Computational Physics Group

Thermomechanical Modeling of Regressing
Heterogeneous Solid Propellants

K.R. Srinivasan², K. Matous¹, P.H. Geubelle² and T.L. Jackson<sup>3

1</sup>Department of Aerospace and Mechanical Engineering
University of Notre Dame
Notre Dame, IN 46556, USA.

²Department of Aerospace Engineering
³Computational Science and Engineering
University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA.

Abstract

A numerical framework based on the generalized finite element method (GFEM) is developed to capture the coupled effects of thermomechanical deformations and thermal gradients on the regression rate of a heterogeneous solid propellant. The thermomechanical formulation is based on a multiplicative split of the deformation gradient and regression of the heterogeneous solid propellant is simulated using the level set method. A spatial mesh convergence study is performed on a nonregressing solid heterogeneous propellant system to examine the consistency of the coupled thermomechanical GFEM solver. The overall accuracy (spatial and temporal) of the coupled thermomechanical solver for regressing solid propellants is obtained from a periodic sandwich propellant configuration, where the effects of thermomechanical deformations on its regression rate is investigated. Finally, the effects of thermomechanical deformations in a regressing two-dimensional heterogeneous propellant pack are studied and time-average regression rates are reported.

Conclusions

This manuscript has described a numerical framework that combines the generalized mixed finite element method with the assumed gradient level set method to model regression of thermomechanically deforming heterogeneous solid propellants. Spatial convergence of the coupled thermomechanical solver was numerically assessed and found to be optimal. Spatial convergence of the thermomechanical solver with surface regression was also assessed using a periodic sandwich propellant with the average regression rate used to quantify error measures. The scheme was found to have an overall order O_I , close to an optimal rate while employing a first-order backward Euler method. Finally, the regression of an idealized two-dimensional heterogeneous solid propellant pack was chosen to demonstrate the capability and robustness of the developed framework. It was found that the deformable heterogeneous propellant pack had smaller regression rates than the rigid one. It was also observed that, within the thermal boundary layer, the binder regions close to AP/binder interfaces experienced large thermomechanical strains.

Acknowledgment

 
This work was supported by the Center for Simulation of Advanced Rockets (CSAR) under contract number B523819 by the U.S. Department of Energy. K. Matous also acknowledges support from ATK/Thiokol, ATK-21316 (J. Thompson and Dr. I. L. Davis - Program managers).

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