Phase spectral evidence for vortex structures in turbulent mixing

Abstract

It is shown that a quantitative schlieren system which senses over a complete cross section of the mixing flow from a nozzle gives rise to signals which have a quadrature phase relationship to near field microphone signals when vortex structures are present in the flow. This was confirmed by signal recovery observations for the transient step induced by a shock tube behind the nozzle settling chamber. The unexcited flow from the circular nozzle showed the phase relation expected for regular vortex structures only for the first two or three diameters downstream of the nozzle. Discrete frequency components did not predominate, but there was a general decrease of the Strouhal number of the spectral maximum with distance from the nozzle. The constraint of a protruding centrebody, shock tube or spark excitation gave rise to sets of discrete components in the flow which appeared to preserve their vortex ring-like character as evidenced by phase spectral observations to a greater distance from the nozzle. However beyond the end of the potential core at five diameters from the nozzle the phase spectra with impulse excitation no longer indicated vortex structures for the large scale disturbances sensed by the schlieren system. Pure tone acoustic excitation produced signals identifiable from their phase as due to vortex structures at the discrete excitation frequency. However, whilst broader band peaks corresponding to vortex pairing in the flow were observed these did not appear to be due to complete vortex rings and it was concluded that the pairing process involved distortion or fragmentation of the initial ring structures.