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This paper deals with a theoretical analysis of the low-frequency combustion instability induced by the combustion time lag of liquid oxidizer in small-scale hybrid rocket motors. We obtained the determined linear stability limit using the following parameters: the combustion time delay of liquid oxidizer, the residence time of a combustion chamber, injector pressure, chamber pressure, mass flux exponent, O/F, and the polytropic exponent of mixture gas in a combustion chamber. Kitagawa and Yuasa sometimes observed low-frequency oscillations, such as chugging, in their swirling-oxidizer-flow-type hybrid rocket engine. The obtained theoretical stability limit was compared with these experimental data.

Marxman's diffusion-limited analysis of hybrid rocket combustion has been often used to investigate various combustion problems in hybrid rocket motors. This analysis was developed on the basis of the Reynolds analogy in turbulent boundary layers. This analogy assumes that both molecular and turbulent Prandtl numbers are equal to one. In the present study, a semi-empirical correlation between the Stanton number and the skin-friction coefficient in a turbulent boundary layer was obtained. This is applicable to hybrid rocket combustion, and also includes the effects of the Prandtl numbers variation. Using this correlation, a fuel regression rate equation for standard-flow hybrid rocket motors was obtained, and its characteristics were examined. In addition, the calculated regression rate characteristics were compared with the experimental data from the laboratory-scale hybrid rocket motors that used gaseous oxygen (GOX) as oxidizer and polymethylmethacrylate (PMMA) as fuel.

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