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.
Highlights
Modelling of chemical reaction terms in turbulent combustion simulations is complicated by the non-linear dependence of reaction rates on fluctuations in composition and temperature
The predictions are presented alongside DNS flame speed data for freely propagating stoichiometric methane-air flames by Nivarti and Cant [27] with similar LT /δL, and based on a one-step chemical reaction model similar to that used in the Stochastic Fields simulations
The Stochastic Fields formulation is an attractive way to apply the transported probability density function approach to turbulent reacting flows, the spatial resolution requirements become very demanding when applied to turbulent premixed combustion
Summary
Modelling of chemical reaction terms in turbulent combustion simulations is complicated by the non-linear dependence of reaction rates on fluctuations in composition and temperature. The Probability Density Function (PDF) modelling approach is attractive because, once the joint-scalar PDF for composition and temperature is known, the chemical reaction terms needed for Reynolds-Averaged Navier-Stokes (RANS) or Large Eddy Simulation (LES) appear in closed form. The joint-scalar transported PDF approach is applicable in RANS and LES across all modes of turbulent combustion—including the limiting cases of non-premixed and perfectly-premixed combustion—provided that turbulent transport and micro-mixing effects are modelled adequately and that the PDF equation is solved accurately. The present study investigates the use of the Stochastic Fields approach [1, 2] for modelling the joint-scalar PDF evolution, and considers the requirements for obtaining numerically accurate solutions in the challenging case of turbulent premixed combustion.
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