Adjoint-based swirling flow injection control in a model combustion chamber: A numerical study

In the present work, an adjoint-based flow control strategy to suppress the precessing vortex core (PVC) in a swirl-stabilized model combustion chamber was studied. A global linear stability analysis of the mean flow yielded a marginally stable mode with azimuthal wavenumber m=1, accounting for the PVC oscillations. The structural sensitivity map, constructed from the direct and adjoint eigenfunctions, identified the wavemaker region near the flow separation point, which was parametrically tested for the PVC suppression. In the main-flow simulations, a constant airflow of 2%–8% of the total flow rate was injected at different positions inside the area of the highest sensitivity. Pressure probe spectra indicated that injection at the wavemaker achieved around 50% attenuation with a modest 4% flow rate, while off-wavemaker positions yielded stronger suppression (70%–80%) at higher injection rates. However, a more detailed analysis using spectral proper orthogonal decomposition revealed the following: injection at the wavemaker x0 and at the downstream position x1 both suppressed the PVC by approximately 70% at 8% flow rate, with shifting the PVC frequency. In contrast, injection at the upstream position x2 led to an increase in the PVC energy, which was not captured by the pressure probe spectra. The results demonstrated that the sensitivity map reliably guides actuator placement, achieving effective PVC mitigation.