Testing premixed turbulent combustion models by studying flame dynamics

First, the following universal feature of premixed turbulent flame dynamics is highlighted: During an early stage of flame development, the burning velocity grows much faster than the mean flame brush thickness, because the two processes are controlled by the small-scale and large-scale turbulent eddies, respectively. Second, this feature of developing flames is exploited in order to test a number of different models of premixed turbulent combustion by theoretically and numerically studying an interaction of an initially laminar, planar, one-dimensional flame with a statistically stationary, planar, one-dimensional, and spatially uniform turbulent flow not affected by combustion. To test as many models as possible in a simple and unified manner, various combustion models are divided into three generalized groups: (i) algebraic models, which invoke an algebraic expression for the mean rate of product creation, (ii) gradient models, which involve a gradient-type source term in a balance equation for the mean combustion progress variable, and (iii) two-equation models, which deal not only with a balance equation for the mean combustion progress variable but also with either a balance equation for the flame surface density or a balance equation for the mean scalar dissipation rate. Analytical and numerical results reported in the paper indicate that solely the gradient models are able to yield substantially different growth rates of the turbulent burning velocity and the mean flame brush thickness.