Characterization of High Speed and Arbitrary Headwall Injection Effects on the Trkalian Swirling Mean Flowfield in Rocket Motors

Abstract

In this work, the bulk gaseous motion inside cylindrical chambers driven by wall normal injection with and without reactive headwalls is explored. The base model is of the Trkalian type and is here extended to include approximations for arbitrary headwall injection patterns as well as compressibility effects for an exact similarity conforming headwall injection profile. The inviscid, non-reacting, swirling flow model is first generalized to capture a variety of headwall injection patterns through the concept of orthogonality. This leads to an approximation with some error which is quantified in the analysis. The velocity and vorticity fields are characterized for four representative injection patterns including a similarity conforming injection profile in the form of a Bessel function. The exact similarity conforming injection profile is then used in the development of a compressible approximation. Dilational effects are captured through a compressible Brag--Hawthorne framework in conjunction with a Rayleigh-Janzen expansion. Here again, the velocity and vorticity fields are obtained, along with the pressure, density, and temperature. These field variables are then compared to the incompressible case as well as the compressible complex-lamellar solution without swirl. Furthermore, the sonic length which functions as a normalizing parameter is calculated for several specific heat ratios and injection coefficients.