The effect of pressure on the hydrodynamic stability limit of premixed flames

Intrinsic instabilities in premixed hydrogen flames: Parametric variation of pressure, equivalence ratio, and temperature. Part 1 - Dispersion relations in the linear regime

“…An increase of the expansion ratio or a reduction of the Lewis number are shown to increase growth rates and also lead to an increase of the cut-off wave number, which represents the wave number when the dispersion relation changes sign at high wave numbers. A similar observation regarding the cut-off wave number is reported by Attili et al [10], who numerically investigated dispersion relations of lean methane/air flames at different pressures using detailed chemistry. They demonstrated that an increase of pressure leads to an increase of the cut-off wave number even for unity Lewis number flames; a trend that is not observed in theoretical models, which predict a pressure independent value.…”

“…However, uncertainties for λ c are significantly lower (< 1% for all cases if allowing for the same amount of error, namely an error of 1% of the peak growth rate, for the determination of the growth rate, where the dispersion relation changes sign) and generally, a weak tendency of an increasing cut-off wave λ c length towards unstable conditions is observed, most prominently visible during the increase of pressure at elevated temperatures. This is interesting if compared to the study of Attili et al [10], who reported the opposite trend for lean methane/air mixtures, namely a decrease of λ c for increasing pressure. This difference is discussed in detail in the remainder of this paper.…”

“…Theoretical models are presently not capable of accurately describing the evolution of lean premixed hydrogen flames, as either Lewis numbers close to unity are assumed, whereas the Lewis number of hydrogen is significantly lower than unity, or small variations of density are assumed, while significant density variations are observed in actual flames. Attili et al [10] showed that even for methane/air flames, whose Lewis number is close to unity and which do not feature thermodiffusive instabilities, the theoretical models are missing certain trends and lack an accurate description. Thus, since thermodiffusive instabilities can significantly affect the flame evolution, a comprehensive quantification of intrinsic instabilities in lean hydrogen/air flames is necessary.…”

Data-driven subfilter modelling of thermo-diffusively unstable hydrogen–air premixed flames

“…The cutoff wavelength has been estimated by numerical reconstruction of the dispersion relation, i.e. by subjecting a planar flame to small perturbations of variable wavenumber and monitoring the initial flame amplitude growth rate, as illustrated in [29,30]. Figure 1 shows the reaction rate fields of the three TD flames.…”

Comparison of Flame Propagation Statistics Extracted from Direct Numerical Simulation Based on Simple and Detailed Chemistry—Part 1: Fundamental Flame Turbulence Interaction

“…Furthermore, it has previously been shown that several models developed based on simple chemistry data [25,26] perform equally well in the context of detailed chemistry and transport [27,28]. Recent analysis indicated that the pressure effects on hydrodynamic instability agree between simple and detailed chemistry simulations, provided the Arrhenius parameters are chosen in a physically consistent manner [29]. Finally, it was shown that the effect of pressure and Lewis number on hydrodynamic and thermodiffusive instability from simple chemistry is in qualitative agreement with experimental data [30].…”