Axisymmetric and flapping global instabilities of a Ma = 1 jet

The global instabilities of a perfectly expanded jet at Ma = 1 are investigated. Two configurations are compared. A reference setup represents the full geometry including the walls of the convergent nozzle within the computational domain. A second case indirectly models the effect of the nozzle on the flow. Both configurations are found to be globally unstable, indicative of the presence of an absolute instability mechanism. The results ascribe the generation of the absolute instability to the instantaneous transformation of the boundary layer within the nozzle into a rapidly expanding free shear layer past the nozzle exit. The constraining effect of the nozzle walls in the reference configuration leads to a lower instability growth rate than in the modeled case. The eigenfunctions are split into upstream- and downstream-traveling parts, and decomposed into vortical, acoustic and thermal components using momentum potential theory (Doak 1989). The most highly amplified axisymmetric and flapping modes are found to have a common structure. In the reference case, the eigenfunctions consist of upstream-traveling acoustic waves and downstream-traveling Kelvin-Helmholtz modes. The eigenfunctions in the modeled case are concentrated at the location of the rapidly expanding shear layer.