Quantitative focused laser differential interferometry with hypersonic turbulent boundary layers.

The effect of turbulent wind-tunnel-wall boundary layers on density change measurements obtained with focused laser differential interferometry (FLDI) was studied using a detailed direct numerical simulation (DNS) of the wall from the Boeing/AFOSR Mach-6 Quiet Tunnel run in its noisy configuration. The DNS was probed with an FLDI model that is capable of reading in three-dimensional time-varying density fields and computing the FLDI response. Simulated FLDI measurements smooth the boundary-layer root-mean-square (RMS) profile relative to true values obtained by directly extracting the data from the DNS. The peak of the density change RMS measured by the FLDI falls within 20% of the true density change RMS. A relationship between local spatial density change and temporal density fluctuations was determined and successfully used to estimate density fluctuations from the FLDI measurements. FLDI measurements of the freestream fluctuations are found to be dominated by the off-axis tunnel-wall boundary layers for lower frequencies despite spatial suppression provided by the technique. However, low-amplitude (0.05%-5% of the mean density) target signals placed along the tunnel centerline were successfully measured over the noise of the boundary layers (which have RMS values of about 12% of the mean). Overall, FLDI was shown to be a useful technique for making quantitative turbulence measurements and to measure finite-width sinusoidal signals through turbulent boundary layers, but may not provide enough off-focus suppression to provide accurate freestream noise measurements, particularly at lower frequencies.