independent of the Reynolds-number. This is in accordance to observations by [41] in non-reacting swirling flows.
Separate from these characteristic frequencies the PSDs show a typical shape of fully developed turbulence. Due to the finite slot width Dt used in the data post-processing, the inertial sub-range can be resolved only partly and the dissipation range is not accessible at all. Higher seeding den- sities to access higher data rates and thereby high- er temporal resolution, however, are prohibitive as they would have changed the flame appearance. The finite sized probe volume acts additionally as a spatial filter suppressing high frequencies. Focal lengths of sending and detection optics in connec- tion with forward scattering are already designed for an exceptional small probe volume size.
The reason for the observed characteristic fre- quencies is multifarious. The high frequencies of 1290 and 2920 Hz are associated with high shear. Based on PIV measurements at the identical noz- zle geometry within a water channel [42], these measured coherent motions are caused most likely by a pair of rotating vortex filaments. These vor- tex filaments spin around the centreline giving rise to the high frequency peaks in the PSDs. The pair of vortex filaments is probably formed at the sep- aration of the annular air flow upstream the recir- culation bubble reaching back into the nozzle. Direct numerical simulations (DNS) [43] as well as large eddy simulations (LES) [44] of non-react- ing swirling flows have shown very similar pairs of vortex filaments.
The lower frequency of 480 Hz is not associat- ed with the presence of a shear layer. It is present in the fuel–air mixing zone upstream the flame front (compare next section). It is speculated that this frequency is linked to an axial oscillation of the heat release zone. In the corresponding non- reacting cases [34,35], it was not observed at all. However, further experimental investigations using for example high-speed PIV will be neces- sary to provide a more sound explanation of this observation.
Far downstream at x = 50 mm a very weak oscillation associated with a frequency of 75 Hz is observed (no PSD shown). This frequency is most likely caused by a precessing vortex core (PVC). PVCs have been often observed in swirling flows and are linked to central recirculation zones [45]. Compared to vortex filaments, PVCs in gen- eral exhibit much lower frequencies. In the present case the PVC is clearly detached from the nozzle. This is due to the high momentum of the central fuel jet and was not observed for nozzle geome- tries without a central jet [7].