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A study of the effects of pressure-driven transport on developing turbulent flame structure and propagation

The properties of solutions of a generalized normalized balance equation for the Favre-averaged combustion progress variable are numerically studied in the simplest case of a statistically planar, one-dimensional, stationary and uniform flow of unburned mixture. The focus is placed on the dependence of the solutions on pressure-driven transport for several closures of the mean rate of product creation. The results show the following: (1) the flame structure is self-similar if the pressure-driven transport is sufficiently strong, but the self-similarity can be obtained even for zero pressure-driven transport by using a particular closure of the mean rate of product creation; and (2) both burning velocity and flame thickness decrease if the pressure-driven transport increases, and this effect can be reduced to a decrease in the asymptotically fully developed quantities. An analysis of a more general progress variable balance equation, performed by invoking the sole assumption of the self-similarity of the flame structure, quantitatively confirms many numerical results, in particular: (1) the profile of the progress variable; (2) the scaling of the asymptotically fully developed flame brush thickness and burning velocity; and (3) the development of the flame brush thickness and burning velocity in the cases of weak and strong pressure-driven transport. The analysis shows straightforwardly that the above general balance equation may be reduced to the Zimont equation with modified diffusivity provided that the flame structure is self-similar.