Here cp is the average specific heat of the combustion gases in kcal/kg-K, ¡x the gas viscosity in kg/m-sec, Pr the dimensionless Prandtl number (¡icp/k) based on the molecular properties of the gases, k the thermal conductivity of the gas, cs the heat capacity of the solid propellant in kcal/kg-K, T\ the combustion gas reaction absolute temperature, Ts the solid propellant surface temperature, and Tp the initial ambient temperature within the solid propellant grain.
Figure 11-10 shows the augmentation ratio r/r0, or the ratio of the burning rate with and without erosive burning, as a function of gas velocity for two similar propellants, one of which has an iron oxide burn rate catalyst. Augmentation ratios up to 3 can be found in some motor designs. There is a pressure drop from the forward end to the aft end of the port passage, because static pressure energy is converted into kinetic gas energy as the flow is accelerated. This pressure differential during erosive burning causes an extra axial load and deformation on the grain, which must be considered in the stress analysis. The erosion or burn rate augmentation is not the same throughout the length of the port passage. The erosion is increased locally by turbulence if there are discontinuities such as protrusions, edges of inhibitors, structural supports, or gaps between segmented grains.
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