Investigation of numerical resolution requirements of the Eulerian Stochastic Fields and the Thickened Stochastic Field approach

Abstract

The stochastic fields approach is an effective way to implement transported Probability Density Function modelling into Large Eddy Simulation of turbulent combustion. In premixed turbulent combustion however, thin flame-like structures arise in the solution of the stochastic fields equations that require grid spacing much finer than the filter scale used for the Large Eddy Simulation. An investigation into numerical resolution requirements is conducted through simulation of a series of one-dimensional stochastic fields simulations of freely-propagating turbulent premixed flames. The investigation involved various stochastic field simulations at different combustion regimes and numerical resolutions. It was concluded that the conventional approach of using a numerical grid spacing equal to the filter scale can yield substantial numerical error; specifically towards the flamelet regime. However, using a numerical grid spacing much finer than the filter length scale is computationally-unaffordable for most industrially-relevant combustion systems. A Thickened Stochastic Fields approach is developed in this thesis in order to provide physically and numerically-accurate solutions of the stochastic fields equations with reduced compute time compared to a fully resolved simulations. The Thickened Stochastic Fields formulation bridges between the conventional stochastic fields and conventional Thickened-Flame approaches depending on the sub-filter combustion regime and numerical grid spacing utilised. One-dimensional stochastic fields simulations of freely-propagating turbulent premixed flames are used in order to obtain a criteria for the thickening factor required as a function of relevant physical and numerical parameters, and to obtain a model for an efficiency function that accounts for the loss of resolved flame surface area caused by applying the thickening transformation to the stochastic fields equations. The Thickened Stochastic Fields formulation is tested by performing LES of a laboratory premixed Bunsen flame. The results demonstrate that the Thickened Stochastic Fields method produces accurate predictions even when using a grid spacing equal to the filter scale.

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ORCID for Edward Richardson: orcid.org/0000-0002-7631-0377

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