Flame standoff distance

If the reactive gas produced at the burning surface of an energetic material reacts slowly in the gas phase and generates a luminous flame, the distance Lg between the burning surface and the luminous flame front is said to be the flame standoff distance. In the gas phase shown in Fig. 3-8, the temperature gradient appears to be small and the temperature increases relatively slowly. In this case, heat flux by conduction, the first term in Eq. (3.41), is neglected. Similarly, the rate of mass diffusion, the first term is Eq. (3.42), is assumed to be small compared with the rate of mass convection, the second term in Eq. (3.42). Thus, one gets 

The reaction rate for an m th order reaction is given by (ignoring the temperature dependence of pg) 

The mass flow continuity relation between the gas phase and solid is 

The temperature gradient, dT/dx, in the gas phase is approximately equal to ATg/Lg, where ATg is the temperature change across the gas phase zone. Thus, the flame standoff distance Lg is represented by 

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Section 5.1.3 in this chapter. The flame standoff distance log plot is represented by versus pressure in a log-... 

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 6-7. Dark zone length (flame standoff distance) decreases as pressure increases.

The flame structures of the noncatalyzed and catalyzed propellants shown in Fig. 6-25 are similar except for the flame standoff distance, i.e., dark zone length, as shown in Fig. 6-26. The dark zone lengths of both propellants decrease with increas-... 

Figure 6-30. Flame standoff distance is increased by the addition of LiF in the super-rate burning region.

Figure 6-32. Flame standoff distance is decreased significantly by the addition of nickel powder even though the burning rate remains unchanged (see Fig. 6-31).

Figure 7-22. Burning rate and flame standoff distance of non-catalyzed and catalyzed GAP-HMX composite propellants.

Surface Temperature, Heat Feedback, and Flame Standoff Distance... 

Fig. 5 Non-dimensional flame standoff distance and Peclet number based on flame standoff distance (ratio of bulk-to-diffusion velocity) for benchmark case (Table 1). Note that in dimensional terms xg for small Eg is actually greater than that for large Eg for comparable...

Figure 5 also shows the Peclet number based on the flame standoff distance, Pe = Xgfh, which can be interpreted as the ratio of the bulk convective velocity to diffusion velocity Pe = ul DIXg) = ul ag IXg)). In the intermediate pressure... 

The combustion wave structure at 100 atm is shown in Figs. 13 and 14, exhibiting a close similarity to that at 1 atm except for the shorter flame-standoff distance (6 vs. 600 pm) and molten-layer thickness (2.1 vs. 66 pm). 

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