Improved Mean-Flow Solution for Slab Rocket Motors with Regressing Walls

Abstract

The Navier‐Stokes equations are solved to obtain an approximate description of the mean e ow in a slab rocket motor with two evenly regressing walls. The scope is limited to two-dimensional incompressible and chemically nonreactive viscous e ow. The transformed governing equation is solved numerically, using e nite differences, and asymptotically, using variation of parameters and small parameter perturbations in the blowing Reynolds number R. Results are correlated and compared via variations in R and the dimensionless wall regression rate. For hard blowing and moderate regression rates the effect of wall motion on the velocity is found to be small. Conversely,forfast-burningpropellants,suchasthosebeing developed forhigh-accelerationvehicles,regressioneffects seem ine uential. Inclusion of viscous dissipation is also found to be important in assessing the total e ow vorticity, especially when R<102. The current geometric cone guration is relevant to motor simulations using ducted channels with porous walls. For validation purposes comparisons with numerical solutions are carried out alongside end-process verie cations. Because the resulting model incorporates viscosity and wall motion, it allows for an improved description of the unsteady acoustico-vortical solution whose assessment is strongly ine uenced by the mean e ow.