Lie group analysis of an internal flow and heat transfer inside a combustion chamber of a solid rocket motor

Abstract

This research project presents semi-analytical solutions for flow and heat transfer during solid rocket motor operation. Proficient modelling process is followed to construct a mathematical representation based on conservation of mass, momentum and energy. According to the dynamics of flow behaviour and temperature distribution during solid rocket motor operation, forces affecting the ow and heat transfer are derived from physical postulates. To understand the dynamics of a solid rocket motor, the current study investigates the ow and heat transfer inside a pipe in two folds. The first fold is to understand the effects of buoyancy force on axial-velocity and pressure field during solid rocket motor operation. The last fold is to understand temperature distribution inside the combustion chamber. Lie group analysis along with double perturbation method is used to carry out the integration of the problem at hand. To integrate equations representing the ow and heat transfer during solid rocket motor operation, momentum and energy equations are reduced to a single fourth order ordinary differential equation and second order differential equation respectively. Thereafter, double perturbation method is used to find the semi-analytical solutions of the resulting ordinary differential equations. The effects of dimensionless parameters arising from the design such as cross-ow Reynolds number Re, wall expansion ratio a, Grashof number Gr, Prandtl number Pr and radiation R on axial-velocity and temperature are represented graphically. Lastly, analysis is performed to seek the best combination of dimensionless parameters that lead to optimal thrust during operation.