Assessment and application of wavelet-based optical flow velocimetry (wOFV) to wall-bounded turbulent flows

Abstract

The performance of a wavelet-based optical flow velocimetry (wOFV) algorithm in extracting high accuracy and high-resolution velocity fields from tracer particle images in wall-bounded turbulent flows is assessed. wOFV is first evaluated using synthetic particle images generated from a channel flow DNS of a turbulent boundary layer. The sensitivity of wOFV to the regularization parameter ($$\lambda$$ λ ) is quantified and results are compared to cross-correlation-based PIV. Results on synthetic particle images indicated different sensitivity to under-regularization or over-regularization depending on which region of the boundary layer is being analyzed. Nonetheless, tests on synthetic data revealed that wOFV can modestly outperform PIV in vector accuracy across a broad $$\lambda$$ λ range. wOFV showed clear advantages over PIV in resolving the viscous sublayer and obtaining highly accurate estimates of the wall shear stress and thus normalizing boundary layer variables. wOFV was also applied to experimental data of a developing turbulent boundary layer. Overall, wOFV revealed good agreement with both PIV and a combined PIV + PTV method. However, wOFV was able to successfully resolve the wall shear stress and correctly normalize the boundary layer streamwise velocity to wall units where PIV and PIV + PTV showed larger deviations. Analysis of the turbulent velocity fluctuations revealed spurious results for PIV in close proximity to the wall, leading to significantly exaggerated and non-physical turbulence intensity in the viscous sublayer region. PIV + PTV showed only a minor improvement in this aspect. wOFV did not exhibit this same effect, revealing that it is more accurate in capturing small-scale turbulent motion in the vicinity of boundaries. The enhanced vector resolution of wOFV enabled improved estimation of instantaneous derivative quantities and intricate flow structure both closer to the wall and more accurately than the other velocimetry methods. These aspects show that, within a reasonable $$\lambda$$ λ range that can be verified using physical principles, wOFV can provide improvements in diagnostics capability in resolving turbulent motion occurring in the vicinity of physical boundaries. Graphical abstract

3D wind field profiles from hyperspectral sounders: revisiting optic-flow from a meteorological perspective

“…latter studied in [26,20,33,28], the optimization procedure avoids the heuristic and standard multiresolution optic flow initialization, and relies instead on the estimation of wavelet expansions of the displacement variable d (Coiflets with 10 vanishing moments). The strategy consists in estimating wavelet series with an increasing number of terms over the iterations of the algorithm, the added terms being related to increasingly fine spatial scales.…”

“…These latter problems remain non-convex and high-dimensional. We rely on the wavelet expansion of the AMV fields [12,26,20,33,28] and employ large scale quasi-Newton methods [29] to deal efficiently with these problems. This paper is organized as follows.…”

Accurate near-wall measurements in wall bounded flows with optical flow velocimetry via an explicit no-slip boundary condition

“…In wall bounded turbulent flows such as boundary layers and channel flows, steep gradients exist close to the wall(s) due to the no-slip condition. As noted in the study conducted by Nicolas et al [20], because of the spatial averaging inherent in cross correlation-based PIV methods, these gradients are virtually impossible to resolve with PIV. Hence, large uncertainties in the velocity field measurements persist for y + ≲ 10-20 where the inner maximum of the RMS streamwise velocity (σ u ) is located [22], which is key to measuring the turbulence intensity and estimating the wall shear.…”

“…In OFV, on the other hand, instead of using the cross correlations between interrogation windows across a pair of images to determine the averaged displacement of each window, the velocity field is estimated by calculating the displacement at each pixel using optical flow, a technique originating from the computer vision community [2,3]. OFV has been demonstrated by the authors and others to yield a higher resolution estimate of the velocity field with increased global accuracy compared to correlation-based PIV [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. A subset of OFV methods are wavelet-based OFV, or wOFV, which is described in section 2.1.…”

“…a Neumann condition. In a recent study, Nicolas et al [20] applied wOFV to a wall-bounded turbulent flow to study the effects of regularization, described in equation ( 1) in section 2.1, on the near wall velocity structures. They observed that while wOFV increases the fidelity of the velocity measurements compared to cross correlation-based PIV with an appropriately chosen regularization parameter, it still fails to resolve the full turbulent boundary layer profile close to the wall without sacrificing the far-field velocity estimates made by wOFV.…”