Turbulent Mixing Time Research Articles

The Dual Nature of Entrainment-Mixing Signatures Revealed Through Large-Eddy Simulations of a Convection-Cloud Chamber

Abstract Entrainment of subsaturated air into a cloud can influence its optical and microphysical properties in various ways, depending on the droplet evaporation and turbulent mixing time scales. Previous experiments in the Pi Convection-Cloud Chamber have revealed that, given a fixed entrained air property, the mixing of entrained subsaturated air results in complete evaporation of some cloud droplets, with the rest remaining unchanged. This is a signature of inhomogeneous mixing. While comparing the results of entrainment with varying air properties, the mixing signature appears as if the subsaturated air is well mixed with the cloud to evenly reduce the droplets’ size. In other words, taken together, the experiments appear to have the signature of homogeneous mixing. To explore these results in a greater depth, we conduct large-eddy simulations combined with a bin microphysics scheme. Our results reproduce the similar signatures of inhomogeneous and homogeneous mixing, implying that LES can resolve the inhomogeneous mixing when the grid spacing is smaller than the entrained air parcel. Additionally, we observe that increasing aerosol injection rate enhances the signature of inhomogeneous mixing, while coarser grid spacing diminishes it. Finally, the change in wall fluxes in response to various entrained air properties confirms that the homogeneous signature seen in the analysis of an ensemble of simulations is the result of various equilibrium states. This further strengthens the suggestion that the homogeneous mixing signature found in aircraft observations near the cloud top may result from combining entrainment events of different intensities, possibly caused by various-sized eddies.

Development and Validation of a Compressible Reacting Gas-Dynamic Flow Solver for Supersonic Combustion

An approach based on the OpenFOAM library has been developed to solve a high-speed, multicomponent mixture of a reacting, compressible flow. This work presents comprehensive validation of the newly developed solver, called compressibleCentralReactingFoam, with different supersonic flows, including shocks, expansion waves, and turbulence–combustion interaction. The comparisons of the simulation results with experimental and computational data confirm the fidelity of this solver for problems involving multicomponent high-speed reactive flows. The gas dynamics of turbulence–chemistry interaction are modeled using a partially stirred reactor formulation and provide promising results to better understand the complex physics involved in supersonic combustors. A time-scale analysis based on local Damköhler numbers reveals different regimes of turbulent combustion. In the core of the jet flow, the Damköhler number is relatively high, indicating that the reaction time scale is smaller than the turbulent mixing time scale. This means that the combustion is controlled by turbulent mixing. In the shear layer, where the heat release rate and the scalar dissipation rate have the highest value, the flame is stabilized due to finite rate chemistry with small Damköhler numbers and a limited fraction of fine structure. This solver allows three-dimensional gas dynamic simulation of high-speed multicomponent reactive flows relevant to practical combustion applications.

Multiphase condensation in cluster haloes: interplay of cooling, buoyancy, and mixing

ABSTRACT Gas in the central regions of cool-core clusters and other massive haloes has a short cooling time (≲1 Gyr). Theoretical models predict that this gas is susceptible to multiphase condensation, in which cold gas is expected to condense out of the hot phase if the ratio of the thermal instability growth time-scale (tti) to the free-fall time (tff) is tti/tff ≲ 10. The turbulent mixing time tmix is another important time-scale: if tmix is short enough, the fluctuations are mixed before they can cool. In this study, we perform high-resolution (5122 × 768–10242 × 1536 resolution elements) hydrodynamic simulations of turbulence in a stratified medium, including radiative cooling of the gas. We explore the parameter space of tti/tff and tti/tmix relevant to galaxy and cluster haloes. We also study the effect of the steepness of the entropy profile, the strength of turbulent forcing and the nature of turbulent forcing (natural mixture versus compressive modes) on multiphase gas condensation. We find that larger values of tti/tff or tti/tmix generally imply stability against multiphase gas condensation, whereas larger density fluctuations (e.g. due to compressible turbulence) promote multiphase gas condensation. We propose a new criterion min (tti/min (tmix, tff)) ≲ c2 × exp (c1σs) for when the halo becomes multiphase, where σs denotes the amplitude of logarithmic density fluctuations and c1 ≃ 6, c2 ≃ 1.8 from an empirical fit to our results.

Impact of atomization and spray flow conditions on droplet [formula omitted]-explosions and temporal self-similarity in the FSP process

Flame spray pyrolysis (FSP) is a technique for the synthesis of metal oxide nanoparticles by combusting precursor solutions in a spray flame. The combustion of certain precursor solutions is known to lead to severe droplet disruptions (μ-explosions) in the spray flame that are linked to the synthesis of homogeneous and phase-pure nanoparticles. In this work, a broad spectrum of suitable subsonic operating conditions for the synthesis of iron oxide nanoparticles by FSP is investigated to understand the influence of the jet Reynolds number and turbulence on the onset of μ-explosions and droplet dynamics in spray flames. In order to enable a coherent comparison between differently operated spray flames using an iron(III) nitrate nonahydrate solution, the gas-to-liquid mass ratio and, hence, the oxygen/fuel ratio have been kept constant in order to identify the influence of flow conditions on the droplet dynamics. From the analysis of the droplet sizes in the spray and in the spray flame, it is found that in all combusting sprays, the droplet sizes convert from unimodal (after atomization) to bimodal droplet size distribution (DSD) due to the presence of μ-explosions. The occurrence and evolution of the bimodal DSD reveal that high jet Reynolds numbers result in narrower DSD and in a sharper separation of both DSD probability peaks (modal values). A straightforward 1-step kinematic model is presented to describe the conversion of unimodal to bimodal DSD considering the evaporation of droplets as well as the disruption of droplets to mimic the effect of μ-explosions. The temporal evolution of droplets in FSP is investigated by spatially resolved velocity data that reveal the formation of a temporal self-similarity. The resulting iron oxide nanoparticle size decreases with increasing jet Reynolds number. The turbulent mixing and residence times in the flame, primarily set by the jet Reynolds number, are identified as key design parameters for FSP.

Internal solitary waves enhancing turbulent mixing in the bottom boundary layer of continental slope

The importance of internal solitary waves (ISWs) to the energy and material transport in the upper ocean has been confirmed, but how ISWs affect turbulent mixing in the bottom boundary layer is lack of direct field observation. To reveal the characteristics of ISWs and the turbulent mixing they cause in the bottom boundary layer, a 36-h fine-scale observation of ISWs and their influence on turbulent mixing was conducted at the South China Sea slope (water depth: 659 m). During the observation, a group of ISWs passed by with horizontal and vertical velocities of 0.2 and 0.04 m/s at 0.1 m above bottom (mab) respectively, resulting in strong velocity shear exceeding 0.5 m/s per meter. When the ISWs passed through the slope, although they did not deform and break near the seabed, they increased the bottom shear stress, turbulent kinetic energy production rate and turbulent kinetic energy dissipation rate ( ε ) at 0.6 mab several times. The ISWs induced ε reached O (10 −6 ) W/kg, which was one order of magnitude higher than the previously observed ε in the upper ocean of the South China Sea slope. At the same observation site, the internal tides induced ε in the bottom boundary layer was O (10 −5 ) W/kg, which indicated that the internal tides played a more important role than the ISWs in enhancing bottom turbulent mixing. • Direct observation reveals strong internal solitary waves near seabed of slope. • Solitary waves cause strong velocity (0.2 m/s) near seabed at depth of 659 m. • Internal solitary waves increase bottom layer turbulent mixing several times.

Experiments and fully transient coupled CFD-PBM 3D flow simulations of disperse liquid-liquid flow in a baffled stirred tank

Liquid-liquid disperse multiphase flow in a baffled tank stirred by a Rushton turbine is investigated by experiments and 3D simulations for different impeller speeds and volume fractions. Droplet size distributions are experimentally measured with an inline shadowgraphic probe and compared with fully transient coupled CFD-PBM simulations using the Eulerian multi-fluid framework, the inhomogeneous Multiple Size Group approach and a statistical turbulence model. The simulation model is assessed by a variation of size class and velocity group numbers, grid resolution and simulation domain extent. The model parameters for the breakup and coalescence kernels are fitted to match the measured droplet size distribution at a selected operation point. A subsequent application to different operation points shows that experimental droplet size trends are captured, albeit aside from the fitting point, deviations to data increase. The resulting droplet size distribution is analyzed by an assessment of the turbulent mixing, breakup and coalescence time scales.

Computationally efficient prediction of cycle-to-cycle variations in spark-ignition engines

Cycle-to-cycle variations are important to consider in the development of spark-ignition engines to further increase fuel conversion efficiency. Direct numerical simulation and large eddy simulation can predict the stochastics of flows and therefore cycle-to-cycle variations. However, the computational costs are too high for engineering purposes if detailed chemistry is applied. Detailed chemistry can predict the fuels’ tendency to auto-ignite for different octane ratings as well as locally changing thermodynamic and chemical conditions which is a prerequisite for the analysis of knocking combustion. In this work, the joint use of unsteady Reynolds-averaged Navier–Stokes simulations for the analysis of the average engine cycle and the spark-ignition stochastic reactor model for the analysis of cycle-to-cycle variations is proposed. Thanks to the stochastic approach for the modeling of mixing and heat transfer, the spark-ignition stochastic reactor model can mimic the randomness of turbulent flows that is missing in the Reynolds-averaged Navier–Stokes modeling framework. The capability to predict cycle-to-cycle variations by the spark-ignition stochastic reactor model is extended by imposing two probability density functions. The probability density function for the scalar mixing time constant introduces a variation in the turbulent mixing time that is extracted from the unsteady Reynolds-averaged Navier–Stokes simulations and leads to variations in the overall mixing process. The probability density function for the inflammation time accounts for the delay or advancement of the early flame development. The combination of unsteady Reynolds-averaged Navier–Stokes and spark-ignition stochastic reactor model enables one to predict cycle-to-cycle variations using detailed chemistry in a fraction of computational time needed for a single large eddy simulation cycle.

Flame stabilization mechanism study in a hydrogen-fueled model supersonic combustor under different air inflow conditions

Flame stabilization mechanisms of a hydrogen-fueled laboratory model scramjet combustor are numerically studied. The combustor consists of a sonic fuel jet injected paralleling into a supersonic air flow at the base of a wedge-shaped strut. The numerical calculations are based on an Open Source Field Operation and Manipulation (OpenFOAM) solver using the large eddy simulation method. A skeletal mechanism for hydrogen-air chemistry including 9 species 27 reactions is used to depict the combustion dynamics. Three cases with air stagnation temperature of 568 K, 460 K, and 960 K, are respectively studied under the same equivalence ratio and entrance Mach number. Damköler number based on the subgrid turbulent mixing time scale and the instantaneous chemical time scale is used to distinguish the role of mixture self-igniting from flame propagation in different air inflows. Flame stabilization in such strut-based combustor is compared with that of cavity-based one. It is found that the basic working principles for the two types of combustor are similar. However, the strut shows more simplicity in flame stabilization locations.

Effect of turbulence on NOx emission in a lean perfectly-premixed combustor

In order to provide validation data for high-fidelity CFD simulation to predict the NOx emission in turbulent premixed combustion, the effect of turbulence on NOx emissions is studied for a perfectly-premixed combustor running on methane/air at the mixture inlet temperature of 495K and the combustor pressure of 5atm over a range of equivalence ratios (0.54–0.85). Turbulence level is varied by a factor of 2–3 by changing the length of a portion of channels in a perforated plate on which the flame is stabilized. Simultaneous PIV and OH-PLIF measurements are used to calculate the required turbulence parameters for the model such as turbulence intensity and turbulence mixing time scales, and define the flame structure such as average flame height and hence flame zone residence time scales. Effect of turbulence level is found to have negligible effect on overall NOx emissions level. NOx emissions are predicted by using a partially-stirred reactor (PaSR) model with the measured turbulence parameters as the input. The modeling results agree very well with the measured NOx emission level and show that it slightly increases with the increase of turbulence level. They also show that increasing turbulence level results in increasing NOx formation rate in flame zone. However, as turbulence level increases the flame length decreases and hence flame residence time will decrease. As a result, the total NOx emission in the flame zone will be determined by the net effect of turbulence on turbulent mixing time and flame residence time. The effect of turbulence on NOx formation becomes negligible in the post flame zone.

Design of novel emulsion microgel particles of tuneable size

In this study, we designed a one-step solvent-free route to prepare emulsion microgel particles, i.e., microgel particles containing several sub-micron sized emulsion droplets stabilised by heat-treated whey protein. The heat treatment conditions were optimized using aggregation kinetics via fluorimetry and dynamic light scattering. Emulsions were gelled and microgel particles were formed simultaneously via turbulent mixing with calcium ions using two specific processing routes (Extrusion and T-mixing). By varying the calcium ion concentration and mixing conditions, we identified the optimal parameters to tune the size and structure of the resultant emulsion microgel particles. Microscopy at various length scales (confocal laser scanning microscopy, scanning electron microscopy) and static light scattering measurements revealed a decrease in particle size (100–10 μm) with lower turbulent mixing time (ca. 4 × 10−4 s) and lower concentrations of calcium ions (0.1–0.02 M). Larger particle sizes (500–1000 μm) were achieved with an increase in the turbulent mixing time (ca. 2 × 10−2 s) and higher concentrations of calcium ions (1–1.4 M). Using gelation kinetics data (small deformation rheology) and theoretical considerations, creation of smaller sized emulsion microgel particles was explained by the increased flux of calcium ions to the denatured whey protein moieties coating the emulsion droplets, enabling faster gelation of the particle surfaces. These novel emulsion microgel particles of tuneable size formed as a result of complex interplay between calcium ion concentration, heat treatment of whey protein, gelation kinetics and mixing time, may find applications in food, pharmaceutical and personal care industries.

Supersaturation Fluctuations during the Early Stage of Cumulus Formation

Abstract On time scales that are long compared to the phase relaxation time, a quasi-steady supersaturation sqs is expected to exist in clouds. On shorter time scales, however, turbulent fluctuations of temperature and water vapor concentration should generate fluctuations in supersaturation. The variability of temperature, water vapor, and supersaturation has been measured in situ with submeter resolution in warm, continental, shallow cumulus clouds. Several cumuli with horizontal extents of order 100 m were sampled during their first appearance and development to depths of ~100 m in a growing boundary layer. Fluctuations of the saturation ratio are observed to be approximately normally distributed with standard deviations on the order of 1%. This variability is almost one order of magnitude larger than sqs calculated using simultaneous measurements of the vertical velocity component and the droplet size distribution. It is argued that, depending on the ratio of the phase relaxation and the turbulent mixing time, substantial fluctuations in the supersaturation field can exist on small spatial scales, centered on sqs for the mean state. The observations also suggest that, on larger scales, fluctuations of the supersaturation field are damped by cloud droplet growth. Droplets with diameters of up to 20 μm were observed in the shallow cumulus clouds, whereas the adiabatic diameter was less than 10 μm. Such large droplets may be explained by a few droplets experiencing the highest observed supersaturations for a certain time. Consequences for aerosol activation and droplet size dispersion in a highly fluctuating supersaturation field are briefly discussed.

Turbulent mixing and removal of ozone within an Amazon rainforest canopy

AbstractSimultaneous profiles of turbulence statistics and mean ozone mixing ratio are used to establish a relation between eddy diffusivity and ozone mixing within the Amazon forest. A one‐dimensional diffusion model is proposed and used to infer mixing time scales from the eddy diffusivity profiles. Data and model results indicate that during daytime conditions, the upper (lower) half of the canopy is well (partially) mixed most of the time and that most of the vertical extent of the forest can be mixed in less than an hour. During nighttime, most of the canopy is predominantly poorly mixed, except for periods with bursts of intermittent turbulence. Even though turbulence is faster than chemistry during daytime, both processes have comparable time scales in the lower canopy layers during nighttime conditions. Nonchemical loss time scales (associated with stomatal uptake and dry deposition) for the entire forest are comparable to turbulent mixing time scale in the lower canopy during the day and in the entire canopy during the night, indicating a tight coupling between turbulent transport and dry deposition and stomatal uptake processes. Because of the significant time of day and height variability of the turbulent mixing time scale inside the canopy, it is important to take it into account when studying chemical and biophysical processes happening in the forest environment. The method proposed here to estimate turbulent mixing time scales is a reliable alternative to currently used models, especially for situations in which the vertical distribution of the time scale is relevant.

Surface waves propagating on a turbulent flow

We study the propagation of monochromatic surface waves on a turbulent flow of liquid metal, when the waves are much less energetic than the background flow. Electromagnetic forcing drives quasi-two-dimensional turbulence with strong vertical vorticity. To isolate the surface-wave field, we remove the surface deformation induced by the background turbulent flow using coherent-phase averaging at the wave frequency. We observe a significant increase in wavelength, when the latter is smaller than the forcing length scale. This phenomenon has not been reported before and can be explained by multiple random wave deflections induced by the turbulent velocity gradients. The shift in wavelength thus provides an estimate of the fluctuations in deflection angle. Local measurements of the wave frequency far from the wavemaker do not reveal such systematic behavior, although a small shift is visible. Finally, we quantify the damping enhancement induced by the turbulent flow and compare it to the existing theoretical predictions. Most of them suggest that the damping increases as the square of the Froude number, whereas our experimental data show a linear increase with the Froude number. We interpret this linear relationship as a balance between the time for a wave to cross a turbulent structure and the turbulent mixing time. The larger the ratio of these two times, the more energy is extracted from the wave. We conclude with possible mechanisms for energy exchange.

Cross-Shelf Exchange.

Cross-shelf exchange dominates the pathways and rates by which nutrients, biota, and materials on the continental shelf are delivered and removed. This follows because cross-shelf gradients of most properties are usually far greater than those in the alongshore direction. The resulting transports are limited by Earth's rotation, which inhibits flow from crossing isobaths. Thus, cross-shelf flows are generally weak compared with alongshore flows, and this leads to interesting observational issues. Cross-shelf flows are enabled by turbulent mixing processes, nonlinear processes (such as momentum advection), and time dependence. Thus, there is a wide range of possible effects that can allow these critical transports, and different natural settings are often governed by different combinations of processes. This review discusses examples of representative transport mechanisms and explores possible observational and theoretical paths to future progress.

Gasoline engine simulations using zero-dimensional spark ignition stochastic reactor model and three-dimensional computational fluid dynamics engine model

A simulation process for spark ignition gasoline engines is proposed. The process is based on a zero-dimensional spark ignition stochastic reactor model and three-dimensional computational fluid dynamics of the cold in-cylinder flow. The cold flow simulations are carried out to analyse changes in the turbulent kinetic energy and its dissipation. From this analysis, the volume-averaged turbulent mixing time can be estimated that is a main input parameter for the spark ignition stochastic reactor model. The spark ignition stochastic reactor model is used to simulate combustion progress and to analyse auto-ignition tendency in the end-gas zone based on the detailed reaction kinetics. The presented engineering process bridges the gap between three-dimensional and zero-dimensional models and is applicable to various engine concepts, such as, port-injected and direct injection engines, with single and multiple spark plug technology. The modelling enables predicting combustion effects and estimating the risk of knock occurrence at different operating points or new engine concepts for which limited experimental data are available.

Turbulent flow and mixing performance of a novel six-blade grid disc impeller

A novel six-blade grid disc impeller (RT-G) was designed and the single-phase turbulent flow and mixing in a baffled stirred tank agitated by this impeller were numerically studied by detached eddy simulation (DES) model. For comparison, a standard Rushton impeller (RT) with the same dimension was also investigated. The numerical results were compared with the reported experimental data and good agreements were obtained. Comparisons of the mean velocity, turbulent kinetic energy, power consumption and mixing time of RT and RT-G were performed. Results show that, for the tank stirred with RT-G, the velocity components can be increased in comparison with RT when the same power is consumed. The increase of the turbulent kinetic energy is about 20–30%. Besides, the mixing time for the tank stirred with RT-G is about 11% shorter than that of RT stirred tank operated at the same condition.

Extension of the eddy dissipation concept and smoke point soot model to the LES frame for fire simulations

The eddy dissipation concept (EDC) is extended to the large eddy simulation (LES) framework following the same logic of the turbulent energy cascade as originally proposed by Magnussen but taking into account the distinctive roles of the sub-grid scale turbulence. A series of structure levels are assumed to exist under the filter width “Δ” in the turbulent energy cascade which spans from the Kolmogorov to the integral scale. The total kinetic energy and its dissipation rate are expressed using the sub-grid scale (SGS) quantities. Assuming infinitely fast chemistry, the filtered reaction rate in the EDC is controlled by the turbulent mixing rate between the fine structures at Kolmogorov scales and the surrounding fluids. In order to extend the laminar smoke point soot model (SPSM) to LES, the partially stirred reactor (PaSR) concept is used to relate the filtered soot formation rate to the soot chemical time scale, which is assumed to be proportional to the laminar smoke point height (SPH) of the fuel. The turbulent mixing time scale for soot is computed as a geometric mean of the Kolmogorov and integral time scale. A new soot oxidation model is also developed by imitating the gas phase combustion within EDC. The newly extended EDC and SPSM are implemented in the open source FireFOAM solver and tested with two medium scale heptane and toluene pool fires with promising results.

Large Eddy Simulation of Turbulent Flow and Mixing Time in a Gas–Liquid Stirred Tank

Mixing time is a key parameter relevant to the scale-up and design of agitated reactors. Although there have been many published papers on mixing times in stirred tanks predicted by computational fluid dynamics (CFD), there are few reports on the large eddy simulation (LES) based prediction of the mixing time in a gas liquid stirred tank. In this work, an LES method based on an Eulerian-Eulerian model is presented for predicting the mixing time in a gas liquid stirred tank agitated by a Rushton turbine. In order to verify the simulated results, mixing time experiments were carried out using a conductivity technique. In the present LES, the Smagorinsky subgrid scale model was used to model the effect of subgrid scale on the resolved scales. The concentration distributions and operating parameters such as feed positions, impeller speeds, and gas flow rates on the mixing time were examined. It is shown that the predicted concentration distributions of tracers are more irregular and realistic by using LES. Also, the mixing time decreases with the increase of impeller speed. However, with increasing gas flow rate, the mixing time first increases and then levels off. The predicted mixing time by the LES method shows good agreement with the measured values.

Evaluation of a combustion model for the simulation of hydrogen spark-ignition engines using a CFD code

The present work deals with the evaluation of a combustion model that has been developed, in order to simulate the power cycle of hydrogen spark-ignition engines. The motivation for the development of such a model is to obtain a simple combustion model with few calibration constants, applicable to a wide range of engine configurations, incorporated in an in-house CFD code using the RNG k– ɛ turbulence model. The calculated cylinder pressure traces, gross heat release rate diagrams and exhaust nitric oxide (NO) emissions are compared with the corresponding measured ones at various engine loads. The engine used is a Cooperative Fuel Research (CFR) engine fueled with hydrogen, operating at a constant engine speed of 600 rpm. This model is composed of various sub-models used for the simulation of combustion of conventional fuels in SI engines; it has been adjusted in the current study specifically for hydrogen combustion. The basic sub-model incorporated for the calculation of the reaction rates is the characteristic conversion time-scale method, meaning that a time-scale is used depending on the laminar conversion time and the turbulent mixing time, which dictates to what extent the combustible gas has reached its chemical equilibrium during a predefined time step. Also, the laminar and turbulent combustion velocity is used to track the flame development within the combustion chamber, using two correlations for the laminar flame speed and the Zimont/Lipatnikov approach for the modeling of the turbulent flame speed, whereas the (NO) emissions are calculated according to the Zeldovich mechanism. From the evaluation conducted, it is revealed that by using the developed hydrogen combustion model and after adjustment of the unique model calibration constant, there is an adequate agreement with measured data (regarding performance and emissions) for the investigated conditions. However, there are a few more issues to be resolved dealing mainly with the ignition process and the applicability of a reliable set of constants for the emission calculations.

Turbulent mixing and residence time distribution in novel multifunctional heat exchangers–reactors

Multifunctional heat exchanger–reactors show significant promise in increasing the energy efficiency of industrial chemical processes. The performance of these systems is conditioned by flow properties and is strongly geometry dependent. Here CFD simulation and laser Doppler anemometry (LDA) measurements are used to investigate the redistributing effects of the longitudinal vorticity generated by rows of inclined trapezoidal tabs on turbulent mixing in static mixers. Studies are carried out on three different configurations: in the first, the tabs are aligned and inclined in the direction of flow (the reference geometry for a high-efficiency vortex (HEV) static mixer), in the second, a periodic 45° tangential rotation is applied to the tab arrays with respect to one another, and in the third the reference geometry is used in the direction opposite to the flow direction (reversed direction). The mixing efficiency, taken as the resultant of the momentum-transfer efficiency of the “mean” flow at different scales, is studied. Macro-mixing entails the dispersive capacity of the flow at the heat exchanger–reactor scale, and is generally measured by the residence time distribution (RTD). At the intermediate scale, meso-mixing is governed by the turbulent fluctuations; this process of turbulent mixing can be characterized by the turbulence kinetic energy (TKE). Micro-mixing is characterized by the local rate of turbulence energy dissipation and is related to the progress of fast chemical reactions and selectivity. It is shown here that the reversed-array arrangement (the third configuration) provides the best performance in micro- (50%) and meso-mixing (25%), but exhibits an approximately 40% increase in power consumption over the classical HEV (reference) geometry and somewhat pronounced bimodal behavior in the RTD.