Performance of Kenics static mixer over a wide range of Reynolds number

The present study deals with the numerical simulation of flow patterns and mixing behaviour in Kenics static mixer over a wide range of Reynolds number. Three different sets of Kenics mixer (aspect ratio = 1.5) comprised of 3, 9 and 25 elements each have been characterized. The Reynolds number was varied in the range of 1 to 25,000 (i.e., from laminar to turbulent flow regime). The numerical approach takes into account the aspects of the fluid flow at higher Reynolds number values including circumferential velocity profiles at different cross-sections within the Kenics mixer, which were neglected in previous studies. It was observed that cross-sectional mixing in the turbulent flow regime takes place up to 30% of each element length at element-to-element transition; beyond that velocity profiles were uniform. The experiments were also carried out to measure the circumferential and axial velocity profiles and pressure drop in three different Kenics Mixers using air as fluid. The pressure drop per unit element (ΔP/η) was found to be independent of the number of Kenics mixing elements used in the system. The total pressure drop across Kenics mixer obtained by CFD simulations were compared with the experimental pressure drop values and correlations available in the literature. The numerical results were found in good agreement with the experimental as well as the results reported in the literature. A new pressure drop correlation in the Kenics static mixer has been developed.     

Finite element modeling of the laminar and transition flow of the Superblend dual shaft coaxial mixer on parallel computers

The macro-mixing mechanisms of the Superblend coaxial mixer consisting of a Maxblend impeller and a double helical ribbon agitator mounted on two independent coaxial shafts rotating at different speeds are numerically investigated. The simulations are based on the resolution of the Navier-Stokes equations with help of a parallel three-dimensional finite element solver exploiting the capabilities of high performance computers. To model the rotation of agitators a hybrid approach based on a novel finite element sliding mesh and fictitious domain method is used. The power consumption, the flow patterns, the shear rate distribution, the pumping capacity and the mixing time of the Superblend mixer are calculated from the simulated hydrodynamics. The simulations allow observing the flow as it evolves from deep laminar (Re=0.1) to transition (Re=520) regime. As Reynolds number increases, several recirculation zones above and below the middle of the tank are formed. It is found that operating the agitators in co-rotation mode requires less power consumption and exhibits equal or shorter mixing time than counter-rotation mode. The larger power consumption in counter-rotating mode is caused by the presence of high shear vortices generated between the two coaxial agitators. Furthermore it is shown that the shear distribution throughout the Superblend coaxial mixer operating in co-rotation mode is almost homogenous, which is highly desirable for shear sensitive products. In view of the results obtained in this work, the Superblend coaxial mixer is found as a good alternative for tough mixing applications.     

Velocity profiles and frictional pressure drop for shear thinning materials in lid-driven cavities with fully developed axial flow

A finite element numerical study has been carried out on the isothermal flow of power law fluids in lid-driven cavities with axial throughflow. The effects of the tangential flow Reynolds number (Re_U), axial flow Reynolds number (Re_W), cavity aspect ratio and shear thinning property of the fluids on tangential and axial velocity distributions and the frictional pressure drop are studied. Where comparison is possible, very good agreement is found between current numerical results and published asymptotic and numerical results. For shear thinning materials in long thin cavities in the tangential flow dominated flow regime, the numerical results show that the frictional pressure drop lies between two extreme conditions, namely the results for duct flow and analytical results from lubrication theory. For shear thinning materials in a lid-driven cavity, the interaction between the tangential flow and axial flow is very complex because the flow is dependent on the flow Reynolds numbers and the ratio of the average axial velocity and the lid velocity. For both Newtonian and shear thinning fluids, the axial velocity peak is shifted and the frictional pressure drop is increased with increasing tangential flow Reynolds number. The results are highly relevant to industrial devices such as screw extruders and scraped surface heat exchangers.     

Experimental and numerical characterization of viscous flow and mixing in an impinging jet contactor

The laminar flow in an impinging jet contactor is examined as a first step toward the development of new technology for fast mixing of viscous fluids. The flow, velocity, and stretching fields in an impinging jet contactor are quantified for low Reynolds number flow using three-dimensional numerical simulations and particle image velocimetry measurements. Computational and experimental velocity fields are in close agreement, as quantified by the velocity probability density functions. Two steady-state flow regimes are found to exist: for jet Reynolds numbers (Re_j) < 10, the jets do not impinge and the velocity field scales linearly with Reynolds number; for Re_j > 10, the jets begin to impinge and recirculation regions form above and below the impingement point. The magnitude of the rate-of-strain tensor is calculated as a function of Re_j. While areas of essentially zero stretching occupy most of the flow domain, very high rates of stretching occur at specific locations in the flow. The maximum and average rates of stretching in the contactor increase roughly linearly as a function of Reynolds number. Mixing simulations show that no mixing occurs for the steady flow in a symmetric-jet contactor. However, mixing is improved substantially by a slight modification of the impinging jet geometry that disrupts geometric symmetry.     

Residence Time and Concentration Distribution in a Kenics Static Mixer

Static mixers, often referred to as motionless mixers, are in-line mixing devices that consist of mixing elements inserted into a length of pipe. Most of the experimental works in this field have concentrated on establishing design guidelines and pressure drop correlations. Due to experimental difficulties, few articles have been published on the investigation of the flow and mixing mechanisms. In this work, a Kenics KMX static mixer was utilized to study concentration and residence time distribution (RTD) and effect of Reynolds number on mixing. The static mixer had six mixing elements arranged in-line along the length of the tube, and the angle between two neighboring elements was 90°. The length of the mixer was 0.98 m with internal and external diameters of 5.0 cm and 6.0 cm, respectively. The main continuous fluid was water, and NaCl solution was used as a tracer. All experiments were conducted with three replications at three Reynolds numbers, Re = 1188.71, 1584.95, and 1981.19. A dispersion model was used to model the RTD data. The experimental results were compared with the model results and reasonable agreement was achieved.     

Transition of the flow in a symmetric channel with periodically expanded grooves

Transition of the flow in a periodically grooved channel is numerically investigated for periodicity indices m=1 up to 6 by assuming the two-dimensional and fully developed flow field, where m is defined as a number of grooves in which the flow repeats periodically. Critical Reynolds numbers for the onset of a self-sustained oscillatory flow from a steady-state flow are evaluated by numerical simulations. It is found that the bifurcations occur at the critical Reynolds numbers as a result of Hopf bifurcation, and a period in the streamwise direction of the oscillatory flow is twice as long as the groove pitch of the channel. In addition, flow visualization with the aluminum dust method is carried out to confirm the results obtained from the numerical simulations. The experimental results are in good agreement with the numerical ones.     

Hydrodynamics characterization of the Maxblend impeller

The hydrodynamic characteristics of the Maxblend^TM impeller have been investigated in the case of viscous Newtonian fluids. Both laboratory experiments and 3D finite element based computational fluid dynamics (CFD) simulations have been carried out. The power consumption, the mixing evolution yielding the mixing time, and the effect of baffles in the laminar and transition flow regimes have been determined. It was found that the limit Reynolds number between the laminar and transition regimes is approximately 25 and 38 for the unbaffled and baffled configurations, respectively. Based on the range of Reynolds numbers studied in this work, the best window performance of the Maxblend^TM mixer where fast and homogenous mixing is achieved is the end of the laminar regime and the early transition regime with baffles.     

Single and two-phase flows in a horizontal pipe with a Kenics static mixer: Effect of pressure drop on mixing

Single and two-phase flows pressure drops through a Kenics static mixer were investigated, for liquid and gas Reynolds numbers ranging from 8110 < Re_L < 18 940 to 1730 < Re_G < 8680, respectively. New friction factor correlations were established for single and two-phase flows, showing better agreement than those available in the literature. Dissipated energy and characteristic time constants were estimated from experimental data. For instance, a dissipated energy with a maximum value of 510 W/kg was calculated in two-phase flow with the drift-flux model. The dispersed phase reduced the characteristic mixing times and its influence was more important than the continuous phase for all the characteristic mixing time investigated. Furthermore, the macroscopic characteristic mixing time was shown to be the governing mixing process for almost all gas and liquid flow rates explored.     

A model for gas-solid flow in a horizontal duct with a smooth merge of rapid-intermediate-dense flows

Granular flow in the rapid flow regime is dominated by particle-particle collisions and the constitutive relations for the solid stress are obtained from the classic kinetic theory of granular flow. In the dense flow regime, on the other hand, particles interact via enduring contacts and the solid stress can be deduced from soil mechanics theories. In this paper, constitutive equations, recently proposed by Tardos et al. [2003. Slow and intermediate flow of frictional bulk powder in the Couette geometry. Powder Technology 131, 23-39.] has been incorporated in the simulation of gas-solid flow in a horizontal duct. These equations smoothly merge the rapid granular flow solution with the so-called “intermediate” regime (where both kinetic/collisional and frictional contributions might play a role) and reduce to Coulomb yield condition for slow frictional flow (shear rate → 0). The results of this new modelling approach have shown good qualitative agreement with the reported experimental observation on wide range of gas-solid flow conditions. In this study, we also present the definition of boundaries between rapid-intermediate-dense flow regimes based on the dimensionless shear rate (λ), and a modified Reynolds number (Re). We have shown that the intermediate flow regime can be classified at approximately 0.1<λ<1.0 and 100<Re<3000.     

Numerical characterisation of folding flow microchannel mixers

Micromixers have been considered in numerous recent studies with the aim of mixing different liquid streams for the common circumstance of non-inertial flow, i.e., in the Stokes flow regime. Under such conditions, the diffusion of momentum is dominant but the diffusion of species remains weak because the Schmidt number of liquids is large. Most mixers that have potential for application in the Stokes regime make use of a folding flow pattern that approximates the baker's transformation. In the work presented here, the general scaling of mixers of this type is developed from the exact equation for species transport and computations are made for a specimen mixer geometry to test the effectiveness of the resulting scaling. The scaling relation developed is found to give an excellent representation of the actual mixing characteristics of the specimen mixer over the entire range of Péclet number of practical interest. Finite volume computations are employed to solve the governing equations up to around Pe=10³. At higher Péclet numbers, where finite volume numerical solution becomes inaccurate with affordable mesh sizes, the species equation is solved using a Monte Carlo method instead. Finally, the scaling relation is used to develop the design relations needed to determine the number of mixing elements, the pressure drop incurred and the Péclet number of operation to achieve a given mixture uniformity within a specified mixing time.     

Laminar mixing of shear thinning fluids in a SMX static mixer

Flow and mixing of power-law fluids in a standard SMX static mixer were simulated using computational fluid dynamics (CFD). Results showed that shear thinning reduces the ratio of pressure drop in the static mixer to pressure drop in empty tube as compared to Newtonian fluids. The correlations for pressure drop and friction factor were obtained at Re_MR?100. The friction factor is a function of both Reynolds number and power-law index. A proper apparent strain rate, area-weighted average strain rate on the solid surface in mixing section, was proposed to calculate pressure drop for a non-Newtonian fluid. Particle tracking showed that shear thinning fluids exhibit better mixing quality, lower pressure drop and higher mixing efficiency as compared to a Newtonian fluid in the SMX static mixer.     

Optimal designs of staggered dean vortex micromixers

A novel parallel laminar micromixer with a two-dimensional staggered Dean Vortex micromixer is optimized and fabricated in our study. Dean vortices induced by centrifugal forces in curved rectangular channels cause fluids to produce secondary flows. The split-and-recombination (SAR) structures of the flow channels and the impinging effects result in the reduction of the diffusion distance of two fluids. Three different designs of a curved channel micromixer are introduced to evaluate the mixing performance of the designed micromixer. Mixing performances are demonstrated by means of a pH indicator using an optical microscope and fluorescent particles via a confocal microscope at different flow rates corresponding to Reynolds numbers (Re) ranging from 0.5 to 50. The comparison between the experimental data and numerical results shows a very reasonable agreement. At a Re of 50, the mixing length at the sixth segment, corresponding to the downstream distance of 21.0 mm, can be achieved in a distance 4 times shorter than when the Re equals 1. An optimization of this micromixer is performed with two geometric parameters. These are the angle between the lines from the center to two intersections of two consecutive curved channels, θ, and the angle between two lines of the centers of three consecutive curved channels, ϕ. It can be found that the maximal mixing index is related to the maximal value of the sum of θ and ϕ, which is equal to 139.82°.     

Segregated regions in continuous laminar stirred tank reactors

Using visualization techniques, including acid/base reactions and UV fluorescence, we provide experimental evidence of segregated regions (islands) during mixing of viscous Newtonian fluids under laminar flow conditions in continuous stirred tank reactors (CSTRs). The effect of inlet/outlet stream position and Reynolds number on the dynamics of the mixing processes is examined. Numerical experiments in 3-D map were able to capture the main features of the CSTR flow by perturbing a Batch system using an imposed axial flow. Asymmetric flow patterns produced by off-center positioning of inlet and outlet pipes cause a reduction in size of the segregated region, enlarging the chaotic region and leading to more efficient mixing. Under dynamic inlet flow conditions, the laminar steady flow is perturbed, giving rise to an asymmetric flow pattern that is able to destroy toroidal segregated regions. Counter-intuitively, higher agitation speed (higher Re) did not enhance overall mixing efficiency. Faster agitation stabilized the toroidal regions, making it harder to destroy them. In addition, dynamic mixing protocols are investigated to enhance mixing performance. We demonstrate that time-dependent pumping and stirring protocols are able to efficiently destroy long-lasting toroidal regions.     

Drag of non-spherical solid particles of regular and irregular shape

The drag of a non-spherical particle was reviewed and investigated for a variety of shapes (regular and irregular) and particle Reynolds numbers (Re_p). Point-force models for the trajectory-averaged drag were discussed for both the Stokes regime (Re_p ? 1) and Newton regime (Re_p ? 1 and sub-critical with approximately constant drag coefficient) for a particular particle shape. While exact solutions were often available for the Stokes regime, the Newton regime depended on: aspect ratio for spheroidal particles, surface area ratio for other regularly-shaped particles, and min-med-max area for irregularly shaped particles. The combination of the Stokes and Newton regimes were well integrated using a general method by Ganser (developed for isometric shapes and disks). In particular, a modified Clift-Gauvin expression was developed for particles with approximately cylindrical cross-sections relative to the flow, e.g. rods, prolate spheroids, and oblate spheroids with near-unity aspect ratios. However, particles with non-circular cross-sections exhibited a weaker dependence on Reynolds number, which is attributed to the more rapid transition to flow separation and turbulent boundary layer conditions. Their drag coefficient behavior was better represented by a modified Dallavalle drag model, by again integrating the Stokes and Newton regimes. This paper first discusses spherical particle drag and classification of particle shapes, followed by the main body which discusses drag in Stokes and Newton regimes and then combines these results for the intermediate regimes.     

Accessing multidimensional mixing via 3D printing and showerhead micromixer design

We present a 3D metal printing showerhead mixer to blend effectively two reagent streams into a confined mixing volume. Each stream is predistributed to multiple channels to increase the contact area in the mixing zone, which enables high mixing performance with smaller pressure drop. The showerhead mixer shows excellent mixing performance owing to its ability to intersperse rapidly the two streams as characterized by the diazo coupling reactions and computational fluid dynamics (CFD) simulations. Experimental results demonstrate superior performance of the showerhead mixer compared to two common commercial micro T-mixers, especially in low Reynolds number regime. CFD results are employed to (a) help understand the mixing mechanism, (b) reproduce the experimental observations, and (c) inform the design specifications for optimal performance. Good agreement between experiments and simulations is achieved. The final design includes multiple side-fed inlets for improved mixing performance of the showerhead mixer, as suggested by the validated CFD models.     

Mixing in a multi-inlet vortex mixer (MIVM) for flash nano-precipitation

Rapid precipitation of both organic and inorganic compounds at high supersaturation requires homogenous mixing to control the particle size distribution. We present the design and characterization of a new multi-inlet vortex mixer (MIVM). The four-stream MIVM allows control of both the supersaturation and the final solvent quality by varying stream velocities. The design also enables the separation of reactive components prior to mixing. Finally, the design enables mixing of streams of unequal volumetric flows, which is not possible with alternate confined impinging jet mixing geometries. We characterize the mixing performance of the MIVM using competitive fast reactions (the so-called “Bourne reactions”). Adequate micromixing is obtained with a suitably defined Reynolds number when Re>1600. The experimental results are compared to computational fluid dynamics (CFD) simulations of the fluid mechanics and parallel reactions in the MIVM. Excellent correspondence is found between the simulation and the experimental results with no adjustable parameters. The CFD simulations provide a powerful tool for the optimization of these complex mixing geometries.     

A new expression for spherical aerosol drag in slip flow regime

A 3D simulation study for an incompressible slip flow around a spherical aerosol particle was performed. The full Navier–Stokes equations were solved and the velocity jump at the gas–particle interface was treated numerically by imposition of the slip boundary condition. Analytical solution to the Stokesian slip flow past a spherical particle was used as a benchmark for code verification, and excellent agreement was achieved. The simulation results showed that in addition to the Knudsen number, the Reynolds number affects the slip correction factor. Thus, the Cunningham-based slip corrections must be augmented by the inclusion of the effect of Reynolds number for application to Lagrangian tracking of fine particles. A new expression for the slip correction factor as a function of both Knudsen number and Reynolds number was developed. The particle total drag coefficient was also correlated against Re and Kn over the range of gas–particle relative speeds yielding the incompressible slip flow from the Stokesian regime up to the threshold of compressibility. Inclusion of gas slip on the particle surface enhances the accuracy of particle drag force prediction up to 40.9% in the range of 0.01<Kn<0.1 and 0.125<Re<20 compared to the no-slip continuum drag values.     

Two-dimensional unsteady flow of power-law fluids over a cylinder

The unsteady flow of incompressible power-law fluids over an unconfined circular cylinder in cross-flow arrangement has been studied numerically. The two-dimensional (2-D) field equations have been solved using a finite volume method based solver (FLUENT 6.3). In particular, the effects of the power-law index (0.4?n?1.8) and Reynolds number (40?Re?140) on the detailed kinematics of the flow (streamline, surface pressure and vorticity patterns) and on the macroscopic parameters (drag and lift coefficients, Strouhal number) are presented in detail. The periodic vortex shedding and the evolution of detailed kinematics with time are also presented to provide insights into the nature of flow. The two-dimensional flow transits from steady to unsteady behaviour at a critical value of the Reynolds number Re∼(40-50) and the von-Karman vortex street is observed beyond the critical Reynolds number (Re). Obviously, both the lift coefficient and Strouhal number values are zero for the steady flow, but their values increase with the increasing Reynolds number (Re) in the unsteady flow regime. For highly shear-thickening fluids (n=1.8), the flow becomes unsteady at Re=40 and unsteadiness in the flow appears at Re=50 for all values of power-law index (n). As expected, the evolution of the kinematics and vortex shedding show a complex dependence on the flow parameters near the transition in the flow. For a fixed value of the Reynolds number (Re), the drag coefficient increases and lift coefficient decreases with increasing value of the power-law index (n). For a fixed value of the power-law index (n), the drag coefficient gradually increases with the Reynolds number (Re). Similar to the drag coefficient, lift coefficient also shows a complex dependence on the power-law index (n) near the transition zone. The value of the Strouhal number (St) decreases with the increasing value of the power-law index (n) at a fixed value of the Reynolds number (Re).     

Computational study of convective–diffusive mixing in a microchannel mixer

Scalar mixing due to convection and diffusion in a microchannel mixer is studied using CFD. A method is developed to quantitatively measure the effect of false diffusion on scalar decay rate. This method computes an average false diffusivity from a given numerical solution and it is not limited to any particular numerical scheme. It is found that a range of molecular diffusivity exist in which average false diffusion is smaller than molecular diffusion and scalar decay rates can be computed accurately with CFD in the mixer. This range of molecular diffusivity covers most of the liquid solutions encountered in chemical and biochemical engineering. When effective diffusivity is used, this range can be further expanded. The predicted mixing structures agree well with experimental results in literature. The classical lamellar structures of the baker's transformation are strongly affected by diffusion. The striation doubling process is destroyed by diffusion broadening at very early stage in the mixer. The optimal mixing is achieved at low Re when the mixing mechanism in the mixer is the baker's transformation. At higher Re, secondary flow is generated and the mixing mechanism is the competition of the kinematics of the baker's transformation and the dynamics of the cross sectional flow. Results show that the secondary flow hinders mixing and the scalar decays at lower exponential rates than when the mixing is due to the baker's transformation alone.     

Experimental and Numerical Investigation of a Novel Spiral Micromixer with Sinusoidal Channel Walls

A novel spiral micromixer with sinusoidal channel walls was designed to enhance the mixing index in the low to intermediate Reynolds number range (1 < Re < 100). To analyze the fluid flow, a set of numerical simulations were performed using the finite-difference method. The microchip was fabricated from polydimethylsiloxane, employing the soft-lithography technique. The degree of mixing was increased by 99.11 % when using the proposed micromixer, compared to 59.44 % for a simple spiral micromixer. The introduced microchannel drastically reduced the mixing length, increasing the mixing index of a 0.5-loop spiral-sinusoidal microchannel compared to that of the simple spiral microchannel with 1.5 loops. The mixing index of the 3-loop mixer was higher than that of the microchannel with 1.5 loops, and its pressure drop was increased.