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Turbulence generated by venting process

For gaseous explosions the venting process itself is known to cause the flame to accelerate [1]. Gov-erning equations for turbulent vented gaseous deflagrations were derived from the first principles in paper [2]. The inverse problem method for vented gaseous deflagrations has been developed [3] and efficiently used over the years of research allowing to gather unique data on venting generated turbu-lence. For example, an analogue to the Le Chatelier-Brown principle for vented gaseous deflagrations [3] was revealed by this method. The universal correlation for vented deflagrations was developed for the first time in 1995 [4] followed by the closure of this fundamentally new vent sizing approach with the correlation for venting generated turbulence, presented for the first time two years later in 1997 [5]. Two of our previous articles were devoted to the problem of inertial vent covers in explosion protection [6-7]. Recently our original correlations for vent sizing were developed further to include experimental data on fast burning mixtures, such as near stoichiometric and rich hydrogen-air mixtures, and test data on elevated initial pressures [8-11].

The attempts to produce any reasonable correlations for venting generated turbulence have failed for another reason as well – due to a neglect of the role of the generalised discharge coefficient, \mu, which is dependent on vented deflagration conditions. This fact of discharge coefficient dependence on con-ditions was recognised already about 20 years ago by various authors, e.g. [12]. It has been demon-strated in a series of studies that reduced explosion pressure correlates with the deflagration-outflow interaction (DOI) number, that is the ratio of the turbulence factor, \chi, to the discharge coefficient, \mu, rather than with the turbulence factor alone.

The following correlation for venting generated turbulence has been obtained by processing a wide range of experimental data on vented gaseous deflagration [11, 13]

\chi / \mu = \alpha {\left[ \frac(1 + 10V{_{\#}}{^{1/3}} )(1 + 0.5 Br{^{\beta}}) {1 + \pi{_{\nu}} } \right]}^{0.4} \pi{_{i\#}}^{0.6}

where the empirical coefficients \alpha and \beta are equal for hydrogen-air mixtures to \alpha=1.00 and \beta=0.8 and for hydrocarbon-air mixtures to \alpha=1.75 and \beta=0.5; V_\# - dimensionless volume (numerically equal to enclosure volume in m3), V{_\#} = V / V{_{1 m^3}} ; \pi{_{i\#}} - dimensionless initial pressure, ; \pi{_{\nu}} - dimensionless vent closure release pressure, \pi{_{\nu}} = P{_\nu} / P{_i} = (P{_{stat}} / P{_i} + 1) with P_\nu - vent closure release pressure, bar abs., P_{stat} - vent closure release pressure used in the NFPA 68, bar gauge, and P_i - initial pressure, bar abs.; and the Bradley number is

Br = \frac {F} {V^{2/3}} \frac {c_{ui}} {S_{ui} (E{_i} - 1)} ,

where F – vent area, m2; V – enclosure volume, m3; c_{ui} – speed of sound, m/s; S_{ui} – burning velocity at initial conditions, m/s; Ei – combustion products expansion coefficient.

The empirical correlation for the DOI number gives the dependence of turbulence level as enclosure scale in power 0.4. This is in agreement with conclusions of fractal theory with corresponding fractal dimension 2.4 for turbulent premixed flame characteristic for vented deflagrations.

The turbulent combustion intensifies with increase of the Bradley number as follows from the correla-tion. It means that an increase of venting area F will be accompanied by an increase of turbulence factor. The increase of burning velocity has opposite effect, i.e. a growth of laminar burning velocity will decrease turbulent factor at other conditions being conserved.

The DOI number is increasing with increase of initial pressure in enclosure. The turbulence level for vented deflagration in conditions of experiments [14] increased from 4-6 at initial atmospheric pres-sure to 15-20 at initial pressure 7 atmospheres. Hence the increase of initial pressure from 1 to 7 at-mospheres leads to about four-fold increase of the turbulence level. It has been found that there is only 20% increase of the turbulence factor for the stage of deflagration in closed vessel for the same in-crease of initial pressure [13]. This result demonstrates explicitly that it is venting that is responsible for a substantial increase in the turbulence level, but not just an elevated initial pressure itself.

1. Tamanini, F., 1996, Modelling of panel inertia effects in vented dust explosions, Process safety Progress, 15: 247-257.
2. Molkov, V.V. and Nekrasov, V.P., 1981, Dynamics of Gaseous Combustion in a Vented Constant Volume Vessel, Combustion, Explosion and Shock Waves, 17: 363-369.
3. 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.
4. Molkov, V.V., 1995, Theoretical Generalization of International Experimental Data on Vented Explosion Dynamics, Proceedings of the First International Seminar on Fire-and-Explosion Haz-ard of Substances and Venting of Deflagrations, 17-21 July 1995, Moscow - Russia, 166-181.
5. Molkov, V.V., 1997, Scaling of Turbulent Vented Deflagrations, Proceedings of the Second Inter-national Seminar on Fire-and-Explosion Hazard of Substances and Venting of Deflagrations, 10-15 August 1997, Moscow - Russia, 445-456.
6. Molkov, V.V., Nikitenko, V.M., Filippov, A.V. and Korolchenko, A.Ya., 1993, Dynamics of Gas Explosion in a Vented Vessel with Inertial Vent Covers, Proceedings of Joint Meeting of the Rus-sian and Japanese Sections of The Combustion Institute, Chernogolovka - Moscow Region, 2-5 October 1993, 183-185.
7. Molkov, V.V., 1999, Explosions in Buildings: Modelling and Interpretation of Real Accidents, Fire Safety Journal, 33: 45-56.
8. Molkov, V.V., 1999, Explosion Safety Engineering: NFPA 68 and Improved Vent Sizing Tech-nology, Proceedings of the 8th International Conference INTERFLAM’99 Fire Science and Engi-neering, 29 June – 1 July 1999, Edinburgh, Scotland, 1129-1134.
9. Molkov, V.V., Dobashi, R., Suzuki, M. and Hirano, T., 1999, Modeling of Vented Hydrogen-Air Deflagrations and Correlations for Vent Sizing, Journal of Loss Prevention in the Process Indus-tries, 12: 147-156.
10. Molkov, V.V., Dobashi, R., Suzuki, M. and Hirano, T., 2000, Venting of Deflagrations: Hydro-carbon-Air and Hydrogen-Air Systems, Journal of Loss Prevention in the Process Industries,13: 397-409.
11. Molkov, V.V., 2000, Unified Correlations for Vent Sizing of Enclosures against Gaseous Defla-grations at Atmospheric and Elevated Pressures, Proceedings of the Third International Sympo-sium on Hazards, Prevention, and Mitigation of Industrial Explosions, 23-27 October 2000, Tsu-kuba, Japan, 289-295.
12. Tufano, V., Crescitelli, S. and Russo, G., 1981, On the design of venting systems against gaseous explosions, Journal of Occupational Accidents, 3: 143-152.
13. Molkov, V.V., 2000, Explosion Safety engineering: Design of Venting Areas for Enclosures at Atmospheric and Elevated Pressures, FABIG Newsletter, Issue No.27, 12-16.
14. Pegg, M.J., Amyotte, P.R. and Chippett, S., 1992, Confined and Vented Deflagrations of Propane / Air Mixtures at Initially Elevated Pressures, Proceedings of the Seventh International Symposium on Loss Prevention and Safety Promotion in the Process Industries, Toormina, Italy, 4-8 May, 110/1-110/14.

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