Grain burnback and nonlinear vibration analysis of solid rocket motors: A section-coupled Quasi-3D level set method with Timoshenko beam theory

초록

Predicting propellant burnback, which determines the performance of solid rocket motors (SRMs), along with analyzing mass changes and structural dynamic characteristics during combustion, are critical elements for robust modeling. As a burnback prediction technique, the Quasi-3D level set method offers high efficiency but lacks accuracy for grain structures involving axial cross-sectional variations and end-burning effects. Conversely, full 3D level set methods require excessive computational costs. To overcome these issues, this study proposes a Section-Coupled Quasi-3D (SC-Q3D) level set method. By correcting the burning rate of each section using a physics-based slope correction factor (Sz,t) derived from the SRM axial profile, the method precisely predicts burnback characteristics. It effectively captures sectional burning rate changes due to axial gradients, end-burning, and complex topological changes, achieving burning surface area prediction accuracy comparable to full 3D analysis at a 2D computational cost. Furthermore, based on the time-varying shape information derived from the SC-Q3D level set technique, the structural nonlinear vibration characteristics of the SRM were analyzed using a Timoshenko beam model that considers shear deformation and rotary inertia. By predicting the nonlinear frequency shifts during propellant combustion for NAWC No. 6 and No. 13 SRMs, this study presents an improved predictive model that enables precise design and overcomes the limitations of traditional Euler-Bernoulli theory.

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