Turbulent swirling flows with vortex breakdown occur in various engineering flows such as on delta wings of aircraft at high angles of attack, in water turbines at part load or in combustors of gas turbines. Under certain conditions, vortex breakdown is accompanied by a strong flow instability called precessing vortex core (PVC).
In gas turbines, the influence of the PVC on flame stability and pollutant emissions is a current focus of research. In order to perform systematic parameter studies, it is essential to design an efficient actuator that allows the PVC to be controlled at will (be it attenuation, amplification or suppression). The goal of this project is to apply adjoint linear stability analysis to determine an optimal placement for the actuator.
Proper orthogonal decomposition is used to extract the PVC from experimental data. Linear stability analysis (LSA) is used for quantitative modeling. The LSA-based models provide valuable insights into the physical causes of the PVC and of coherent structures in general that would otherwise be inaccessible with purely numerical simulations or with experiments. The adjoint form of the LSA allows us to locate the origin of the instability driving the coherent structures. Furthermore, the regions with the highest receptivity to flow modifications through passive or active flow control can be identified. In this way, optimal actuator positions can be derived without the need for extensive actuator tests in a trial-and-error procedure beforehand.
The figure below shows contours of the PVC instability mode for all three velocity components, extracted with proper orthogonal decomposition, in a generic combustor flow with an upstream mixing tube. The mode quantifies the coherent fluctuations of the instability at a given phase angle, with positive fluctuations in red and negative fluctuations in blue. Thus, the mode visualizes the strong precession and helical Kelvin-Helmholtz vortices inside the combustor flow.
The first figure in the upper right shows contours of the magnitude of the adjoint PVC mode. Here, the white color denotes no receptivity and the dark blue color denotes maximum receptivity. Therefore, maximum receptivity is reached inside the mixing tube, and an actuator positioned in this region has the greatest effect on the PVC (illustrated by the speaker symbols).