology is to be resolved.

Scale-up effects on the time-averaged and dynamic behavior in bubble column reactors

Scale-up effects on the dynamic and time-averaged behavior are investigated in bubble columns with diameters of 200, 400 and 800 mm , respectively. Using a hot-wire probe, the local instantaneous heat transfer rates and the local time-averaged gas holdups were measured at the different locations of the columns over the gas velocity range from 20 to 90 mm/ s . The dyanamic behavior of local heat transfer was characterized by frequency domain and state-space analysis in terms of power spectrum, correlation dimension and Kolmogorov entropy. The power spectra of heat transfer rate fluctuations were found to be insensitive to the bubble column size. The state-space analysis indicates that heat transfer rate exhibits a chaotic behavior with the correlation dimension varying from 2.0 to 3.0. No significant effect of column size on the correlation dimension was observed, whereas the Kolmogorov entropies are apparently dependent on the column diameter. With the increase in column diameter, Kolmogorov entropy decreases significantly and exhibits rather flat radial distribution in the large-scale column. With respect to the time-averaged behavior of local gas holdup, the effects of column size on the radial distribution of gas holdup was examined. It was found that the 800 mm column exhibited a relatively uniform distribution of gas holdup. The dependence of both dynamic and time-averaged behavior on the column scale is considered to be closely related to the different macroscopic flow structure, which is a function of the scale of the column.

三相系における粒子及び気泡濃度分布測定用の超音波ＣＴ法

An ultrasonic computed tomography (UCT) developed for measuring time-averaged cross-sectional distributions of gas and solid concentrations in three-phase flow is described. The ultrasonic computed tomography is a coupling of a transmission mode ultrasonic sensor developed in Department of Chemical Engineering, Shizuoka University and a tomographic reconstruction technique based on dynamic neural network optimization algorithm developed in Department of Chemical Engineering, The Ohio State University. The ultrasonic sensor is based on measurements of the energy attenuation and the velocity change of ultrasonic pulse waves transmitted through the three-phase medium, enabling the measurements of the gas and the solid concentrations in the system simultaneously. The tomographic reconstruction technique has been proven to reconstruct simulated tomographic data accurately even with a very small number of projection data as used in the measurement. The application of the technique to a water-air-particles flow system in a bubble column is described.Glass-beads with diameters of 100, 260 and 350 micron meters are used as the solid phase. The time-averaged macroscopic flow structure and the behavior of the gas bubbles and solid particles distributions are investigated. The effects of gas velocity, solid loading and particle diameter to the behaviors of bubbles and particles distributions in the three-phase system are also discussed.

Flow Characteristics of Coal Ash in a Circulating Fluidized Bed

Solids flow characteristics of coal ash are investigated with the measurement of the local solids flux, local solids concentration, and spatial distribution of particle size. Two sets of the solids sampling probe are used to quantify the local solids flux at different radial and axial locations. The macroscopic flow structure is presented by analyzing the radial profiles of solids flux and the local particle size distributions, while the mesoscale flow structure is illustrated on the basis of probability density function of instantaneous solids concentration, the intermittency index, and the cluster frequency. It is found that both macroscopic and mesoscopic structures of gas−solid flow of coal ash are different from those of commonly studied fluid catalytic cracking and sand particles. The differences include higher upward and downward solids fluxes in the lower dense region, significant particle segregation, and more uniform annular flow. Furthermore, a semiempirical model taking into consideration the ...