Receptivity of the turbulent precessing vortex core: synchronization experiments and global adjoint linear stability analysis

Abstract: The Precessing Vortex Core (PVC) is a coherent structure that can arise in swirling jets from a global instability. In this work, the PVC is investigated under highly turbulent conditions. The goal is to characterize the receptivity of the PVC to active flow control, both theoretically and experimentally. Based on stereoscopic particle image velocimetry and surface pressure measurements, the experimental studies are facilitated by Fourier decomposition and proper orthogonal decomposition. The frequency and the mode shape of the PVC are extracted and a very good agreement with the theoretical prediction by global linear stability analysis (LSA) is found. By employing an adjoint LSA, it is found that the PVC is particularly receptive inside the duct upstream of the swirling jet. Open-loop zero net mass flux actuation is applied at different axial positions inside the duct with the goal of frequency synchronization of the PVC. The actuation is shown to have the strongest effect close to the exit of the duct. There, frequency synchronization is reached primarily through direct mode-to-mode interaction. Applying the actuation farther upstream, synchronization is only achieved by a modification of the mean flow that manipulates the swirl number. These experimental observations match qualitatively well with the theoretical receptivity derived from adjoint LSA. Although the process of synchronization is very complex, it is concluded that adjoint LSA based on mean field theory sufficiently predicts regions of high and low receptivity. Furthermore, the adjoint framework promises to be a valuable tool for finding ideal locations for flow control applications.