Resolution Requirements in Stochastic Field Simulation of Turbulent Premixed Flames

Abstract

The spatial resolution requirements of the Stochastic Fields probability density function approach are investigated in the context of turbulent premixed combustion simulation. The Stochastic Fields approach is an attractive way to implement a transported Probability Density Function modelling framework into Large Eddy Simulations of turbulent combustion. In premixed combustion LES, the numerical grid should resolve flame-like structures that arise from solution of the Stochastic Fields equation. Through analysis of Stochastic Fields simulations of a freely-propagating planar turbulent premixed flame, it is shown that the flame-like structures in the Stochastic Fields simulations can be orders of magnitude narrower than the LES filter length scale. The under-resolution is worst for low Karlovitz number combustion, where the thickness of the Stochastic Fields flame structures is on the order of the laminar flame thickness. The effect of resolution on LES predictions is then assessed by performing LES of a laboratory Bunsen flame and comparing the effect of refining the grid spacing and filter length scale independently. The usual practice of setting the LES filter length scale equal to grid spacing leads to severe under-resolution and numerical thickening of the flame, and to substantial error in the turbulent flame speed. The numerical resolution required for accurate solution of the Stochastic Fields equations is prohibitive for many practical applications involving high-pressure premixed combustion. This motivates development of a Thickened Stochastic Fields approach (Picciani et al. Flow Turbul. Combust. X, YYY (2018) in order to ensure the numerical accuracy of Stochastic Fields simulations.

A Thickened Stochastic Fields Approach for Turbulent Combustion Simulation

“…The numerical setup is identical to previous Stochastic Fields simulations in Ref. [4], however the formulation is repeated in Sections 3.1 and 3.2 for completeness. The flame is characterised by Karlovitz numbers of order unity, indicating that combustion takes place across the flamelet and thin reaction zone regimes.…”

“…The improved resolution case with x = 0.5mm displays faster flame propagation than the less well-resolved case with x = 1.0mm. Under-resolution affects the flame speed in three main ways [4]: first, numerical diffusion increases the local propagation speed of the individual stochastic field reaction fronts; second, thickening of the stochastic field reaction fronts caused by the numerical diffusion reduces the amount of flame wrinkling produced by a given velocity field; third, the numerical viscosity reduces the strength of small-scale eddies that wrinkle the reaction fronts. Since the present Bunsen flame exhibits combustion in the flamelet regime, the scales of the reaction fronts are generally smaller than the scales of the velocity field that wrinkles the flame.…”

“…Stochastic Fields PDF-LES has been used to model both non-premixed [2] and premixed combustion [3]. However, in Stochastic Fields simulation of premixed combustion, flame-like structures arise that may be thinner than the LES filter length scale [4]. In order to solve the Stochastic Fields equations accurately it is then necessary to have grid spacing finer than the filter length scale substantially adding to the computational time required for the Stochastic Fields simulation.…”

“…In order to solve the Stochastic Fields equations accurately it is then necessary to have grid spacing finer than the filter length scale substantially adding to the computational time required for the Stochastic Fields simulation. Conversely, following the conventional practice of setting the LES filter length scale equal to the numerical grid spacing can lead to substantial numerical error for two reasons [4]. First, numerical diffusion caused by under-resolution changes the local propagation speed of the reaction fronts in the Stochastic Fields solution.…”

“…Having identified the difficulty and importance of spatially-resolved Stochastic Fields solutions for premixed combustion in Ref. [4], the present contribution seeks to develop a practical approach to alleviate the demanding resolution requirements.…”