Mean flow stability analysis of oscillating jet experiments

TL;DR

This study applies linear stability analysis to the mean flow of an oscillating jet, demonstrating the model's accuracy in predicting flow oscillations and its limitations at high forcing amplitudes and downstream regions.

Contribution

It extends mean flow stability analysis to externally forced oscillating jets, validating the approach across a range of forcing amplitudes and identifying its limitations.

Findings

Stability wave model accurately predicts flow oscillations during growth and decay phases.

Model shows robustness over a wide range of forcing amplitudes with minimal sensitivity to nonlinear saturation.

Prediction deteriorates at very strong forcing and downstream regions due to flow interactions.

Abstract

Linear stability analysis is applied to the mean flow of an oscillating round jet with the aim to investigate the robustness and accuracy of mean flow stability wave models. The jet's axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry and decomposed into a mean and periodic part utilizing proper orthogonal decomposition. Local linear stability analysis is applied to the measured mean flow adopting a weakly nonparallel flow approach. The resulting global perturbation field is carefully compared to the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pronounced sensitivity to the strength of nonlinear saturation. The upstream displacement of the neutral point and the successive reduction of gain with increasing forcing amplitude is very well captured by the stability wave model. At very strong forcing (>40%), the flow becomes essentially stable to the axisymmetric mode. For these extreme cases, the prediction deteriorates from the measurements due to an interaction of the forced wave with the geometric confinement of the nozzle. Moreover, the model fails far downstream in a region where energy is transferred from the oscillation back to the mean flow. This study supports previously conducted mean flow stability analysis of self-excited flow oscillations in the cylinder wake and in the vortex breakdown bubble and extends the methodology to externally forced convectively unstable flows.