Scalar Mixing In Turbulent Flows Research Articles

A strategy for large-scale scalar advection in large eddy simulations that use the linear eddy sub-grid mixing model

PurposeThe purpose of this numerical work is to present and test a new approach for large-scale scalar advection (splicing) in large eddy simulations (LES) that use the linear eddy sub-grid mixing model (LEM) called the LES-LEM.Design/methodology/approachThe new splicing strategy is based on an ordered flux of spliced LEM segments. The principle is that low-flux segments have less momentum than high-flux segments and, therefore, are displaced less than high-flux segments. This strategy affects the order of both inflowing and outflowing LEM segments of an LES cell. The new splicing approach is implemented in a pressure-based fluid solver and tested by simulation of passive scalar transport in a co-flowing turbulent rectangular jet, instead of combustion simulation, to perform an isolated investigation of splicing. Comparison of the new splicing with a previous splicing approach is also done.FindingsThe simulation results show that the velocity statistics and passive scalar mixing are correctly predicted using the new splicing approach for the LES-LEM. It is argued that modeling of large-scale advection in the LES-LEM via splicing is reasonable, and the new splicing approach potentially captures the physics better than the old approach. The standard LES sub-grid mixing models do not represent turbulent mixing in a proper way because they do not adequately represent molecular diffusion processes and counter gradient effects. Scalar mixing in turbulent flow consists of two different processes, i.e. turbulent mixing that increases the interface between unmixed species and molecular diffusion. It is crucial to model these two processes individually at their respective time scales. The LEM explicitly includes both of these processes and has been used successfully as a sub-grid scalar mixing model (McMurtry et al., 1992; Sone and Menon, 2003). Here, the turbulent mixing capabilities of the LES-LEM with a modified splicing treatment are examined.Originality/valueThe splicing strategy proposed for the LES-LEM is original and has not been investigated before. Also, it is the first LES-LEM implementation using unstructured grids.

Simultaneous velocity-temperature measurements in the heated wake of a cylinder with implications for the modeling of turbulent passive scalars

Two principal quantities of interest in applications of scalar mixing in turbulent flows are the mean scalar and the scalar variance. Reynolds-averaged approaches are computationally efficient numerical methods that predict these fields. They require, however, the introduction of models to close the governing equations. Oftentimes, the numerical constants employed in these models include, or depend upon, the turbulent Prandtl number (PrT) and the mechanical-to-thermal time-scale ratio (r), which are generally assumed to be constant, but flow dependent. The present work studies the sensitivity of PrT and r to differences in their injection method within the same flow. To this end, mixed velocity-temperature statistics were measured in the wake of a circular cylinder. The wake was heated by one of two ways: heating the cylinder or heating an array of fine parallel wires (called a mandoline) placed downstream of the cylinder. The experimental results demonstrate that the magnitude of PrT varies throughout the wake for both scalar fields (and is consistently greater than the typical value of 0.7 generally used in turbulence models). Likewise, the values of r vary across the wake for both scalar fields and are lower than the generally accepted value of 2. The principal result of this paper, however, is that the measured values of both PrT and r differ for the two scalar injection methods, despite being within the same flow field. Hence, both PrT and r not only depend on the type of flow but also on the scalar field injection mechanism method as well—a result that is generally not taken into account when modeling the mixing of scalars within turbulent flows.

Effects of rotation on turbulent mixing: Nonpremixed passive scalars

We study by direct numerical simulations the effects of uniform solid-body rotation on passive scalar mixing in turbulent flow, with a focus on the unsteady problem of nonpremixed scalars in forced rotating turbulence with isotropic initial conditions in the velocity field. The expectation of reduced mixing as a result of reduced spectral transfer is readily verified in several aspects, including slower decay rates for the scalar variance, increased scalar mixing times, and slower relaxation of the probability density function from its initially bimodal form to a near-Gaussian shape. Spectral transfer in the scalar field is shown to be dominated by very low-wavenumber velocity modes, and strongly suppressed at higher wavenumbers in the scalar field. Considerable departure from local isotropy is observed in the scalar gradient fluctuations, which are smaller in the direction along the axis of rotation where there is less mixing than in the orthogonal plane. A partial explanation is given in terms of the influence of a modified turbulence velocity structure on directional characteristics of spectral transfer, which leads to anisotropy in the scalar gradient spectra as well as one-dimensional spectra of the scalar field. The observed anisotropy is stronger than that for the velocity field, especially for high rotation rates, and is more pronounced at Schmidt number 1 than at 1/8. A reduction in intermittency compared with nonrotating turbulence is also observed.

Strained dissipation and reaction layer analyses of nonequilibrium chemistry in turbulent reacting flows

A physically based formulation relating the chemical state of nonequilibrium combustion in turbulent flows to the mixing state of a conserved scalar is presented. The present strained dissipation and reaction layer approach is motivated by results from detailed imaging studies of scalar mixing in turbulent flows, which show that essentially all the instantaneous scalar energy dissipation rate field is confined to locally one-dimensional layer-like structures. These dissipation layers are a direct consequence of the dynamics of scalar mixing in turbulent flows and are independent of the extent of chemical nonequilibrium in the flow. The presence of these layer-like scalar dissipation structures in turn indicates a locally one-dimensional structure in the underlying chemical species fields. The resulting strained dissipation and reaction layer model has certain similarities with the classical “flamelet” model; however, it is based on entirely different physical observations, derived from entirely different arguments, and limited by an entirely different and more widely applicable set of conditions. Moreover, the boundary conditions for solution of the local chemical state differ fundamentally from those used in flamelet models. Results for OH concentration fields obtained from experimental imaging measurements of conserved scalar fields in turbulent flows for conditions ranging from near equilibrium to deep nonequilibrium demonstrate remarkable resemblances to direct OH PLIF measurements under similar combustion conditions. In particular, species concentration and reaction rate fields obtained clearly show the predominance of thin (flamelet-like) reaction zones under conditions of relatively weak chemical nonequilibrium, and the natural emergence and dominance of broad (distributed) reaction zones for increasing equilibrium departures. Detailed nonequilibrium O-atom concentration fields obtained via this formulation, unattainable by direct experimental techniques, provide insights into Zel'dovich NO formation in turbulent jet diffusion flames.

Assumed joint probability density function approach for supersonic turbulent combustion

In a recent experiment, Cheng et al. used UV spontaneous vibrational Raman scattering and laser-induced predissociative fluorescence techniques for simultaneous measurements of temperature and concentrations of O2, H2, H2O, OH, and N2 (and the rms of their fluctuations) in supersonic turbulent reacting shear layers. Because present computational techniques are not suited for the prediction of all of the above measurements, a new approach has been developed and is being used to predict all relevant flow properties and the rms of their fluctuations (where appropriate). The approach explores the use of a multivariate Beta PDF for concentrations. In particular, a version developed by Girimaji to model scalar mixing in turbulent flows is employed. Predictions using this model were, in general, satisfactory in regions preceding ignition, but not in regions downstream of ignition. Part of the discrepancy is a result of our current inability to relate Favre and time averages. 10 refs.

Johnson-Edgeworth Translation for Probability Modeling of Binary Scalar Mixing in Turbulent Flows

Abstract A family of Probability Density Functions (PDF's) generated by Johnson-Edgeworth Translation (JET) is used for statistical modeling of the mixing of an initially binary scalar in isotropic turbulence. The frequencies obtained by this translation are shown to satisfy some of the characteristics of the PDF's generated by the Amplitude Mapping Closure (AMC) (Kraichnan, 1989; Chen et al., 1989). In fact, the solution obtained by one of the members of this family is shown to be identical to that developed by the AMC (Pope, 1991). Due to this similarity and due to the demonstrated capabilities of the AMC, a justification is provided for the use of other members of JET frequencies for the modeling of the binary mixing problem. This similarity also furnishes the reasoning for the applicability of the Pearson Family (PF) of frequencies for modeling of the same phenomena. The mathematical requirements associated with the applications of JET in the modeling of the binary mixing problem are provided, and all the results are compared with data generated by Direct Numerical Simulations (DNS). These comparisons indicate that the Logit-Normal frequency portrays some subtle features of the mixing problem better than the other closures. However, none of the models considered (JET, AMC, and PF) are capable of predicting the evolution of the conditional expected dissipation and/or the conditional expected diffusion of the scalar field in accordance with DNS. It is demonstrated that this is due to the incapability of the models to account for the variations of the scalar bounds as the mixing proceeds. A remedy is suggested for overcoming this problem which can be useful in probability modeling of turbulent mixing, especially when accompanied by chemical reactions. While in the context of a single-point description the evolution of the scalar bounds cannot be predicted, the qualitative analytical-computational results portray a physically plausible behavior.

Assumed β-pdf Model for Turbulent Mixing: Validation and Extension to Multiple Scalar Mixing

Abstract Many engineering calculations of turbulent reacting flows employ the assumed-pdf approach. On the form of the assumed pdf, however, there has been little consensus and the choice has often been ad hoc. The objective of this work is to investigate the validity of the assumed β-pdf model for the case of the inert mixing of two scalars and extend the applicability of the model to multiple scalar mixing. By comparing the β-pdf model favorably with the two-scalar mixing data obtained from direct numerical simulations (DNS), it is demonstrated that the use of this model is justified for all stages of the mixing process in statistically-stationary, isotropic turbulence. It is also shown analytically that during the final stages of mixing the model β-pdf reduces to a Gaussian-pdf, consistent with the observations from experiments and DNS, The suggested multivariate β-pdf model for multiple-scalar mixing relates algebraically, The mean scalar concentrations and the turbulent scalar-energy—to the joint pdf of the scalar concentrations. The model requires that only one extra transport equation—for the turbulent scalar-energy—be solved, apart from the mean equations. The model can be used in conjunction with any model for the turbulence velocity field and is expected to provide a simple method for calculating scalar mixing in turbulent flows.