Hydrogen/air burner-stabilized flames at elevated pressures
Introduction
Burner-stabilized flames remain one of most investigated topics in combustion theory. The flat porous plug burner experimental setup [1] is widely used to measure flame height, speed, structure, dynamics as well as for calibration of optical techniques [2], [3], [4], [5], [6], [7], [8], [9], [10]. This is due to the very simple geometry and the possibility to access the flame structure by using different direct and indirect measurements. The flame can be efficiently controlled and maintained at different stationary regimes. However, increasing demand for reliable combustion mechanisms describing transient regimes of combustion near stability limits and in a view of recent progress made in the detailed modelling (e.g. molecular transport, chemical kinetics etc.) and in numerical integration open new perspectives of the burner-stabilized flames. It provides a unique opportunity to directly compare the results of numerical modelling and experiments (see e.g. [11] for relevant detailed review of the experimental studies). This can be used efficiently to verify the reaction and transport models similarly as in [8] and investigate the complex dynamics of various non-trivial combustion regimes [5], [6], [7]. So far such verification has been made for combustion of hydrogen under low, atmospheric and moderately elevated (up to 5 atm) pressures [8]. Nevertheless, understanding the chemistry of hydrogen oxidation under the high pressure and near stationary limit conditions is crucial for applications in development of engines and propulsion. Further development of reliable mechanisms of chemical kinetic describing combustion systems in such conditions represents a very interesting and challenging task.
Starting from the first experiments there were several very interesting phenomena observed. Particularly, it was demonstrated that the response curves, e.g. flame height vs. mass flow rate, admit the co-existence of two solutions [2], [12]. Thus the same flame height can be realized for two different mass flow rates or temperatures. In [12] by using the flame sheet model for temperature only and empirical correlation [13] it was shown that the stand off distance is a U-shaped function of flame temperature and there exists a minimum distance of the flame sheet from the burner surface. As the flow velocity approaches the speed of freely propagating flame the temperature tends to adiabatic flame temperature and blow-off occurs. In the opposite limit as the flow rate is reduced the flame temperature decreases and the flame height above the burner grows in order to reduce the heat loss to the burner surface and balance the reduction of the rate of heat release. This behaviour is governed by heat exchange between the flame and the burner surface and it was confirmed in all subsequent papers on asymptotic analysis [14], [15], [16], [17]. Note that most of the studies of the unsteady burner-stabilized flames have been done within the framework of the single-step reaction, except maybe [18], [19].
The flame stability is analysed in a number of papers using the activation energy asymptotic approach. In [18] by means of asymptotic and numerical analysis it was shown that the flame-wall interaction between the hot reacting gas and burner can significantly promote the onset of pulsating instabilities. In [15] the emergence of one-dimensional pulsating instabilities is studied in the model with infinitely thin burner, which played a role of a heat sink. Nearly equidiffusional approximation was employed. It was found that for a given mass flow rate the pulsating instabilities occur provided the Lewis number is sufficiently large. The calculations confirmed that the flame-burner thermal interaction enhanced the onset of pulsations. In [17] the asymptotic analysis was carried out in the nearly equidiffusional approximation, however different model of the burner was used. It was assumed that the thermal inertia of the burner was large, the temperature of the burner was fixed and the temperature of the fresh gas mixture at the surface of the burner was also constant and equal to it. The mixed boundary conditions were imposed for the mass fraction of fuel taking into account the depletion of fuel concentration inside of the burner due to diffusion. These conditions are quite often used in the analysis and appropriate for the thick (in comparison to flame thickness) plate and/or small porosity. Several conclusions on the characteristics of pulsating instabilities can be drawn based on the results obtained in [17]. Again, the heat exchange with the burner significantly promotes the onset of flame pulsations: it is possible to encounter flame oscillations for mixtures with the Lewis number less than one, moreover the stationary planar flame may become completely unstable for all values of the Lewis number. The dominating type of oscillatory instability is planar one-dimensional as it follows from the dispersion relation in [17]. The dynamics of flame oscillations for the mixture with Lewis number equals to one was studied in [16], where the evolution equation for the location of the flame front was derived. It was shown that the low-temperature branch is unstable, while the high-temperature branch loses stability before the minimum stand-off distance is reached and flame pulsations emerge as a result of the supercritical Hopf bifurcation. The amplitude of oscillations of the flame front position and the period of pulsations grow as the bifurcation parameter is increased. As the parameters are further modified away from the critical value for Hopf bifurcation the oscillations become relaxational and are characterized by the presence of rapid and slow stages in dynamics of pulsations. The minimal distance from the surface of the burner can be significantly smaller than the flame thickness, while the maximum stand-off distance can be of order of magnitude larger than the flame thickness. All these conclusions qualitatively agree with the results of detailed numerical simulations of burner stabilized hydrogen-oxygen flame calculated with the thirteen step skeletal mechanism for rich mixture under ambient pressure and elevated temperature of the burner [18].
In [20] the asymptotic results are generalized to include the effects of product dissociation. In the non-dissociative case the results of the asymptotic analysis were successfully used to interpret the experimental data in [2], [12]. It was shown that flame can be destabilized with respect to pulsating instabilities for both lean and rich mixtures. In [21] the stability of the burner stabilized flame is revised to take into consideration the transport processes inside of the porous media of the burner. The investigation is carried out both analytically and numerically using the flame-sheet and finite rate chemistry models, respectively. It was demonstrated that the burner thickness and porosity can affect the flame stability. In particular, if the ratio of burner plate thickness in units of flame thickness to its porosity is finite, then the low-temperature branch of solutions can regain the stability for sufficiently large stand-off distances. The effect of radiation or volumetric linear heat losses on burner stabilized flame properties and stability was studied in [22], [23]. It was demonstrated that the region of existence of steady solutions in the space of parameters shrinks with the intensification of heat losses, which eventually leads to flame quenching. The heat losses also promote the onset of both pulsating and cellular instabilities.
In several earlier papers [18], [19], skeletal reaction mechanisms to investigate the characteristics and pulsations of rich hydrogen-oxygen flames at elevated burner temperature and atmospheric pressure was used. The aim of our current work is to extend these results to the case of hydrogen-air flames and to study their properties and dynamics using the detailed reaction mechanism. The effect of the key parameters which can be easily controlled in experiments such as mixture composition, temperature of the burner, pressure is studied. The special attention is paid to the comparison of the model predictions obtained with different kinetic mechanisms.
Section snippets
Mathematical model and numerical methods
The mathematical model for burner stabilized one-dimensional flame is described in detail in e.g. [18], [24]. In our current paper it is used for modelling and numerical study of the flat burner and includes the detailed chemistry mechanisms and detailed transport models. More specifically, a number of detailed chemical reaction mechanisms is considered, namely, Warnatz [25], [26], San-Diego [27], GRI3.0 [28], Keromnes [29], Li [30], USC2.0 [31]. Both well-established mechanisms as well as
Dynamics of flame oscillations
As discussed in the introduction the variation of the mass flow rate may result in the loss of stability of the stationary solutions and the emergence of flame oscillations. In this section typical numerical results for the steady and pulsating solutions are summarized. They are illustrated for the case of a rich hydrogen-air mixture with the equivalence ratio, and ambient pressure of 5 bar. In Fig. 4 the dependence of flame height above the burner (left axis) and burned temperature (right
Effect of the mixture composition
In this section we investigate the effect of the equivalence ratio on the characteristics and stability of flames anchored near the burner surface. We are interested here in pulsating instabilities, so mixtures with ϕ ≥ 1 are considered, since flame oscillations in hydrogen-air flames are expected to occur for sufficiently rich mixtures (see [41] and references therein). The typical dependence of the stand-off distance and flame temperature on the equivalence ratio is illustrated in Fig. 9 for
Effect of the burner temperature
It was assumed in the model that the temperature of the burner is constant. This can be achieved by using the water cooling system. The temperature of the burner thus can be manipulated in experiments and provide a suitable control parameter. In this paragraph we investigate the influence of burner temperature T0 on the flame characteristics.
In Fig. 12 the dependence of flame height and temperature on T0 is plotted for kg/m2s, bar using the circles connected with the solid and
Dependence of flame characteristics on kinetics
In the previous analysis we used one specific reaction mechanism. Here we study how the predictions of the numerical calculations depend on the choice of the kinetic scheme. The sensitivity of the onset of pulsation, the loss of stability and blow-off phenomena to chemical mechanisms is discussed here. As it follows from the consideration above, the properties of burner stabilized flame are strongly related to the adiabatic flame speed. In Fig. 14 the mass flow rate for freely propagating
Conclusions
In this paper stability and dynamics of pulsations of one-dimensional flat burner stabilized hydrogen-air flames under elevated pressure are investigated. The numerical calculations showed that the stand-off distance is U-shaped function of mass flow rate and flame temperature. As theoretically predicted, there are two branches, the high-temperature (or fast) and low-temperature (or slow) branches, between them the condition of the minimum stand-off distance is met. As the mass flow rate tends
Acknowledgments
This research was partly supported by the Deutsche Forschungsgemeinschaft (DFG) within SFB/TRR 150. VVG acknowledges the support of TSNIIMASH through the ‘s-Flame’ project.
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