A near-exact analytic solution of progress variable and pdf for single-step Arrhenius chemistry

A new chemical reaction rate source term in the transport equation of a single progress variable is proposed and implications for premixed flame modelling are discussed. This surrogate source term approximates the Arrhenius one over a large range of activation energies and density ratios almost perfectly. An analytic, invertible flame profile and the corresponding 1D laminar flame pdf are derived. The laminar flame Eigenvalue is evaluated analytically for unity and non-unity Lewis number and compared to classical results. A method to evaluate the progress variable pdf from DNS data is introduced. It is based on regularized delta functions and a transformation of the DNS progress variable field with the inverse of the 1D laminar flame profile, which behaves like a signed distance function. The pdf factorizes into the flat flame pdf, a geometrical wrinkling factor and a correction factor accounting for changes in the inner flame structure. The pdfs of RANS-like filter volumes and their ingredients are evaluated from DNS datasets of statistically flat turbulent flames featuring different turbulence intensity levels. For all DNS cases the wrinkling and correction factors vary little with progress variable. The wrinkling factor rises with turbulence intensity. The pdf is similar to that of a 1D laminar flame pdf, scaled by the wrinkling factor. Opportunities for improvements to premixed turbulent flame modelling are discussed. (c) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Automated summary

A new chemical reaction rate source term is proposed and its implications for premixed flame modeling are discussed. Analytic flame profiles, 1D laminar flame pdfs, and the evaluation of laminar flame Eigenvalues are derived and compared to classical results. A method to evaluate progress variable pdf from DNS data is introduced, which factorizes into flat flame pdf, geometrical wrinkling factor, and correction factor.