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Effect of obstacles on flame propagation and pressure build up

Flame acceleration which is typically followed an ignition and laminar burning of hydrogen-air mixtures can have different origin. in fact, flame acceleration in all cases is connected with the presence and / or production of turbulence. One can distinguish at least three sources for turbulence production and therefore for flame acceleration:
- Self-generated turbulence; for large-scale flames it will be connected with Raleigh-Taylor or Landay-Darrieus instabilities;
- Obstacle-generated turbulence; it will be turbulence generated due to interaction of the flow resulted from combustion process and obstacles congesting the flow;
- External sources of turbulence; there can be technological sources as jets, fans, etc and natural sources as wind, natural convection, etc.
In most cases the second reason is responsible for the strong flame acceleration and deflagra-tion-to-detonation transition. The pressure development during flame accelearion and possi-bility for detonation onset depends on the following main characteristics:
- The size of the combustible gas region or the size of the enclosure;
- The concentration of the combustible mixture;
- The arrangement of the obstacles.
In case of high degree of confinement and obstruction of the burning volume it is very likely that hydrogen combustion will end up with DDT event. As indicated by (CravenAD:1968), the pressure produced by DDT depends on the flame propagation process prior to DDT. The worst case scenario proposed by Craven and Greig involves the transition to detonation on a reflected shock produced by a fast flame. Calculations indicate that the peak pressure produced on the wall of an enclosure by such an event can be an order of magnitude higher than the detonation pressure for the mixture. The Craven and Greig scenario has been observed in the laboratory ((KogarkoSM:1958), (ChanCK:1998) and (ZhangF:1998)). In the latter study, a peak reflected pressure of 250 atm was observed for a hydrocarbon-air mixture at an initial pressure of 1 atm. Numerical studies of detonations (e.g., (BreitungW:1994)) show that such hight values are not unusual and even typical for 2D and 3D focusing and multi-shock interactions.

Figure 1. Accelerating flame (left column), DDT,
and quasi-detonation (two right columns) in 2D
half-channel with obstacles computed for d/2 = 2 cm,
L = 64 cm, dxmin = 1/512 cm. Times in milliseconds
are shown in frame corners [Gamezo et al. 2007]

The particular process of the flame acceleration is a complex non-linear evolution of pressure perturbations linked to the combustion processes. However, generally it can be considered as a result of interaction of a series of relatively simple events. A flame during its propagation generates acoustic waves that can interact after reflections from the obstacles and channel walls with the flame front and develop flame perturbations through a variety of instability mechanisms. Such instabilities have been observed by Guenoche (1949) and Leyer & Manson (1971) in tubes, by Kogarko & Ryzkor (1992) in spherical chambers, and by van Wingerden & Zeeuwen (1983) and Tamanini & Chaffee (1992) in vented enclosures. Flame acoustic instabilities are usually associated with relatively slow flames in open atmosphere or enclosures that are free of obstacles. Turbulence inducing obstacles have shown to reduce relative contribution of acoustic instabilities on flame propagation and pressure build-up (Tamanini & Chaffee 1992). It has been also shown experimentally that such instabilities can be successfully eliminated by lining the enclosure or tube walls with materials that can absorb acoustic waves (TeodorczykA:1995a).

The nature of the acoustic-flame instabilities have been reviewed by Oran & Gardner (1985) and Searby&Rochwerger (1991), Joulin (1994), Jackson et al.(1993) and Kansa&Perlee (1976) studied them in detail. These mechanisms cause flame distortion and wave amplification.

Generally, if confinement and/or obstacles are present, several powerful instabilities may strongly influence flame propagation. These are Kelvin-Helmholtz (K-H) shear instability and Rayleigh-Tailor (R-T) density difference instability. In compressible flows the R-T instability is known as Richtmyer-Meshkov (R-M) instability. Both K-H and R-T instabilities are triggered when the flame is accelerated over an obstacle or through a vent. Detailed studies of flame propagation over single obstacle were performed by Wolanski&Wojcicki (1981) and Tsuruda&Hirano (1987).

Finally, sufficient fast flames can produce a shock wave that can reflect off a wall and/or an obstacle and interact with the flame. As shown by Markstein&Somers (1953), Scarinci et al.(1993) and Thomas et al.(1997) this can result in severe flame distorsion and in extreme cases cause DDT.

Gamezo et al.(2007) have studied flame acceleration in channels with obstacles using advanced 2D and 3D reactive Navier-Stokes numerical simulations. Computations have shown that during flame acceleration shock-flame interactions, R-T, R-M and K-H instabilities, and flame-vortex interactions in obstacle wakes are responsible for the increase of the flame surface area, the energy-release rate, and, eventually, the shock strength. As the flame passes obstacles (Fig. 1), it wrinkles due to R-T instability caused by the flow acceleration. The unreacted flow ahead of the flame becomes sonic. Noticeable shocks begin to form ahead of the flame and they reflect from obstacles and side walls, and interact with the flame triggering R-M instabilities. The K-H instabilities develop at the flame surface when a jet of hot burned material passes through a narrow part of the channel and a shear layer forms downstream of the obstacle. The elevated temperature behind shocks also contributes to the increased energy-release rate.

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Kogarko S.M. (1958) Investigation of the pressure at the end of a tube in connection with rapid nonstationary combustion. Soviet Physics - Technical Physics, 28:1875-1879.(BibTeX)
Chan C.K. and Dewitt W.A. (1998) DDT in end gases. In Proceedings of the Twenty-Seventh Symposium (International) on Combustion. Pittsburgh. The Combustion Institute, pages 2679-2684.(BibTeX)
Zhang F., Thibault P.A. and Murray S. (1998) Transition from deflagration to detonation in multi-phase slug. Combustion and Flame, 114:13-24.(BibTeX)
Breitung W., Dorofeev S.B., Efimenko A.A., Kochurko A.S., Redlinger R. and Sidorov V.P. (1994) Large-scale experiments on hydrogen-air detonation loads and their numerical simulation. In ANS/ARS 1994 International Topical Meeting on Advanced Reactor Safety, Pittsburgh, Pennsylvania. 17--21 April, page 733.(BibTeX)
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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
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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. and Thomas G.O. (1995) Experimental methods for controlled deflagration to detonation transition (DDT) in gaseous mixtures. Archivum Combustionis, 15:59-80.(BibTeX)

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