Dependence of heat release on the progress variable in premixed turbulent combustion

Abstract

An analysis of various experimental data obtained for different turbulent flames under a wide range of conditions shows that spatial profiles of the progress variable across the flame brush, presented in the dimensionless form by using the flame brush thickness, are described by a universal curve or, in other words, are self-similar. This observation offers the opportunity to suggest the following simple test for any model of premixed turbulent combustion: It should be able to predict such universal profiles for the simplest, one-dimensional planar flames propagating in frozen turbulence, as a minimum. Various models of premixed turbulent combustion, utilizing the balance equation for the mean progress variable, are tested in this simple case. For these purposes, balance equations for the mean progress variable, resulting from different models, are written in the same dimensionless general form by using model-dependent time and length scales and a gradient-diffusion closure of the transport term. The results of numerical computations show that a proper definition of the mean flame brush thickness δt is of importance when performing such tests. When the evaluation of δt in the numerical simulations corresponds to the measurements, the dependencies like Q ∼ c ¯ ( 1 − c ¯ ) or Q ∼ p ¯ c ˜ ( 1 − c ˜ ) , invoked by many submodels of the mean heat release rate Q in the Favre-averaged balance equation, cannot lead to the aforementioned universal profile, whereas the dependence of Q ∼ c ˜ ( 1 − c ˜ ) , not commonly used in the simulations, can do so. The gradient-type, Q ∼ | ∇ c ˜ | , and the flame surface density closures can also lead to the universal profiles discussed. The ability of certain numerical models invoking the gradient closure of the transport term to predict the measured dimensionless spatial profiles of the progress variable reasonably well shows that modeling this transport term is of secondary importance for many applications.