In the spring of 2017, just before I graduated from school, I began a small C++/Allegro project to predict solid rocket motor performance. This project started as a simple 0-D ballistic model based on basic primitives, but quickly grew into something more as I continued adding features. By the end of the summer, I had a program that could take arbitrary 2-D solid rocket propellant and case geometry, and simulate ballistic performance in real time.
The software takes an input file that defines the geometry and solid propellant characteristics. The initial as-cast propellant boundary is input by a series of coordinates and indices. This will define the bounding volume that the gaseous products will initially burn into. Propellant parameters can be found with a thermochemistry code such as NASA CEA. The final section of the input file defines nozzle throat and expansion data that is used for thrust and pressure calculations. These assume the 1-D isentropic nozzle flow equations for simplicity.
After the program reads in an input file, it computes a level-set that represents the data. This level-set is internally held as a non-uniform signed distance field. To speed computation, the level-set is maintained as a quadtree with the highest resolution clustered about the burning “interface” between the solid propellant and free volume. The level-set is recalulcated as it diverges from the typically slow-moving interface. This does not usually need to be performed every time step, which saves some computer cycles.
For each time step, the level-set is recalculated using a Lagrangian scheme. A burning “flow field” is computed against the level-set using the interface normals. The next interface is extracted from the current level-set using an algorithm based on Dual-Contouring. The surface area can then be found by computing the length of the lines composing the contour, and then scaling that value by the input length of the motor. Moving to a 3-D regression simulation, the surface area of the triangles that compose the contour will be used instead.
From the current burning surface area, which is found via the previously described algorithm, the internal ballistics of the motor may now be calculated. The mass flow rate of the propellant grain, and therefore the pressure of the motor, can be found using parameters from the last time step. The current burn rate can be found using the chamber pressure and St. Robert’s burning rate law. Once the motor pressure is known, it is a trivial task to compute the current thrust using the isentropic nozzle relations.
This brief blog post does not cover all of the features of this software, or all of the details of its implementation. I would like to go into detail about some of its inner workings, and maybe even one day extend the functionality to 3-D. I have included some sample output clips from two solid rocket performance runs: an 11-point star, and a double anchor shape. I hope that these make some of the methodology described in this post a little more clear. Thanks for reading!