NUMERICAL INVESTIGATION OF ACOUSTIC- FLUID DYNAMIC INTERACTIONS IN AN SRM CHAMBER/NOZZLE MODEL

Multidimensional, rotational transient flow dynamics in a planar model of a solid rocket motor chamber/nozzle geometry are predicted from the solution to the parabolized unsteady, compressible Navier-Stokes equations. The Two-Four explicit scheme, combined with the Navier-Stokes Characteristics Boundary Condition (NSCBC), is used to obtain solutions in a chamber/nozzle model. After convergence to the steady state, driven by constant side-wall injection, the flow field is disturbed by transient side-wall mass addition of similar amplitude. This mimics unsteady propellant gasification. The solution is carried out for small subsonic Mach numbers ( M<1), and a weakly viscous internal shear flow (Re » 1) in a chamber where the aspect ratio is A»l. The computational analysis shows that intensive vorticity is generated at the Copyright © 1998 by the American Institute of Aeronautics and Astronautics Inc. All rights reserved. chamber side-wall. Then, the vorticity is converted into the chamber by the unsteady injected flow field. Eventually, the wall generated rotational flow fills the entire chamber. Unsteady vorticity is also generated in the nozzle within the viscous boundary layer. Finally, the effect of the nozzle on the generation and evolution of the chamber-generated unsteady vorticity is studied by comparing results with those in a chamber without a nozzle. Physical and Mathematical Model The flow occurs in a planar chamber/nozzle geometry of a length L and chamber-half height H, with a pressure node at the exit and an impermeable wall at the head end. Inert gas, injected through the porous side walls with a characteristic velocity V' , induces Jo an axial flow characterized by U. =AVV ^ o Jo to mimic the evolution of combustion products from solid propellant burning. The mathematical model is based on the following non-dimensional conservation form of the unsteady, compressible, 2-D, 1 American Institute of Aeronautics and Astronautics Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc. Navier-Stokes equations describing both fluid dynamics and acoustics in a perfect gas within a rectangular chamber; dQ dE dF —— + — + — = 0 dt GX dy (1) where Q, E, and F are column vectors given by;