Abstract
The unstrained and strained flamelet closures for filtered reaction rate in large eddy simulation (LES) of premixed flames are studied. The required sub-grid scale (SGS) PDF in these closures is presumed using the Beta function. The relative performances of these closures are assessed by comparing numerical results from large eddy simulations of piloted Bunsen flames of stoichiometric methane–air mixture with experimental measurements. The strained flamelets closure is observed to underestimate the burn rate and thus the reactive scalars mass fractions are under-predicted with an over-prediction of fuel mass fraction compared with the unstrained flamelet closure. The physical reasons for this relative behaviour are discussed. The results of unstrained flamelet closure compare well with experimental data. The SGS variance of the progress variable required for the presumed PDF is obtained by solving its transport equation. An order of magnitude analysis of this equation suggests that the commonly used algebraic model obtained by balancing source and sink in this transport equation does not hold. This algebraic model is shown to underestimate the SGS variance substantially and the implications of this variance model for the filtered reaction rate closures are highlighted.
Highlights
High combustion efficiency with low emissions in practical devices can be achieved using lean premixed combustion, which will be invariably turbulent offering considerable challenge for mathematical treatment and modelling
Two grids of 1.5M and 4.2M are employed and these grids resolve more than 80% of turbulent kinetic energy and show a negligible difference in the computed mean velocity and turbulent kinetic energy, and compare well with the measured values for cold flows of the piloted Bunsen flames in [33]
The averaged streamwise velocity and various scalar mass fractions including temperature obtained using the unstrained flamelet (UF) and strained flamelets (SF) models show a weak sensitivity to the numerical grid, but the turbulent kinetic energy (TKE) computed using the SF model shows a substantial sensitivity, which is observed to be weak for the UF model
Summary
High combustion efficiency with low emissions in practical devices can be achieved using lean premixed combustion, which will be invariably turbulent offering considerable challenge for mathematical treatment and modelling. The premixed combustion is usually a sub-grid phenomenon requiring modelling, and various approaches used for this modelling are reviewed and summarised in [1,2,3,4,5]. These approaches can be broadly categorised into flamelet and non-flamelet or geometrical and statistical [3] approaches. The non-flamelet methodology includes the transported PDF and the conditional moment closure (CMC) approaches. The conditional source term estimation approach has been developed for premixed combustion modelling, and details can be found elsewhere – for example in [30,31]
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