Dimensional Analysis and Self-Similarity Theory for Regenerative Liquid Propellant Guns

Regenerative liquid propellant guns (RLPGs) have been studied for many years. RLPG firings almost always show large, high-frequency pressure oscillations. To study this phenomenon, a fluid dynamics model of the combustion chamher/gun tube of an RLPG has been developed. High-frequency oscillations are generated naturally by the physics modeled in the code. Dimensional analysis has been applied to the governing equations to furnish insight into the dynamic relationships among pressure, density, temperature, droplet size, etc. The dimensional analysis predicts a scaling law between different-sized fixtures. The computational results exactly match these predictions. This agreement establishes the basis of self-similarity in the physical processes (e.g., tradeoff between droplet size and burning rate) and, in addition, helps verify the computational model.