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Quantitative Analysis of Flame Instabilities in a Hele-Shaw Burner

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Abstract

We show in this paper that a Hele-Shaw burner can be used for studying the development of premixed flame instabilities in a quasi-two dimensional configuration. It is possible to ignite a plane flame at the top of the cell, and to measure quantitatively the growth rates of the instability by image analysis. Experiments are performed with propane and methane-air mixtures. It is found that the most unstable wavelength, and the maximum linear growth rate of perturbations, directly measured in the present experiments, have the same order of magnitude as those previously measured on flames propagating freely downwards in wide tubes.

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Acknowledgements

We thank Guy Joulin for many stimulating discussions on the Hele-Shaw configuration.

Funding

This work was supported by the French National Research Agency (project PDF) under agreement ANR-14-CE05-0006. The project leading to this publication has received funding from Excellence Initiative of Aix-Marseille University - A*MIDEX, a French “Investissements d’Avenir” program. It has been carried out in the framework of the Labex MEC.

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  1. Aix-Marseille Université, CNRS, Centrale Marseille, IRPHE, 13451, Marseille Cedex 20, France

    Elias Al Sarraf, Christophe Almarcha, Joël Quinard, Basile Radisson & Bruno Denet

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  1. Elias Al Sarraf
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  2. Christophe Almarcha
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  3. Joël Quinard
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  5. Bruno Denet
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Appendix: Gas Expansion

Appendix: Gas Expansion

We have shown in this article that the growth rates of the hydrodynamic instability in the Hele-Shaw cell, are generally smaller than those in a tube, which suggests that heat losses play a role. It would be interesting to measure the temperature profile in the burner, but this is a difficult task. We show in this section that by measuring the velocity field on both sides of the flame, burnt and fresh gasses, by a PIV technique using cesium oxide particles as seeding material, experimental values of the expansion ratio E can be obtained. It is known [24] that the normal mass flux is not exactly conserved across the flame, so measuring the velocity jump between fresh and burnt gasses does not give exactly the expansion ratio, however for our purpose we only need approximate values of the expansion ratio (these values will be used to discuss in more detail the Darrieus Landau instability in the Hele-Shaw burner in future papers). Figure 19 (propane ϕ = 0.9) shows the velocity field in the fresh and burnt gasses and the normals at different positions on the front in a small cell (60 cm × 1.5 cm × 5 mm). We use a smaller cell here in order to reduce the presence of cusps on the front, the heat losses however are slightly increased.

Fig. 19
figure 19

Velocity field and normals at different positions on the front in a small cell 60 cm × 1.5 cm × 5 mm

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Figure 20 shows the normal velocity profile deduced from the previous figure at different positions on the front. Taking the average of velocity ratio between burnt and fresh gasses in the different curves of Fig. 20, we obtain a gas expansion E = 6.1 ± 0.25, which can be compared to the value obtained by Cantera [25] with a San Diego mechanism [26] E = 7.57 for propane at ϕ = 0.9. As expected the value obtained experimentally is slightly lower, probably because of heat losses. The typical thickness of the velocity profile is also close to the one given by complex chemistry, shown as a dashed line on the figure. Note that these profiles are obtained by PIV, it is possible that out-of-p] heat losses have an important role in the Hele-Shaw cell, which could be described by a lower gas expansion.

Fig. 20
figure 20

Normal velocity profiles in a small cell 60 cm × 1.5 cm × 5 mm, dashed line: velocity profile of a 1D flame with complex chemistry

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Sarraf, E.A., Almarcha, C., Quinard, J. et al. Quantitative Analysis of Flame Instabilities in a Hele-Shaw Burner. Flow Turbulence Combust 101, 851–868 (2018). https://doi.org/10.1007/s10494-018-9940-4

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