Spatial density fluctuation of supersonic flow over a backward-facing step measured by nano-tracer planar laser scattering

Spatial density fluctuation of supersonic flow over a backward-facing step is studied by nano-tracer planar laser scattering, aero-optic method and proper orthogonal decomposition analysis. Measurements were carried out in a Ma = 3.0 low-noise indraft wind tunnel. By varying the superficial roughness of the wall upstream from the step, supersonic laminar flow and supersonic turbulent flow were generated over a backward-facing step. The reattachment regions of these two flows were focused on. Flow structures of supersonic boundary layer, free shear layer, \(Kelvin - Helmholtz\) vortices and reattachment shock were revealed. Based on the density-grayscale calibration of the flow field, the density distribution and optical path difference were calculated. Proper orthogonal decomposition was applied to 400 samples of optical path difference distributions which were generated by performing ray tracing method. According to the principle of proper orthogonal decomposition and the aero-optic basic equations, peaks in the first mode of proper orthogonal decomposition could reveal intensive spatial density fluctuations. The results showed that around the location of the reattachment point, density changed dramatically in both of two flows spatially. The location of reattachment point judged by the intensive density variation basically agreed with that judged by velocity field or flow structures. Thus, it was found that reattachment of supersonic backward-facing step occurred with intensive spatial density fluctuation which caused complex aero-optic aberration.