Micromixing Model Research Articles

Experimental study and turbulence dissipative scale modelling of the rapid micromixing of impinging thin sheets of liquids

Previous studies have shown that the impingement of thin liquid sheets produces high energy dissipation rates due to the release of kinetic energy in a very small mass of liquid (0.0001–0.01 g), even though flowrates are on the order of L/min. Rapid micromixing occurs because the dissipated energy leads to a substantial reduction in the initial segregation size scale of the liquids, which is the single-sheet thickness at impingement (~ 100 μm). In the present study, the micromixing was investigated by following the progress of an acid-base neutralization accompanied by a change in fluorescence intensity of a fluorophore. Micromixing was modeled using a framework that assumes diffusion and reaction of species occur within slabs of fixed thickness (2L). The slabs are fixed in size because the released kinetic energy is dissipated within one turnover time of the large energy-containing eddies produced in the turbulent impingement zone. A simulation, which included a module for calculating the fluorescence intensity, determined 2L for experimental energy dissipation rates (ϵ) ranging from 4×104 to 7.7×106 W/kg. 2L was found to lie in the range of turbulent dissipative scales less than the Taylor microscale but greater than the Kolmogorov microscale. 2L/v′ was found to be a function of ReΛ−1/4 and ν/ϵ1/2, where v′ is the velocity associated with the turbulent kinetic energy, ReΛ is the large-eddy Reynolds number and ν is the kinematic viscosity. Similar to η/Λ, 2L/Λ is a function of ReΛ−3/4, where ηis the Kolmogorov microscale and Λ is the size of the large energy-containing eddies.

Liquid flow field and residence time distribution in a baffleless oscillatory flow coil reactor

Baffleless coils can operate as continuous oscillatory flow reactors to produce pharmaceutical products where process intensification is intended. A method to evaluate mixing performance and its impact on reaction conversion is residence time distribution (RTD) analysis. Liquid macromixing in a long baffleless coil reactor (L = 24 m, dt = 4.57 mm) at ranges of oscillation amplitude (11.75–58.75 mm), frequency (0–3.68 Hz), and net flow rate (30–120 g⋅min−1) was investigated based on measured RTDs fitted to the skewed normal distribution model. The impact of operating conditions on the RTD was supported by analyzing the liquid flow field derived from CFD simulations. The RTD variance under different oscillation conditions suggests a near plug flow pattern, although deviations from ideality such as skewness and long tailing were always observed. The model parameters, along with the RTD variance, were correlated to the operating conditions lumped in an oscillatory Dean number that used the flow amplitude as characteristic length (Deox). Values of Deox varied between 150 and 11000, and the RTD variance at the different net flow rates was minimized for 300 < Deox < 600, as also evidenced from the minimum cross-sectional variance of the simulated time-averaged axial velocity profile. Normalizing the data allowed comparison to similar coil studies with different geometrical dimensions and operating conditions, leading to generalized correlations for the RTD model parameters. Finally, chemical conversion was assessed for first- and second-order single phase reactions at different Damköhler numbers using the segregation and maximum mixedness micromixing models combined with the fitted RTDs. The performance of the coil remained consistent with a plug flow reactor despite its departures from ideal flow.

Investigation of Modified EMST Micromixing Model Performance on Lagrangian PDF Transported in Lifted Hydrogen/Air Fames

This article presents a numerical simulation of high hydrogen/air flames using the Lagrangian transported PDF method. This method enables the calculation of fluid composition changes resulting from convection and reaction without the need for modelling, while requiring modelling for molecular mixing. Consequently, the accuracy of calculations in this L-PDF method heavily relies on an accurate representation of the mixture model term. The Euclidean model, which provides a better description of physical mixing processes, is well-suited for modelling the molecular mixing term EMST. Additionally, the accuracy of this model depends on the value of the mixing constant, representing the ratio between the mechanical time scale and the scalar time scale. Two algebraic models for the mixing constant have been implemented in the computational code, employing a well-defined function to calculate this ratio for each cell. These models contribute to memory and CPU time savings. To account for turbulence and its interaction with physical phenomena, the RSM model is employed due to its ability to identify different areas of turbulent stresses. Hence, the primary objective of this study is to evaluate the capabilities of these algebraic models in predicting scalar fields within such flames. Overall, the predictions align well with experimental data, affirming the validity of these models.

Local estimation of the mixing model constant for transported PDF combustion models

This work presents a novel method for the local estimation of the mixing constant in transported, joint-composition, probability density function (TPDF) combustion models. In the literature, the micro-mixing model’s constant, denoted as Cϕ which represents the ratio between the integral and the mixing time-scale, is usually set to a fixed and uniform value. The selection of the appropriate value of the aforementioned constant is mostly done by trial-and-error procedures, which entails a considerable computational cost considering the complexity of TPDF models. In addition, the assumption of a uniform value for this constant may affect the performance of such models, as local effects are neglected. For these reasons, an approach for the local estimation of the mixing constant based on the transport of a passive scalar is developed in this work. The approach is tested by performing Reynolds-Averaged Navier–Stokes simulations on the Adelaide Jet-In-Hot-Coflow (AJHC) flames at different Reynolds numbers (i.e., 5,000 and 10,000) and oxygen concentrations in the coflow (i.e., 3 and 9% in mass basis). The model is validated against experimental data of temperature and species. The local approach can help to overcome the issues related to the tuning of Cϕ, which in many cases may result in time-consuming trial-and-error procedures.

Image‐based measurement of engulfment vortex to quantitatively assess micromixing efficiency in a gas–liquid stirred tank

AbstractMicromixing in reactors is typically characterized by chemical test reactions. A novel image‐based measurement system of engulfment vortex (IMEV system) is developed to assess the micromixing efficiency. Over 2000 vortices were recognized from images captured under various experimental cases, and key frames for their formation, engulfment and dissipation were identified. Inspired by the engulfment model (i.e., E model), this work quantified the micromixing time and local turbulent energy dissipation rate with the vortex lifetimes. The micromixing time obtained through the IMEV method is comparable to its value estimated by the micromixing model and segregation index of the test reaction, with a deviation of less than 20%. In turbulent gas–liquid systems, bubbles play a dual role on the local micromixing due to frequent disturbance and phase interface limitation. To summarize, this work offers an alternative approach for micromixing studies and provides valuable insights into dispersed phase effects on the micromixing efficiency.

Computational Modeling of Magnesium Hydroxide Precipitation and Kinetics Parameters Identification.

Magnesium is a critical raw material and its recovery as Mg(OH)2 from saltwork brines can be realized via precipitation. The effective design, optimization, and scale-up of such a process require the development of a computational model accounting for the effect of fluid dynamics, homogeneous and heterogeneous nucleation, molecular growth, and aggregation. The unknown kinetics parameters are inferred and validated in this work by using experimental data produced with a T2mm-mixer and a T3mm-mixer, guaranteeing fast and efficient mixing. The flow field in the T-mixers is fully characterized by using the k-ε turbulence model implemented in the computational fluid dynamics (CFD) code OpenFOAM. The model is based on a simplified plug flow reactor model, instructed by detailed CFD simulations. It incorporates Bromley's activity coefficient correction and a micro-mixing model for the calculation of the supersaturation ratio. The population balance equation is solved by exploiting the quadrature method of moments, and mass balances are used for updating the reactive ions concentrations, accounting for the precipitated solid. To avoid unphysical results, global constrained optimization is used for kinetics parameters identification, exploiting experimentally measured particle size distribution (PSD). The inferred kinetics set is validated by comparing PSDs at different operative conditions both in the T2mm-mixer and the T3mm-mixer. The developed computational model, including the kinetics parameters estimated for the first time in this work, will be used for the design of a prototype for the industrial precipitation of Mg(OH)2 from saltwork brines in an industrial environment.

Numerical Analysis and Moth Flame Optimization of Passive T-Micromixer with Twist and Bend mixing channel

In this study, we investigate a novel micromixer for numerical analysis with evolutionary algorithm optimization, using Computational Fluid Dynamics (CFD) and Machine Learning (ML) tools while maintaining relatively low computational costs. The initial design is motivated by a simple-T micromixer using different twists and bends. Ansys fluent with finite volume analysis, conducts a simulation for this parameter. We investigate the impact of twist and bend on mixing performance and pressure drops. For data analysis, we consider the twist, bend angle, and Reynold number as input variables and mixing index and pressure drop as outputs variables for training using a neural network. With the moth flame optimization algorithm, the micromixer model was optimized for the maximum mixing performance and the minimum pressure drop. The optimal value for the twist and bend angle is 4 and 700, respectively, at Reynold number (Re) 10. This technique has a significant benefit for microfluidic channel optimization.

A novel passive micromixer model computational analysis with twist and bend

A dynamic mixing model for a microfluidic platform that uses bending and twisting characteristic is proposed in this work. The action of twisting and bending on mixing efficient in the microchannel is tested using Navier-Stokes equations. Micromixers being broadly applied in micro total analysis systems (µTAS). Passive micromixers are largely preferred from their heftiness, serenity of amalgamation and cost effective. However rapid mixing in this model is difficult but can be achieved with a twist in the model and offset. From the past study, we know that with a high Reynolds number mixing efficiency effectively improved. Chaotic advection allows the micromixer model to generate secondary flow which led to a drop in high-pressure drop in the model.

Large-Eddy Simulation of flameless combustion with neural-network driven chemistry

Large eddy simulation of a flameless combustion furnace is discussed with comparison against experimental measurements of the mean thermochemical quantities. The focus is on the introduction in flow simulations of complex chemistry through the training of neural networks, in order to simulate the oxidation of a gaseous fuel representative of recycled gases available in the steel industry. A canonical problem, based on a non-adiabatic stochastic micro-mixing model and combined with a detailed description of chemistry, is setup to train the neural networks prior to the flow simulation. For these networks to be predictive, the thermochemical composition space is decomposed into sub-domains from a partitioning algorithm. A neural network is trained in every sub-domain to return the increments in time of the most influential thermochemical quantities, from the knowledge of temperature and species mass fractions solved with the flow. Implemented in an open-source low-Mach number fluid mechanics code, the neural networks complex chemistry is shown to be very efficient in terms of CPU time, with an overhead of only 60% compared to the non-reactive multi-species simulation of the furnace.

Development of a cellular mixing model for competitive-consecutive reactions

This work presents experimental and theoretical investigations into the effects of mixing on third-order reaction kinetics in a semibatch reactor with high feed rates. Minimization of the thiourea impurity in this synthetic step constituted the main objective. The kinetic data were obtained in laboratory experiments, whereas the characteristic mixing time-constants at low stirring speeds were measured using a purposely developed asymptotic pH method in linear buffer. A general mixing model combining both mass- and heat-transfer was created using cellular automata (CA) principles, and in conjunction with the engulfment (E) model of micromixing. This new approach included the effects of concentration gradients and interacting mixing-reaction zones and predicted a significant increase of the impurity formation under low mixing conditions. The predictions were also extended to an industrial scale.

Assessment of critical species for differential mixing in transported PDF simulations of a non-premixed ethylene DNS flame

The difference in the mixing timescale among species, i.e., differential mixing, is a combined result due to the difference in molecular diffusivity and the difference in reaction-induced scalar gradient. Being a key component for micro-mixing, incorporating differential mixing is a desirable feature for a transported probability density function (TPDF) simulation. Nevertheless, the lack of understanding of differential mixing hinders its model development. This paper intends to address that whether there exist critical species for differential mixing, such that considering only the differential mixing of these species can reproduce the prediction with the full differential mixing of all species. To achieve so, TPDF simulations have been performed for a temporally evolving, non-premixed ethylene DNS flame, with the DNS-extracted mean velocity, turbulent diffusivity and species mixing timescales to enable a clean assessment on the critical species for differential mixing. An algorithm based on active subspace (AS) method is proposed to identify the critical species. It is found that the identified 10 critical species are neither the ones having the highest mixing frequency nor the ones causing the largest temperature change. The TPDF simulation with the differential mixing of the 10 critical species can well reproduce the mean and conditional mean quantities of the reference simulation with the full differential mixing of all species, illustrating the effectiveness of the AS method. Compared to the crude single-species trial method, the AS method better identifies the critical species as it accounts for the coupling nature of the chemical reaction system. By analyzing the reaction pathway in 1D opposed jet flames, it is found that the critical species all involve in the controlling reactions for the overall combustion process, thus providing a physical interpretation for the identified critical species. The effects of quantity of interest and micro-mixing model on critical species are also analyzed.

Predicting jet ignitability using a PDF transport model

For the first time the probability of ignition is calculated successfully using a PDF transport model. At present the model is only accurate where jet intermittency effects are small, away from the jet boundary. A conclusion of this investigation is the probability of ignition field is sensitive to the micro-mixing model used. In this article, four micro-mixing models are implemented and the modified Curl model demonstrated to be the most accurate for the jet ignitability experiments simulated.

Solvent-antisolvent precipitation in a spinning disc reactor: Precipitation kinetics and mathematical modelling of starch nanoparticles

Experimentally determined kinetics for the precipitation of starch nanoparticles in ethanol antisolvent are reported in a spinning disc reactor. Induction times (tind) obtained from visualisation studies are estimated to be between 13 and 144 ms, with lower tind obtained at higher shear and supersaturations. Nucleation rates are measured to be of the order of 1016 mL−1s − 1, with higher values obtained on a smooth disc at the highest shear conditions and 9:1 antisolvent/solvent ratio. The grooved texture is deemed more advantageous in the low shear regions (i.e. at low flow rate and disc speed) where the passive mixing induced by the flow disrupting grooves produces more nuclei than the smooth surface under similar conditions. Modelling of particle size distribution via population balance equations combined with an engulfment micromixing model has been validated against the experimental profiles with good agreement for most of the conditions studied, even in the presence of agglomerates.

Modeling of sawdust drying in spouted beds using solar energy and phase change materials

In the present work, the modeling and simulation of the continuous drying of sawdust using spouted beds connected in series and a solar energy accumulator panel to heat the drying air was carried out. The modeling approach for the solar energy accumulator panel was based on energy balances, whereas for the dryer a combination of residence time distribution, drying kinetics and micro-mixing models was considered. Model parameters were adjusted with available experimental data. Simulations results were validated using experimental values, observing that the predicted outlet air temperature of the solar collector presented root mean squared errors lower than 1.9 °C for 5 different air flows, while the outlet sawdust moisture deviated less than 5.6%. Finally, the effect of increasing the number of spouted beds and the solids feed rate on the moisture content leaving the dryer was evaluated, showing a greater influence of the increase in spouted bed units compared to increasing the drying air temperature by 10 °C.

A fully dynamic mixing time‐scale model for the sparse Lagrangian multiple mapping conditioning approach

Multiple mapping conditioning / large eddy simulation (MMC-LES) is a promising model for turbulence-chemistry interactions, successfully applied to simulate different combustion regimes involving gaseous, liquid, and solid fuels. MMC-LES attempts to produce accurate molecular mixing by localising mixing in an independent, composition-like reference space. In the MMC mixing model, mixing between two stochastic particles is defined based on the Lagrangian mixing time-scale τL, which is defined as the ratio of the Lagrangian subgrid-scale mixture fraction variance (fL′2˜) and the scalar dissipation rate (χL), typically modelled algebraically, based on fixed values of global constants at all spatial locations. Accurate modelling of τL is essential towards predicting the conditional scalar fluctuations, which is otherwise highly challenging if the same set of static constants are used at all spatial locations for complex flames with varying extinction/re-ignition. Herein, a fully dynamic mixing time-scale model (dyn-aISO) is proposed within the MMC-LES framework, which dynamically evaluates fL′2˜ and χL, essentially based on a local variance coefficient and variable turbulent Schmidt number, respectively, eliminating the need for specifying tuneable model constants. This novel dyn-aISO model is used to simulate the pilot-stabilised Sandia flame series with increasing local extinction levels. The conditional and unconditional profiles of compositional scalars from the new dynamic model are compared with those from a fully static model (st-aISO) and a model which uses a static constant for fL′2˜ (stCf-aISO). Numerical results from different timescale models deviate from each other for Sandia flame F having a high jet Reynolds number. With the proposed improvement of the micro-mixing time-scale model, the dyn-aISO model accurately captures the transient behaviour of the complete flame series, which could otherwise be obtained by the tuning of static constants. The role of molecular and turbulent mass diffusivities, coefficient of residual variance of mixture fraction, mixing distance, and the mixing time-scale on the predictions of the reactive scalars is also explored.

Mixing performance enhancement and parametric investigation of swirl-inlets split-and-recombine micromixer with pulsatile flow

The current study develops a pulsatile flow micromixing model, and investigates the performance of swirl-inlets split-and-recombine micromixer. A three-dimensional transient flow numerical model solving Navier-Stokes and diffusion equation is prepared to model the species mixing in a microchannel. The effect of pulsatile flow parameters, i.e., Strouhal number, amplitude ratio, and phase difference, on mixing performance is investigated along with the nature and extent of performance enhancement. A significant improvement in the mixing index is observed with the application of pulsatile flow. The pulse phase difference was found to be the more effective parameter to enhance the mixing index compared to Strouhal number and amplitude ratios investigated in the present study.

CFD-PBE modelling of continuous Ni-Mn-Co hydroxide co-precipitation for Li-ion batteries

A modelling framework is proposed to simulate the co-precipitation of Ni-Mn-Co hydroxide as precursor of cathode material for lithium-ion batteries. It integrates a population balance equation with computational fluid dynamics to describe the evolution of the particle size in (particularly continuous) co-precipitation processes. The population balance equation is solved by employing the quadrature method of moments. In addition, a multi-environment micromixing model is employed to consider the potential effect of molecular mixing on the fast co-precipitation reaction. The modelling framework is used to investigate the co-precipitation of Ni0.8Mn0.1Co0.1(OH)2 in a multi-inlet vortex micromixer, as a suitable candidate for the study of fast co-precipitation processes in continuous mode. Finally, the simulation results are discussed, and the role of the different phenomena involved in the formation and evolution of particles is identified by inspecting the predicted trends.

A comprehensive investigation of the incorporation model for micromixing time calculation

The incorporation model is a widely applied micromixing model for the interpretation of micromixing experiments conducted by the Villermaux–Dushman test reaction. In this work, a deeper look into the model is taken and a modified incorporation model is proposed which leads to more reasonable results regarding the time to equalize concentration gradients, which corresponds to a micromixed state. The original definition of the micromixing time, tm, is revised and two characteristic times are introduced which can be deduced from the modified incorporation model. First, the time in which the acid–base and Dushman reaction are completed, tR, and the time until a complete equalization of concentration gradients is reached, tE, which corresponds to the actual micromixing time. In addition, an instruction to easily revise historical micromixing time calculations from the original incorporation model is given. From the incorporation model, concentration ranges for the kinetic investigation of the Dushman reaction relevant to mixing studies were extracted and are proposed for future kinetic studies of the Dushman reaction. The MatLab codes for implementing the incorporation model are published in GitHub for further scientific exchange.

Numerical study of a high-hydrogen micromix model burner using flamelet-generated manifold

The flamelet-generated manifolds (FGM) method was adopted in this study to consider the preferential diffusion in a high-hydrogen micro-mixing model burner. That is, when solving the FGM flamelet, accurate diffusion rate was obtained from two methods: multicomponent formulation and constant detailed Lewis numbers assumption. Then a new method of filling the thermochemical state and the source term in the mixture fraction and the process variable space also was proposed, namely the linear triangular dissection interpolation method, to predict the position of the hydrogen-rich micro-mixing flame front. Compared with the Fluent approach to establish the diffusion FGM flamelet, the results showed that the two FGMs have similar flame predictions in high hydrogen content fuels, and both can accurately capture the location of the internal and external shear layer boundaries of the micro-mixing multi-jet flame in the steady state, while the Fluent approach based on the uniform Lewis number assumption predicts results that deviated significantly from the experimental results. However, for the internal shear layer, both methods have large predicted OH gradients compared to the experimental results due to the lack of effective Lewis number correction for the control variable transport equation. The results using linear triangular dissection interpolation maybe superior to the method with linear interpolation of the process variable quenching boundary toward zero, which leads to flashback due to overestimation of the process variable source term in the region below the diffusion FGM quenching boundary.

An improved model for interpretation of micromixing experiment with iodide–iodate method and sulphuric acid

The Villermaux–Dushman test reaction for micromixing characterization has been used by many researchers to investigate homogeneous mixing systems. Due to the complexity of the iodine-forming reaction, the strong effect of ionic strength of reaction medium on its reaction rate constant, as well as the dependence of the sulfuric acid dissociation on its concentration, the kinetic model of the iodide/iodate test reaction with sulfuric acid is complicated. Therefore, a quantitative evaluation of such a test reaction is challenging and remains an open problem. In this paper, the pH of the sulfuric acid solutions with different values of ionic strength is investigated using the model of Pitzer. The numerical results of the simulation are compared with the experimental data and good agreement is obtained. It is also shown that simple equilibrium calculations for sulfuric acid do not give correct pH results when the ionic strength of its solution is increased by the addition of sulfate salts. However, such an assumption yields satisfactory results for the cases without additional salt and with an acid concentration lower than 0.2 M. Finally, the engulfment model of micromixing using activities to calculate proton concentrations is applied to analyze the experimental results from previous papers employing the iodide/iodate method.