Quad-plane stereoscopic PIV for fine-scale structure measurements in turbulence

Abstract

The fine-scale structure in turbulence is investigated by quad-plane stereoscopic particle image velocimetry (QPSPIV). The quad-plane consists of two each of different polarizations and wavelengths, and it provides three velocity components at four independent parallel planes. Measurements have been undertaken in the developed region of a turbulent round jet with a spatial resolution sufficient to capture the small-scale structures. The advantage of the QPSPIV is presented in terms of the spectral response in the evaluation of the out-of-plane velocity gradient. The full velocity gradient tensor is computed with a fourth-order finite difference scheme in the out-of-plane direction as well as the in-plane directions. The turbulence quantities, such as the vorticity components, the energy dissipation rate and the second and third invariants of the velocity gradient tensor, are computed according to their faithful definitions. The coherent fine-scale eddies are extracted from the present QPSPIV data. The probability density functions of the diameter and the maximum azimuthal velocity of the extracted eddies exhibit their peak at approximately $$8\eta $$ and $$1.5u_k$$ , respectively, where $$\eta $$ and $$u_k$$ are the Kolmogorov length and velocity. These values agree well with the data in the literature. The phase-averaged distributions of turbulence quantities around the coherent fine-scale eddy indicate an apparent elliptic feature around the axis. Furthermore, the state of the strain rate exerting the eddy is quantified from the phase-averaged distributions of eigenvalues of the strain rate tensor and the alignment of the corresponding eigenvectors against the axis. The present study gives a solid experimental support of the coherent fine-scale structures in turbulence, and the technique can be applied to various flow fields and to the higher Reynolds number condition.