Erosive Burning Design Criteria for High Power and
This article covers erosive burning design criteria for high power and experimental/amateur solid rocket motors. Easy to implement design criteria are presented that allow high power and experimental/amateur rocketeers to determine the maximum length-to-diameter (L/D) ratio for a motor design, or the minimum diameter for the motor core to maximize propellant loading, for either non-erosive burning or max recommended erosive burning. The author proposes a unique approach of using combined core Mach number/core mass flux erosive burning design criteria, design criteria which are applicable whether the motor propellant is sensitive to velocity-based or mass flux-based erosive burning. An innovative constant core mass flux core design is proposed by the author that maximizes the L/D of a motor design, or minimizes the motor port area (core cross-sectional area) for maximum propellant loading. Design criteria for the constant core mass flux core design are presented for both non-erosive and max recommended erosive burning.
Non-Erosive: Core Mach Number £ 0.50
For g = 1.2;
³ 1.36_{th}Max Recommended Erosivity: Core Mach Number = 0.70
For g = 1.2;
= 1.10_{th}
Non-Erosive:
^{2}
^{2}
^{2}Max Recommended Erosivity:
^{2}
^{2}
^{2}
Based on the data presented in the article, it appears that a
core mass flux £ 1.0
lb/sec-in
Copyright ©2005 by Charles E. Rogers.
All rights reserved. Used with permission. A major advantage of using combined core Mach number/core mass flux erosive burning design criteria for either non-erosive or max recommended erosivity motor designs is that irregardless of whether the motor propellant is sensitive to velocity-based or mass flux-based erosive burning, provisions for both have been included as both core Mach number limits and core mass flux limits have been considered. Note that an important analysis technique presented by the author and included in the figure above is to simplify the calculations for the core mass flux at the aft end of the core (the “core mass flux” for the motor), by calculating the core mass flux for ignition only, and basing the calculated core mass flux on the propellant non-erosive burn rate. The highest core mass flux, and thus the highest mass flux-based erosive burning will be at ignition. If the core mass flux limit for non-erosive burning is not exceeded, then the fact that the core mass flux calculations were done assuming a non-erosive propellant burn rate will have no effect since erosive burning will not be present. Basing the core mass flux calculations on the propellant non-erosive burn rate provides easy to use erosive burning design criteria, which through experience experimental/amateur rocketeers can use to calibrate what level of core mass flux based on the non-erosive propellant burn rate produces an acceptable level of erosive burning for their propellants.
Copyright ©2005 by Charles E. Rogers.
All rights reserved., Used with permission. As shown in the figure above, when using the constant core mass flux core design, once a design point core mass flux is achieved, the core is then opened up (the core diameter is increased) to maintain the same core mass flux down the rest of the core. As more propellant burning surface area is added down the core, the core has to be proportionately opened up to hold the core mass flux constant. For the BATES grain generic motor design presented in the figure above, the core mass flux versus motor length will “stair-step” in discrete steps as each subsequent grain core diameter increases based on the core mass flux halfway down the length of each grain. Note that the constant core mass flux core design can also be used for monolithic grains, where the port area can be gradually increased once the design point core mass flux is achieved, versus the step-wise increase in core diameter for a motor with BATES grains. This article was Part 6 of
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