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The influence of reactive scalar mixing physics on turbulent premixed flame propagation is studied, within the framework of turbulent flame speed modelling, by comparing predictive
ability of two algebraic flame speed models: one that includes all relevant physics and the other ignoring dilatation effects on reactive scalar mixing. This study is an extension of a previous
work analysing and validating the former model. The latter is obtained by neglecting modelling terms that include dilatation effects: a direct effect because of density change across the
flame front and an indirect effect due to dilatation on turbulence-scalar interaction. An analysis of the limiting behaviour shows that neglecting the indirect effect alters the flame speed scaling
considerably when

The propagation of a deflagration wave in turbulent medium is a classical problem of turbulent premixed combustion and is of great practical significance in the current climate of energy and environment. Expressions for the mean propagation velocity, referred to as “turbulent flame speed” or “turbulent burning velocity”, are often required in practical computational fluid dynamics (CFDs) codes employed in the design of combustion systems. Furthermore, from a theoretical standpoint, turbulent flame speed is a useful analytical tool to assess the general validity of turbulent combustion models [

The KPP theorem [

Substituting (

Early theories for turbulent flows have taken the scalar dissipation rate to be purely a function of the turbulence parameters. While this is true for turbulent flows with passive scalars, recent studies [

The aim of the present work is to illustrate the influence of the two-way coupling of heat release effects and the associated physics on turbulent premixed flame propagation. This is done, within the turbulent flame speed framework, by comparing the predictive capability of the flame speed model with and without the terms signifying the physics behind the two-way coupling. In principle, one could also do this within the scalar dissipation rate framework, since the two models have the same terms with the same model parameters [

The outline of this paper is as follows. The two-way coupling and the physics associated with the turbulent mixing of a reactive scalar in premixed flames are discussed in Section

The physics behind the two-way coupling is explained best using the scalar dissipation rate transport equation, which also helps us to identify the mathematical terms signifying these physical processes. This transport equation has been derived in earlier studies for unity [

For a passive chemical reaction,

Schematics showing the alignment of scalar gradient with the two principal components of turbulent strain rate tensor

A model for the scalar dissipation rate,

The constant

It is evident that the terms pertaining to the two-way coupling are

The case of passive chemical reaction is trivial for this study and has been discussed already in [

If one were to retain only the direct part of the two-way coupling, then

To study the limiting behaviour of (

In the limit of small

In the limit of large

It is interesting to note that neglecting

Finally, it is worth commenting on why we have not considered the case where

The original flame speed model, (

the planar flame data from the Taylor-Couette apparatus of Aldredge et al. [

the high pressure Bunsen flame data of Kobayashi et al. [

the very high turbulence intensity data of Il'yashenko and Talantov [

This is to emphasis the relative roles of direct and indirect effects of density change on the propagation speed of the flame brush leading edge for wide conditions of turbulent flames. As noted earlier, ignoring the effects of density change completely will give the classical result analysed in many earlier studies.

Comparisons of (

The predictions of turbulent flame speed expressions, (

The predictions of the flame speed expressions, (

Comparisons of turbulent flame speed predictions to the experimental data of [

The present study illustrates the influence of dilatation effects on the propagation speed of turbulent premixed flames, by assessing their contribution to turbulent flame speed calculation. An algebraic model for turbulent flame speed, (

If both of these terms are ignored, then the original model proposed in [

The turbulent flame speed values obtained using these two equations differ largely in the limit of weak turbulence (about 66% for