The minimum ignition energy (MIE) requirements for ensuring successful thermal runaway and self-sustained flame propagation have been analysed for forced ignition of homogeneous stoichiometric biogas-air mixtures for a wide range of initial turbulence intensities and CO2 dilutions using three-dimensional Direct Numerical Simulations under decaying turbulence. The biogas is represented by a CH4 + CO2 mixture and a two-step chemical mechanism involving incomplete oxidation of CH4 to CO and H2O and an equilibrium between the CO oxidation and the CO2 dissociation has been used for simulating biogas-air combustion. It has been found that the MIE increases with increasing CO2 content in the biogas due to the detrimental effect of the CO2 dilution on the burning and heat release rates. The MIE for ensuring self-sustained flame propagation has been found to be greater than the MIE for ensuring only thermal runaway irrespective of its outcome for large root-mean-square (rms) values of turbulent velocity fluctuation, and the MIE values increase with increasing rms turbulent velocity for both cases. It has been found that the MIE values increase more steeply with increasing rms turbulent velocity beyond a critical turbulence intensity than in the case of smaller turbulence intensities. The variations of the normalised MIE (MIE normalised by the value for the quiescent laminar condition) with normalised turbulence intensity for biogas-air mixtures are found to be qualitatively similar to those obtained for the undiluted mixture. However, the critical turbulence intensity has been found to decrease with increasing CO2 dilution. It has been found that the normalised MIE for self-sustained flame propagation increases with increasing rms turbulent velocity following a power-law and the power-law exponent has been found not to vary much with the level of CO2 dilution. This behaviour has been explained using a scaling analysis and flame wrinkling statistics. The stochasticity of the ignition event has been analysed by using different realisations of statistically similar turbulent flow fields for the energy inputs corresponding to the MIE and it has been demonstrated that successful outcomes are obtained in most of the instances, justifying the accuracy of the MIE values identified by this analysis.

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Three-dimensional compressible Direct Numerical Simulations have been used to investigate the localised forced ignition of statistically planar biogas/air mixing layers for different levels of turbulence intensity and biogas composition. The biogas is represented by a $$\hbox {CH}_4$$ CH 4 /$$\hbox {CO}_2$$ CO 2 mixture and a two-step mechanism capturing the variation of the unstrained laminar flame speed with equivalence ratio and $$\hbox {CO}_2$$ CO 2 dilution was used. The mixture composition was found to significantly affect the flame kernel development which was reflected in the diminished growth rate of the burned gas volume with increasing $$\hbox {CO}_2$$ CO 2 dilution. A successful ignition of $$\hbox {CH}_4$$ CH 4 /$$\hbox {CO}_2$$ CO 2 /air mixing layer gives rise to a tribrachial flame structure involving fuel-rich and lean premixed branches on either side of the diffusion flame stabilised on the stoichiometric mixture fraction iso-surface. The most probable edge flame speed decreases in time and converges to a value that is at most equal to its laminar theoretical limit, and can even locally become negative for large values of the dilution and/or turbulence intensity. The decomposition of the edge flame speed showed a negligible or negative contribution of the mixture fraction surface displacement speed, while the displacement speed of the fuel mass fraction surface appeared as the dominant contributor. Finally, the edge flame speed dependences to the fuel mass fraction and mixture fraction gradients, fuel mass fraction iso-surface curvature and tangential strain rate have been analysed and found, within the dilution values considered, qualitatively similar to those of undiluted mixtures regardless of the amount of $$\hbox {CO}_2$$ CO 2 , although quantitative differences were observed.