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.Key words: Authors should not enter keywords on the manuscript, as these must be chosen by the author during the online submission process and will then be added during the typesetting process (see http://journals.cambridge.org/data/relatedlink/jfmkeywords.pdf for the full list) †

Stochastic modelling of a noise-driven global instability in a turbulent swirling jet

“…(2015) and Müller et al. (2020).

Figure 2.Schematic of the experimental set-up and the utilised measurement systems: HS PIV, high-speed particle image velocimetry; AMP, amplifier; DAQ, data acquisition system.

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“…In these cases, the failure of the mean-flow model is related to a strong nonlinear interaction between the fundamental mode and the first harmonic. The present investigation covers the global mode in a swirling jet, for which it was shown that the saturation is governed by the mean-flow change (Müller et al 2020).…”

“…The jet is emanating into a large space (4 m wide, 3 m high) that constitutes unconfined boundary conditions in radial and streamwise directions. Further details of the experimental set-up can be found in Rukes et al (2015) and Müller et al (2020).…”

“…The present investigation covers the global mode in a swirling jet, for which it was shown that the saturation is governed by the mean-flow change (Müller et al. 2020).…”

On the relevance of the runner crown for flow instabilities in a Francis turbine

“…One of the greatest benefits of the LSA framework lies in its adjoint formulation. The adjoint LSA allows, amongst others, for identifying regions of receptivity to periodic forcing [3,4,5] and sensitivity to mean flow modifications [6,7,8]. Previous works have already discussed the PVC in the light of the LSA [9,10].…”