DEM investigation of mixing indices in a ribbon mixer

Mixing index is an important parameter to understand and assess the mixing state in various mixers including ribbon mixers, the typical food processing devices. Many mixing indices based on either sample variance methods or non-sample variance methods have been proposed and used in the past, however, they were not well compared in the literature to evaluate their accuracy of assessing the final mixing state. In this study, discrete element method (DEM) modelling is used to investigate and compare the accuracy of these mixing indices for mixing of uniform particles in a horizontal cylindrical ribbon mixer. The sample variance methods for mixing indices are first compared both at particle- and macro-scale levels. In addition, non-sample variance methods, namely entropy and non-sampling indices are compared against the results from the sample variance methods. The simulation results indicate that, among the indices considered in this study, Lacey index shows the most accurate results. The Lacey index is regarded to be the most suitable mixing index to evaluate the steady-state mixing state of the ribbon mixer in the real-time (or without stopping the impeller) at both the particle- and macro-scale levels. The study is useful for the selection of a proper mixing index for a specific mixture in a given mixer.     

超音速混合层稳定性分析及增强混合的研究

利用流动稳定性提高超音速混合层的混合效率,对于提高超音速流的高效混合是一个有效途径。研究结果表明,有展向曲率的三维混合层中,三维扰动的增长率很大,且法向的掺混能力也较强,可以有效地增强混合。对于高马赫数来流的超音速混合层,这一特性依然存在,这将有利于提高高超音速混合层的混合能力。     

Influence of a combustion-driven oscillation on global mixing in the flame from a refinery flare

An assessment of the influence of strong combustion-driven oscillations on mixing rates and visible radiation in the flame from a full-scale refinery flare is reported. Importantly, the oscillations were generated naturally, with no external forcing, and at a high Reynolds number of 4 × 10⁶. These conditions differentiate this study from those of previous investigations, which all involved some external forcing and were at a Re too low to ensure fully turbulent flow within the flame. A frame-by-frame analysis of video footage, providing good resolution of the instantaneous edge of each flame, was used to assess flame dimensions, and so to determine a global residence time. Since the flames are in the fast-chemistry regime, the visual imagers can be used to determine a global mixing rate. The analysis reveals a consistent picture that the combustion-driven oscillations do not result in a significant change to the global mixing rate, but do increase the visible radiation. This is in contrast to previous investigations, using externally forced jets, where forcing at the preferred mode has been found to increase mixing rates and reduce radiation.     

Analysis of Experiments on Determining the Turbulent Mixing Constant on the Basis of Two-Dimensional Calculations

Based on numerical calculations, the experiments on mixing at the interface of gases are analyzed. Single-mode and random disturbances of the interface and superposition of random disturbances onto long-wave perturbations are considered. Possible reasons for the higher value of the mixing constant obtained in the experiments are discussed.     

Study of the membrane effect on turbulent mixing measurements in shock tubes

The effect of the thin membrane on the time evolution of the shock wave induced turbulent mixing between the two gases initially separated by it is investigated using two different sets of experiments. In the first set, in which a single-mode large-amplitude initial perturbation was studied, two gas combinations (air/SF and air/air) and two membrane thicknesses were used. The main conclusion of these experiments was that the tested membrane has a negligible effect on the evolution of the mixing zone, which evolves as predicted theoretically. In the second set, in which similar gas combinations and membrane thicknesses were used, small amplitude random-mode initial perturbation, caused by the membrane rupture, rather than the large amplitude single-mode initial perturbation used in the first set, was studied. The conclusions of these experiments were: (1) The membrane has a significant effect on the mixing zone during the initial stages of its growth. This has also been observed in the air/air experiment where theoretically no growth should exist. (2) The membrane effect on the late time evolution, where the mixing zone width has reached a relatively large-amplitude, was relatively small and in good agreement with full numerical simulations. The main conclusion from the present experiments is that the effect of the membrane is important only during the initial stages of the evolution (before the re-shock), when the perturbations have very small amplitudes, and is negligible when the perturbations reach relatively large amplitudes. Received 29 August 1998 / Accepted 25 December 1998     

Effect of mixing structure on the hygroscopic behavior of ultrafine ammonium sulfate particles mixed with succinic acid and levoglucosan

Understanding the interactions between water and atmospheric aerosols is critical for estimating their impact on the radiation budget and cloud formation. The hygroscopic behavior of ultrafine (<100 nm) ammonium sulfate particles internally mixed with either succinic acid (slightly soluble) or levoglucosan (soluble) in different mixing structures (core-shell vs. well-mixed) were measured using a hygroscopicity tandem differential mobility analyzer (HTDMA). During the hydration process (6–92% relative humidity (RH)), the size of core-shell particles (ammonium sulfate and succinic acid) remained unchanged until a slow increase in particle size occurred at 79% RH; however, an abrupt increase in size (i.e., a clear deliquescence) was observed at ∼72% RH for well-mixed particles with a similar volume fraction to the core-shell particles (80:20 by volume). This increase might occur because the shell hindered the complete dissolution of the core-shell particles below 92% RH. The onset RH value was lower for the ammonium sulfate/levoglucosan core-shell particles than the ammonium sulfate/succinic acid core-shell particles due to levoglucosan's higher solubility relative to succinic acid. The growth factor (GF) of the core-shell particles was lower than that of the well-mixed particles, while the GF of the ammonium sulfate/levoglucosan particles was higher than that of ammonium sulfate/succinic acid particles with the same volume fractions. As the volume fraction of the organic species increased, the GF decreased. The data suggest that the mixing structure is also important when determining hygroscopic behavior of the mixed particles.     

Numerical research on the coherent structure in the viscoelastic second-order mixing layers

I.IntroductionViscoelastict'olwsareprevalentinstiring,mixingandchemicalreactionofdilutepolymersolutions.SinceTomsdiscoveredthedragreducingeffectofpolylllerudditivesontul.bulent11owsin1948,1llilnystudiesonitsmechanisms11acebeendoneinviewofitsenormouspr'tcticillalld[lleorcticill\'al[Ics.UPtodata,1ilorcasonilbicilltcrl,rclilti')lls,II()wcvcr,ill'cstillun'lvtlilabjedLlctotiledilllcultiesillfoeviscoelasticdyllalnicsalldthetLlrbulellcetllcory.Al'cwpolymericadditiveshavinglittleeffectonthesolvent…     

The mixing layer instability of wind over a flexible crop canopyInstabilité de couche de mélange dans le vent sur un couvert végétal souple

A coupled fluid-stucture model is proposed to study the dynamics of a flexible crop canopy exposed to wind. The canopy is represented by an elastic continuous medium and coupled to the wind mixing layer through a drag load. The mixing layer instability is shown to remain the principle instability mechanism but its characteristics are modified when taking into account the flexible canopy. The size of the coherent structures is decreased as well as the instability growth rate. To cite this article: C. Py et al., C. R. Mecanique 332 (2004).     

Numerical study on the stability and mixing of vertical round buoyant jet in shallow water

IntroductionAsimplewaytodisposeofthelargequantitiesofwasteheatresultingfromsteamelectricpowergeneration ,istodischargetheheatedcondenserwaterthroughasubmergedroundoutfalllocatedatthebottomofthereceivingwater.Inrecentyears,suchkindsofhighvelocityinjectionsystemshaveincreasinglybeenusedaseffectivemixingdevices,frequently ,thesedevicesarelocatedinwatersofonlyafewportdiametersdeep ,anddischargingareaisrelativelysmall.Thusanunderstandingoftheinducedexcesstemperaturedistribution ,inrelationshiptothe…     

Formation and evolution of the streamwise vortices in mixing layers

The evolution of the three-dimensional time-developing mixing layer is simulated numerically using the pseudo-spectral method. The initial perturbations used in this study consisted of the two-dimensional fundamental wave and the streamwise-invariant three-dimensional disturbance. A comparison of the formations of the streamwise vortices with different amplitude functions for three-dimensional disturbances is made. In one case the results are similar to that of Rogers & Moser^[1], whereas a different way in which the quadrupole forms and sudden expansion of the rib are observed in another case. The simulation also confirms that the stretching by the forming roller rather than Rayleigh centrifugal instability is responsible for the formation of the rib. Finally, numerical flow visualization results are presented. The project supported by the Zhejiang Province Natural Science Special Fund for Youth Scientistis' Cultivation.     

Spanwise domain effects on the evolution of the plane turbulent mixing layer

Large Eddy Simulation is used to simulate a series of plane mixing layers. The influence of the spanwise domain on the development of the mixing layer, and the evolution of the coherent structures, are considered. The mixing layers originate from laminar conditions, and an idealised inflow condition is found to produce accurate flow predictions when the spanwise computational domain extent is sufficient to avoid confinement effects. Spanwise domain confinement of the flow occurs when the ratio of spanwise domain extent to local momentum thickness reaches a value of ten. Flow confinement results in changes to both the growth mechanism of the turbulent coherent structures, and the nature of the interactions that occur between them. The results demonstrate that simulations of the two-dimensional mixing layer flow requires a three-dimensional computational domain in order that the flow will evolve in a manner that is free from restraints imposed by the spanwise domain.     

Numerical investigation of the turbulent energy budget in the wake of freely oscillating elastically mounted cylinder at low reduced velocities

We present a numerical study of the turbulent kinetic energy budget in the wake of cylinders undergoing Vortex-Induced Vibration (VIV). We show three-dimensional Large Eddy Simulations (LES) of an elastically mounted circular cylinder in the synchronization regime at Reynolds number of Re=8000. The Immersed Boundary Method (IBM) is used to account for the presence of the cylinder. The flow field in the wake is decomposed using the triple decomposition splitting the flow variables in mean, coherent and stochastic components. The energy transfer between these scales of motions are then studied and the results of the free oscillation are compared to those of a forced oscillation. The turbulent kinetic energy budget shows that the maximum amplitude of VIV is defined by the ability of the mean flow to feed energy to the coherent structures in the wake. At amplitudes above this maximum amplitude, the energy of the coherent structures needs to be fed additionally by small scale, stochastic energy in form of backscatter to sustain its motion. Furthermore, we demonstrate that the maximum amplitude of the VIV is defined by the integral length scale of the turbulence in the wake.     

Influence of drag reducing additives on the structure of turbulence in a mixing layer

The structure of a free turbulent mixing layer in Newtonian and drag reducing fluids is discussed using results from visualization and LDA-techniques. Particular emphasis is placed on results for the turbulent shear stress and the time correlation function.     

Effects of dual jets distance on mixing characteristics and flow path within a cavity in supersonic crossflow

A rectangular open cavity with upstream dual injectors at a freestream Mach number of 1.9 was investigated experimentally. To evaluate the effect of the distance between the jets, the flow characteristics were investigated using the high-speed schlieren photography, particle image velocimetry, and surface oil flow techniques. The dual jet distances of 18 and 54 mm were used. Unstable flow occurs over the cavity in all cases and is not improved by changing the distance between the dual jets. Although the distance between the dual jets does not influence the flow stability, the flow field varies decidedly depending on the dual jets distance. The enhancement of air mixing depends on the distance between the jets. A long dual jets distance was found to yield better mixing characteristics within the cavity than a short one. When the jets are further apart, the mainstream between two counter-rotating vortex pairs behind the jets flows strongly into the cavity because of the increased blow-down occurring between the vortex pairs. Additionally, a counterflow with a low velocity magnitude occurs behind the jets. Hence, mixing is enhanced within the cavity by effects of the opposed flow. When the jet pairs are closer to each other, the counter-rotating vortex pairs are in contact; as a result, the blow-down effect does not occur between them. The flow drawn into the cavity from the mainstream is supplied from the sides of the test section into the cavity.     

可压缩气固混合层中离散相与连续相的相互作用研究

尽管已有许多文献采用数值模拟方法研究两相流问题,但主要是集中不可压流动方面.本文采用Eul-er-Lagrange颗粒-轨道双向耦合模型对时间模式下含有固粒的二维可压缩混合层流动进行了研究.气相流场采用非定常全Navier-Stokes方程描述,并应用具有空间三阶精度的WNND(Weighted Non-Oscillatory, Contai-ning No Free Parameters and Dissipative)格式进行数值高散.固相方程采用二阶单边三点差分离散.在考虑流场对固粒作用的同时,也计及颗粒对流场的反作用.主要研究混合层大尺度涡对颗粒扩散特性的影响及颗粒对流场结构的影响问题.在对流马赫数为0.5时,研究不同Stokes数颗粒在连续流场中的扩散特性,而在对流马赫数为0.8时研究了不同Stokes数颗粒对流场小激波结构的影响.     

Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface

Results of flow visualization experiments of an impulsively accelerated plane interface between air and SF₆ are reported. The shock tube used for the experiments has a larger test section than in previous experiments. The larger extent of uniform test flow relative to nonuniform boundary-layer flow permits unambiguous interpretation of flow-visualization photographs, and the influence of shock-wave/boundary-layer interactions is no longer dominant. The strong wall vortex observed in previous studies is not observed in these experiments. It is found that the thin membrane, which forms the initially plane interface, has a significant influence on the initial growth rate of the interface thickness. However, the measured growth rates after the first reflected shock are independent of membrane configuration and are in good agreement with analytical predictions.On leave from Stosswellenlabor (Shock Wave Laboratory), RWTH Aachen, Templergraben 55, D-52056 Aachen, Germany.This article was processed by the author using theLAT_EX style filepljour2 from Springer-Verlag.     

The effect of side walls on particles mixing in rotating drums

In this paper, we study the effects of the presence and shape of side walls and of the overall length of rotating cylindrical drums on the mixing of particles with differing sizes by application of the discrete element method (DEM). By varying the semi-axis of the spheroidally shaped side walls and the length of the overall drum, we observe the formation of circulation patterns near the side walls. Although there is a vast amount of literature studying mixing regimes in rotating drums, little is known about the effect of the side walls of the drum on particle mixing. The results of our study demonstrate that introducing curved side walls induces a strong circulation pattern near these side walls, but has, paradoxically, a negative impact on mixing and actually promotes segregation. The cause for this segregation is the difference in velocity of differently sized particles near the curved side walls. Large particles accumulate at the curved side walls, whereas small particles move away from the curved side walls. When the length of the drum is increased, the overall effect of the side walls is decreased, although it does remain observable, even in very large drums.     

Using the discrete element method to assess the mixing of polydisperse solid particles in a rotary drum

Despite the wide applications of powder and solid mixing in industry, knowledge on the mixing of polydisperse solid particles in rotary drum blenders is lacking. This study investigates the mixing of monodisperse, bidisperse, tridisperse, and polydisperse solid particles in a rotary drum using the discrete element method. To validate the model developed in this study, experimental and simulation results were compared. The validated model was then employed to investigate the effects of the drum rotational speed, particle size, and initial loading method on the mixing quality. The degree of mixing of polydisperse particles was smaller than that for monodisperse particles owing to the segregation phenomenon. The mixing index increased from an initial value to a maximum and decreased slightly before reaching a plateau for bidisperse, tridisperse, and polydisperse particles as a direct result of the segregation of particles of different sizes. Final mixing indices were higher for polydisperse particles than for tridisperse and bidisperse particles. Additionally, segregation was weakened by introducing additional particles of intermediate size. The best mixing of bidisperse and tridisperse particles was achieved for top–bottom smaller-to-larger initial loading, while that of polydisperse systems was achieved using top–bottom smaller-to-larger and top–bottom larger-to-smaller initial loading methods.