Structural sensitivity of the precessing vortex core instability in swirled jets

Abstract

This thesis performs an LES study of the flow through a swirling nozzle. The nozzle has one single stream with swirl being generated by vanes mounted on an axially aligned centrebody. The end face of the centrebody coincides with the nozzle exit. The nominal Reynolds number based on the jet diameter and bulk flow velocity is 82,000 and the swirl number is 0.8. Two simulations are performed at this condition for a nominal end face diameter, Dc = 10mm (LES85A) and Dc = 5mm (LES85B). An additional test case for an Re ∼ 50, 000(LES50) was performed to validate the LES method against experimental flow field measurements for this nozzle at this condition. The LES results agree closely with PIV measurements. Coherent PVC oscillations are observed in the LES85B case. A linear stability analysis around the time averaged flow reveals the presence of a marginally stable helical mode that shows strong radial flow oscillations at the centreline, as may be expected. The mode is stable in the LES85A case. Structural sensitivity analysis reveals that the complex eigenfrequency of the mode is sensitive to changes in the linearised governing equations (structural perturbation) due to changes in the time averaged flow in the region corresponding to the merger of the wake behind the centrebody and the leading edge of the vortex breakdown bubble. Comparing mean fields between LES85A and LES85B shows that the reduction in Dc results in a large change in mean radial velocity alone at a z/D ∼ 0.1 , where the bubble and the centerbody wake meet. This can be conceptualised as the resultant of a localised radial force proportional to the oscillating velocities, being applied at the wake-bubble merger region. The relevant components of the structural sensitivity tensor terms that characterise the response of the eigenvalue to such a force suggests an increase in the growth rate and frequency. This is consistent with the marginally higher growth rate and frequency of the unstable linear mode and the presence of PVC oscillations in the LES for the LES85B case. Therefore, we conclude that the larger value of Dc in the LES85A case results in a nominally longer recirculation zone in the wake of the centerbody which then merges with the vortex breakdown bubble. This stabilises the PVC eigenmode and thereby, suppresses PVC oscillations.