Rs Cant

A flame surface density approach to large-eddy simulation of premixed turbulent combustion

The flame surface density approach to the modeling of premixed turbulent combustion is well established in the context of Reynolds-averaged simulations. For the future, it is necessary to consider large-eddy simulation (LES), which is likely to offer major advantages in terms of physical accuracy, particularly for unsteady combustion problems. LES relies on spatial filtering for the removal of unresolved phenomena whose characteristic length scales are smaller than the computational grid scale. Thus, there is a need for soundly based physical modeling at the subgrid scales. The aim of this paper is to explore the usefulness of the flame surface density concept as a basis for LES modeling of premixed turbulent combustion. A transport equation for the filtered flame surface density is presented, and models are proposed for unclosed terms. Comparison with Reynolds-averaged modeling is shown to reveal some interesting similarities and differences. These were exploited together with known physics and statistical results from experiment and from direct numerical stimulation in order to gain insight and refine the modeling. The model has been implemented in a combustion LES code together with standard models for scalar and momentum transport. Computational results were obtained for a simple three-dimensional flame propagation test problem, and the relative importance of contributing terms in the modeled equation for flame surface density was assessed. Straining and curvature are shown to have a major influence at both the resolved and subgrid levels.

Implications of a flame surface density approach to large eddy simulation of premixed turbulent combustion

Abstract Large eddy simulation (LES) is now widely regarded as an improvement on existing computational fluid dynamics (CFD) techniques in addressing classes of combustion problems where traditional CFD approaches have experienced some difficulty 1 , 2 , 3 . This is particularly true in situations where there is significant unsteadiness that is characterized by large-scale flow-flame interactions. The flame surface density (FSD) approach to the modeling of premixed turbulent combustion is well established in the context of Reynolds-averaged simulations, and has shown potential as a technique for LES [4] . In this paper, results are presented by using the flame surface density model of Hawkes and Cant [4] in a flame propagation test case that further demonstrates the feasibility of the approach. Firstly, the response of the model to variations in turbulence intensity is examined, and an assessment of the relative importance of the source terms in the balance equation for FSD is made. Secondly, it is shown how LES can exploit the effects of large-scale coherent structures in the prediction of FSD through an analysis of the resolved strain source term. Lastly, the model behavior under variations of the filter size is examined. It is an essential but difficult test for FSD models for LES that the results are independent of the filter size. It is shown that the FSD responds to variations in filter size as expected. An increase in filter size results in a decrease in resolved wrinkling, but an increase in sub-grid wrinkling. The net propagation rate of the turbulent flame is shown to be largely independent of the chosen filter size.

Modelling of flamelet surface-to-volume ratio in turbulent premixed combustion

A model is proposed, valid in the laminar flamelet regime, for the surface-to-volume ratio of a turbulent premixed flame. The new model is in a form suitable for incorporation into an existing model of turbulent premixed combustion. Exact equations are derived which describe the dynamics of the constant-property surface representing the flame interface. Unknown terms in the exact equations are modelled for the simplified case of constant-density combustion in a specified turbulence field. Numerical solutions of the modelled equations are carried out for a one-dimensional test case. Preliminary results indicate that the model is capable of predicting effects present in turbulent flame propagation, and a parametric study shows that correct trends are observed.

Some Applications of Kolmogorov's Turbulence Research in the Field of Combustion

This paper reviews recent developments in understanding of ways in which various characteristic scales in the Kolmogorov energy cascade control the wrinkling and stretching of thin laminar premixed flames in turbulent flows. Some unresolved problems are identified. Results of recent direct numerical simulations of turbulent combustion are discussed. Distributions of flame strain and curvature, obtained from constant density simulations, are presented and a parametrization of these results is suggested. This parametrization is then used to derive a new theoretical model to allow for effects of detailed finite chemical reaction rate mechanisms in engineering calculations of turbulent combustion.

Influence of Lewis number on curvature effects in turbulent premixed flame propagation in the thin reaction zones regime

The influence of differential diffusion on the statistical behavior of the local displacement speed (Sd) in relation to flame curvature is studied based on three-dimensional compressible direct numerical simulations (DNS) of statistically planar flames with single-step Arrhenius-type chemistry. Three different Lewis number cases (Le=0.8, 1.0, and 1.2) are considered. In order to study the influence of differential diffusion on curvature effects in flame propagation, temperature statistics are presented in terms of standard probability density functions (pdfs) and also joint pdfs with curvature for the nonunity Lewis number cases. Temperature statistics are found to be consistent with previous incompressible combustion DNS studies. It is found that both dilatation and tangential strain rate are negatively correlated with curvature. The relative strength of these two correlations determines the nature of the correlation between surface density function (SDF) (∣∇c∣) and curvature. It is also found that the v...

Effects of strain rate and curvature on surface density function transport in turbulent premixed flames in the thin reaction zones regime

Strain rate and curvature effects on Surface Density Function (SDF) transport in the thin reaction zones regime are studied using a three-dimensional direct numerical simulations (DNS) with a single-step Arrhenius type chemistry. It is shown that if the tangential strain rate on a flame isosurface exceeds a critical value, then a negative normal strain rate is induced, which acts to bring the isoscalar lines closer to each other and hence leads to a higher value of SDF. This is reflected in a positive correlation between SDF and tangential strain rate. Curvature is also found to affect SDF through the correlation between tangential strain rate and curvature on a given flame isosurface. Strain rate and curvature are found to have an appreciable effect on various terms of the SDF transport equation. The SDF straining term is correlated positively with tangential strain rate as expected and is also correlated negatively with the curvature. The combined SDF curvature and propagation terms operate as a source ...

EFFECTS OF TURBULENCE ON SPARK IGNITION IN INHOMOGENEOUS MIXTURES: A DIRECT NUMERICAL SIMULATION (DNS) STUDY

Spark ignition in inhomogeneous mixtures is numerically studied using three-dimensional compressible Direct Numerical Simulations (DNS) with simplified chemistry. The thermal effect of the spark is represented by a Gaussian power distribution in the energy transport equation. Success of the spark ignition and subsequent self-sustained flame propagation is shown to be heavily dependent on the turbulent velocity fluctuation. It has been found that high levels of turbulent velocity fluctuation have detrimental effects on the spark ignition event, which ultimately may lead to misfire. It is observed that the flame shows a tribrachial structure following successful ignition. The local flame propagation speed may attain values equal to several times the laminar burning velocity of an unstrained premixed stoichiometric flame S L , but may also be negative, in agreement with previous findings. The mean flame propagation speed decreases with increasing turbulent intensity.

A priori analysis of the curvature and propagation terms of the flame surface density transport equation for large eddy simulation

The statistical behavior of the propagation and curvature terms in the transport equation for flame surface density (FSD) is studied in the context of large eddy simulation (LES) of premixed combustion in the thin reaction zones regime. It is found that the propagation term is strongly influenced by curvature effects on displacement speed, and it is shown that the propagation term can be closed exactly without any additional modelling provided that the surface averaged displacement speed is accurately represented. The FSD curvature term is decomposed into resolved and subgrid contributions and three different model expressions for the resolved curvature term are studied. It is shown that the choice of expression for the resolved curvature term affects the modelling of the subgrid curvature term. This is important since the treatment of the subgrid curvature term involves the largest modelling uncertainties. Following this, it is argued that the most preferable expression for the resolved curvature term is...

Effects of Lewis number on scalar transport in turbulent premixed flames

The effects of global Lewis number on scalar transport in turbulent premixed flames are studied using direct numerical simulation. Under the same initial conditions of turbulent flow field, it is observed that flames with global Lewis numbers significantly smaller than unity tend to exhibit countergradient transport, whereas the extent of gradient transport is shown to increase with increasing global Lewis numbers. The velocity difference between reactants and products in the flame normal direction is shown to be significantly affected by the global Lewis number. The flame normal acceleration is shown to increase with decreasing Lewis number, leading to an increase in the magnitude of the mean pressure gradient in the mean direction of flame propagation. This effect is shown to be is responsible for promoting countergradient transport in low Lewis number flames. It is also shown that turbulent transport of flame surface density tends to exhibit countergradient behavior for the flames with Lewis number sig...

An introduction to turbulent reacting flows

Introduction: Motivation, Audience, Governing Equations, Main Closure Problem Turbulence and Mixing: Molecular Mixing, Reaction-Diffusion Problems, Random Walks, Turbulent Scales, Averaged Equations, Modeling Turbulent Transport, Scalar Mixing, Scalar Dissipation Methods for Flows with Non-Premixed Reactants: Moment Methods, the Mixture Fraction, Flamelet Theory, Conditional Moment Closure, the PDF Method Applications Methods for Flows with Premixed Reactants: Laminar Flamelet Modelling, the Bray-Moss-Libby Formulation, the G-Equation, Flame Surface Density, Applications Numerical Methods for Reacting Flows: Density Change, Unsteady Flames, Boundedness of Scalars, Stiffness, Special Features Experimental Methods for Reacting Flows: Resolution, Uncertainties, Probes, Laser-Based Techniques.