Numerical simulation of geometry effect on mixing performance in L-shaped micromixers

Abstract

This study accomplishes a numerical analysis of mixing in a microchannel with repeating L-shaped units in order to research the effect of the extension of L-shaped units in a three-dimensional (3D) space and the angle of repeating units on the process of mixing. In the first part, Geometry 2 and Geometry 3 are designed by extending the units of Geometry 1 in a 3D space. In the second part, an L-shaped micromixer, a 90° V-shaped micromixer, and a 60° V-shaped micromixer are analyzed. It is observed that Geometry 1 and Geometry 2 perform better than Geometry 3 in terms of mixing due to the spiral path with 360° rotation of the flow. The L-shaped micromixer is more efficient than the 90° and 60° V-shaped micromixers. A maximum mixing index of about 88% is achieved in all serpentine microchannels at the following Reynolds numbers: Re = 150 and Re = 200.     

On the mixing properties of spherically symmetric helical coherent structures in turbulence

A paradigmatic family of flow fields for localized, spherically symmetrical flow with maximal helicity—a model for helical coherent structures that are localized—is introduced. The Lagrangian mixing of the lowest order member of the family that is truly 3-D due to spiral arms is analyzed with linear theory, demonstrating that trajectory growth rates for the short, convective time scale are exponential and bounded by the extremal eigenvalues of the Jacobian. However, these rates show strong inhomogeneity and anisotropy associated with anomalous mixing. It was found for nonlinear Lagrangian mixing times that for this paradigm helical coherent structure, 22% of the trajectory pairs were bounded by the initial separation (non-mixing) and 78% mixed in various classifications of convective dispersal. All non-local studies of 10,000 Lagrangian trajectories could be categorized into five classes of growth (decay) patterns which exhibit the effects of localized, finite helicity/momentum associated with this class of velocity field. A scalar dispersion simulation confirms that the “patch” of fluid near the origin is slowly mixing—on the diffusive time scale—and is convected “unmixed” when the influence of molecular diffusion is still not pronounced (short times relative to Pe=100).     

Propane combustion in non-adiabatic microreactors: 1. Comparison of channel and posted catalytic inserts

The reduction in size of catalytic microreactors results in high heat and mass transfer rates and a significant increase in the surface area to volume ratio. A further increase in the catalytic surface area can be achieved in a scaled-down version of fixed bed reactors. Since micro-fixed bed reactors are often deemed impractical due to their large pressure drops, one could use precisely structured inserts to increase the surface area, enhance mixing and manipulate the flow distribution. Catalytic propane combustion in microreactors with multi-channel and posted inserts, which consist of multiple static structures (walls separating various channels and pillar-like structures, respectively) in the flow channel of a microreactor, is considered in this series of two papers. In this first paper, we present numerical comparison of multi-channel and posted catalytic inserts for non-adiabatic self-sustained propane combustion. The inserts are oriented axially along the flow direction. We show that channel and post microreactors have similar performance for low thermal conductivity of the inserts. The in-line arrangement of the posted structures is preferred over a staggered arrangement because the former provides higher propane conversion and more stable combustion. The role of thermal conductivity of the microreactor wall structure and the catalytic inserts is investigated. The thermal conductivity of the microreactor structure affects the performance of the posts but not the channels; this is contrary to the effect of catalyst insert thermal conductivity where it is vice-versa. The channel microreactor is more stable towards high flow-rate blowout limit, whereas the post microreactor is significantly more stable at the lower flow-rate extinction limit. This results in stable operation of the post microreactor under more fuel-lean mixtures than the channel microreactor.     

Pressure drop in monolith reactors

A theoretical model for the computation of pressure drop in bubble-train flow inside capillaries of square cross-section was developed. The model is based on three contributions: hydrostatics, viscous pressure drop, and capillary pressure drop. Capillary pressure drop is related to the shape of the fronts and ends of the bubbles. The model does not include entrance or exit effects, has no adjustable parameters, and agrees very well with available experimental data.

For a given set of flow parameters, bubble velocity and liquid slug average velocity are computed as a function of gas and liquid superficial velocities. The length of the unit cell determines the number of bubbles inside the capillary for a given flow situation. The model requires experimental information of average bubble lengths to compute the length of a unit cell consisting of a bubble and a liquid slug.

The three pressure contributions for a unit capillary length are linear functions of the number of bubbles inside the capillary. The length of the bubbles in bubble-train flows is a critical parameter in the computation of pressure drop.     

Experimental characterization and multi-scale modeling of mixing in static mixers

Mixing in static mixers is studied using a set of competitive-parallel chemical reactions and computational fluid dynamics (CFD) in a wide range of operating conditions. Two kinds of mixers, a wide angle Y-mixer and a two jet vortex mixer, referred to as Roughton mixer, are compared in terms of reaction yields and mixing times. It is found that the Roughton mixer achieves a better mixing performance compared to the Y-mixer. The effect of flow rate ratio on mixing in the Roughton mixer has been studied as well and it is shown that the mixing efficiency is not affected by the flow rate ratio. Moreover, experimental results and model predictions are in good agreement for all mixer geometries and operating conditions. CFD is used to calculate absolute mixing times based on the residence time in the segregated zone and it is shown that mixing times of less than 1 ms can be achieved in the Roughton mixer. In addition, CFD provides insight in local concentrations and reaction rates and serves as a valuable tool to improve or to scale-up mixers.     

Pressure drop across vortex diodes: Experiments and design guidelines

Vortex diodes are used as leaky non-return valves in applications where it is desirable to avoid valves with moving parts. Despite their use in practice for several decades, no clear guidelines for design and optimization of vortex diodes are available. Detailed experimental study on flow and pressure drop characteristics of vortex diodes was therefore carried out to evolve such guidelines. The study covered a wide range of vortex diodes. The variation of diodicity (ratio of pressure drop for reverse and forward flow for the same flow rate) with respect to diode geometry, diode size (d_C), aspect ratio (d_C/h), nozzle configuration and Reynolds number (Re) was studied. The experimental results were critically analyzed to develop a design methodology. The methodology is shown to be useful for obtaining the diode dimensions that would yield the desired diodicity for the required operating flow rate.     

Pressure drop in pulsed extraction columns with internals of discs and doughnuts

A study on the pressure drop in pulsed extraction columns with internals of immobile discs and rings, usually called Discs and Doughnuts Columns (DDC) is carried out. The local pressure at a desired level of the column is obtained by resolving of turbulent flow model based on Reynolds equations coupled with k–? model of turbulence. Consequently, the pressure drop for a column stage or for a unit of column length is determined. The results are used for development of correlations for determination of pressure drop as a function of plate free area, interplate distance and pulsation parameters – amplitude and frequency. Good correspondence to experimental data is observed. The developed quantitative relations are useful for non-experimental numerical optimization of stage geometry in view of lesser energy consumption.     

Studies on frictional pressure drop of gas-non-Newtonian two-phase flow in a cocurrent downflow bubble column

An exclusive study has been done on experimental investigation of the two-phase frictional pressure drop with air-non-Newtonian liquid (CMC solutions) system in cocurrent downflow bubble column. The effects of gas and liquid flowrate on two-phase frictional pressure drop have been illustrated. An attempt has been made to fit the experimental two-phase frictional pressure drop data by modified Lockhart and Martinelli correlation and Aoki correlation. In another approach, friction factor method was adopted to correlate the experimental results in terms of dimensionless groups of the operating and system variables and the predicted values were found to be in good agreement with the experimental result. The experiments were performed in the bubbly flow regime because of its stability and uniformity.     

Pressure drop and gas bypassing in recirculating fluidized beds

The effect of different operating and design parameters on the pressure drop profile for a recirculating fluidized bed has been studied. A mathematical model was developed for the pressure drop in the recirculating fluidized bed. The different parameters considered were flow rate, inventory of solids and spacing between the draft-tube bottom and the distribution plate. Geldart D and B particles were used for the study. The gas bypassing from the jet towards the downcomer was calculated on the basis of the mathematical model and the effect of various parameters on gas bypassing were analyzed.     

Pressure drop and mixing behaviour of non‐Newtonian fluids in a static mixing unit

Static or motionless mixers have received wide application in chemical and allied industries due to their low cost and high efficiency. The pressure drop and mixing behaviour of such mixers have been widely studied. However, the available information for non‐Newtonian fluids is scanty. The results of pressure drop and mixing studies conducted with a locally made motionless mixer (MALAVIYA mixer) and four non‐Newtonian fluids—aq. CMC, PVA, and PEG solutions are reported in this article. The new mixer causes less pressure drop compared to some of the commercial mixers. Mixing behaviour of the unit is more closer to plug flow and a two‐parameter model correlates the dispersion data.     

Pressure drop modelling in cellular metallic foams

A theoretical model is presented for the prediction of pressure drop in a Newtonian fluid flowing through highly porous, isotropic metallic foams. The model is based on a rigorous assumption of piece-wise plane Poiseuille flow and a simplistic geometrical model, and shows promise to accurately predict the hydrodynamic conditions in both the Darcy and Forchheimer regimes, without a priori knowledge of the flow behaviour of the particular metallic foam.     

竖直上升管中密相气力输送压降特性

研究了内径20 mm的竖直上升不锈钢管道中粉煤密相气力输送单位管长压降随输送参数的变化规律,并得到了Zenz相图。结果表明,在实验操作范围内管道压降主要由固相自身静压降和固相摩擦压降组成,气相产生的压降不超过总压降的1%;固相体积分数是影响压降变化的主要因素,并讨论了粉煤流速以及固相体积分数对固相静压降和摩擦压降的影响规律;考察了粉煤流速和固相体积分数对固相摩擦系数的影响,对实验数据拟合得到了固相摩擦系数的关系式,计算结果与实验值吻合较好。     

气固并流式轴向移动床过滤器的压降特性

通过冷模实验,改变移动床表观气速、颗粒循环速率、入口气体含尘浓度等操作参数,研究了轴向移动床过滤器的压降特性和合适的操作条件,结合移动床内气固两相运动特点,修正了Ergun公式,在加尘条件下分析了床内滤饼对压降稳定性的影响。结果表明,在无尘负荷条件下(“纯”移动床操作),颗粒的循环速率由0增至2.26 kg/(m2?s)时,设备的压降减小0.03 kPa。表观气速为0.126 m/s、入口气体含尘浓度为89.10 g/m3时,移动床内滤饼形成和破损呈动态平衡,过滤500 s后,压降可稳定在0.88 kPa,此时设备具有较高的除尘性能,粉尘捕集效率可达96%以上。     

CFD modeling of mixing intensification assisted with ultrasound wave in a T-type microreactor

This paper aims to demonstrate the effect of ultrasound wave on mixing in a T-type microreactor. In order to create vibration in this microreactor, a low frequency (42 kHz) piezoelectric transducer was used. A well-known parallel-competitive reaction (Villermaux–Dushman reaction) was employed to study the mixing in the microreactor and the segregation index values were found for layouts with and without sonication. Results show that the ultrasound waves have a significant favorable influence on product distribution and the segregation index at various total flow rates. In all cases, the segregation index decreased with increase in total flow rate. The results reveal that the segregation index improved up to 10–20% by consuming a low energy (2.45 W Kg⁻¹) by the piezoelectric transducer. Finally, the computational fluid dynamics (CFD) modeling was carried out to explain the observed experimental results.     

Pressure drop measurements and modeling on SiC foams

Foam-structured beds are likely to be the next generation of catalyst supports due to their interesting specific properties (large exchange area, low pressure drop, easy control of external porosity, etc.). Nevertheless, chemical engineering parameters of this new catalyst support types are still not completely clear for the scientific community and many approaches are attempted to solve this problem. SiC foams offer the dual advantages of the interesting properties of structured beds and the intrinsic thermal and mechanical properties of silicon carbide as a catalytic support. In the present work, the problem of pressure drops along foam beds is studied with a new simplistic geometrical model as a first step in the understanding of the peculiar hydrodynamic behavior of SiC foams in chemical processes. The proposed model was successfully validated by experimental results on a relatively large range of parameters which fully confirm the validity of the model.     

Evaluation of models and correlations for pressure drop estimation in dense phase pneumatic conveying and an experimental analysis

This study reviews the models and correlations for dense phase conveying in an effort to explore existing and new data on the subject and to provide guidance to the designer on the best pressure drop model. Using various data sets the Mi (Konrad)-based model was found to be best for predicting the pressure drop across dense phase plugs. A series of industrial scale tests also shows agreement with the Mi (Konrad)-based model.     

The NETmix reactor: Pressure drop measurements and 3D CFD modeling

NETmix is a new static mixing technology based on a network of mixing chambers interconnected by channels. Three NETmix reactors with different geometries were used to obtain experimental data for pressure drop and a generalized model for pressure drop in NETmix reactors has been developed. This model features a single adjustable parameter and it is only dependent on the geometric configuration of the NETmix design. The Z factor and the power number were also determined to compare the performance of different NETmix configurations with other existing mixers. The dynamic measurement of pressure drop was used to evaluate the mixing dynamics in the NETmix chambers and, above the critical Reynolds number, the natural oscillation frequency was quantified. Furthermore, a three-dimensional computational fluid dynamic transport model was also developed and validated. The energy performance of the three NETmix prototypes was quantified and shown to be very competitive with the compared existing static mixers. The developed 3D CFD transport model, validated by the reported experimental data, enables the computation of transport properties for any geometrical design and fluid properties, and avoids the need for experimental data each time a new NETmix configuration is designed.     

Liquid phase axial mixing in bubble columns operated at high pressures

Liquid phase axial mixing was measured in a 100 mm i.d. bubble column operated in the pressure range of 0.1-0.5 MPa. Water, ethanol and 1-butanol were used as the liquid phase and nitrogen as the gas phase. The temperature and superficial gas velocity were varied in the range of 298-323 K and 0.01-0.21 m/s, respectively. The axial dispersion coefficient increased with an increase in the gas density due to pressure. The temperature had surprisingly a small effect. A CFD model was developed for the prediction of flow pattern in terms of mean velocity and eddy diffusivity profiles. The model was further extended for the prediction of residence time distribution and hence the axial dispersion coefficient (D_L). The predictions of axial dispersion coefficient agree favorably with all the experimental data collected in this work as well as published in the literature. The model was extended for different gas-liquid systems. The predicted values of axial dispersion coefficient were found to agree very well with all the experimental data.     

Periodic open-cell foams: Pressure drop measurements and modeling of an ideal tetrakaidecahedra packing

Periodic open-cell foams of ideal tetrakaidecahedron geometry were manufactured by selective electron beam melting (SEBM) and characterized with respect to the morphological parameters, namely strut diameter, window diameter and porosity. The pressure drop over these periodic foam samples of different pore size and porosity was determined experimentally. The basic form of the Ergun equation (which contains no empirical coefficients) was modified to develop a new correlation for the prediction of the pressure drop in periodic open-cell foams of ideal tetrakaidecahedron geometry. The correlation was successfully validated by the experimental results of the pressure drop measured for the periodic open-cell foam samples. With the new correlation it is possible to predict the pressure drop in periodic open-cell foams by using only two geometrical parameters, namely the open porosity and the window diameter.The applicability of the new correlation for a large range of porosities was examined by comparing the experimental and simulated friction factors for the porous media with both high (foam structure) and low porosities (packed beds) for a large range of the Reynolds number. It was demonstrated that the correlation can successfully predict the pressure drop of foam structures as well as packed beds.