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Le Chatelier-Brown principle analogue for vented deflagrations

The following relationship could be extracted from a conservative form of the universal correlation for vented gaseous deflagrations [1] and will be used to discuss the Le Chatelier-Brown principle analogue for vented gaseous deflagrations [2]

\pi_{red} \sim \left[ S_{ui} \frac{\chi}{\mu} \frac{1}{F} \right]^{25}

where \pi_{red} reduced explosion pressure; S_{ui} burning velocity, m/s; \chi turbulence factor; \mu generalized discharge coefficient; F vent area, m2.

The Le Chatelier-Brown principle analogue states that gasdynamics of premixed turbulent combustion in vented vessel responds to external changes in the process conditions in such a way as to weaken the effect of external influence. Response action is always weaker than primary one.

Let us say one would like to reduce explosion pressure \pi_{red} simply through an increase of the venting area F. However, an increase of the vent area F is always (!) accompanied by increase of deflagration-outflow-interaction number \chi/\mu. For example, in experiments on hydrogen-air deflagration [3] 1.5 increase of F is accompanied by 1.25 increase of \chi/\mu. In experiments on 10-20% hydrogen-air defla-grations in spherical vessel of 2.3-m diameter [4] ninefold growth of vent area F was accompanied by 2.79 increase of \chi/\mu for 10% hydrogen-air and 2.93 increase for 20% hydrogen-air mixture. Thus effective increase of venting area for this case is about 3 rather than 9. The same manifestation of the Le Chatelier-Brown principle analogue was observed for hydrocarbon-air mixtures. For propane-air deflagration [3] twofold increase of F is accompanied by 1.57 times increase of \chi/\mu. In experiments by Harrison and Eyre in 30.4 m3 vessel with natural gas-air mixture 2.06 times increase in F was practi-cally compensated by 1.87 increase of \chi/\mu. As a result an effective increase of vent area, i.e. F/(\chi/\mu) is often much less than expected. In the last case the effective increase of vent area is just 2.06/1.87=1.1 (10% only), but not as much as 2.06.

Sixfold increase of initial burning velocity Sui, when hydrogen concentration in air increased from 10% to 20% [4], is accompanied by slight, but nevertheless 1.15 decrease of urbulence factor \chi.

The significant decrease of the discharge coefficient \mu at the same series of experiments on vented hydrogen-air deflagrations [4] in 2.25 times, when vent diameter changed from 15 to 45 cm due to duct effect, is accompanied by 1.12 decrease of the turbulence factor \chi.

Another demonstration of this principle: 1.5 times increase of the turbulence factor \chi in FM Global experiments [5] was compensated partially by 1.25 increase of the discharge coefficient \mu.

The Le Chatelier-Brown principle analogue explains why, for example, an increase of venting area is not always so efficient in engineering practice to mitigate explosions to safe level as expected.

1. Molkov V.V., Accidental gaseous deflagrations: modelling, scaling and mitigation, Journal de Physique IV, 2002, Vol.12, pp.7-19 7-30.
2. Molkov, V.V., Baratov, A.N. and Korolchenko, A.Ya., 1993, Dynamics of Gas Explosions in Vented Vessels: A Critical Review and Progress, Progress in Astronautics and Aeronautics, 154: 117-131.
3. Pasman, H.J., Groothuisen, Th.M. and Gooijer, P.H., 1974, Design of Pressure Relief Vents, In Loss Prevention and Safety Promotion in the Process Industries, Ed. Buschman C.H., New-York, 185-189.
4. Kumar R.K., Dewit W.A., Greig D.R., Vented Explosion of Hydrogen-Air Mixtures in a Large Volume, Combustion Science and Technology, 1989, V.66, pp.251-266.
5. Yao C., Explosion venting of low-strength equipment and structures, Loss Prevention, 1974, Vol.8, pp.1-9.

Content: Deflagration

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