The heat release kernel is about m far from
The heat release kernel is about 6 μm far from the burning surface when AP particle diameter is 140 μm at 20 atm. It works as a flame holder followed by a trailing atp citrate lyase flame. Price et al.  calls the structure as leading edge flame (LEF). The typical structure is shown in Fig. 8. When the AP decomposition products and HTPB pyrolysis products leave the burning surface, the temperature of gas phase is lower than the initiation temperature of diffusion reaction. Low temperature means low Da number, and the diffusion mixing process is enhanced. There is a pre-mixed zone before the diffusion ignition temperature is reached. The temperature of the pre-mixed zone raises as the pre-mixed species approaches the diffusion flame. Once the temperature of the pre-mixed species reaches the ignition temperature of diffusion flame, the chemical reaction initiates with rapid heat release. In the process, a pre-mixed diffusion flame structure, LEF, is formed. It can be seen that the diffusion flame is influenced by both the reaction time scale and diffusion time scale. In order to further study this phenomenon, a calculation was made with the pre-exponential factor reduced by 10 and 100 times. So the chemical reaction time scale is reduced to 0.1 and 0.01 of origin value, respectively. Fig. 9 shows the reaction rate distribution of different pre-exponential factors at 40 atm. It can be seen from Fig. 9 that the heat release kernel move far away from the burning surface at maximum heat release rate decreased by about 0.1 and 0.01 of its original value. The separate diffusion flame gets gradually merges when 0.01D2 is used. The order of magnitude of Da is about 1 when the pre-exponential factor is 0.01D2. In this condition, the diffusion transport rate is relatively high, and the total chemical reaction is similar to pre-mixed combustion. It\'s obvious that the gas phase reaction will be totally pre-mixing reaction and LEF structure will be vanished if a much smaller reaction rate constant is used. This implies that LEF is depended on the reaction rate. In addition, unlike the Burke–Schuman flame sheet model with infinite Da number (Da→∞), the chemical reaction between the decomposition products of oxidizer and binder occurs in a wider zone. Therefore, the existence of LEF is largely dependent on Da number, and also is largely dependent on chemical reaction rate.
Fig. 10 shows the diffusion reaction rate distribution when AP particle diameter is 60 μm at 40 atm. The diffusion time scale td is reduced as the diffusion length scale decreases and so is the Da number. The diffusion mixing between the oxidizer and fuel species is much stronger than that of 140 μm AP diameter. It can be shown by comparing Fig. 10 with Fig. 9(a) that the two diffusion reaction layers merge together above AP solid when a smaller AP particle is used, which indicates a more pre-mixed flame.
Fig. 11 shows that the burning rate of AP particles of different diameters varies with pressure at 20 atm–100 atm. When a smaller AP particle is used, the diffusion length scale is decreased and a more pre-mixed diffusion flame is formed. The heat flux from the gas to the solid is more uniform, and hence the solid binder gets more heat feedback. The burning rate increases as AP particle size decreases. This feature indicates the ability of fine AP to adjust the burning rate. So in the real composite formulations, a different granularity gradation of AP particles is usually used to maintain the burning rate–pressure relationship.
Conclusions A numerical model has been established to study the combustion characteristics of AP/HTPB base bleed propellant. The flame structure is investigated, and the effects of pressure, chemical reaction rate and AP particle diameters on the combustion characteristics are discussed based on Peclet (Pe) number and Damkohler (Da) number.
Acknowledgments The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (No. 51176076).