Modelling of Landau–Darrieus and thermo-diffusive instability effects for CFD simulations of laminar and turbulent premixed combustion

Abstract

An algebraic model is derived that accounts for the effects of non-resolved Landau–Darrieus and thermo-diffusive instabilities on the propagation speed of fully premixed laminar and turbulent flame fronts in the Large Eddy Simulation (LES) context provided that the laminar flame speed appears as a model parameter in the LES combustion model. The model is derived assuming fractal characteristics of flames which exhibit cellular structures due to instabilities. The smallest and largest unstable wavelengths are computed employing a dispersion relation for nominally planar flames. Values for the fractal dimension characterising the flame structures are taken from the literature. A phenomenological model accounts for the stabilising effect of strain. Based on experimental data, a correlation for a critical strain rate, which indicates the onset of instabilities, is formulated. To validate the new model which accounts for instabilities on the effective speed of laminar flame propagation, laminar expanding spherical methane–air flames at p = 5 bar and p = 10 bar are simulated in the LES context. Values for the fractal dimension, as proposed in the literature, are varied. The predicted flame propagation speed is in very good agreement with experimental data when applying a fractal dimension of about D = 2.06. The critical strain turns out to be a suitable parameter to indicate the onset of instabilities and to quantify the influence of instabilities. Simulations applying a second model proposed by Bradley and valid for spherically expanding flames show similar results. LES of turbulent Bunsen flames at 1, 5 and 10 bar, which are characterised by u′/s⁰_L < 1, are performed to evaluate the derived instability model for turbulent flames. The simulated flames (from the Kobayashi database) have already been experimentally investigated in the context of Landau–Darrieus and thermo-diffusive instabilities. In agreement with conclusions from these investigations, for the considered cases the new model does not predict any onset of instabilities.

Keywords:

• Landau-Darrieus and thermo-diffusive instabilities
• premixed combustion
• laminar flame speed
• LES
• high pressure

Notes

1. The coefficient is set to 0.5 as a compromise for best accuracy and convergence.

2. Since the flame propagates with a constant flame thickness, the simulation result is independent of the flame front definition.