The effect of Soret diffusion on stability of rich premixed hydrogen–air flames
Introduction
Molecular transport process have a profound influence on laminar flames. In the case of hydrogen combustion systems they affect and define the main features of the flame. The transport is mainly due to Fickian diffusion caused by the concentration gradient. Total molecular diffusion, however, can be affected by Soret diffusion caused by the temperature gradient [2], [3].
It is well known that the Soret effect tends to drive small and light species towards hotter regions, while large and heavy species towards cold fresh mixture [3]. It causes an additional flux of H atoms and H2 in the downstream direction and an O2 flux in the upstream direction. Thus, the concentration of H radicals in the active reaction region decreases and reaction intensity weakens. This in turn affects the reaction dynamics. In particular, it leads to reduction of laminar planar flame speed. This effect firstly was observed computationally in the pioneering work of Dixon-Lewis [4] for a stoichiometric planar flame. Later it was theoretically investigated in Ref. [5], using a one-step Arrhenius model. It has been shown in Ref. [4] that the exclusion of thermal diffusion of hydrogen atoms increases the value of the burning rate of planar flame by about 6%. By using numerical studies Ern and Giovangigli [6], [7] have shown that the thermal diffusion has a great impact on the structure of both rich and lean hydrogen–air Bunsen flames.
In general, the inclusion of thermal diffusion decreases the flame speed for most equivalence ratios. This phenomenon has been observed for both lean and rich fuels in recent numerical investigations of methane/hydrogen–air [8], [9], CO–air [10], methane–air [11] and syngas–air [12], [13] planar flames (see e.g. Ref. [3] for a review of previous studies on this subject).
In Refs. [8], [11] the effect of H and H2 thermal diffusion was investigated separately. It was shown in both works that the inclusion of H2 Soret diffusion has only a moderate effect on the laminar flame speed, slightly lowering it for all equivalence ratios; the inclusion of the Soret diffusion of H atoms has significant effect on the laminar flame speed. In principle, the combined Soret effect of H and H2 should basically compose the total Soret diffusion because these are very light species and diffuse much stronger than the other.
For wrinkled flames the effect of thermal diffusion on flame propagation speed differs from those for planar flames; for example, in recent theoretical investigations of premixed spherical flames [14] it was found that for light fuels Soret diffusion increases the flame propagation speed, for heavy fuels – decreases. In Refs. [15], [16], [17], the thermal-diffusion is shown to increase the burning rate of lean hydrogen–air flames in narrow channels and in the case of freely propagation, respectively.
It is important to note that in all computational studies with detailed kinetic and transport [4], [6], [7], [8] of the Soret effect on planar hydrogen–air flames, the diffusive-thermal stability has not yet been considered. Such analysis was carried out in Ref. [1] by means of activation energy asymptotics for a model with single-step Arrhenius reaction. It is demonstrated that in the leading order of asymptotic expansion the thermal diffusion has no effect on flame speed and structure, while it strongly modifies the neutral stability boundary. Therefore, the main aim of this study is to investigate the impact of the Soret effect both on the flame propagation and on its stability by using a detailed reaction model. The understanding and quantification of this phenomenon (how thermal diffusion affects the flame stability) represents a challenging and interesting task from both academic as well as from application point of view.
Section snippets
Model
The standard mathematical model for one-dimensional premixed flame is used in this work (see e.g. Ref. [18]). The one-dimensional system of conservation equations with a detailed chemistry mechanism and a detailed transport model was integrated numerically. Calculations were performed using the detailed mechanism by Warnatz [2], [19] accounting for 38 elementary reactions between 9 species.
The rate coefficients of the forward and reverse reactions were calculated using thermodynamic properties
Flame structure and propagation velocity
We investigate the speed and structure of the freely propagating combustion waves using the model described in the previous section. Rich hydrogen/air flames are considered here because pulsating diffusive-thermal instabilities are usually observed for rich flames having equivalence ratio [23].
The diffusion flux is described [2] bywhere ρ is density, wi is the mass fraction of specie i, Vi is diffusion velocity in the centre of mass system (vi = v + Vi with v – the mean mass velocity),
Stability of combustion waves
The onset of the diffusive-thermal pulsating instability is investigated according to the methodology employed in Ref. [23]. For fixed mixture composition and temperature of the fresh mixture, the pressure is increased from the ambient value, P = 1 atm until the oscillations of combustion wave appear. These oscillations are observed as periodic time dependent variations of flame velocity and concentration of species profiles, which settle in the system after certain transient period of time. Due
Conclusions
In this work the role of the Soret effect on the emergence of pulsating diffusive thermal instabilities is investigated. The analysis is undertaken for the model of freely propagating flames in rich hydrogen–air mixtures, which is in accordance with our previous work [23]. In addition the thermal diffusion effect on the velocity of combustion waves is investigated. In terms of flame structure, it is found that the Soret diffusion has a pronounced influence on the molar fractions of reagents,
Acknowledgements
AIK and VVG would like to acknowledge the financial support from the Russian Foundation for Basic Research grant 14-01-00196; Ministry of Education and Science of the Russian Federation (Grant 14.Y26.31.0003). AIK acknowledges The Karlsruhe House of Young Scientists (KHYS) for the aspirant Grant. VB and UM acknowledge the financing support by the DFG (Grant no. SFB/TR 150). We would like to thank V.N. Kurdyumov and C. Jiménez for helpful discussions.
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2021, Combustion and FlameCitation Excerpt :Detailed molecular transport including thermal diffusion is taken into account (see e.g. [31]). In a number of previous studies [35,36] it has been shown that the Soret effect influences significantly the outcome of the numerical integration with respect to the bifurcation and characteristics of the oscillating solutions, though it has only a moderate influence on the laminar flame characteristics. In order to describe this a multi-component transport model based on the Curtiss–Hirschfelder approximation is chosen [37,38].