Recently, the experts at Fauske & Associates (FAI), performed a safety analysis to predict the transient response and potential consequences of hydrogen combustion within nested containers. This analysis can be used to model storage or shipping containers where an inner container contains a flammable mixture which upon combustion can fail the inner container and challenge the integrity of the outer container. This is a particular concern if there are toxic materials present in the containers.
The vented deflagration model developed at FAI (Epstein, Swift, and Fauske, 1986, hereafter referred to as ESF’86) provides the basis for the current model. To model nested storage containers ESF’86 was modified to include time-dependent boundary conditions. The ESF’86 model compares extremely well with an earlier model by Chippett (Chippett, 1984). Moreover, the ESF’86 model has been adopted as the U.S. National Fire Protection Association (NFPA) standard (NFPA, 2013). Equations (21) and (22) of ESF’86 are used for the NFPA standard vent size Equations (7.2.2a) and (7.2.2b); please note there are typographical errors in NFPA Equation (7.2.2a).
In the present example, ignition is assumed to occur in the inner container. Flame propagation to the outer container occurs after the complete combustion in the inner container. The volume undergoing combustion is comprised of burned and unburned gas regions. The regions are at equal pressure, and pressure is related to density via the polytropic exponent relation for isentropic volume change of an ideal gas. The burned gas region is conservatively idealized to be spherical, so that the flame front area increases with the distance squared. The burning process is also treated as adiabatic. Unburned gases are discharged to the outer container when the inner container reaches the pressure failure threshold. This leads to an increased pressure in the outer container, also known as pressure piling, before the burn propagates into the outer container. The consequence is a higher ultimate pressure in the outer container than if pressure piling was neglected. Figure 1 illustrates the model. Note, that while the example application and the illustration is for nested containers, topologically there is no difference between this illustration and two identical containers connected by a short vent path.
Figure 1 Vented Deflagration with Pressure Piling Model
The model requires the determination of the post-combustion pressure and temperature in the absence of venting. These are calculated using a simplified version of the technique employed by the NASA CEA2 code (Gordon and McBride, 1994). The quantities obtained are the equilibrium adiabatic isochoric complete combustion (AICC) values. The post-combustion gas composition is the equilibrium composition at the post-combustion temperature. It is noted that CEA2 has been accepted and used by the Pittsburgh Research Laboratory (PRL, formerly known as the Pittsburgh Research Center of the U.S. Bureau of Mines).
In the example problem presented here, the inner and outer container have the same volume, and are connected by path with a leaky check valve. Both volumes in this sample contain a mixture of air and hydrogen with a hydrogen mole fraction of 15%. Both regions are initially at atmospheric pressure at a temperature of 300 K (27°C). The leaky check valve between the two containers has an area of 0.01 m2 which opens at a very low pressure difference, 100 Pa.
Figure 2 and Figure 3 provide the transient pressure and combustion completeness, respectively for the sample sequence. Figure 2 shows that pressure in the outer container begins to gradually increase after approximately 75 milliseconds. This indicates that the inner container has failed and unburned gas is venting and pressurizing the outer container. When the combustion completeness in the inner container reaches 100%, at approximately 400 milliseconds in Figure 3, the flame propagates into the outer container. The pressure in the outer container at the time of flame propagation into the outer container is approximately 1.7 bara. Figure 2 shows that if this higher pressure in the outer container is neglected at the time of flame propagation, i.e. no pressure piling, the final pressure within the outer container is 42% lower than when pressure piling is considered (5.6 vs. 8 bara).
In summary, a new model has been developed based on ESF’89 to extend analysis of vented deflagrations to accommodate pressure piling effects.
Figure 2 Transient Pressure Response
Figure 3 Transient Hydrogen Concentration in Outer Container
Chippett, S., 1984, Modeling of Vented Deflagrations, Combustion and Flame Vol. 55, pp. 127-140.
Epstein, M., I. Swift, and H.K. Fauske, 1986, Estimation of Peak Pressure for Sonic-Vented Hydrocarbon Explosions in Spherical Vessels, Combustion and Flame Vol. 66, pp. 1-8.
NFPA, 2013, NFPA 68 Standard on Explosion Prevention by Deflagration Venting, 2013 Edition, National Fire Prevention Associates, Quincy, MA.
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