Analytical Prediction for Grain Burn Time and Burning Area Kinematics in a Solid Rocket Combustion Chamber

Abstract

This chapter proposes the application of Newtonian particle mechanics for the derivation of predictive equations for burn time, burning and unburnt area propagation for the case of a core propellant grain. The grain is considered to be inhibited in a solid rocket combu- stion chamber subject to the assumption that the flame propagation speed is constant for the particular solid fuel formulation and formation chemistry in any direction. Here, intricacies surrounding reaction chemistry and kinetic mechanisms are not of interest at the moment. Meanwhile, the physics derives from the assumption of a regressive solid fuel pyrolysis in a cylindrical combustion chamber subject to any theoretical or empirical burn rate characterization law. Essential parametric variables are expressed in terms of the propellant geometrical configuration at any instantaneous time. Profiles from simulation studies revealed the effect of modulating variables on the burning propagation arising from the kinematics and ordinary differential equations models. In the meantime, this mathematical exercise explored the tendency for a tie between essential kernels and mat- ching polynomial approximations. In the limiting cases, closed form expressions are couched in terms of the propellant grain geometrical parameters. Notably, for the fuel burn time, a good agreement is observed for the theoretical and experimental results.