2D3C or Stereo PIV Three-component displacement in a plane
Figure 1: Sketch of a stereoscopic PIV setup arranged to match the Scheimpflug condition (reprinted from Raffel et al. 2007 [1]).
In Stereoscopic PIV, the basic principle of PIV is extended in order to determine the three components of the velocity vector within the light sheet plane, by mimicking binocular vision. The light sheet is imaged by two cameras, which are most often geometrically arranged in order to match the Scheimpflug condition (see Figure 1). Given a camera, this consists in tilting slightly its objective so that the object, lens and image plane intersect in a common line.
Compared to 2D2C PIV, four images are thus used to determine an individual displacement field: one per camera and per time instant. Up to now, PIV codes have all used a two-step paradigm: first, the displacement seen by each camera is determined separately by classical PIV, then the three components of the actual displacement are reconstructed from these data (stereo reconstruction step). FOLKI-SPIV relies on a novel one-step method, which directly uses all the information contained in the images and in the geometrical calibration. Read more about FOLKI-SPIV here.
Example: Study of an axisymmetric mixing layer in the R4Ch wind-tunnel
Instability and turbulence in the near field of a jet play are known to play a fundamental role in the generation of acoustic perturbations, as well as in the mixing between the jet and the surrounding ambient fluid. In that respect, understanding their dynamics is of foremost importance for a large spectrum of applications, principally in aerodynamics and combustion.
Recently, the dynamics of such a jet has been studied experimentally in order to shed new light on the complex interplay between its most important coherent structures [2]. This has been performed in the subsonic R4Ch wind-tunnel. In particular, high-speed stereoscopic PIV has been performed in a cross-sectional plane located two diameters downstream from the jet exit (see Figure 2). Figure 3 shows a sequence of snapshots calculated by FOLKI-SPIV.
Figure 2: Principle sketch of the high-speed stereoscopic PIV measurements in the cross-sectional plane of a circular jet, R4Ch wind-tunnel [2].
Based on these measurements, Davoust and Jacquin [3] have in particular derived a new method to determine local convection velocities of the coherent structures and assess the validity of Taylor's approximation. This approximation allows to reconstruct a three-dimensional flow field from a time-sequence, such as that shown above. An example appears in Figure 4, which shows the benefit of the approach for three-dimensional flow characterization.
Figure 4: Spatial reconstruction of the velocity and vorticity fluctuation in a circular jet, using Taylor's hypothesis, from high-speed stereoscopic PIV measurements [2-3].
References
[1] Raffel M., Willert C., Wereley S., Kompenhans J., Particle image velocimetry: a practical guide, Springer-Verlag, 2007.
[2] Davoust S., Jacquin L., Leclaire B., Dynamics of m=0 and m=1 modes and of streamwise vortices in a turbulent axisymmetric mixing layer, submitted to the J. Fluid Mech.
[3] Davoust S., Jacquin, L., Taylor's hypothesis convection velocities from mass conservation equation, Phys. Fluids 23(5), 2011.
