Spatio-temporal and modal analysis of unsteady fluctuations in a high-subsonic base flow

The high-subsonic flow over an axisymmetric backward facing step is investigated at a Mach number of 0.7, with high-speed particle image velocimetry operating at acquisition frequency up to 20 kHz to resolve the time dependent behavior of the separated flow in the longitudinal plane. The statistical flow properties such as the approaching boundary layer thickness, mean and fluctuating velocity field and shear layer growth are quantified. It is found that the shear layer growth is nearly linear up to x/D = 0.6; downstream this location, the reattachment surface influences the shear layer growth rate, causing it to decrease. The visualization of the high-speed measurements shows a quasi-cyclic behavior of the separated region characterized by a fluctuation of the flow reattachment location. The growing and shrinking of the separated region is accompanied by large-scale fluctuations that dominate the flow motions and the momentum exchange across the shear layer. The analysis of the large-scale fluctuations based on proper orthogonal decomposition (POD) of the velocity field indicates that the separated region exhibits pulsating behaviour as associated to the highest energy mode. The second and third modes are approximately in phase quadrature and can be associated to the growth of large azimuthal vortices that undulate the shear layer approaching the mean reattachment location. Conditional averaging of the data indicates that the second/third mode is associated to either the entrainment of high momentum fluid or ejection of low momentum fluid from the separated region depending on the phase. The high-speed measurements enable the spectral analysis of the velocity; the power spectral density of the POD time coefficients for the first three modes is evaluated. The first mode associated to pulsatile growth and collapse of the separated region yields a dominant frequency at Str(D) = 0.13 (f = 585 Hz) while the second mode features a broader frequency distribution in the range from 1 to 3 kHz (0.22 < Str(D) < 0.67) with a distinguishable peak at Str(D) = 0.4. The dynamical correlation between these two modes shows that time derivative of the first mode temporal coefficient and second mode coefficient are strongly correlated. This suggests that the entrainment of high momentum fluid into the separated region is responsible for the wake growth phenomenon. (C) 2014 AIP Publishing LLC.