A posteriori testing of algebraic flame surface density models for LES

In the application of Large Eddy Simulation (LES) to premixed combustion, the unknown filtered chemical source term can be modelled by the generalised flame surface density (FSD) using algebraic models for the wrinkling factor Xi. The present study compares the behaviour of the various models by first examining the effect of sub-grid turbulent velocity fluctuation on Xi through a one-dimensional analysis and by the LES of the ORACLES burner (Nguyen, Bruel, and Reichstadt, Flow, Turbulence and Combustion Vol. 82 [2009], pp. 155-183) and the Volvo Rig (Sjunnesson, Nelsson, and Max, Laser Anemometry, Vol. 3 [1991], pp. 83-90; Sjunnesson, Henrikson, and Lofstrom, AIAA Journal, Vol. 28 [1992], pp. AIAA-92-3650). Several sensitivity studies on parameters such as the turbulent viscosity and the grid resolution are also carried out. A statistically 1-D analysis of turbulent flame propagation reveals that counter gradient transport of the progress variable needs to be accounted for to obtain a realistic flame thickness from the simulations using algebraic FSD based closure. The two burner setups are found to operate mainly within the wrinkling/corrugated flamelet regime based on the premixed combustion diagram for LES (Pitsch and Duchamp de Lageneste, Proceedings of the Combustion Institute, Vol. 29 [2002], pp. 2001-2008) and this suggests that the models are operating within their ideal range. The performance of the algebraic models are then assessed by comparing velocity statistics, followed by a detailed error analysis for the ORACLES burner. Four of the tested models were found to perform reasonably well against experiments, and one of these four further excels in being the most grid-independent. For the Volvo Rig, more focus is placed upon the comparison of temperature data and identifying changes in flame structure amongst the different models. It is found that the few models which largely over-predict velocities in the ORACLES case and volume averaged Sigma(gen) in a previous a priori DNS analysis (Chakraborty and Klein, Physics of Fluids, Vol. 20 [2008], p. 085108), deliver satisfactory agreement with experimental observations in the Volvo Rig, whereas a few of the other models are only able to capture the experimental data of the Volvo Rig either quantitatively or qualitatively.