The Problems of the Turbulent Burning Velocity

Abstract

The paper reviews the practical problems in measuring a turbulent burning velocity that gives the mass rate of burning. These largely centre on identifying an appropriate flame surface to associate with the turbulent burning velocity, u t , and the density of the unburned mixture. Such a flame surface has been identified, in terms of the mean reaction progress variable, $\bar {c}$ , for explosive flame propagation in a fan-stirred bomb. Measurement of $\bar {c}$ makes possible an estimation of the flame surface density, Σ, from the relationship ${\it \Sigma} =k\bar {c}\left( {1-\bar {c}} \right)$ . It is shown that in such explosions, mass rates of burning derived from the measured total flame surface area agreed well with those found from the measured turbulent burning velocity. Flamelet considerations identify appropriate dimensionless correlating parameters for u t . As a result, correlations of turbulent burning velocity divided by the effective rms turbulent velocity, are plotted against the turbulent Karlovitz stretch factor, K, for different values of the Markstein number for flame strain rate, Masr. These plots cover a wide range of variables, including pressure and fuels, and are indicative of different regimes of turbulent combustion. At the lower values of K, there is some evidence of increases in u t and k due to high-frequency flame surface wrinkling arising from flame instabilities. These increase as Masr becomes more negative. It is found from the developed value of the mean flame surface density throughout the flame brush that, to a first approximation, an increase in u t for a given mixture is accompanied by a proportional increase in the volume of the brush. The analysis shows that the volume fraction of the turbulent flame brush that is reacting is quite small.