Thermo-Diffusive Flames

Responsible: Jens Lang, Bodo Erdmann

Cooperation: J. Fröhlich, University of Karlsruhe

Literature: J. Fröhlich,  J. Lang, Two-dimensional Cascadic Finite Element Computations of Combustion Problems, Comp. Meth. Appl. Mech. Engrg. 158 (1998), 255-267.

J. Lang, B. Erdmann, Adaptive Linearly Implicit Methods for Heat and Mass Transfer, Report ZR-00-21 (2000), Konrad-Zuse-Zentrum.

Combustion problems are known to range among the most demanding for spatial adaptivity when the thin flame front is to be resolved numerically. This is often required as the inner structure of the flame determines global properties such as the flame speed, the formation of cellular patterns or even more important the mass fraction of reaction products (e.g. NOx formation). A large part of numerical studies in this field is devoted to the different instabilities of such flames. The observed phenomena include cellular patterns, spiral waves, and transition to chaotic behaviour.

Laminar Flames through an Obstacle


Reaction Front in a Non-uniformly Packed Solid


Stability of Flame Balls: The profound understanding of premixed gas flames near extinction or stability limits is important for the design of efficient, clean-burning combustion engines and for the assessment of fire and explosion hazards in oil refineries, mine shafts, etc. Surprisingly, the near-limit behaviour of very simple flames is still not well-known. Since these phenomena are influenced by bouyant convection, typically experiments are performed in a micro-gravity environment. Under these conditions transport mechanisms such as radiation and  small Lewis number effects, the ratio of thermal diffusivity to the  mass diffusivity, come into the play, see the next figure.

Configuration of a stationary flame ball. Diffusional fluxes of heat and 
combustion products (outwards) and of fresh mixture (inwards) 
together with radiative heat loss cause a zero mass-averaged velocity.


Seemingly stable flame balls are one of  the most exciting appearances which were accidentally discovered in drop-tower experiments by Ronney (1990) and confirmed later in parabolic aircraft flights. First theoretical investigations on purely diffusion-controlled stationary spherical flames were done by Zeldovich (1944). 40 years later his flame balls were predicted to be unstable (1984). However, encouraged by the above new experimental discoveries, Buckmaster and collaborators (1990) have shown that for low Lewis numbers flame balls can be stabilized including radiant heat loss which was not considered before.

Two-dimensional flame ball with Le = 0.3, c = 0.01.
Iso-thermals T = 0.1, 0.2,..., 1.0 at times t = 10 and 30.


Typically, instabilities occur which result in a local quenching of the flame as can be seen in the figure. After a while the flame is splitted into two seperate smaller flames. Nevertheless, we found quasi-stationary flame ball configurations, fixing the heat loss by radiation and varying the initial radii for a circular flame.

Last update: July 2007
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