Solenoidal and potential velocity fields in weakly turbulent premixed flames

TL;DR

This study analyzes how thermal expansion influences turbulence in premixed flames by decomposing velocity fields into solenoidal and potential components, revealing their distinct roles in flame dynamics and flow perturbations.

Contribution

It introduces a combined Helmholtz-Hodge and natural decomposition approach to study velocity fields in turbulent flames, highlighting the impact of thermal expansion on flow structures.

Findings

Thermal expansion significantly alters upstream turbulence via potential velocity fluctuations.

Potential and solenoidal velocity fields show opposite correlations in unburned and burned regions.

Strain rates and curvature are differentially correlated in leading and trailing flame regions.

Abstract

Direct Numerical Simulation data obtained earlier from two statistically 1D, planar, fully-developed, weakly turbulent, single-step-chemistry, premixed flames characterized by two significantly different (7.53 and 2.50) density ratios {\sigma} are analyzed to explore the influence of combustion-induced thermal expansion on the turbulence and the backward influence of such flow perturbations on the reaction-zone surface. For this purpose, the simulated velocity fields are decomposed into solenoidal and potential velocity subfields. The approach is justified by the fact that results obtained adopting (i) a widely used orthogonal Helmholtz-Hodge decomposition and (ii) a recently introduced natural decomposition are close in the largest part of the computational domain (including the entire mean flame brushes) except for narrow zones near the inlet and outlet boundaries. The results show that combustion-induced thermal expansion can significantly change turbulent flow of unburned mixture upstream of a premixed flame by generating potential velocity fluctuations. Within the flame brush, the potential and solenoidal velocity fields are negatively (positively) correlated in unburned reactants (burned products, respectively) provided that {\sigma}=7.53. Moreover, correlation between strain rates generated by the solenoidal and potential velocity fields and conditioned to the reaction zone is positive (negative) in the leading (trailing, respectively) halves of the mean flame brushes. Furthermore, the potential strain rate correlates negatively with the curvature of the reaction zone, whereas the solenoidal strain rate and the curvature are negatively (positively) correlated in the leading (trailing, respectively) halves of the mean flame brushes.