An internal flow and heat transfer inside a solid rocket motor combustion chamber; A Lie symmetry approach

Abstract

The validity of Solid Rocket Motor (SRM) stability calculations critically depends on the sufficiently detailed and physically correct representation of propellant velocity flow-field, which leads to well behaved flow. A theoretical analysis of propellant flow and heat distribution is presented to study the thermal effects on propellant velocity flow-field to understand rocket stability dynamics better. Analysis based on Lie symmetry and perturbation technique is used to construct semi-analytical propellant flow and heat distribution solutions. Effects of various non-dimensional parameters arising from the Solid Rocket Motor design are graphically represented, analysed and parameter values leading to unstable and stable propellant flow are quantified. The study mainly gives an insight of thermal parameters affects rocket momentum. Among other findings, the study found that for Prandtl number values Pr>0.1 while sucking propellant out of the combustion chamber leads to instabilities on the propellant velocity flow field. In contrast, same Pr values lead to stable operation during injection. Also, the results show that for Grashof number values Gr>0.1 while injecting propellant into the combustion leads to unstable propellant velocity field but stable flow velocity during suction. The obtained temperature profiles agree with the experimental and theoretical results from the literature.