Investigation of the influence of combustion-induced thermal expansion on two-point turbulence statistics using conditioned structure functions

Journal article, 2019

The second-order Structure Functions (SFs) of velocity field, which characterize velocity difference in two points, are widely used in research into non-reacting turbulent flows. In the present paper, the approach is extended in order to study the influence of combustion-induced thermal expansion on turbulent flow within a premixed flame brush. For this purpose, SFs conditioned to various combinations of mixture states in two different points
(reactant-reactant, reactant-product, product-product, etc.) are introduced in the paper and a relevant exact transport equation is derived in appendix.
Subsequently, in order to demonstrate capabilities of the newly developed approach for advancing understanding of turbulent reacting flows, the conditioned SFs are extracted from 3D Direct Numerical Simulation data obtained from two statistically 1D, planar, fully-developed, weakly turbulent, premixed, single-step-chemistry flames characterized by significantly different (7.53 and 2.50) density ratios, with all other things being approximately equal. Obtained results show that the conditioned SFs differ significantly from standard mean SFs and convey a large amount of important information on various local phenomena that stem from the influence of combustion-induced thermal expansion on turbulent flow. In particular, the conditioned SFs not only (i) indicate a number of already known local phenomena discussed in the paper, but also (ii) reveal a less recognized phenomenon such as substantial influence of combustion-induced thermal expansion on turbulence in constant-density unburned reactants, and even (iii) allow us to detect a new phenomenon such as appearance of strong local velocity perturbations (shear layers) within flamelets. Moreover, SFs conditioned to heat release zones indicate highly anisotropic influence of combustion-induced thermal expansion on the evolution of small-scale two-point velocity differences within flamelets, with the effects being opposite (an increase or a decrease) for different components of the local velocity vector.