| A hybrid holographic system is developed for three-dimensional particle image velocimetry. This new-generation experimental technique enables measurements of whole field, 3-D velocity distributions within a finite volume at an unprecedented level of spatial resolution. As a demonstration of the potential of this robust diagnostic tool for studying turbulent flows, the current system is successfully implemented to measure the instantaneous, 3-D velocity field of a square duct flow at ReH ≈ 1.2 × 105. Nine such realizations are obtained, each containing ∼1303 vectors with a minimum vector spacing of 0.33 mm. These vector maps constitute the first ever full 3-D, high Reynolds number experimental data to be used for fundamental turbulence research.; Employing spatial filtering of the measured 3-D velocity distributions, the subgrid-scale (SGS) stress, the filtered strain-rate and the filtered vorticity are computed directly from the filtered velocity field. In the context of large-eddy simulation, we study the scale and geometrical relationships between the parameters of the resolved and subgrid scales. Specifically, probability density functions (Pdf) of scalar parameters characterizing tensorial eigenvalue structures are used to examine the most probable states in both the filtered strainrate and SGS stress fields. The relative spatial alignment configurations between the vorticity vector and eigenvectors of the strain-rate and SGS stress tensors are investigated using 3-D alignment pdfs. A priori tests of common SGS models, such as the Smagorinsky and similarity/non-linear models, are performed to check how well they reproduce the geometrical trends identified from the experimental data. Furthermore, employing conditional sampling, the effects of the preferred strain-rate and SGS stress states, magnitudes of strain-rate and vorticity, and SGS dissipation rate, are analyzed in detail. New, intriguing geometrical trends are observed and their implications on the SGS modeling are discussed. Conclusions in the present study may provide new insight into better understanding of the dynamics of SGS stresses and constructing of improved, physics-based SGS models. Finally, the tensor geometrical approach developed here can be readily applied to investigating significant structural characteristics of other turbulent flows obtained from either experiments or direct numerical simulations. |
