Experimental Investigation of Compliant Wall Surface Deformation in a Turbulent Channel Flow using Tomographic Particle Image Velocimetry and Mach-Zehnder Interferometry
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Interaction of a compliant wall with a turbulent channel flow is investigated experimentally by simultaneously measuring the time-resolved, three-dimensional flow field and the two-dimensional surface deformation. The optical setup integrates tomographic particle image velocimetry to measure the flow with Mach-Zehnder interferometry to map the deformation. The Reynolds number is Reτ=2300, and the Young’s modulus of the wall is 0.93 MPa, resulting in a ratio of shear speed, ct, to the centerline velocity, U0, of 6.8. The 3D distributions of pressure are calculated by spatially integrating the material acceleration. To resolve sub-micron surface deformations, several fringe image enhancement and phase evaluation algorithms are developed and compared. Extensive synthetic validations are performed to estimate measurement uncertainty and determine relevant filtering parameters. The deformation wavenumber-frequency spectra show the surface motion contains a non-advected low-frequency component and advected modes, some traveling downstream at U0 and others at 0.72U0. The amplitudes of the detrended deformations are much smaller than the wall-unit, hence they do not affect the flow statistics. Predictions by the Chase (1991) model are calculated and compared to the measured trends. Conditional correlations are calculated between deformation and flow variables, including pressure. The deformation-pressure correlations peak at y/h~0.12 (h is channel half-height), the elevation of Reynolds shear stress maximum in the log-layer. Streamwise lagging of the deformation behind the pressure is caused in part by phase lag of the pressure with decreasing distance from the wall, and in part by material damping. By correlating deformation with flow velocity, vorticity and λ2, the relevant flow structures are identified. Positive deformations (bumps) caused by negative pressure fluctuations are preferentially associated with ejections involving spanwise vortices located downstream and quasi-streamwise vortices with spanwise offset. Results of conditional correlations are consistent with presence of hairpin-like structures. The negative deformations (dimples) are preferentially associated with positive pressure fluctuations at the transition between an upstream sweep to a downstream ejection.