Surface Propagation

In Rocstar, the interface must be tracked as it regresses due to burning. In recent years, Eulerian methods, especially level set methods, have made significant advancements and become the dominant methods for moving interfaces.[5,6] In our context, Lagrangian representation of the interface is crucial to describe the boundary of volume meshes of physical regions. However, preexisting numerical methods, either Eulerian or Lagrangian, have difficulties in capturing the evolving singularities (such as ridges and corners) in solid rocket motors.

To meet this challenge, we have developed a novel method, called face-offsetting methods,[7] based on a new entropy-satisfying Lagrangian formulation. Our face-offsetting methods deliver an accurate and stable entropy-satisfying solution without requiring Eulerian volume meshes. A fundamental difference between face-offsetting and traditional Lagrangian methods is that our methods solve the Lagrangian formulation face by face, and then reconstruct vertices by constrained minimization and curvature-aware averaging, instead of directly moving vertices along some approximate normal directions. This method allows part of the surface to be fixed or to be constrained to move along certain directions (such as constraining the propellant to burn along the case). It supports both structured and unstructured meshes, with an integrated node redistribution scheme that suffices to control mesh quality for moderately moving interfaces. Figure 3 shows the propagation of a block-structured surface mesh for the fluids domain of the Attitude Control Motor (ACM) rocket, where the front and aft ends burn along the cylindrical case.

Figure 3: Simulation of burning of Attitude Control Motor along the case with block-structured meshes using face offsetting. Left subfigure shows initial geometry; middle and right subfigures show meshes of initial geometry and after 30% burn, respectively. Colors indicate magnitude of total displacements of vertices.

When coupled with mesh adaptation, the face-offsetting method can capture significant burns. Figure 4 shows a sample result of the burning of a star grain section of a rocket motor using the face offsetting method coupled with surface remeshing using MeshSim from Simmetrix (http://www.simmetrix.com). The interior (the fins) of the propellant burns at uniform speed and exhibits rapid expansion at slots and contraction at fins. The fin tips transform into sharp ridges during propagation, as captured by the face offsetting method.

Figure 4: Simulation of uniform burning of section of star grain of solid rocket using face offsetting and mesh repair. Green curves indicate ridges in evolving geometry.