Micromixing Model Research Articles

Numerical investigation of DQMoM-IEM as a turbulent reaction closure

This paper investigates a mean reaction rate closure for turbulent reacting flows called the Direct Quadrature Method of Moments using the Interaction by Exchange with the Mean micromixing model (DQMoM-IEM). The method was first introduced for reacting flows by Fox (Computational Models for Turbulent Reacting Flows, Cambridge University Press, 2003). We present a systematic study that considers several important new aspects of the method. In particular we introduce a new analytic expression for the DQMoM-IEM source terms. We present a rigourous numerical investigation and discuss problems of boundedness and singularity in detail. We introduce a filter function to overcome these issues in the general case and present analytic integrals for special cases of specific terms. We extend the methodology to take advantage of these developments and show details of the implementation in a commercial computational fluid dynamics (CFD) code. We present an extensive set of numerical experiments and validation. The method is proven for a problem known from the literature which includes an isothermal dimerisation process. Experimental and transported probability density function (PDF) data compare reasonably well. The method is discussed critically and areas for further research are suggested to make the method more practical.

A coupled Eulerian and Lagrangian mixing model for intermittent concentration time series

The time series of scalar concentration at fixed points in space is modeled by a system of Eulerian stochastic differential equations for velocity and concentration using statistics obtained from a Lagrangian micromixing model. The interaction by exchange with the conditional mean model is used in both the Eulerian and Lagrangian frameworks allowing the natural representation of the external, large scale, scalar intermittency due to meandering. The calculated time series includes both the meandering and the relative dispersion time scales. The model is compared to experimental data in decaying grid turbulence and to Lagrangian simulations in stationary homogeneous turbulence. Scalar probability density functions conditioned on the velocity are calculated at two downwind distances from the source along with the corresponding time series to illustrate the separate effects of meandering and relative dispersion.

Numerical modelling of hydrothermal flames. Micromixing effects over turbulent reaction rates

Determining turbulent reaction rates in hydrothermal combustion is a difficult task due to the high sensitivity with mixing of this type of flames. Combining a micromixing model for liquid reactions along with the Eddy dissipation concept (EDC) allows for a good estimation method of the turbulent reaction rates. This novel method is validated for the combustion of methanol in supercritical water, predicting the temperature of the flame and its structure with absolute average deviations below than 10% for most of the cases tested. The influence of different operational variables, i.e. inlet temperature, inlet mass fraction and inlet flow of the fuel have been estimated with high accuracy. The methodology proposed lays the foundations for the subsequent design of supercritical combustion devices, where the geometry of the system has a great influence in the yield of the combustion.

Elimination of Fast Modes in the Coupled Process of Chemistry and Diffusion in Turbulent Nonpremixed Flames: An Application of the REDIM Approach

A computational study has been made of bluff-body stabilized turbulent jet flames with strong turbulence-chemistry interaction (Sydney Flames HM1 and HM3). The wide range of scales in the problem is described using a combination of a standard second moment turbulence closure, a joint scalar transported probability density function (PDF) method and the Reaction-Diffusion Manifold (REDIM) technique. The latter provides a reduction of a detailed chemistry mechanism, taking into account effects of laminar diffusion. In an a priori test it is evaluated to what extent the single shot experimental data are located on the reaction-diffusion manifold. Next, computed spatial profiles of mean and variance of independent and dependent scalar variables and profiles of conditional averages and variances (conditional on mixture fraction) are compared to the experimental results. The quality of these predictions is interpreted in relation to the a priori analysis. In general, simulations using the REDIM approach for reduction of detailed C2-chemistry confirm earlier findings for micro-mixing model behavior, obtained with a skeletal Cl-mechanism. Nevertheless it is concluded that the experiments show important features that are not described by the currently used REDIM.

Micromixing models for turbulent flows

In transported probability density function and filtered density function methods, micromixing models are required to close the molecular mixing term. The accuracy and computational efficiency of improved versions of the parameterized scalar profile (PSP) model are assessed and compared with commonly used mixing models such as Curl, modified Curl, interaction by exchange with the mean and Euclidean minimum spanning tree. Different generalizations of the PSP mixing model for spatially inhomogeneous flow configurations are presented. The selected test cases focus on molecular mixing and avoid interference with other models. Simulation results for a three-stream problem, involving two inert scalars, and a multi-scalar test case with mean-scalar-gradients are presented.

Modeling of the Joint PDF of a Scalar and Its Gradient in Turbulent Mixing

A joint probability distribution function of a conservative scalar (mixture fraction) and its gradient is predicted numerically. Statistical moments of this function are compared to their approximations, direct numerical simulation data, and also to the results obtained by simplified models for a conditional rate of scalar dissipation, the surface density function, and the one-point PDF of scalar fluctuation under homogeneous isotropic turbulence. The results allow to evaluate the performance of existing statistical micromixing models.

Joint Scalar versus Joint Velocity-Scalar PDF Simulations of Bluff-Body Stabilized Flames with REDIM

Two transported PDF strategies, joint velocity-scalar PDF (JVSPDF) and joint scalar PDF (JSPDF), are investigated for bluff-body stabilized jet-type turbulent diffusion flames with a variable degree of turbulence–chemistry interaction. Chemistry is modeled by means of the novel reaction-diffusion manifold (REDIM) technique. A detailed chemistry mechanism is reduced, including diffusion effects, with N 2 and CO 2 mass fractions as reduced coordinates. The second-moment closure RANS turbulence model and the modified Curl’s micro-mixing model are not varied. Radiative heat loss effects are ignored. The results for mean velocity and velocity fluctuations in physical space are very similar for both PDF methods. They agree well with experimental data up to the neck zone. Each of the two PDF approaches implies a different closure for the velocity-scalar correlation. This leads to differences in the radial profiles in physical space of mean scalars and mixture fraction variance, due to different scalar flux modeling. Differences are visible in mean mixture fraction and mean temperature, as well as in mixture fraction variance. In principle, the JVSPDF simulations can be closer to physical reality, as a differential model is implied for the scalar fluxes, whereas the gradient diffusion hypothesis is implied in JSPDF simulations. Yet, in JSPDF simulations, turbulent diffusion can be tuned by means of the turbulent Schmidt number. In the neck zone, where the turbulent flow field results deteriorate, the joint scalar PDF results are in somewhat better agreement with experimental data, for the test cases considered. In composition space, where results are reported as scatter plots, differences between the two PDF strategies are small in the calculations at hand, with a little more local extinction in the joint scalar PDF results.

An Extension to the Incorporation Model of Micromixing and Its Use in Estimating Local Specific Energy Dissipation Rates

The incorporation model of micromixing first developed conceptually and quantified by Villermaux and co-workers has been extended to cover both higher rates of micromixing (higher mean and local sp...

Probability density function modeling of scalar mixing from concentrated sources in turbulent channel flow

Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is represented by a large number of Lagrangian particles. A stochastic near-wall PDF model combines the generalized Langevin model of Haworth and Pope [Phys. Fluids 29, 387 (1986)] with Durbin's [J. Fluid Mech. 249, 465 (1993)] method of elliptic relaxation to provide a mathematically exact treatment of convective and viscous transport with a nonlocal representation of the near-wall Reynolds stress anisotropy. The presence of walls is incorporated through the imposition of no-slip and impermeability conditions on particles without the use of damping or wall-functions. Information on the turbulent time scale is supplied by the gamma-distribution model of van Slooten et al. [Phys. Fluids 10, 246 (1998)]. Two different micromixing models are compared that incorporate the effect of small scale mixing on the transported scalar: the widely used interaction by exchange with the mean and the interaction by exchange with the conditional mean model. Single-point velocity and concentration statistics are compared to direct numerical simulation and experimental data at Reτ=1080 based on the friction velocity and the channel half width. The joint model accurately reproduces a wide variety of conditional and unconditional statistics in both physical and composition space.

Experimental study and nonlinear dynamic analysis of time-periodic micro chaotic mixers

The efficiency of MEMS-based time-periodic micro chaotic mixers is experimentally and theoretically investigated in this study. A time-periodic flow perturbation was realized using digitally controlled solenoid valves to activate a source and sink alternately, acting together as a pair, with different driving frequencies. Working fluids with and without fluorescent dye were used in the micromixing experiments. The spatio-temporal variation of the mixing concentration during the mixing process was characterized at different Strouhal numbers, ranging from 0.03 to 0.74, using fluorescence microscopy. A simple kinematical model for the micromixer was used to demonstrate the presence of chaotic mixing. Specific stretching rate, Lyapunov exponent, and local bifurcation and Poincaré section analyses were used to identify the emergence of chaos. Two different numerical methods were employed to verify that the maximum Lyapunov exponent was positive in the proposed micromixer model. A simplified analytical analysis of the effect of Strouhal number is presented. Kolmogorov–Arnold–Mose (KAM) curves, which are mixing barriers, were also found in Poincaré sections. From a comparative study of the experimental results and theoretical analysis, a finite-time Lyapunov exponent (FTLE) was shown to be a more practical mixing index than the classical Lyapunov exponent because the time spent in mixing is the main concern in practical applications, such as bio-medical diagnosis. In addition, the FTLE takes into account both fluid stretching in terms of the stretching rate and fluid folding in terms of curvature.

Impact of Turbulent Flow and Mean Mixture Fraction Results on Mixing Model Behavior in Transported Scalar PDF Simulations of Turbulent Non-premixed Bluff Body Flames

Numerical simulation results are presented for three turbulent jet diffusion flames, stabilized behind a bluff body (Sydney Flames HM1-3). Interaction between turbulence and combustion is modeled with the transported joint-scalar PDF approach. The focus of the study is on the impact of the quality of simulation results in physical space on the behavior of two micro-mixing models in composition space: the Euclidean Minimum Spanning Tree (‘EMST’) model and the modified Curl coalescence dispersion (‘CD’) model. Profiles of conditional means and variances of thermo-chemical quantities, conditioned on the mixture fraction, are discussed in the recirculation region and in the neck zone behind. The impact of the flow and mixing fields in physical space on the mixing model behavior in composition space is strong for the CD model and increases as the turbulence – chemistry interaction becomes stronger. The EMST conditional profiles, on the contrary, are hardly affected.

INTERACTION BETWEEN CHEMISTRY AND MICRO-MIXING MODELING IN TRANSPORTED PDF SIMULATIONS OF TURBULENT NON-PREMIXED FLAMES

A comparative study is presented of the impact of chemistry modeling on the behavior of 2 micro-mixing models in transported scalar PDF simulations of turbulent non-premixed flames. The micro-mixing models are CD (modified Curl's Coalescence/Dispersion) and EMST (Euclidean Minimum Spanning Tree). A first order non-linear k-ε turbulence model is applied for the turbulent flow and mixing fields. Three C1 chemistry models are considered: 2 skeletal schemes containing 16 species and 31, resp. 41 elementary reactions, and one augmented reaction scheme (ARM), consisting of 9 independent species and 5 global reaction steps. The test cases considered are the piloted turbulent Delft Flame III jet diffusion flame and the bluff-body stabilized turbulent non-premixed Sydney HM1 flame. With EMST the chemistry model choice has a negligible effect on the micro-mixing model behavior or on the results in physical space. With CD on the other hand, larger differences appear.

CFD Modelling of Nano-Particle Precipitation in Confined Impinging Jet Reactors

Predictive design of nano-particle production via precipitation requires that the different steps through which particle formation occurs are deeply understood in order to control the final product properties and quality. In this work nano-particle precipitation in a confined impinging jet reactor (CIJR) is studied from the modelling point of view. The mathematical model, based on computational fluid dynamics (CFD), includes a micro-mixing model, the interchange by exchange with the mean (IEM) model coupled with the direct quadrature method of moments (DQMOM) approach, and solves the population balance equation (PBE) with the quadrature method of moments (QMOM). Eventually CFD predictions are compared with experimental data and good agreement is found.

Modelling of concentration fluctuations in canopy turbulence

The knowledge of the concentration probability density function (pdf) is of importance in a number of practical applications, and a Lagrangian stochastic (LS) pdf model has been developed to predict statistics and concentration pdf generated by continuous releases of non-reactive and reactive substances in canopy generated turbulence. Turbulent dispersion is modelled using a LS model including the effects of wind shear and along-wind turbulence. The dissipation of concentration fluctuations associated with turbulence and molecular diffusivity is simulated by an Interaction by Exchange with the Conditional Mean (IECM) micromixing model. A general procedure to obtain the micromixing time scale needed in the IECM model useful in non-homogeneous conditions and for single and multiple scalar sources has been developed. An efficient algorithm based on a nested grid approach with particle splitting, merging techniques and time averaging has been used, thus allowing the calculation for cases of practical interest. The model has been tested against wind-tunnel experiments of single line and multiple line releases in a canopy layer. The approach accounted for chemical reactions in a straightforward manner with no closure assumptions, but here the validation is limited to non-reacting scalars.

An efficient algorithm for scalar PDF modelling in incompressible turbulent flow; numerical analysis with evaluation of IEM and IECM micro-mixing models

In this paper, we investigate the application of probability density function (PDF) Monte Carlo methods to scalar release from small sources in a turbulent flow spanning a large physical domain. This is a typical situation encountered when modeling the dispersion of a gaseous substance in the atmosphere. Monte Carlo PDF methods have recently been applied to atmospheric modeling responding to the need for predicting the higher statistics and the concentration PDF generated by the continuous release of reactive and non-reactive substances. In this work we introduce some optimized numerical techniques based on the paradigm that the main field of interest is the scalar field and not the fluid dynamic field; the scalar are considered dynamically passive and the statistical characteristics of the turbulence velocity field are assumed known. These techniques are a block-structured grid coupled with a particle splitting/erasing algorithm and a localized time stepping. The proposed technique is different from others presented before since the particle splitting and erasing is done in a more straightforward and consistent manner. This method has been applied to the study of scalar dispersion from localized line sources in a canopy generated boundary layer. The line source has been treated as a point source in a two-dimensional space but the extension to three dimensions is straightforward. Our framework allows for an evaluation of the effects induced by different levels of discretization in the velocity space of the involved micro-mixing model, starting from the interaction by the exchange with the mean (IEM) toward the more physically consistent interaction by exchange with the conditional mean (IECM). Therefore, aside from the algorithm description and a complete numerical analysis of the code, a comparison between the IEM and IECM micro-mixing models has been investigated.

A consistent LES/filtered-density function formulation for the simulation of turbulent flames with detailed chemistry

A hybrid large-Eddy simulation/filtered-density function (LES–FDF) methodology is formulated for simulating variable density turbulent reactive flows. An indirect feedback mechanism coupled with a consistency measure based on redundant density fields contained in the different solvers is used to construct a robust algorithm. Using this novel scheme, a partially premixed methane/air flame is simulated. To describe transport in composition space, a 16-species reduced chemistry mechanism is used along with the interaction-by-exchange with the mean (IEM) model. For the micro-mixing model, typically a constant ratio of scalar to mechanical time-scale is assumed. This parameter can have substantial variations and can strongly influence the combustion process. Here, a dynamic time-scale model is used to prescribe the mixing time-scale, which eliminates the time-scale ratio as a model constant. Two different flame configurations, namely, Sandia flames D and E are studied. Comparison of simulated radial profiles with experimental data show good agreement for both flames. The LES–FDF simulations accurately predict the increased extinction near the inlet and re-ignition further downstream. The conditional mean profiles show good agreement with experimental data for both flames.

Comparison of transported scalar PDF and velocity-scalar PDF approaches to ‘Delft flame III’

Numerical simulation results are presented for the turbulent piloted jet diffusion flame ‘Delft Flame III’. In this flame, which is one of the target flames of the International Workshop on Measurements and Computations of Turbulent Nonpremixed Flames (TNF), effects of turbulence-chemistry interaction are strong and modelling the turbulence-chemistry interaction is a challenge. After an outline of the theoretical framework, a comparison is presented of results with on the one hand the velocity-scalar transported probability density function (PDF) approach with reduced chemistry (ILDM) and on the other hand the scalar PDF approach with detailed chemistry (C 1-mechanism). The same micromixing model (modified coalescence-dispersion model, CD) is used in both studies. The reasons for the significantly better prediction of the mean temperature field by the scalar PDF calculations are discussed. Results of other micromixing models are briefly mentioned. To cite this article: D. Roekaerts et al., C. R. Mecanique 334 (2006).

Lagrangian modeling of scalar statistics in a double scalar mixing layer

Statistics of scalar concentration in a double scalar mixing layer are calculated using a Lagrangian stochastic model coupled to the interaction by exchange with the conditional mean micromixing model. Excellent agreement is obtained with recent direct numerical simulation results. The model accurately reproduces a wide variety of behavior across both physical and concentration space and over both unconditional and conditional scalar statistics.

Comparative study of micromixing models in transported scalar PDF simulations of turbulent nonpremixed bluff body flames

Numerical simulation results are presented for turbulent jet diffusion flames with various levels of turbulence–chemistry interaction, stabilized behind a bluff body (Sydney Flames HM1–3). Interaction between turbulence and combustion is modeled with the transported joint-scalar PDF approach. The mass density function transport equation is solved in a Lagrangian manner. A second-moment-closure turbulence model is applied to obtain accurate mean flow and turbulent mixing fields. The behavior of two micromixing models is discussed: the Euclidean minimum spanning tree model and the modified Curl coalescence dispersion model. The impact of the micromixing model choice on the results in physical space is small, although some influence becomes visible as the amount of local extinction increases. Scatter plots and profiles of conditional means and variances of thermochemical quantities, conditioned on the mixture fraction, are discussed both within and downstream of the recirculation region. A distinction is made between local extinction and incomplete combustion, based on the CO species mass fraction. The differences in qualitative behavior between the micromixing models are explained and quantitative comparison to experimental data is made.

Precipitation of nanoparticles in a T-mixer: Coupling the particle population dynamics with hydrodynamics through direct numerical simulation

Mixing is a key parameter to tailor the particle size distribution (PSD) in nanoparticle precipitation. In this study we present two model approaches to simulate the impact of mixing on the PSD, using barium sulfate as exemplary material. In the first model, we combine a Lagrangian micromixing model with the population balance equation. This approach was found successful in predicting the influence of mixing on mean particle sizes but fails to predict the shape and width of the PSD. This is attributed to the neglect of spatial and temporal fluctuations in that model. Therefore, an improved CFD-based approach using direct numerical simulation (DNS) in combination with Lagrangian particle tracking strategy is applied. We found that the full DNS-approach, coupled to the population balance and a derived micromixing model, is capable of predicting the full PSD in nanoparticle precipitation.