Application of Tomographic Wavelet-Based Optical Flow Velocimetry (wOFV) to Hypersonic Flows

Tomographic wavelet-based optical flow velocimetry (TwOFV) is demonstrated a hypersonic (Mach 5) boundary layer flow. Improvements to a previous prelimary implementation of TwOFV are presented that enable improved measurements in a high-speed wall-bounded flows. wOFV algorithm advancements, previous developed for 2D, planar applications, are non-trivially extended to 3D, volumetric applications. This includes the application of the wavelet transform from a lifting implementation to matrix-tensor product to provide an efficient and intuitive basis for the adaptation of continuous regularization in three dimensions. Both the matrix-tensor product and continuous regularization are demonstrated to enable accurate velocity estimates on non-cubic regions of varying sizes. Additional features are implemented to improve the experimental performance and usability of TwOFV, such as adoption of a pyramidal scheme and application of the no-slip boundary condition for wall-bounded flows. TwOFV is experimentally demonstrated on a sub-volume of the tomographic reconstruction produced from M=5 hypersonic flow over a flat plate model. Initial results include qualitative visualization of enhanced spatial resolution afforded by TwOFV and qualitative comparisons to planar wOFV results acquired for the same operating condition.