# A Unified Theory for Combustion-driven Flow Dynamics in a Model of a Solid Rocket Motor Chamber

Monday, September 27, 1999 - 9:30am - 10:30am

Keller 3-180

David Kassoy (University of Colorado)

Asymptotic techniques are integrated with numerical solution development to study the velocity and temperature dynamics in a cylinder with transient propellant combustion occuring on the sidewall. Earlier efforts of this type have focused on the velocity and temperature responses in the cylinder when the prescribed initial steady mass addition from the sidewalls (injection) is incremented by a similar size transient component. Unsteady mass injection is the source of acoustic disturbances which interact with the injected fluid to create unexpectedly large transient vorticity and radial temperature gradients on the sidewall of the cylinder. It follows that the surface is scoured by large oscillatory axial shear stresses and subjected to large transient heat transfer. Radial gradients of axial velocity and temperature are convected into the cylinder and downstream by the bulk motion of the internal flow. As a result, one finds significant radial variations in the instantaneous axial velocity (vorticity) and temperature (conductive heat transfer) distributions at any axial location in the cylinder. The total energy of the fluid is partitioned between the original steady flow, the acoustic field and an intense transient rotational flow field. The latter is entirely absent from traditional acoustic stability analyses of solid rocket motors. The prescribed mass injection boundary condition used in the earlier modeling is replaced by an elementary model of propellant combustion in order to enable nonlinear coupling of the flow dynamics and the gasification of the propellant which is present in real systems. It is the latter which is the basic source of transient dynamics in a motor chamber. The effects of large radial gradients of axial velocity and temperature which extend through the gaseous combustion zone down to the degrading propellant surface are expected to play essential roles in the coupling process. One objective of the study is to demonstrate that asymptotic methodologies can be used to describe basic chemico-physical processes that must be included in comprehensive models of motor chamber flow dynamics. A secondary aim is to encourage the solid rocket motor stability community to move beyond traditional response function approaches to propellant combustion by including physically viable forms of chemically induced exothermic heat release in their analytical and computational models