Scalar Mixing Layer Research Articles

Scalar structures around the mixing interface of a thermal mixing layer in multiscale-generated decaying turbulent flows visualized using DNS database

This study shows the results for the visualization of a scalar mixing layer in decaying turbulence produced by a multiscale-generated turbulence grid. For this purpose, a thermal mixing layer in the air is used as the scalar mixing layer. A fractal generating grid proposed in the previous study is used for the generation of multiscale-generated turbulence. In addition, a parameter for determining the grid shape is varied. The scalar field is then visualized using a database given by direct numerical simulations. The instantaneous scalar field, the instantaneous scalar fluctuation field, the instantaneous scalar variance field, and the scalar dissipation field are visualized, and the visualization results are discussed using the wake interaction length scale.

Small transparent prism for the cross-sectional visualization for a turbulent scalar mixing layer using a water-channel PLIF method

This study introduces a simple method that enables cross-sectional visualization in the measurement of the planer-laser induced fluorescence (PLIF) method. The concentration field of the high Schmidt number scalar mixing layer generated by grid-generated turbulence is measured by a water-channel experiment in this tudy. The high Schmidt scalar mixing layer is produced by Rhodamine B aqueous solution and water. A small transparent prism, installed on the outside wall of the test section, aids in applying cross-sectional visualization. The small transparent prism is an isosceles triangular shaped prism filled with the working fluid through the test section of the water channel. The setting and details of the small transparent prism are shown in this study. By using the small transparent prism, the concentration field on the plane set into the test section is shown as a result of the cross-sectional visualization. In this result, a scalar structure like a mushroom is visualized around the mixing interface of the scalar mixing layer, as found in a previous experiment.

Implicit large eddy simulation of a scalar mixing layer in fractal grid turbulence

A scalar mixing layer in fractal grid turbulence is simulated by the implicit large eddy simulation (ILES) using low-pass filtering as an implicit subgrid-scale model. The square-type fractal grid with three fractal iterations is used for generating turbulence. The streamwise evolutions of the streamwise velocity statistics obtained in the ILES are in good agreement with the experimental results. The ILES results are used for investigating the development of the scalar mixing layer behind the fractal grid. The results show that the vertical development of the scalar mixing layer strongly depends on the spanwise location. Near the fractal grid, the scalar mixing layer rapidly develops just behind the largest grid bars owing to the vertical turbulent transport. The scalar mixing layer near the fractal grid also develops outside the largest grid bars because the scalar is transported between the outside and back of the largest grid bars by the spanwise turbulent transport. In the downstream region, the scalar mixing layer develops more rapidly near the grid centerline by the vertical turbulent transport and by the spanwise one which transports the scalar between the back of the largest grid bars and both the centerline and outer edge of the fractal grid. Then, the mean scalar profile becomes close to be homogeneous in the spanwise direction.

Turbulent mixing of a passive scalar in grid turbulence

Fractal grids have attracted attention as a new-type of turbulence-generating grid due to their unique characteristics. Recent studies have revealed that such uniqueness appears in the near field of regular grid-generated turbulence. Scalar transport in those flows is also of great interest as it is not yet fully understood. In this study, we investigate the scalar mixing in the near field of regular grid-generated turbulence with various grid configurations. Experiments have been carried out in liquid mixing layers with a Reynolds number of 5000 based on the mesh size of the grid and uniform velocity. Simultaneous measurements of two-component velocities and concentration have been performed by particle image velocimetry and a planar laser-induced fluorescence technique, respectively. The results show that the scaling law using the wake-interaction length scale is applicable for the turbulence intensity in the grid turbulence with different mesh sizes and the same thickness of the grid bar. The turbulence intensity increases as the thickness of the grid bar increases; thus, consequently increasing the scalar diffusion. The streamwise development of the scalar mixing layer thickness collapses onto a single curve by normalization based on the thickness of the grid bar.

Lagrangian micromixing modelling of reactive scalar statistics: scalar mixing layer in decaying grid turbulence

A Lagrangian micro-mixing numerical model estimates the concentration statistics of reactive pollutants (NO, O3 and NO2) of a scalar mixing layer in decaying grid turbulence. A stochastic macro-mixing scheme computes the fluid particle trajectories, which describe the turbulent flow (Lagrangian turbulence), whereas the micro-mixing scheme interaction by the exchange with the conditional mean (IECM), implementing a new formulation for the mixing time, represents the dissipation of concentration turbulent fluctuations due to molecular diffusion. The non-homogeneous reaction-dominated limit (NHRDL) of the conserved scalar theory simulates chemical reactions. The numerical model integrates these three schemes and is validated by comparison with experimental and direct numerical simulation (DNS) data, whereas inter-comparisons with other numerical models are also reported. The study focuses on the reliability of Lagrangian stochastic models in representing micro-scale pollutant dispersion (air quality) and the importance of representing chemical reactions depending on instantaneous concentrations rather than their means.

Assessment of the presumed mapping function approach for the stationary laminar flamelet modelling of reacting double scalar mixing layers

This paper assesses the Presumed Mapping Function (PMF) approach in the context of the Stationary Laminar Flamelet Modelling (SLFM) of a reacting Double Scalar Mixing Layer (DSML). Starting from a prescribed Gaussian reference field, the PMF approach provides a presumed Probability Density Function (PDF) for the mixture fraction that is subsequently employed to close the Conditional Scalar Dissipation Rate (CSDR) upon doubly-integrating the homogeneous PDF transport equation. The PMF approach is unique in its ability to yield PDF and CSDR distributions that capture the effect of multiple fuel injections of different composition. This distinct feature overcomes the shortcomings of the classical SLFM closures (the β-distribution for the PDF and the counterflow solution for the CSDR). The current study analyses the impact of the binary (two-stream) and trinary (three-stream) PMF approaches on the structure of laminar flamelets in a DSML formed by the mixing of a fuel stream and an oxidiser stream separated by a pilot. The conditions of a partially-premixed methane/air piloted jet flame are considered. A parametric assessment is performed by varying the local mixing statistics and the findings are compared to those of the classical SLFM approach. Further, the influence of the PMF approach on flamelet extinction and transport by means of differential diffusion is thoroughly investigated. It is shown that the trinary PMF approach captures the influence of the pilot stream as it is capable of yielding bimodal CSDR and trimodal PDF distributions. It is further demonstrated that, when the influence of the pilot is significant, flamelets generated using the trinary CSDR closure extinguish at higher strain levels compared to flamelets generated using the binary and counterflow closures. Lastly, it is shown that the trinary PMF approach can be critical for accurate SLFM computations of DSMLs when differential diffusion effects are important.

A study on effects of temporally varying/ fluctuating noises on statistical profiles measured by means of PLIF method (Development of prediction formulas of the effects, and validation by high-Sc-number scalar mixing layer in grid turbulence)

In planar laser induced fluorescence (PLIF) measurement, temporally varying and fluctuating noises affect measured statistical profiles, significantly. In this study, the former φ is caused by a ratio of temporally varying quantum yield φ between measurement and reference images, and the latter sβI is mainly due to temporal fluctuations of a ratio of camera sensitively β and a ratio of incident laser I to excite a fluorescent dye, where sβI ≡ βI - 1. These noises can significantly affect statistical profiles of fluctuating concentration field. The aim of this study is to develop predictive formulas for the effects on fundamental statistical profiles. The effects of φ and sβI are reconstructed to mean of φ, αT/2, mean of sβI, SβI and intensity of fluctuation of sβI, <e2>, where α is rate of temporal change of φ, T is required time of the experiment, SβI = <sβI>, e = sβI, sβI = SβI + sβI and <> denotes ensemble average. Then, we show a series of the formulas to predict the effects on mean scalar, intensity of scalar fluctuation, 3rd-order statistics and 4th-order statistics of scalar fluctuation. The predictive formulas are validated by using experimental results of high-Sc-number scalar mixing layer in grid-generated turbulence measured by PLIF method, where the mesh Reynolds number was 2,500 and the Schmidt number was about 2,100, respectively. The effects of <e2> is analytically found to be the most significant among αT, SβI and <e2> by expanding the predictive formulas. In fact, the profile of <c2> is significantly affected by variation of <e2>. The predictive formulas can be used as formulas to correct the profiles when given values of the three parameter are appropriate.

A model for turbulent mixing based on shadow-position conditioning

In the modeling and simulation of mixing and reaction in turbulent flows using probability density function (PDF) methods, a key component is the mixing model, which represents the mixing effected by molecular diffusion. A new model, called the shadow-position mixing model (SPMM), is introduced and its performance is illustrated for two test cases. The model involves a new variable—the shadow position—and mixing is modeled as a relaxation of the composition to its mean conditional on the shadow position. The model is constructed to be consistent with turbulent dispersion theory, and to be local in the composition space, both to adequate approximations. The connections between the SPMM and previous mixing models are discussed. The first test case of a scalar mixing layer shows that the SPMM yields scalar statistics in broad agreement with experimental data. The second test case of a reactive scalar mixing layer with idealized non-premixed combustion shows that the SPMM correctly yields stable combustion, whereas simpler models incorrectly lead to extinction. The model satisfies all required realizability and transformation properties and correctly yields Gaussian distributions in appropriate circumstances. The SPMM is generally applicable to turbulent reactive flows using different PDF approaches in the contexts of both Reynolds-averaged Navier-Stokes modeling and large-eddy simulation.

Numerical Simulation of Reactive Turbulent Scalar Mixing Layer by the Random Fourier Modes Method and Lagrangian Molecular Mixing Model

A new computational scheme using Lagrangian model of the velocity and molecular mixing for the fluid particle is developed to calculate the reactive scalar field in grid generated turbulence. The model is composed of three parts. The Lagrangian velocity of fluid particle which carries the reacting species is generated by the Random Fourier Modes method. The molecular mixing model(the modified Curl's model)is used to calculate the mixing and diffusion of reactive concentration field, and the chemical reaction model is a second-order and irreversible reaction in the scalar mixing layer. It is shown that the simulated results of the first and second moments of reactive and productive species show the good agreements with of the experimental data.

Scalar energy fluctuations in Large-Eddy Simulation of turbulent flames: Statistical budgets and mesh quality criterion

Large-Eddy Simulation (LES) provides space-filtered quantities to compare with measurements, which usually have been obtained using a different filtering operation; hence, numerical and experimental results can be examined side-by-side in a statistical sense only. Instantaneous, space-filtered and statistically time-averaged signals feature different characteristic length-scales, which can be combined in dimensionless ratios. From two canonical manufactured turbulent solutions, a turbulent flame and a passive scalar turbulent mixing layer, the critical values of these ratios under which measured and computed variances (resolved plus sub-grid scale) can be compared without resorting to additional residual terms are first determined. It is shown that actual Direct Numerical Simulation can hardly accommodate a sufficiently large range of length-scales to perform statistical studies of LES filtered reactive scalar-fields energy budget based on sub-grid scale variances; an estimation of the minimum Reynolds number allowing for such DNS studies is given. From these developments, a reliability mesh criterion emerges for scalar LES and scaling for scalar sub-grid scale energy is discussed.

0140 マルチスケール格子乱流による高シュミット数スカラー混合層の基本特性(OS1-8 噴流,後流および剥離流れ現象の解明と制御,オーガナイズドセッション)

High-Schmidt-number scalar mixing layers in the multiscale grid generated turbulence are experimentally investigated in a water channel by means of planar laser induced fluorescence (PLIF) technique and particle image velocimetry (PIV). The Reynolds number based on the effective mesh size and mean velocity is 2,500. Fluorescent dye (Rhodamine B; Schmidt number is about 2,100) is homogeneously premixed only in the upper stream, and therefore, the scalar mixing layer with an initial step profile develops downstream of the grid. Various turbulence quantities are evaluated and discussed.

S0502-7-3 高精度PLIFによる高Sc数スカラー乱流混合の実験解析([S0502-7]噴流,後流および剥離流れ現象の解明と制御(7))

High-Schmidt-number scalar mixing layers in the grid turbulence are experimentally investigated in a water channel by means of the planar laser induced fluorescence (PLIF) technique and the time-resolved particle image velocimetry (PIV). A biplane square grid and a fractal square grid are used to generate turbulence. The Reynolds number based on the effective mesh size and mean velocity is 2,500 in both flows. Fluorescent dye (Rhodamine B; Schmidt number is about 2,100) is homogeneously premixed only in the upper stream, and therefore, the scalar mixing layer with an initial step profile develops downstream of the grid. Various turbulence quantities are evaluated and comparisons are made between turbulence and scalar fields generated by the regular and fractal grids.

Hydrogen autoignition in a turbulent jet with preheated co-flow air

The autoignition of hydrogen in a turbulent jet with preheated air is studied computationally using the stand-alone one-dimensional turbulence (ODT) model. The simulations are based on varying the jet Reynolds number and the mixture pressure. Also, computations are carried out for homogeneous autoignition at different mixture fractions and the same two pressure conditions considered for the jet simulations. The simulations show that autoignition is delayed in the jet configuration relative to the earliest autoignition events in homogeneous mixtures. This delay is primarily due to the presence of scalar dissipation associated with the scalar mixing layer in the jet configuration as well as with the presence of turbulent stirring. Turbulence plays additional roles in the subsequent stages of the autoignition process. Pressure effects also are present during the autoignition process and the subsequent high-temperature combustion stages. These effects may be attributed primarily to the sensitivity of the autoignition delay time to the mixture conditions and the role of pressure and air preheating on molecular transport properties. The overall trends are such that turbulence increases autoignition delay times and accordingly the ignition length and pressure further contribute to this delay.

Conditional velocity statistics in the double scalar mixing layer – A mapping closure approach

In this work we use 3D direct numerical simulations (DNS) to investigate the average velocity conditioned on a conserved scalar in a double scalar mixing layer (DSML). The DSML is a canonical multistream flow designed as a model problem for the extensively studied piloted diffusion flames. The conditional mean velocity appears as an unclosed term in advanced Eulerian models of turbulent non-premixed combustion, like the conditional moment closure and transported probability density function (PDF) methods. Here it accounts for inhomogeneous effects that have been found significant in flames with relatively low Damköhler numbers. Today there are only a few simple models available for the conditional mean velocity and these are discussed with reference to the DNS results. We find that both the linear model of Kutznetzov and the Li and Bilger model are unsuitable for multi stream flows, whereas the gradient diffusion model of Pope shows very close agreement with DNS over the whole range of the DSML. The gradient diffusion model relies on a model for the conserved scalar PDF and here we have used a presumed mapping function PDF, that is known to give an excellent representation of the DNS. A new model for the conditional mean velocity is suggested by arguing that the Gaussian reference field represents the velocity field, a statement that is evidenced by a near perfect agreement with DNS. The model still suffers from an inconsistency with the unconditional flux of conserved scalar variance, though, and a strategy for developing fully consistent models is suggested.

Derivation of the conditional moment closure equations for spray combustion

In this work we derive the fundamental equations for conditional moment closure (CMC) modelling of individual phases set in a two-phase flow. The derivation is based on the instantaneous transport equations for the single phase that involve a level set/indicator function technique for accounting for interfaces. Special emphasis is put on spray combustion with the CMC equations formulated for the gas phase. The CMC equations are to be viewed as an adjunct to existing methods for the modelling of the dynamics of sprays: they provide a refinement of the modelling of chemical reactions in the gas phase. The resulting CMC equations differ significantly from those already in use in the literature. They contain, of course, unclosed terms that need to be modelled. Investigation of the unclosed terms associated with evaporation at the droplet surface is well beyond the capabilities of laboratory measurement or direct numerical simulation. It is proposed that modelling of these terms be based on the well-established ‘laws’ of similarity between heat and mass transfer: an example is detailed for one example of the general modelling of the spray dynamics. Other unclosed terms are important throughout the gas phase. Models used for these terms in single-phase flows are reviewed and it is proposed that any modifications needed for these models be investigated by DNS of suitable model problems having good resolution of the flow and mixing in the inter-droplet space. It is proposed that a spray analogue of the scalar mixing layer that has been widely studied in single-phase flows be used as the model problem for such DNS studies and also for LES and RANS modelling.

Direct numerical simulations of the double scalar mixing layer: Part II: Reactive scalars

The reacting double scalar mixing layer (RDSML) is investigated as a canonical multistream flow and a model problem for simple piloted diffusion flames. In piloted diffusion flames, the reacting fuel and oxidizer streams are initially separated by a central pilot stream at stoichiometric composition. The primary purpose of this pilot is to delay the mixing of the pure streams until a stable flame base can develop. In such multistream systems, the modeling of turbulent scalar mixing is complicated by the multiple feed streams, leading to more complex fine-scale statistics, which remain as yet an unmet modeling challenge compared to the simpler two-feed system. In Part I we described how multimodal mixture fraction probability density functions (PDFs) and conditional scalar dissipation rates can be modeled with a presumed mapping function approach. In this work we present an efficient and robust extension of the modeling to a general multistream reacting flow and compare predictions to three-dimensional direct numerical simulations (DNS) of the RDSML with a single-step reversible chemistry model and varying levels of extinction. With high extinction levels, the interaction with the pilot stream is described. Additionally, state-of-the-art combustion modeling calculations including conditional moment closure (CMC) and stationary laminar flamelet modeling (SLFM) are performed with the newly developed mixing model. Excellent agreement is found between the DNS and modeling predictions, even where the PDF is essentially a triple-delta shape near the flame base, so long as extinction levels are moderate to low. The suggested approach outlined in this paper is strictly valid only for flows that can be described by a single mixture fraction. For these flows the approach should provide engineers with fine-scale models that are of accuracy comparable to those already available for binary mixing, at only marginally higher complexity and cost.

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.

Direct numerical simulations of the double scalar mixing layer. Part I: Passive scalar mixing and dissipation

The double scalar mixing layer (DSML) is a canonical problem for studying the mixing of multiple streams and, with reaction, combustion of the partially premixed type. In a DSML, a third stream consisting of a premixture of the reactants is introduced in between the pure fuel and air streams of the classic twin-feed or binary mixing problem. The well-known presumed probability density function (PDF), such as the β-PDF, can adequately model passive scalar mixing for the binary mixing problem on which state-of-the-art turbulent combustion models such as conditional moment closure and flamelet approaches rely. However, the β-PDF model, now a standard in CFD simulation, cannot describe turbulent mixing involving multiple streams; e.g., the asymmetric three-stream mixing characterizing the DSML. In this paper, direct numerical simulations of the DSML are performed to make available a high-fidelity database for developing more general, fine-scale mixing models required to compute turbulent combustion problems of practical engineering interest, which usually involve mixing between multiple streams. In this first part of two investigations, nonreacting numerical experiments are presented with emphasis on the nontrivial distributions of the passive scalar and its dissipation rate. Mapping closure modeling is applied to describe the PDFs and conditional dissipation rates of a single mixture fraction.

Presumed Mapping Functions for Eulerian Modelling of Turbulent Mixing

The mapping closure of Chen et al. [Phys. Rev. Lett., 63, 1989] is a transported probability density function (PDF) method that has proven very efficient for modelling of turbulent mixing in homogeneous turbulence. By utilizing a Gaussian reference field, the solution to the mapping function (in homogeneous turbulence) can be found analytically for a range of initial conditions common for turbulent combustion applications, e.g. for binary or trinary mixing. The purpose of this paper is to investigate the possibility of making this solution a presumed mapping function (PMF) for inhomogeneous flows. The PMF in turn will imply a presumed mixture fraction PDF that can be used for a wide range of models in turbulent combustion, e.g. flamelet models, the conditional moment closure (CMC) or large eddy simulations. The true novelty of the paper, though, is in the derivation of highly efficient, closed algebraic expressions for several existing models of conditional statistics, e.g. for the conditional scalar dissipation/diffusion rate or the conditional mean velocity. The closed form expressions nearly eliminates the overhead computational cost that usually is associated with nonlinear models for conditional statistics. In this respect it is argued that the PMF is particularly well suited for CMC that relies heavily on manipulations of the PDF for consistency. The accuracy of the PMF approach is shown with comparison to DNS of a single scalar mixing layer to be better than for the β-PDF. Not only in the shape of the PDF itself, but also for all conditional statistics models computed from the PDF.

Lagrangian Stochastic Modelling of Chemical Reaction in a Scalar Mixing Layer

Statistics of conserved and reactive scalar concentration in a scalar mixing layer are calculated using a Lagrangian particle model coupled to a micro-mixing model and using conserved scalar theory for the chemistry. Good agreement is obtained with laboratory experiments for temperature statistics in a thermal mixing layer. For conserved scalar statistics in a reacting mixing layer, good agreement is obtained with direct numerical simulations, but enhanced mixing is necessary in order to account approximately for the effects of a flow instability in the experiments. With this enhanced mixing, good agreement is obtained with laboratory data for reactive scalars on the edges of the mixing layer using conditional moment closure, but discrepancies remain in the middle of the layer. Calculations show that in conditional moment closure modelling, the scalar dissipation conditioned on the scalar concentration can be replaced by its unconditional counterpart with negligible error.