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Criteria for spontaneous flame acceleration to supersonic flame speed Figure 1. Observed combustion regime as a function of expansion ratio \sigma and dimension- less activation energy Ea/RTu for hydrogen-air and hydrocarbon-air mixtures for closed systems. Picture reproduced with permission from (DorofeevSB:2001). The next phenomenon which strongly influences the route of combustion process is flame acceleration. As it was shown in (DorofeevSB:2001), the possibility of flame acceleration is defined by mixture properties. The experimental data on the combustions in confined volumes from a wide variety of test facilities with the different characteristic lengths and the geometric configurations were analyzed. The analysis showed that strong flame acceleration was observed only for the sufficiently sensitive mixtures (Figure 1). The parameter, which controls the possibility of flame acceleration, was identified as an expansion ratio \sigma (ratio between density of unburned and burned mixture at constant pressure). An expression of critical expansion ratio (below which the flame acceleration is not observed) reads as \sigma^* = 0.9 \times 10^{-5} \cdot x^3 - 0.0019 \cdot x^2 + 0.1807 \cdot x + 0.2314, \ \ \ \ \ (1)
where x is dimensionless activation energy x = Ea/RTu . For hydrogen-air mixtures this parameter is approximately equal to 25 and, therefore, for critical value \sigma^* gives approximately value of 3.7. In case of systems with partial transverse venting (as it was shown in [4], see Figure 2) the critical value \sigma^* is modified proportionally to vent ratio \alpha (ratio between surface of vent and surface of enclosure). The larger is the vent area the more reactive mixtures is necessary for development of fast flames. The resulting expression for critical expansion ratio reads as \sigma_{cr} = \sigma^* \cdot (1 + 2.24 \cdot \alpha)
where \sigma^* is critical expansion ratio for closed systems (Eq. (1)). On the basis of findings of [(DorofeevSB:2001), (AlekseevVI:2001)], it is possible to formulate a criterion for strong flame acceleration: the mixture can exhibit strong flame acceleration only if its expansion ratio is larger than critical expansion ratio \sigma^{cr} . This statement has to be supplemented with the following: strong flame acceleration can take place only if there is enough room for actual development of supersonic flame. This geometric limitation is connected with necessity of run-up distance for flame acceleration process, which can be evaluated for tube-like configurations as having value of 20-40 diameters (see, e.g., [5]). Such formulated criterion has a character of necessary condition and thus can be directly used for evaluation of flame acceleration potential in CFD simulations.  Figure 2. Observed combustion regime as a function of expansion ration \sigma and vent ratio\alpha . Dependence of critical expansion ratio \sigma^{cr} on \alpha . Picture reproduced with permission from (AlekseevVI:2001). Note, that the proposed criterion has, unfortunately, only limited range of applicability, since it was deduced on the basis of data obtained in confined and confined with partial venting systems. The generalization of this criterion to lower degrees of confinement and to open systems should provide extremely useful information for evaluation of flame acceleration potential in safety analysis. Dorofeev S.B., Kuznetsov M.S., Alekseev V.I., Efimenko A.A. and Breitung W. (2001) Evaluation of limits for effective flame acceleration in hydrogen mixtures. Journal of Loss Prevention in the Processes Industries, 14:583-589.(BibTeX) << Effect of chemical composition, pressure, temperature, geometry, system physical scale, non-uniformity (SWACER) and presence of venting | Content | Criteria for establishment of stable detonation >> |