Summary
The numerical simulation of flame-acoustic interactions is very demanding due to the multiple length scales involved: There are chemical scales of about 1/10 mm and vortical flow structures of about 1–10 cm, while acoustic wave lengths are tens of centimeters to several meters.
Here we describe the current state of development of numerical techniques allowing us to overcome these scaling discrepancies. These include a multi-scale grid representation of long wave acoustics, its coupling to a quasi-incompressible flow solver and a capturing/tracking hybrid scheme for flame front discontinuities in the zero Mach number limit.
Experiments and theory reveal a stabilizing effect of acoustics at low forcing but a parametric flame instability at higher forcing. Using quasisteady flame jump conditions, as in the flame tracking method, one obtains these effects theoretically, but he fails to correctly assess the influence of Lewis number. Improved insight is gained by a more expensive numerical approach which resolves the flame structure. These computations correctly capture the influence of Lewis number.
We conclude that a flame front tracking approach must resort to modified jump conditions for highly unsteady flows in order to correctly operate under high acoustic forcing.
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References
Karki, K.C., Patankar, S.V., Pressure Based Calculation Procedure for Viscous Flows at All Speeds in Arbitrary Configurations, AIAA Journal, 27 (9), 1167–1174, (1989).
Klein, R., Semi-Implicit Extension of a Godunov-Type Scheme Based on Low Mach Number Asymptotics I: One-dimensional Flow, J.Comput.Phys., 121, 213–237, (1995).
Munz, C. D., Klein, R., Roller, S., Geratz, K.J. The Extension of Incompressible Flow Solvers to the Weakly Compressible Regime, submitted to “Theoretical and Computational Fluid Dynamics”, August 1997.
Roller S., Dissertation, Institut für Aerodynamik Gasdynamik, Univ. Stuttgart, (1998), in preparation.
Smiljanovski V., Moser V., Klein R., A Tracking/Capturing Hybrid Scheme for Deflagration Discontinuities, Combustion Theory Si Modelling, 1, 183–215, (1997).
Terhoeven P., Ein numerisches Verfahren zur Berechnung von Flammenfronten bei kleiner Mach-Zahl, Dissertation, Institut für Technische Mechanik, RWTH Aachen, (1997), in preparation.
Markstein G.H., Instability Phenomena in Combustion Waves, Fourth Symposium in Combustion, 44, Baltimore, Williams and Wilkins (1953).
Clavin P., Pelce P. and He L., One-dimensional Vibratory Instability of Planar Flames Propagating in Tubes, J. Fluid Mech. 216, 299–322, (1990).
Searby G., Experimental Investigations of Acoustic Instabilities in Laminar Premixed Flames, Proceedings of the NATO ASI Summer School “Non linear phenomena related to growth and form”, Edited by Ben Amar M., Pelcé P. and Tabeling P., Plenum Press (1991).
Searby G., Acoustic Instability in Premixed Flames,Combust. Sci.Tech. 81 221–231, (1992).
Searby G., Rochwerger D., A parametric Acoustic Instability in Premixed Flames, J. Fluid Mech. 231, 529–543, (1991).
Joulin G., On the response of premixed Flames to Time-dependent stretch and curvature,Combust. Sci. Tech. 97 219, (1994).
Denet B., Haldenwang P., A numerical study of premixed Flames Darrieus-Landau instability, Combust. Sci. Tech. 104 (1–3), 143, (1995).
Denet B., Toma A., Numerical study of premixed Flames parametric acoustic instability, Combust. Sci. Tech. 109, 23–33, (1995).
Clavin P., Joulin G., High frequency response of premixed Flames to weak stretch and curvature: a variable density analysis, to appear in Combust. Theor. Mod., (1997).
Pelce P., Rochwerger D., Vibratory instability of cellular Flames propagating in tubes, J. Fluid Mech. 239, 293, (1992).
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Klein, R. et al. (1998). Numerical Techniques for Multi-Scale Weakly Compressible Reactive Flows. In: Hirschel, E.H. (eds) Numerical Flow Simulation I. Notes on Numerical Fluid Mechanics (NNFM), vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44437-4_12
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DOI: https://doi.org/10.1007/978-3-540-44437-4_12
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