Influence of the Lewis Number on Effective Strain Rates in Weakly Turbulent Premixed Combustion

ABSTRACT

The influence of the global Lewis number, Le, on the statistical behavior of the “effective” normal and tangential strain rates have been analyzed based on three-dimensional direct numerical simulation data of freely propagating statistically planar turbulent premixed flames with Le = 0.34, 0.60, 0.80, 1.00, and 1.20. The volumetric dilatation rate is found to be mostly positive and its magnitude increases with decreasing Le. The flow normal strain rate predominantly assumes positive values and thus tends to pull adjacent iso-scalar surfaces apart, which reduces scalar gradients. By contrast, the “added” normal strain rate due to derivatives of the displacement speed normal to iso-surfaces has the propensity to push them closer together, and therefore increase the magnitude of scalar gradients. The balance between flow and added normal strain rates along with the advective transport determines whether scalar gradients are enhanced or destroyed. Iso-surface elementary area stretching by the fluid flow increases with decreasing Lewis number, and the added tangential strain rate exhibits predominantly negative values and is determined by the correlation between displacement speed components and flame curvature. It has been found that turbulent flames with small values of Lewis number exhibit flame thinning and high values of the flame surface area and these tendencies strengthen with decreasing Lewis number. This behavior has been explained in detail in terms of the statistical behaviors of effective normal and tangential strain rates.

KEYWORDS:

• “Added” and “effective” normal and tangential strain rate
• Direct numerical simulation
• Flow
• Iso-scalar non-material surfaces
• Premixed flames
• Volumetric dilation rate

Acknowledgments

C.D. and L.C. gratefully acknowledge the support of this research by the Spanish Ministry of Economy and Competitiveness, under the CONSOLIDER-INGENIO Program, Project CS D2010-00011-SCORE. NC acknowledges N8/ARCHER for computational resources.

Notes

¹ The agreement of transient term of the transport equation evaluated from the transport equation and the actual evaluation from two time snapshots has been found to be very good (i.e., maximum deviation is smaller than 2%).