Divergence-Free Wavelets and High Order Regularization

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

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 ( 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 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 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.

Blood Flow Velocimetry in a Microchannel During Coagulation Using Particle Image Velocimetry and Wavelet-Based Optical Flow Velocimetry

This article describes novel measurements of the velocity of whole blood flow in a microchannel during coagulation. The blood is imaged volumetrically using a simple optical setup involving a white light source and a microscope camera. The images are processed using particle image velocimetry (PIV) and wavelet-based optical flow velocimetry (wOFV), both of which use images of individual blood cells as flow tracers. Measurements of several clinically relevant parameters such as the clotting time, decay rate, and blockage ratio are computed. The high-resolution wOFV results yield highly detailed information regarding thrombus formation and corresponding flow evolution that is the first of its kind.