Iso-surface mass flow density and its implications for turbulent mixing and combustion

Abstract

A new result is derived for the mass flow rate per unit volume through a scalar iso-surface – called here the ‘iso-surface mass flow density’. The relationship of the surface mass flow density to the local entrainment rate per unit volume in scalar mixing and to the local reaction rate in turbulent premixed combustion is considered. In inhomogeneous flows, integration of the surface mass flow density across the layer in the direction of the mean scalar inhomogeneity yields the mean entrainment velocity in scalar mixing and the turbulent burning velocity in premixed combustion. For non-premixed turbulent reacting flow, this new result is shown to be consistent with the classical result of Bilger (Combust. Sci. Technol. vol. 13, 1976, p. 155) for fast one-step irreversible chemical reactions. Direct numerical simulation data for conserved scalar mixing, isothermal reaction front propagation and turbulent premixed flames are analysed. It is found that the entrainment velocity in the conserved scalar mixing case is sensitive to a threshold value. This suggests that the entrainment velocity is not a well-defined concept in temporally developing mixing layers and that scaling laws for the viscous superlayer warrant further investigation. In the isothermal reaction fronts problem, the characteristics of iso-surface propagation in a low Damköhler number regime are investigated. In premixed flames, the effects of non-stationarity on the turbulent burning velocity are addressed. The difference from the existing methods for determining turbulent burning velocity, and the implications of the present results for flames with multi-dimensional complex geometry are discussed. It is also shown that the surface mass flow density is related to the turbulent scalar flux in statistically stationary one-dimensional premixed flames. Variations of the local propagation characteristics due to departure from an unstretched laminar flame structure are shown to decrease the tendency to counter-gradient transport in turbulent premixed flames.