Modeling of Regressing
Heterogeneous Solid Propellants
K.R. Srinivasan2, K. Matous1,
P.H. Geubelle2 and T.L. Jackson3
1Department of Aerospace and Mechanical
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.
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
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 OI
, 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.
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
Thompson and Dr. I. L. Davis - Program managers).
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