Mass-burning rate

A.C. McIntosh. The linearised response of the mass burning rate of a premixed flame to rapid pressure changes. Combustion Science and Technology, 91 329-346, 1993. 

Turbulent mass burning rate versus the turbulent root-mean-square velocity by Karpov and Severin [18]. Here, nis the air excess coefficient that is the inverse of the equivalence ratio. (Reprinted from Abdel-Gayed, R., Bradley, D., and Lung, F.K.-K., Combustion regimes and the straining of turbulent premixed flames. Combust. Flame, 76, 213, 1989. With permission. Figure 2, p. 215, copyright Elsevier editions.)... 

Herrera, Vargas, et al. (2) report experimental measurements of the behavior of energetic materials burning in a compartment. The results indicate that as the critical loading density, Mc (kg/m3) Increases, the mass burning rate inside the compartment reaches a steady state condition and unburned material is carried out in the plume. Burning of the unburned material then takes place outside the compartment, thereby contributing to the destructive potential of the fire in adjacent spaces. 

The mass burning rate is determined from the ordinary expression for chemical kinetic rates that is, the fuel consumption rate is given by... 

Although most analyses assume no radiant energy transfer, as will be shown subsequently, the addition of radiation poses no mathematical difficulty in the solution to the mass burning rate problem. 

Three parameters are generally evaluated the mass burning rate (evaporation), the flame position above the fuel surface, and the flame temperature. The most important parameter is the mass burning rate, for it permits the evaluation of the so-called evaporation coefficient, which is most readily measured experimentally. 

Law [23] points out that since imoco is generally much less than 1, the denominator of the second term in Eq. (6.135) becomes [im0J(Le) a ], which indicates that the effect of (Le)foo is to change the oxygen concentration by a factor (LeA as experienced by the flame. Obviously, then, for (Le)lco > 1, the oxidizer concentration is effectively reduced and the flame temperature is also reduced from the adiabatic value obtained for Le = 1, the value given by Eq. (6.126). The effective Lewis number for the mass burning rate [Eq. (6.134)] is... 

The development of the mass burning rate [Eq. (6.118)] in terms of the transfer number B [Eq. (6.120)] was made with the assumption that no oxygen reaches the fuel surface and no fuel reaches °°, the ambient atmosphere. In essence, the only assumption made was that the chemical reactions in the gas-phase flame zone were fast enough so that the conditions mos = 0 = m[m could be met. The beauty of the transfer number approach, given that the kinetics are finite but faster than diffusion and the Lewis number is equal to 1, is its great simplicity compared to other endeavors [20, 21],... 

For infinitely fast kinetics, then, the temperature profiles form a discontinuity at the infinitely thin reaction zone (see Fig. 6.11). Realizing that the mass burning rate must remain the same for either infinite or finite reaction rates, one must consider three aspects dictated by physical insight when the kinetics are finite first, the temperature gradient at r = rs must be the same in both cases second, the maximum temperature reached when the kinetics are finite must be less than that for the infinite kinetics case third, if the temperature is lower in the finite case, the maximum must be closer to the droplet in order to satisfy the first aspect. Lorell et al. [22] have shown analytically that these physical insights as depicted in Fig. 6.15 are correct. 

The consequence of this small B assumption may not be immediately apparent. One may obtain a physical interpretation by again writing the mass burning rate expression for the two assumptions made (i.e., B 1 and B = [im<, H]/Lw)... 

If flame radiation occurs in the mass burning process—or any other radiation is imposed, as is frequently the case in plastic flammability tests—one can obtain a convenient expression for the mass burning rate provided one assumes that only the gasifying surface, and none of the gases between the radiation source and the surface, absorbs radiation. In this case Fineman [32] showed that the stagnant film expression for the burning rate can be approximated by... 

This simple form for the burning rate expression is possible because the equations are developed for the conditions in the gas phase and the mass burning rate arises explicitly in the boundary condition to the problem. Since the assumption is made that no radiation is absorbed by the gases, the radiation term appears only in the boundary condition to the problem. 

Consider each of the condensed phase fuels listed to be a spherical particle burning with a perfect spherical flame front in air. From the properties of the fuels given, estimate the order of the fuels with respect to mass burning rate per unit area. List the fastest burning fuel first, etc. 

Experimental evidence from a porous sphere burning rate measurement in a low Reynolds number laminar flow condition confirms that the mass burning rate per unit area can be represented by... 

What is sought is the mass burning rate in terms of m00 . It follows that... 

Of course, Eq. (9.20) also gives one the mass burning rate of the fuel... 

The mass burning rate of a fuel is a key factor in the correlations that have been developed for calculating the energy released from a fire. Mass burning rates for some materials are provided in Appendix B. 

Once sustained combustion is achieved, liquid fires quickly reach steady-state burning with a near constant mass-burning rate. As such, the heat release rate for the fire becomes a function of the liquid surface area exposed to air. 

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