Construction of three-dimensional images of flow structure via particle tracking techniques

Construction of three-dimensional images of flow structure, based on the quantitative velocity field, is assessed for cases where experimental data are obtained using particle tracking technique. The experimental data are in the form of contiguous planes of particle images. These contiguous data planes are assumed to correspond to successive spatial realizations in steady flow, or to phase-referenced realizations in an unsteady flow.Given the particle images on contiguous planes, the in-plane velocity fields are determined. Then, the out-of-plane velocity field is obtained using a spectral interpolation method. Application of this method allows, in principle, construction of the three-dimensional vorticity field and the streamline patterns.A critical assessment is made of the uncertainties arising from the in-plane interpolation of the velocity field obtained from particle tracking and the evaluation of the out-of-plane velocity component. The consequences of such uncertainties on the reconstructed vorticity distributions and streamline patterns are addressed for two basic types of vortex flows: a columnar vortex, for which the streamlines are not closed and are spatially periodic in the streamwise direction; and for a spherical (Hill's) vortex exhibiting closed streamline patterns, and no spatial periodicity.