# Structural vibrations and internal ballistic modelling of a star-grain solid rocket motor

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- Structural vibrations and internal ballistic modelling of a star-grain solid rocket motor

## Abstract

A numerical model is developed to solve the governing equations for the structural dynamics and internal ballistics of a solid rocket motor (SRM). An explicit finite element method is used to solve for the structural response, and an explicit finite volume method is used to solve for the internal ballistic flow. Together, these two numerical solutions are coupled to model the nonsteady behaviour of axial combustion instability in sleeved cylindrical- and star-grain SRMs.The simulation model is used to predict the axial instability in star-grain SRMs. A parametric analysis is made to record the effects of various parameters on the simulation model. These parameters include the numerical dissipation constant, damping ratio and pulsing strength. It is found that both the numerical dissipation constant and damping ratio can, both artificially and physically, affect the finite element structural response of the motor. The pulsing strength affects only the rate at which the do pressure rises as well as how quickly the limiting wave amplitude is reached.A numerical model is developed to solve the governing equations for the structural dynamics and internal ballistics of a solid rocket motor (SRM). An explicit finite element method is used to solve for the structural response, and an explicit finite volume method is used to solve for the internal ballistic flow. Together, these two numerical solutions are coupled to model the nonsteady behaviour of axial combustion instability in sleeved cylindrical- and star-grain SRMs.The simulation model is used to predict the axial instability in star-grain SRMs. A parametric analysis is made to record the effects of various parameters on the simulation model. These parameters include the numerical dissipation constant, damping ratio and pulsing strength. It is found that both the numerical dissipation constant and damping ratio can, both artificially and physically, affect the finite element structural response of the motor. The pulsing strength affects only the rate at which the do pressure rises as well as how quickly the limiting wave amplitude is reached.The detailed analysis of simulated star-grain SRM axial instability reveals the effect of structural vibrations on burning rate augmentation and wave development in nonsteady operation. The variation in oscillation frequencies about a given grain section periphery, and along the grain with different levels of burnback, influences the means by which the local acceleration drives the combustion and flow behavior. The amount of damping also plays a role in influencing the predicted instability symptoms of the motor.