Laminar cold-flow model for the internal gas dynamics of a slab rocket motor

Abstract

This paper considers the internal fluid dynamics of the slab rocket motor based on a laminar cold-flow model. An idealization process applicable to nonreacting flows leads to a mathematical solution for both steady and unsteady flow variables. Results are compared to the circular-port solution. This brings into focus the effect of a motor's radius of curvature. By comparison to a circular grain, a planar cross section exhibits slower and more gradual flow turning near the wall. It also induces reductions in core velocities and vorticities by 1/2 and 1/4, respectively. On the one hand, it appears that the reduced vortical intensity could make the slab configuration more resilient to vibrations and acoustic combustion instabilities. On the other hand, decreasing the radius of curvature seems to inhibit the inward penetration of vorticity. By comparison with the circular port, the simulated slab exhibits a more spatially uniform pressure and an uneven mass efflux at the aft end. Since the mass efflux is concentrated in a thin sheet near the core, the slab configuration is likely to exhibit improved stealth capabilities. The temporal solution is derived using the composite-scale and multiple-order WKB techniques. Asymptotic results are validated via comparisons with finite-volume solutions of the complete Navier–Stokes equations. Simulated conditions apply to forward motor segments and planar cold-flow experiments.