Pulsating instability in rich hydrogen/air counterflow flames

Pulsating instability in adiabatic, rich hydrogen/air counterflow flames was computationally simulated with detailed chemistry and transport. Results demonstrate that for large Lewis number flames, thermal-diffusive pulsating instability is promoted by the positive stretch of the counterflow flames, that oscillation is initiated at an equivalence ratio much smaller than the onedimensional rich threshold, and that the critical strain rate leading to pulsation is smaller than the corresponding static extinction limit. Furthermore, similar to the one-dimensional, unstretched cases, \vith progressive increase in the strain rate for a sufficiently rich mixture, the pulsation mode changes from that of monochromatic, to period doubling, and to pemlanent extinction. It is also seen that the pulsating flames are quasi-steady in nature in that the period of oscillation is larger than the characteristic flame time. As such, the unsteady flame cannot recover once the instantaneous flame temperature is reduced below the corresponding steady-state extinction temperature. Since pulsating extinction occurs at a smaller strain rate than the steady extinction limit, it implies that the flame extinguishes in the pulsating instead of the steadily propagating mode, and the flammable range is accordingly narrowed. It is expected that when radiative heat loss is considered, the onset of pulsation will be facilitated such that the *Asstant Professor, Department of Mechanical and Aerospace Engineering, Senior Member, AIAA. ‘Robert H. Goddard Professor, Department of Mechanical and Aerospace Engineering, Fellow, AIAA. Copyright 8 2000 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc. \vith permission. regime in strain rate for steady burning will be further narrowed. This pulsation-induced extinction can be a major factor accounting for the discrepancy in the extinction strain rate betlveen the computed values based on static extinction turning points and the experimental data, for large Lewis number mixtures. Introduction Counterflow configuration has been widely used to study the flame dynamics and responses. The relative simplicity of this flow field renders accurate experimental and theoretical specifications and hence direct comparison between them possible. Additionally, the counterflow is quasi-one dimensional in nature, thereby facilitating the computational simulation with detailed chemistry and transport properties. Currently there exist considerable activities in this area. Especially, we can now compare the computational simulation using a detailed mechanism with the experimental data to identify the dominant chemistry. Such comparisons play an important role in developing comprehensive kinetic mechanisms. In this regard, it is also noted that a comprehensive kinetic mechanism must satisfactorily describe various flame phenomena such as steady burning, ignition, and extinction, with wide range of thermodynamic parameteric variations. At the global level, validation of a proposed mechanism can be conducted by comparing calculated and experimental results, including the laminar flame speeds, and the ignition and extinction strain rates. Typically, by using the laminar flame speed data together with the literature data on shock tube ignition delay and the concentration progress in plug flow reactors, detailed kinetic mechanism can be de\peloped, for instance, by applying 1 American Institute of Aeronautics and Astronautics (c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. constrained global optimization. Subsequently, validity of the mechanisms developed can be scrutinized and verified by using data on the ignition and extinction strain rates. This would lead to re-examination of the mechanism if the agreement is not satisfactory. Following the above procedure, a hierarchy of hydrocarbon fuels of increasing molecular weights and complexity has been systematically studied. However, our recent studies [l-6] on counterflow flames have shown that, while the experimental steady-state flame structure, including the hydrodynamic, thermal, and species profiles, can be predicted well for Ci-Cj flames using the existing/developed mechanisms, the experimental extinction strain rates are consistently smaller than the computed ones. Such a discrepancy cannot be accounted for by the experimental uncertainty. There are at least three possibilities for such a disagreement in the determination of the extinction states. First, recognizing that extinction is inherently a kinetics-affected phenomenon, the controlling kinetics -could change from steady burning to extinction. Second, recognizing that flame radiation is an inherent heat loss process of a combustion system and that radiative loss facilitates flame extinction, the radiation effect has to be properly accounted. Hovvever, in the optically-thin limit, which also represents the maximum radiative loss from the flame by neglecting reabsorption, calculated extinction limits of methane/air [7, 81 and propane/air counterflow flames [8] are still significantly higher than the experimental values [9]. The third possibility is related to the self-extinction of an oscillatorily unstable flame. Namely, the flame may become unstable near extinction, and consequently extinction could be governed by an unsteady instead of steady process. In particular, from the theory of diffusional-thermal instability of premixed flames, it is well established that a premixed flame tends to exhibit oscillatory instability when its effective Lewis number (Le) is sufficiently larger than unity, as in the case of rich hydrogen/air and lean, higher-order, hydrocarbon/air flames. For one-dimensional, unstretched flames, the propensity to become unstable increases as the flame further departs from stoichiometry. Furthermore, for rich hydrogen/air flames pulsating instability has been observed to take place at fuel concentrations well below that of the rich flammability limit [lo]. The unsteady flame propagation discussed above for the one-dimensional, freely-propagating flame is expected to be modified in the presence of aerodynamic stretch, which is invariably present in all practical flames, and is manifested through flow nonuniformity, flame curvature, and flame unsteadiness. Indeed, a numerical study on outwardly-propagating flames using one-step chemistry demonstrated that, vvith sufficiently large Lewis numbers, positive curvature appears to encourage oscillation at small radii but is damped out at larger radii [ 111. Furthermore, a recent study [ 121 also investigated the curvature effects of the invvardlypropagating flame on the onset of pulsating instability through linear stability analysis and fully transient calculations with detailed chemistry and transport properties. The results showed that since the inwardlypropagating flame is negatively-stretched, flame curvature tends to suppress pulsating instability. Therefore, it is clear that negative (positive) stretch delays (promotes) the onset of pulsating instability. Since positive straining facilitates pulsating instability, this then leads to the expectation that extinction of such Le>l counterflow flames could be in the oscillatory mode. It is then of interest to describe the extinction of such a self-induced oscillatory flame, particularly the possibility of the self-extinction of an otherwise un-extinguishable flame when it becomes oscillatory unstable. In the present study, we therefore extend our previous study on purely-cuRed, negatively-stretched, imvardly-propagating flames by investigating the purely-strained, positively-stretched, counterflovv flames. Phenomena of interest include the effect of strain rate on the onset of the pulsating instability and the existence of pulsation-induced extinction as well as their implications to the determination of the fundamental flammability limit using the counterflowbased experimentation. Computational Specifications The mathematical model and the governing equations of the steady-state system employed here follow those of Kee et al. [13], while the unsteady behavior of counterflow flames is studied using a second order implicit scheme [14, 151. Calculations are performed for the axisymmetric configuration at one atmosphere pressure, 298 K upstream temperature, and with plugflow boundary conditions. The reaction mechanism used for hydrogen flames is taken from Kim et al. [ 161. Transient calculations are started at time t=O from the velocity, temperature, and species profiles of the steady solution with the same set of the boundary conditions. The local strain rate for the present premixed twin-flame case is simply defined as the