Flame sheet temperature

The combustion wave of HMX is divided into three zones crystallized solid phase (zone 1), solid and/or liquid condensed phase (zone 11), and gas phase (zone 111). A schematic representation of the heat transfer process in the combustion wave is shown in Fig. 5.5. In zone 1, the temperature increases from the initial value Tq to the decomposition temperature T without reaction. In zone 11, the temperature increases from T to the burning surface temperature Tj (interface of the condensed phase and the gas phase). In zone 111, the temperature increases rapidly from to the luminous flame temperature (that of the flame sheet shown in Fig. 5.4). Since the condensed-phase reaction zone is very thin (-0.1 mm), is approximately equal to T . 

After the rapid oxidation that typically occurs in a flame sheet, the temperature is high and the concentration of the O and H radicals may be significant. In the postflame region these radicals react in three-body recombination reactions, mainly... 

The use of laminar flamelet combustion models within FDS have been studied by Yang et al. [42] and Kang and Wen [43], Unfortunately, the performance or advantage over the simple flame-sheet model in large-scale fire simulation was not demonstrated in these studies. In full-scale calculations, the mixture fraction and temperature fields close to the flame sheet have overshoots, caused by the second-order transport scheme. It is still unclear how the laminar flamelet models that require both second and first moments of the local mixture fraction field could work in this situation. 

It may be observed that only the fuel and oxidizer concentration fields have been considered in finding the flame shape. The nature of the boundary conditions makes it unnecessary to study the temperature- and product-concentration fields when the stated assumptions are adopted. If temperature or product concentrations are desired, they may be calculated a posteriori, in terms of the known fuel or oxidizer fields, by solving equation (1-49) for and Pi with = otp, for example. Temperatures at the flame sheet calculated in this way usually are too high (see Section 3.4). 

An alternative to equation (28) is a model in which CO -h jOj CO2 at a flame sheet in the gas and CO2 + C 2CO at the carbon surface [39], [41], [43], [45]. The rate of oxidation of carbon by CO2 is so slow that this alternative seems reasonable only for fairly high surface temperatures and fairly low oxygen concentrations in the gas [41]. Uncertainties remain concerning influences of gas-phase chemistry [44]. 

In many respects, equation (57) is of more general validity than the burning rate expressions usually quoted because arbitrary temperature dependences of (pD) and Cp are permitted in equation (57), and the flame-sheet approximation has not been introduced. However, equation (57) will be useful for computing m only if all quantities appearing on the right-hand side of this equation are known. The specific heat at constant pressure for each pure species i(Cp ), the heat of vaporization per unit mass for the fuel at temperature Ti(L) and the quantity which is the heat of reaction... 

FIGURE 3.6. Temperature and mass-fraction profiles for a burning fuel droplet in the flame-sheet approximation. 

FIGURE 10.3. Illustration of the dependences of the temperature and of the fuel and oxidizer mass fractions on the mixture fraction in the flame-sheet approximation, as given by equations (3-80H3-85). 

FIGURE 10.4. Illustration of probability-density functions for the mixture fraction, fuel mass fraction, oxidizer mass fraction, and temperature for a jet-type diffusion flame in the flame-sheet approximation. 

The near-field analysis provides expressions for the wrinkled-flame motion and the reaction-sheet temperature in terms of the flame shape and the gas velocities at the edge of the wrinkled flame. To the first order in the small parameter bj, the equation for the flame motion may be written, in the nondimensional notation of Section 9.5.1, as... 

The boundary conditions that will be adopted at y = 0 (where conditions will be identified by the subscript 0) are = 0,(Xp = (Xp q = constant (a measure of the sublimation or boiling temperature), and u = 0. The first of these conditions would follow from a flame-sheet hypothesis and is accurate for many liquid fuels (see Section 3.3.4 or [21]). The validity of the second condition is discussed in Section 3.3.4 this condition will be most accurate for a volatile liquid fuel. The third condition is rigorously true only for a solid fuel but is an excellent approximation for liquid fuels if longitudinal flow of the liquid is surpressed (for example, by extruding the liquid through a porous solid material). ... 

The General Discussion of the previous section is equally applicable here, except now proper multicomponent descriptions of the gas-phase transport and the interfacial phase change should be used (50,51, 52). By assuming the gas-phase reactions are again confined to a flame-sheet where the reactants are consumed in a species-weighted stoichiometric proportion, explicit expressions can be derived (50) for y, Tf, H, and the fractional mass evaporation rate of the i species, as functions of the temperature and vapor concentration at the droplet surface. 

The similarity of the profiles of temperature T, fuel (heptane, C7H,6) and oxidizer O2 with the profiles of Figure 3.6 may be seen in Figure 3.8. A rounding of the temperature profile in the reaction sheet is evident. Also, lighter fuel species, such as C2H2, H2, and CH4, are found on the fuel side of the reaction region these are produced by finite-rate pyrolysis of the fuel vapor as it is heated. A small amount of oxygen penetrates the flame sheet and survives on the fuel side some fuel species also penetrate to the oxidizer side, but this is less evident because the downward convection quickly... 

As the premixed-flame temperature decreases, conditions may be calculated for which the second reactant also begins to leak through the reaction zone in appreciable quantities. An asymptotic analysis may be developed for which, in the reaction zone, the factor tp — tf remains effectively constant [184], Departures from equations (82), (83), and (84) then occur even in lowest order on both sides of the flame sheet. This regime has been termed the partial-burning regime [184]. 

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