Abstract
The low-frequency unsteadiness in the direct numerical simulation of a Mach 2.9 shock wave/turbulent boundary layer interaction with mean flow separation is analysed using dynamic mode decomposition (DMD). The analysis is applied both to three-dimensional and spanwise-averaged snapshots of the flow. The observed low-frequency DMD modes all share a common structure, characterized by perturbations along the shock, together with streamwise-elongated regions of low and high momentum that originate at the shock foot and extend into the downstream flow. A linear superposition of these modes, with dynamics governed by their corresponding DMD eigenvalues, accurately captures the unsteadiness of the shock. In addition, DMD analysis shows that the downstream regions of low and high momentum are unsteady and that their unsteadiness is linked to the unsteadiness of the shock. The observed flow structures in the downstream flow are reminiscent of Görtler-like vortices that are present in this type of flow due to an underlying centrifugal instability, suggesting a possible physical mechanism for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions.
Highlights
Shock wave/turbulent boundary layer interactions (STBLIs) are typically unsteady across a broad range of frequencies
The present analysis finds that the low-frequency dynamics observed in STBLIs is not associated with any single dominant dynamic mode decomposition (DMD) mode, but rather, it is the result of interactions between a number of low-frequency DMD modes
The DMD spectrum shows several modes in the range of low frequencies of interest (St < 0.1). These low-frequency modes share a similar structure, consisting of streamwise-elongated regions of low- and high-momentum perturbations, which originate at the separation shock foot and extend downstream into the separated flow and further into the reattached flow on the ramp. In addition to these perturbations in the downstream flow, the low-frequency DMD modes show significant perturbations along the shock, which are consistent with streamwise excursions of the shock about its average location
Summary
Shock wave/turbulent boundary layer interactions (STBLIs) are typically unsteady across a broad range of frequencies. In addition to high-frequency unsteadiness, which is associated with turbulent fluctuations, STBLIs in the supersonic regime display a characteristic low-frequency unsteadiness (Dolling 2001; Smits & Dussauge 2006; Clemens & Narayanaswamy 2014). The low-frequency unsteadiness is present in separated STBLIs, i.e. when the shock is sufficiently strong to separate the boundary layer in the mean. Evidence for low-frequency unsteadiness has been observed when the probability of instantaneous flow separation is high but no mean flow separation is observed (Souverein et al 2010). P. Martín which is broadband, involves oscillations of the shock in the streamwise direction and corresponding variations in the size of the separated flow
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
