Estimation of the shear layer velocity fluctuation in a supersonic jet with single-pixel resolution

The acoustic wave of a supersonic jet is an important issue in the engineering field. The Mach wave which is a dominant noise source of a supersonic jet is generated by the supersonic convection of the turbulent structure in the shear layer. For an understanding of the phenomenon, an acquisiton of two-dimensional velocity distribution by particle image velocimetry (PIV) help us to understand the generation mechanism of acoustic waves. However, it is difficult to obtain the velocity distribution with sufficiently high spatial resolution in the shear layer region because the diameter a lab-scale jet flow is commonly small[1]. The spatial resolution of the PIV is limited by an interrogation window used for calculating cross-correlation in the case of the conventional spatial correlation method (CSC). On the other hand, the single-pixel ensemble correlation method (SPC) proposed by Westerweel enables us to estimate the averaged velocity distribution with high spatial resolution in single-pixel units using the cross-correlation of the time evolution of intensity at each pixel[2]. This technique was improved by Scharnowski to be able to estimate velocity fluctuation and Reynolds stress[3]. However, this technique cannot be applied to the particle image of a supersonic jet flow because this method assumes ideal PIV images which have no blur of particle. In the particle images of supersonic jet flow, the shape of particle on the image extends in streamwise due to the high-speed flow and particle distribution is not uniform all over the image because there are a steep velocity gradient and density difference. Therefore, in this study, we improved the estimation method of the fluctuation component using SPC in order to estimate the velocity distribution of a supersonic jet with high spatial resolution.