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Fast deflagrations

The studies of deflagration in very rough, obstacle-filled tubes have demonstrated that the flame speed in a given combustible mixture can be varied continuously over three orders of magnitude between the slow limit of a laminar flame to the fast limit of a CJ detonation. The steady flame speed is governed by the boundary conditions in the tube: i.e. geometry and obstacle configurations.

It should be noted that the so-called steady flame speed is an averaged value in the direction of propagation over a distance at least of the order of several obstacle spacings or tube diameters, whichever is greater. Large fluctuations are observed locally in the highly three-dimensional transient structure of the flame front. For the so-called quasi-detonation regime (i.e. flame speeds between 1200 m/s and the normal C-J value of about 2500 m/s for fuel-oxygen mixtures) the studies by Teodorczyk et al. and Chan have conclusively demonstrated that the mechanism of propagation is due to auto-ignition via shock reflections. These studies show that normal shock reflections from the obstacle, Mach reflection of the diffracted shock on the bottom wall and Mach reflection of the reflected shock from the top wall can lead to auto-ignition. The role of the obstacle is to promote strong shock reflections leading to high local temperatures for auto-ignition.

Detonations are initiated from these local "hot spots" but are later destroyed by diffraction quenching around the obstacles themselves. Hence for quasi-detonations, the diffraction around the obstacles destroys the initiated detonation while shock reflections resulting from the interactions of the decoupled shock with the obstacle and the tube will give rise to local hot spots and re-initiation of the detonation.

Experimentally, it has also been observed that there exists a fast deflagration regime (flame speeds between 400 m/s to 1200 m/s) in which the shock reflections are observed to be not strong enough to result in auto-ignition. A decoupled shock and reaction zone complex which propagates at an averaged steady speed is observed.

The studies by Teodorczyk have shown that in the fast deflagration regime, shock reflections do not lead to auto-ignition as in the case of quasi-detonations. The mechanism for sustaining the fast propagation speed is intense combustion via flame turbulization by

  1. shock flame interaction,
  2. Rayleigh-Taylor instability as the flame is convected in an accelerating flow, and
  3. auto-ignition by rapid entrainment and mixing in the large recirculating eddies in the obstacles.

The importance of transverse waves (and their interaction with the flame) was clearly demonstrated since their elimination results in a significant decrease in the combustion intensity (and hence the deflagration speed). The elimination of the transverse waves also greatly delays the onset of transition from the deflagration to the detonation regime indicating that the transverse waves not only provide a mechanism to promote intense combustion via interface instability, but also a feedback mechanism where the energy released can be coupled to the leading shock front. In a one-dimensional flow the feedback must proceed via the pressure waves generated. Near the sound speed these pressure waves no longer provide the transfer of energy to the front. The structure of a turbulent high speed deflagration consists of a series of compression waves in the front followed by a highly turbulent reaction zone.

Lee J.H., Knystautas R., Chan C.K. (1984) Proc.Combust.Inst., Vol.20, p.1663
Lee J.H.S. (1984) Fast Flames and Detonations, ACS Symposium Series, No. 249, The Chemistry of Combustion Processes, (Thompson M.Sloane, Ed.) American Chemical Society
Lee J.H.S., Knystautas R., Freeman A. (1984) Comb. Flame 56, 227
Lee J.H.S. (1986) Advances in Chemical Reaction Dynamics, (P.M. Rentzepis and C. Capellos. Eds.), 345, D. Reidel Publishing Company
Teodorczyk A., Lee J.H.S., Knystautas R. (1988) Proc.Combust.Inst., Vol.22, p.1723
Teodorczyk A., Lee J.H.S., Knystautas R. (1989) Photographic Studies of the Structure and Propagation Mechanisms of Quasi-Detonations in a Rough Tube, 12th International Colloquium on the Dynamics of Explosions and Reactive Systems, Ann Arbor, Michigan, July
Chan C.K., Greig D.R. (1988) Proc. of the Combustion Institute, Vol.22, p.1733
Teodorczyk A., Lee J.H.S., Knystautas R. (1990) The Structure of Fast Turbulent Flames In Very Rough, Obstacle-Filled Channels, Proc. of the Combustion Institute, Vol.23, p.735
Teodorczyk A. (1995) Fast Deflagrations and Detonations in Obstacle-Filled Channels, Biuletyn Instytutu Techniki Cieplnej PW, Nr 79, pp.145-178

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