Simulations of scalar transport in developing turbulent flames solving a conditioned balance equation

Journal article, 2010

A balance equation for the difference in the conditioned velocities (u) over bar (b) and (u) over bar (u), derived and validated recently (Lipatnikov, 2008a, 2008b), is numerically solved in a statistically planar, one-dimensional case in order to (a) highlight the influence of premixed turbulent flame development on the direction of the mean scalar flux and (b) assess the equation by comparing computed trends with available experimental and DNS data. Numerical results show that (a) the flux (rho u '' c '') over bar gradient during an early stage of flame development followed by a transition to countergradient scalar transport (i. e., (rho u '' c '') over bar center dot del(c) over bar >0) at certain instant t(tr); (b) the transition time t(tr) is increased by the rms turbulent velocity and decreases when the density ratio or the laminar flame speed increases; and (c) even after the transition from gradient to countergradient scalar transport, the mean flame brush thickness grows because the mean rate of product creation overwhelms the transport term in the combustion progress variable balance equation and serves to not only control the turbulent burning rate, but also cause the growth of the thickness.