Simulations of Scalar Transport in Developing Turbulent Flames Solving a Conditioned Balance Equation

Abstract

A balance equation for the difference in the conditioned velocities and , 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 is gradient during an early stage of flame development followed by a transition to countergradient scalar transport (i.e., ) 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.

Keywords:

• Conditioned velocities
• Countergradient transport
• Flame development
• Modeling
• Premixed turbulent combustion

ACKNOWLEDGMENTS

The author is grateful to Prof. Jerzy Chomiak for valuable discussion. This work was supported by the Swedish Research Council (VR) and by the Combustion Engine Reserch Center (CERC).

Notes

When rewriting these equations from the cited paper, the following equalities valid in the flamelet regime (Bray and Moss, 1977), have been invoked.

The flux still shows the gradient behavior at the leading edge due to the boundary conditions, but this effect is not visible in Figure 1 due to a low magnitude of the flux at . It is worth also noting that the recent experimental data by Troiani et al. (2009) indicate gradient transport in the trailing half of turbulent flame brush, while countergradient transport in the leading half (e.g., see Figure 9) for Φ = 0.8 in the cited paper).

Certainly, computed dependencies of and δ _t (t) are substantially affected by a particular submodel invoked to close the mean rate .