Incipient group combustion

In assuming WF.p to be a constant, we anticipate a heat/mass compensation eflFect which tends to suppress particle temperature variation through a QS cloud. Specifically, the decreased oxidizer concentration found as one penetrates the cloud, which tends to decrease particle temperature, is offset by an increase in the local ambient temperature. (Such an effect has been observed recently for the case of evaporation of interacting particles of low volatility (II). Extension of these results follows, since for the conditions of incipient group combustion, the variable T + [Q/(vCp)](oo satisfies the Laplace equation both inside and outside the cloud. The condition for total heat/mass compensation follows provided that Q >> L),... 

Since is independent of Rc and <, Equation 11 implies that the critical cloud size for which incipient group combustion will occur, (Rc/Rp) scales with the inverse square root of the droplet volume fraction, i.e. ... 

For most hydrocarbons burning in air, coo,oe/v is only about 0.07, and WF.eff is about 2, so that the pseudo-homogeneous source term in Equation 6 depends only weakly on wq. For this case, i/r plays the role of a zero-order Thiele modulus (13). Thus, the present continuum analysis clearly reveals that the dimensionless parameter which dictates the onset of incipient group combustion is simply a Damkohler niunber (Thiele modulus) which takes on a critical value (Equation 15) dependent only on the ambient oxidizer mass fraction, on the fuel vapor mass fraction at the droplet surface, and on the stoichiometric oxidizer/fuel mass ratio. 

The functional form of is the same as that of in Incipient Group Combustion, but these two Thiele moduli will, in general, have different numerical values. Since the total group combustion criteria requires... 

Approach. The use of continuum models is defensible only when the particles are suflBciently far apart that suitable averaged oxidizer and fuel mass fraction can be defined. This implies not only the Rp/L < < 1 but also the Rf/L < < 1, where Rf is the individual envelope flame radius, and L is the interparticle distance. Indeed, the use of a continuum approach to establish the incipient group combustion criterion may be suspect since this last inequality is not met. Further, continuum models cannot be defended when the number of particles in the cloud is small... 

In the light of these possible limitations on continuum methods, an alternative approach was deemed desirable so that the continuum incipient group combustion criterion can be checked and so that continuum results can be extended into the small cloud region. In... 

Combustion ) (%) superposition incipient group combustion criterion (O) superposition total group combustion condition (see ""Calculation of Flame Locations ). 

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