Integrating Mach–Zehnder interferometry with TPIV to measure the time-resolved deformation of a compliant wall along with the 3D velocity field in a turbulent channel flow

A system combining tomographic PIV (TPIV) and Mach–Zehnder interferometry (MZI) simultaneously measures the time-resolved 3D flow field and 2D distribution of wall-normal deformation in a turbulent channel flow over a transparent compliant surface. This paper focuses on the experimental techniques and data analysis procedures, but includes sample results. Standard TPIV analysis resolves the log layer of the mean velocity and the linear decrease in total shear stress with distance from the wall. Single-pixel ensemble correlations reveal the buffer layer and top of the viscous sublayer. Analysis of the MZI data consists of two steps, namely critical spatial filtering of interferograms to remove noise and phase demodulation to calculate the surface shape. A new technique to improve the filtration of noise from interferograms based on spatial correlations of small windows is introduced and optimized. Taking advantage of this enhancement, the phase/deformation distribution is calculated directly from arccosines of the intensity, which avoids edge artifacts affecting spectral calculations. Validations using synthetic noisy interferograms indicate that errors associated with correlation-based enhancement are consistently lower and much less sensitive to fringe shape than spectral band-pass filtering. The experimental wavenumber–frequency spectra show that the deformation consists of patterns that are larger than the field of view, surface waves and small-scale patterns. Some of the latter are advected at the freestream velocity, but mostly at 70 % of the freestream, the mean speed at 10 % of the channel half height. Indeed, spatial correlations of the deformation with velocity components peak at this elevation.