Effects of Turbulent Reynolds Number on the Performance of Algebraic Flame Surface Density Models for Large Eddy Simulation in the Thin Reaction Zones Regime: A Direct Numerical Simulation Analysis
A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different turbulent Reynolds numbers has been used to assess the performance of algebraic flame surface density (FSD) models based on a fractal representation of the flame wrinkling factor. The turbulent Reynolds number Ret has been varied by modifying the Karlovitz number Ka and the Damk？hler number Da independently of each other in such a way that the flames remain within the thin reaction zones regime. It has been found that the turbulent Reynolds number and the Karlovitz number both have a significant influence on the fractal dimension, which is found to increase with increasing Ret and Ka before reaching an asymptotic value for large values of Ret and Ka. A parameterisation of the fractal dimension is presented in which the effects of the Reynolds and the Karlovitz numbers are explicitly taken into account. By contrast, the inner cut-off scale normalised by the Zel’dovich flame thickness does not exhibit any significant dependence on Ret for the cases considered here. The performance of several algebraic FSD models has been assessed based on various criteria. Most of the algebraic models show a deterioration in performance with increasing the LES filter width. 1. Introduction Large eddy simulation (LES) is becoming increasingly popular for computational fluid dynamics (CFD) analysis of turbulent reacting flows due to the advancement and increased affordability of high-performance computing. The exponential temperature dependence of the chemical reaction rate poses one of the major challenges in LES modelling of turbulent reacting flows [1, 2]. Reaction rate closure models based on the concept of flame surface density (FSD) are well established in the context of the Reynolds averaged Navier Stokes simulations [3, 4] of turbulent premixed flames. However, the application of FSD-based modelling in LES is relatively recent [5–10]. The generalised FSD ( ) is defined as [5] where is the reaction progress variable. The overbar indicates the LES filtering operation in which the filtered value of a general quantity is evaluated as , where is a suitable filter function [5]. The combined contribution of the filtered reaction and molecular diffusion rates can be modelled using as , where is the fluid density, is the progress variable diffusivity, is the density-weighted surface-filtered displacement speed , and is the surface-filtered value of a general quantity . Often, is expressed in terms of the wrinkling factor , which is
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