**Article: **Tirunagari, RR; Pope, SB; Hernandez, KA; Spector, JA; Bonassar, LJ; (2016) *“An Investigation of Turbulent Premixed Counterflow Flames Using Large-eddy Simulations and Probability Density Function Methods”*, Combustion and Flame, 166: 229-242

**Abstract: **We report results from a coupled large-eddy simulation (LES)/probability density function (PDF) computational study of turbulent premixed flames in the Yale turbulent counterflow flame (TCF) burner. The Yale TCF burner in the premixed mode consists of two coaxial opposed nozzles: one emitting cold, fresh premixed reactants, CH4/O-2/N-2, and the other hot stoichiometric combustion products. This results in a turbulent premixed flame close to the mean stagnation plane. Four critical parameters are identified in the experiments, namely, the bulk strain rate, the turbulent Reynolds number, the equivalence ratio of the reactants mixture and the temperature of the hot combustion products. These are varied independently. In the conditional statistics approach, the instantaneous centerline profiles of OH mass fraction and its gradient are used to identify (i) the interface between the two counterflowing streams referred to as the gas mixing layer interface (GMLI), and (ii) the turbulent flame front using a binary reaction progress variable, c.

The conditional mean of the progress variable conditioned on distance Delta from the GMLI, < c vertical bar Delta >, and the PDF of the GMLI-to-flame-front distance, Delta(f), are used to quantify the effects of the critical parameters on the interactions of the turbulent premixed flame with the counterflowing hot combustion products, both in the experiments and in the simulations. The LES/PDF simulations are performed in a cylindrical domain between the two nozzle exit planes. A base case simulation involving reference values of the critical parameters is simulated, and the centerline profiles (both unconditional and conditional) of the velocity statistics and the mean progress variable are found to match well with the experimental data.

Additionally, the LES/PDF simulations predict the experimentally-observed trends of the effects of the critical parameters on the turbulent premixed flame very well. More importantly, the probability of localized extinction at the GMLI (i.e., 1 – < c vertical bar Delta = 0 >) and the PDF of the separation distance between the GMLI and flame front, Delta(f), compare well with the experiments for all the flow conditions explored in the parametric study. Three independent key quantities are computed from the LES/PDF simulations of the base case to examine if the simulations can be considered to be in the direct numerical simulation (DNS) limit. They are (i) the ratio of the resolved turbulent diffusivity to the resolved molecular diffusivity, (D) over tilde (T)/(D) over tilde, (ii) the normalized mixing rate, Omega(R)tau(L), and (iii) the normalized grid spacing, h/delta(L). The ratio of (D) over tilde (T)/(D) over tilde is sufficiently small (<=0.02) and the value of Omega(R)tau(L), is sufficiently large (approximate to 22) to be considered to be in the DNS limit. However, the ratio of h/delta(L) is too large (approximate to 0.6) and hence the LES/PDF cannot be considered to be in the DNS limit by this criterion.

In spite of the poor spatial resolution, the particle mesh method yields a flame speed close to the laminar flame speed and this likely explains the success of the present LES/PDF calculations of the TCF premixed flame over the full range of critical parameters. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Funding Acknowledgement: U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences [DE-FG02-90 ER14128]; National Science Foundation [ACI-1053575]

Funding Text: This research is funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under award number DE-FG02-90 ER14128. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575.