Dark zone temperature

The burning rate of a double-base propellant can be calculated by means of Eq. (3.59), assuming the radiation from the gas phase to the burning surface to be negligible. Since the burning rate of a double-base propellant is dominated by the heat flux transferred back from the fizz zone to the burning surface, the reaction rate parameters in Eq. (3.59) are the physicochemical parameters of choice for describing the fizz zone. The gas-phase temperature, Tg, is the temperature at the end of the fizz zone, i. e., the dark-zone temperature, as obtained by means of Eq. (3.60). 

Since the final gas-phase reaction to produce a luminous flame zone is initiated by the reaction in the dark zone, the reaction time is determined by the dark zone length, L4, i. e., the flame stand-off distance. Fig. 6.8 and 6.9 show data for the dark zone length and the dark zone temperature, T, respectively, for the propellants listed in Table 6.3. The luminous flame front approaches the burning surface and... 

Fig. 6.9 Dark zone temperature (temperature at the end of the fizz zone) increases with increasing pressure as well as with increasing KNO2) at constant pressure.

Fig. 6.17 Dark zone temperature, burning surface temperature, surface heat release, and temperature gradient in the fizz zone for high- and low-energy double-base propellants as a function of initial propellant temperature.

Though it is impossible to formulate a complete mathematical representation of the super-rate burning, it is possible to introduce a simplified description based on a dual-pathway representation of the effects of a shift in stoichiometry. Generalized chemical pathways for both non-catalyzed and catalyzed propellants are shown in Fig. 6.26. The shift toward the stoichiometric ratio causes a substantial increase in the reaction rate in the fizz zone and increases the dark zone temperature, a consequence of which is that the heat flux transferred back from the gas phase to the burning surface increases. 

Fig. 8.11 shows the relationship between the dark zone temperature, T, and the adiabatic flame temperature, Tg, at dilferent burning pressures. decreases with increasing Tg. The addition of HMX decreases T. On the other hand, increases slightly with increasing pressure at constant (N02), as shown in Fig. 8.12. The burning rate is correlated with T, as manifested in a straight line in an In r versus...

An important result is that the dark zone temperature, T, decreases even though the flame temperature, Tg, increases with increasing KNOj) at constant pressure. 

Fig. 8.13 Burning rate versus dark zone temperature for an HMX-CMDB propellant at different pressures.

Fig. 8.15 Temperature gradient in fizz zone versus dark zone temperature for an HMX-CMDB propellant at different pressures, showing that the heat flux transferred back to the burning surface increases with increasing dark zone temperature.

Since the final gas phase reaction to produce a luminous flame zone is initiated by the reaction in the dark zone, the reaction time is determined from the dark zone length Ld, i.e., the flame standoff distance. Figures 6-7 and 6-8 show the results for the dark zone length and dark zone temperature, Td, of the propellants listed in Table 6-1, respectively. The luminous flame front approaches the burning surface and the dark zone length decreases as pressure increases for the propellants. There is no clear difference between the propellants with respect to the dark zone length and the pressure exponent of the dark zone, d = n - m, defined in Eq. (3.70) is determined to be approximately -2.0. The overall order of the reaction in the dark zone is also determined to be m= 2.6 for all the propellants. However, the dark zone temperature increases as pressure increases at constant (N02) and also increases as (N02) increases at constant pressure. 

Figure 7-38. Dark zone temperature versus adiabatic flame temperature at different pressures.

Fig. 7-42 as a function of the dark zone temperature, where T is temperature, x is distance, and the subscript fs is the fizz zone above the burning surface. As Td increases, increases linearly in a In cf) versus Td plot. The heat flux transferred back from the fizz zone to the burning surface is the dominant factor in determining the burning rate[27,31]. In fact, the relationship between the burning rate and c > shown in Fig. 7-42 is also similar to the relationship between the burning rate and Td shown in Fig. 7-40. 

Important results are that the dark zone temperature (Tf) decreases even though the flame temperature (Tg) is increased by the increase of Sj(N02) at constant pressure as shown in Fig. 7-38. Furthermore, (f> decreases also as Sj(N02) increases, and thus the burning rate decreases as Sj(N02) increases, i.e., the burning rate of HMX-CMDB propellants decreases as Ij(HMX) increases at a constant pressure. The observed burning rate characteristics of HMX-CMDB propellants are understood without consideration of the diffusional process and the chemical reaction between the decomposed gases of the base-matrix and the HMX particles. This is a significant difference from the burning rate characteristics of AP-CMDB propellants. 

With laser augmentation at 1 atm, HMX will exhibit a dark zone temperature plateau similar to NC/NG at 1300 to 1500 K. In this case, the single-step gas reaction can be applied to the primary flame the secondary flame will have no appreciable effect on steady burning rate, as in NC/NG. If it is desired to simulate the secondary flame, a more complex kinetic mechanism (at least two-step) must be considered. Complex chemical kinetics models have shown the ability to simulate the two-stage gas flame structure of RDX under laser irradiation. (However, complex chemistry models still have difficulty in predicting the correct temperature sensitivity of HMX, as noted below.)... 

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