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Mathematical Formulation and Validation of Muraour's Linear Burning Rate Law for Solid Rocket Propellants

Shekhar H.

Central European Journal of Energetic Materials

2012

Vol. 9, nr 4

353-364

Linear variation of burning rate with pressure (burning rate, r = H + Sp), referred in the literature as Muraour's law, is adopted as the burning rate law for solid rocket propellants. The two constants 'H' and 'S' are the vacuum burning rate and the slope of burning rate variation, respectively. The conventional power law of the burning rate, r = apn, is also analyzed and its practical, anomalous behaviour such as zero burning rate at zero pressure, the reduction in pressure sensitivity of the burning rate at higher pressures, the lower burning rate for the high pressure index in typical situations etc, are explained with illustrations. Like the conventional power law of burning rate, the linear burning rate law considered here is also empirical but mathematically simpler than the power law. Using burning rate and pressure data from various literature sources similar regression coefficients are observed for the conventional power law as well as for the alternative linear burning rate law. The mathematical concept for the evolution of the pressure time profile with the considered linear burning rate law is developed and validated practically with the actual firing of rocket propellants as uninhibited, tubular configurations in a ballistic evaluation motor (BEM). Close matching of the firing curve, predicted by the conventional power law and by the proposed linear burning rate law validates the mathematical formulation. The considered linear burning rate law is simple, easy to apply and gives a better representation of the burning rate behaviour of solid rocket propellants.