A Pseudo-3D Level Set Simulation Method for Propellant Surface Regression by APN / Erosive Burning in Solid Rocket Motors

A "pseudo-3D" level set method is proposed, validated, and demonstrated that enables rapid yet accurate simulations of propellant surface regression under pressure-dependent (APN) burning rates combined with erosive enhancement of the burning rate in solid rocket motors. The method is based on a linked succession of axial propellant segments, in each of which a two-dimensional level set simulation of combined APN / erosive propellant surface regression is conducted, with the resulting combustion product gas mass flow rate generated in each segment adding to the mass flow rate produced by all upstream segments. In this manner the product gas flow speed and thus its effect on erosive burning increases in successive downstream segments. As the burning progresses in time, the current mass flow rate from the final segment provides the mass flow rate through the choked nozzle, which in turn determines the current total pressure in the solid propellant combustion chamber, from which the local static pressure determines the local APN burning rate in each segment, while the current gas flow speed in each segment determines the current erosive enhancement in that segment. This pseudo-3D simulation method is first validated in a simple configuration that allows exact analytical results for comparison. It then is demonstrated by application to a succession of increasingly complex propellant grains to show how it can be used in practical instances to determine the propellant grain burning with time and the resulting chamber pressure vs. time and thrust vs. time.