Michel Champion

Premixed flames in stagnating turbulence part II. The mean velocities and pressure and the Damköhler number

We extend to premixed flames an earlier asymptotic analysis of constant density stagnating turbulence by introducing a specified distribution of mean density, e.g., one obtained from experimental data for the mean progress variable. The small parameter providing the basis for the analysis is again the relative intensity of the turbulence exiting from the jet. The first moment equations are shown to predict the mean velocity components and the mean pressure. Comparison is made with four experiments involving turbulent reactants impinging on a wall and with one involving reactants in opposed streams. A range of rates of strain is covered in these experiments so that we treat flames either adjacent to a wall or to a stagnation plane as well as freestanding flames, i.e., those removed from the wall or stagnation plane. Quantitative agreement is found in three cases and only qualitative agreement in the other two. Conjectural explanations of the absence of quantitative agreement in these latter cases are provided. The first movement equation for the mean progress variable is shown to yield a distribution of a turbulent Damkohler number. Having validated the theory by comparisons with experiment, we then calculate systematically the characteristics of a range of flames: those adjacent to walls and stagnation planes and those which are freestanding. Features of the two classes of flames are found to differ significantly; for example, freestanding flames involve a pressure drop, whereas the pressure is either constant or increasing through flames adjacent to walls or stagnation planes. The Damkohler number is nearly constant in the latter flames, but significantly increases through freestanding flames. The implications of these findings are discussed.

The Interaction Between Turbulence and Chemistry in Premixed Turbulent Flames

Recent studies of turbulent premixed combustion by the authors and their coworkers are reviewed with emphasis on two topics, related to the interaction between turbulence and chemistry. The first is the use of conditional averaging techniques to describe terms in the transport equations for Reynolds stress and flux components. Secondly a laminar flamelet description of the mean reaction rate terms is presented. Some problems which remain to be solved are identified.

Algebraic Models for Turbulent Transports in Premixed Flames

The thermal expansion induced by the chemical reactions taking place in a turbulent reactive flow of premixed reactants affects the velocity field so strongly that turbulent transports can be controlled by reaction rather than by turbulence. Moreover, thermal expansion is well-known to cause countergradient turbulent diffusion as well as flame-generated turbulence phenomena. In the present article, a splitting procedure of the velocity field is used that allows the identification of two different effects of the thermal expansion in the specific flamelets regime of turbulent premixed combustion: (i) the thermal expansion occurring through the local flames (direct effect) and (ii) the effect of thermal expansion on the velocity field associated to the growth of the flame surface (indirect effect). Algebraic closures for the turbulent transport terms of mass and momentum are proposed where the effect of the turbulent mixing (nonreactive effect) is modeled by classical closures, i.e., gradient law, while the contributions associated with thermal expansion are closed by taking advantage of flamelet relationships. Finally, this simple model is applied to the numerical simulation of a turbulent flame stabilized by the sudden expansion of a 2D channel. Corresponding results are satisfactorily compared with experimental data and confirm the ability of the model to represent the behavior of turbulent transports in premixed flames.

Premixed Turbulent Combustion Controlled by Complex Chemical Kinetics

Abstract The combustion of a turbulent homogeneous mixture of propane and air within a duct having a stationary one-dimensional mean flow is modelled. Under the conditions chosen for the study, chemical kinetics factors are important and a relatively detailed chemical model is needed. A semi-global model for the combustion of hydrocarbon is used and simplifying assumptions are made which reduce the system of independent variables to that of temperature and CO2 mass fraction. A two-dimensional probability density function is introduced to close the mean chemical production terms. The required equations for Favre averaged temperature, CO2 mass fraction, turbulence kinetic energy and the mean square fluctuation of the temperature are solved numerically. Predictions are made of the profiles of mean quantities through the combustion zone under different initial temperature, turbulence intensities and dissipation length scales.

Relevance of Two Basic Turbulent Premixed Combustion Models for the Numerical Simulations of V-Shaped Flames

ABSTRACT The present study is devoted to the analysis of basic turbulent premixed combustion closures applied to the numerical simulations of V-shaped flames. It is well known that an important parameter for the numerical simulation of such premixed turbulent flames is the description of the departure from the bimodal limit (thin flame limit), which is associated to the maximum value of the progress variable segregation rate, i.e., S = 1. The evolution of this segregation rate is often deduced from a modeled transport equation written for the progress variable variance. However, the closure of such a transport equation does involve many additional sub-models, which are related to the mean and variance progress variable fluxes and mean scalar dissipation rate of the progress variable variance. In the present work two original closures for the mean chemical rate are considered. Special emphasis is also placed on algebraic closures for S that circumvent the difficulty associated to the modeling of the second moment of the progress variable. In the first step of the analysis these closures are analyzed in the case of the propagation of a one-dimensional turbulent premixed flame brush. They are subsequently applied to the numerical simulation of premixed V-shaped flames that have been studied experimentally by Galizzi (2003) and by Degardin et al. (2006). It is found that these closures provide a satisfactory representation of the turbulent premixed flames.

Density Variations Effects in Turbulent Diffusion Flames: Modeling Of Unresolved Fluxes

Unresolved fluxes in turbulent diffusion flames are investigated by introducing the specific volume to analyze the effects of density variations. Unresolved fluxes are found to be related to scalar correlations involving this specific quantity. The algebraic models proposed for the turbulent scalar and momentum fluxes allow to recover and generalize well-known previously established relations and highlight the possible occurrence of non-gradient diffusion. These correlations are evaluated from the consideration of strained laminar diffusion flames and chemical equilibrium conditions. Finally, the calculations performed confirm that such non-premixed flames may exhibit a strong production of turbulence near stoichiometric conditions.

A Layered Description of a Premixed Flame Stabilized in Stagnating Turbulence

ABSTRACT In the thin-flame regime of turbulent premixed combustion, instantaneous progress variable gradients are essentially fixed by propagating flamelets. The laminar flamelet internal structure thus imposes, at least to some extent, the progress variable one-point one-time statistics, i.e., the progress variable PDF . In the present study a generalized presumed probability density function (PDF) shape is considered to account for possible departures from the thin-flame limit. The parameters that characterize this PDF shape depend on the ratio of the Kolmogorov length scale to laminar flame width. The corresponding framework may be associated to a layered description of the turbulent flame brush (TFB) with the thicknesses of the different sub-layers determined from the knowledge of both the Reynolds and Karlovitz numbers, ReT and Ka. It incorporates boundary layers on both sides of the TFB, which are associated to the finite thickness of the local flamelets, i.e., small but finite values of the Karlovitz number. This description leads to a modeling proposal for premixed turbulent combustion. A tabulation is constructed based on canonical one-dimensional planar unstrained laminar premixed flame computations and the different quantities are tabulated as functions of ReT and Ka. The final closure is applied to the numerical simulations of premixed flames stabilized in stagnating turbulence.

Importance of Physical Modeling for Simulations of Turbulent Reactive Flows

The physical models implemented in practical computational tools are not systematically required for the numerical simulations of turbulent flows. When the grid is sufficiently refined, satisfactory numerical results can be obtained even if the smallest characteristic scales are not solved. However, when reactive flows are considered, the physical mechanisms occurring at the smallest scales may control the main characteristics of the flow such as the flame velocity propagation. Therefore, the development of new physical models is still needed for practical numerical simulations of turbulent reactive flows. A recent work that describes the inner structure of turbulent flames as composed of different layers is presented. This study also evidences the necessity to understand in details the transition between a slow chemistry layers to a fast chemistry layer. The behavior of the scalar variance and turbulent scalar flux between these two limit cases is presented.