Measurement of three-dimensional coherent fluid structure in high Reynolds number turbulent boundary layers

Abstract

The turbulent boundary layer is an aspect of fluid flow which dominates the performance of many engineering systems - yet the analytic solution of such flows is intractable for most applications. Our understanding of boundary layers is therefore limited by our ability to simulate and measure them. Tomographic Particle Image Velocimetry (TPIV) is a recently developed technique for direct measurement of fluid velocity within a 3D region. This allows new insight into the topological structure of turbulent boundary layers. Increasing Reynolds Number increases the range of scales at which turbulence exists; a measurement technique must have a larger 'dynamic range' to fully resolve the flow. Tomographic PIV is currently limited in spatial dynamic range (which is also linked to the spatial and temporal resolution) due to a high degree of noise. Results also contain significant bias error. This work proposes a modification of the technique to use more than two exposures in the PIV process, which (for four exposures) is shown to improve random error by a factor of 2 to 7 depending on experimental setup parameters. The dynamic range increases correspondingly and can be doubled again in highly turbulent flows. Bias error is reduced by up to 40%. An alternative reconstruction approach is also presented, based on application of a reduction strategy (elimination of coefficients based on a first guess) to the tomographic weightings matrix Wij. This facilitates a potentially significant increase in computational efficiency. Despite the achieved reduction in error, measurements contain non-zero divergence due to noise and sampling errors. The same problem affects visualisation of topology and coherent fluid structures. Using Projection Onto Convex Sets, a framework for post-processing operators is implemented which includes a divergence minimisation procedure and a scale-limited denoising strategy which is resilient to 'false' vectors contained in the data. Finally, developed techniques are showcased by visualisation of topological information in the inner region of a high Reynolds Number boundary layer (δ+ = 1890, Reθ = 3650). Comments are made on the visible flow structures and tentative conclusions are drawn.