Does sensitivity of measured scaling exponents for turbulent burning velocity to flame configuration prove lack of generality of notion of turbulent burning velocity?

There exists a large scatter in reported scaling (power) exponents q characterizing response of turbulent flame speed St or burning velocity Ut to changes of various factors such as the root-mean-square turbulent velocity u′, integral length scale L or laminar flame speed SL0, e.g. St∝u′^q. This scatter is often interpreted as lack of generality of the notion of turbulent flame speed or burning velocity in the sense that these quantities may not be extrapolated beyond a particular flame configuration used to evaluate them. The aim of the present paper is to assess this interpretation. For this purpose, a simple model based on the notion of burning velocity Ut as a physically meaningful quantity defined by mixture and turbulence characteristics is used to simulate statistically stationary two-dimensional V-shaped and Bunsen flames. Various St and Ut are evaluated applying five different methods, which were used in earlier measurements and simulations, to numerical solutions obtained for different values of u′, L, or SL0 and three different mean flame surfaces and at three different distances from flame-holder for both flame configurations. So obtained scaling exponents are sensitive both to flame configuration and analysis method. This result (a significant scatter in the scaling exponents can be computed invoking a model based on the notion of Ut) shows that the scatter reported in the literature does not prove that turbulent burning velocity is of minor fundamental value