In-flight formation of slag in spinning solid propellant rocket motors
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Ground tests of solid propellant rocket motors have shown that metal-containing propellants produce various amounts of slag (primarily aluminum oxide), which are trapped in the motor case, causing a reduction, albeit small, of total impulse. Although not yet definitely established, the presence of a liquid pool of slag also may contribute to nutational instabilities that have been observed with certain spin-stabilized, upper-stage vehicles. Because of the rocket's axial acceleration—absent in the ground tests—estimates of in-flight slag mass have been very uncertain. Yet such estimates are needed to determine the magnitude of the control authority of the systems required for eliminating the instability. This paper describes a physical model of the slag transport in the motor and uses it to predict the in-flight slag mass from ground tests. Based on reported ground tests, it is concluded that the distribution function for slag droplet masses in the dynamically significant range is proportional to the -1.50 power of the mass. For geometrically similar motors with a given ratio of radial to axial acceleration, the trapped slag mass is shown to be proportional to the fourth power of the motor diameter. a(t) d(t) C c dd K kd m m0 R(t) ug
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