Multiple Axisymmetric Solutions for Axially Traveling Waves in Solid Rocket Motors

In this article, we consider the vorticoacoustic flowfield arising in a rightcylindrical porous chamber with uniform sidewall injection. Such configuration is often used to simulate the internal gaseous environment of a solid rocket motor (SRM). Assuming closed-closed acoustic conditions at both fore and aft ends of the domain, the introduction of small disturbances in the mean flow give rise to an axially traveling vortico-acoustically dominated wave structure that our study attempts to elucidate. Although this problem has been formulated before, it is reconsidered here in the context of WKB perturbation expansions in the reciprocal of the crossflow Reynolds number. This enables us to uncover multiple distinguished limits along with new asymptotic solutions that are presented for the first time. Among them are WKB approximations of type II and III that are systematically evaluated and discussed. The WKB solutions are shown to exhibit a peculiar singularity that warrants the use of matched asymptotic expansions to produce uniformly valid representations. Our solutions are obtained for any characteristic mean flow function satisfying Berman’s similarity condition for porous tubes. They are also derived to an arbitrary level of precision using a recursive formulation that can reproduce each of the asymptotic solutions to any prescribed order. Finally, our solutions are verified numerically over a wide range of physical parameters and through limiting process approximations.