| A numerical analysis has been conducted to study solid-propellant rocket motor internal flowfields under both steady and oscillatory conditions. The formulation is based on the time-dependent Navier-Stokes equations for compressible flows, with consideration of finite-rate chemical kinetics and variable properties. Turbulence closure is achieved using a modified k-{dollar}epsilon{dollar} two-equation model and a two-layer model. Both models take into account the wall-injection effect arising from the surface combustion of propellants. The analysis consists of two parts: cold-flow simulation of unsteady motions in a porous chamber, and investigation of combustion of homogeneous propellants. A time-accurate finite-difference program based on the four-stage Runge-Kutta scheme, and a finite-volume program based on the dual time-stepping integration technique, were used for the cold-flow and reacting-flow simulations, respectively. The results from cold-flow simulation indicate that while the acoustic pressure field remains one-dimensional, the acoustic velocity exhibits a more complicated oscillation behavior than a plane wave. The flow-turning loss of the acoustic field is as important as the viscous loss which occurs within the acoustic boundary layer. From the reacting-flow simulation, it was found that the strong temperature gradient within the flame zones has an effect on the distribution of acoustic velocity. The interactions between acoustic waves and gas-phase chemical reactions are also demonstrated by the large amplitude of temperature fluctuations when the characteristic time scales of these two mechanisms are closely matched. |
