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Criteria for establishment of stable detonation

One of the most important critical event, which can strongly affect the regime of combustion, is deflagration-to-detonation transition. For many years many efforts was being made to develop a theory of this event, however it is still far from complete understanding. Due to this fact, the DDT predictions from CFD simulations hardly can have reliable character. To avoid uncertainty in forecast of DDT a criterion for detonation onset was proposed.

Figure 1. Critical conditions for onset of detonations
in rooms and channels with obstacles. Deviations from
line L = 7\lambda are within 30%. Picture reproduced with
permission from (DorofeevSB:2000).

For systematization of conditions in which DDT event can take place, numerous sources of data were analyzed in (DorofeevSB:2000). The literature data and the data from experiments carried out by authors were used. It was shown that depending on geometry of the facility, the mixture of the same composition can exhibit different behavior. In the facilities with characteristic length large than certain value (defined by mixture reactivity) the mixture does detonate, and in smaller facilities the detonation does not occur. The results of analysis are summarized in Figure 1. Solid line L = 7\lambda separate analyzed cases with observed detonation from cases without detonation onset. As it was indicated by authors an accuracy of such separation is within 30% of \lambda value.

Parameter \lambda, which is used as characteristic length for characterization of mixture sensitivity, is detonation cell size. Detonation cells are imprint of complex three-dimensional structure of detonation wave and their size is determined by mixture properties only (e.g., H2 concentration, initial temperature) and does not depend on geometric configuration of detonating mixture. The values of detonation cells are often known only with inaccuracy of 100%, therefore an application of 7\lambda correlation has to be made with understanding of accuracy of this correlation.

A criterion built on basis of 7\lambda correlation reads as: for detonation onset to be possible a characteristic size of combustible mixture (cloud or room size) must exceed 7\lambda (necessary condition). If detonation develops as a transition from fast deflagration, the corresponding criterion for flame accelleration has to be fulfilled as well.

Note that this criterion as well as criterion for flame acceleration has limited character of applicability since for non-uniform mixtures with spatially dependent properties (e.g., concentration) assessments of detonation cell size and expansion ratio can have considerable uncertainties in their values. However, by the moment these criteria provide the most reliable methodic on the potential of flame acceleration and DDT events.

Dorofeev S.B., Sidorov V.P., Kuznetsov M.S., Matsukov I.D. and Alekseev V.I. (2000) Effect of scale on the onset of detonations. Shock Waves, 10:137-149.(BibTeX)

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