Development of Scalable Space-Time Averaged Regression Rate Expressions for Hybrid Rockets

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DOI: 10.2514/1.19226 The fuel regression rate expressions reported in the hybrid literature often depend explicitly on the physical dimensions of the system such as the fuel port diameter. Typically, when these dimensional formulas are applied to systems with significantly different scales, they produce grossly inaccurate results. This paper addresses the development of scalable space–time averaged regression rate formulas for hybrid rockets. The derivation process hingesonthe assumption thatthe local instantaneous regression rateisa function of the local mass fluxandthe axial port distance in the power law format as predicted by the classical theory developed by Marxman. In this study, we have developed physics-based nondimensional formulas for the space–time averaged regression rate and used these expressions to develop a scalable regression rate law for a selected propellant combination, paraffin-based SP-1a/ GOX,fromlimitedmotordata.Initially,spaceandtimeaveragingaretreatedseparately,whichwerelatercombined to develop a technique that allows for the coupling between the spatial and time variations to predict the port diameter and mass flow rate profiles as functions of time. Finally, a comprehensive technique to estimate the systematic and random errors on the regression rate and mass flux data is also outlined.