Spectral proper orthogonal decomposition of external flow at high Reynolds number

Abstract

Spectral proper orthogonal decomposition(SPOD) has been recently used to capture temporal and spatial characteristics of complex flows. Applying SPOD analysis to such flow fields can deepen the understanding of flow mechanism. To further study the external flow at high Reynolds numbers, large eddy simulation(LES) is applied to acquire the flow field data while SPOD is utilized to extract important flow structures. The considered external flow includes incompressible flow around the cylinder and transonic shock oscillation. For the flow around the cylinder, flow field under three different Reynolds numbers is studied. Power spectral density(PSD) results of lift coefficient show that the vortex shedding frequency of low Reynolds number is $St=0.24$, which of moderate Reynolds number is $St=0.203$, and $St=0.27$ for high Reynolds number flow. The increment of Reynolds number will lead to early instability of shear layer on the cylindrical surface. The modal results of SPOD and dynamic mode decomposition(DMD) at different Reynolds numbers show two antisymmetric structures at shedding vortex frequencies, indicating the resemblance in the process of vortex formation. For the shock wave/boundary layer interaction(SBLI) of transonic Royal Aircraft Establishment(RAE) 2822 airfoil, flow field under $M_{\infty }=0.729$, ${Re}_c=1.94\times 10^7$ is studied. The results show that the occurrence of unsteadiness is closely related to the normal shock wave/turbulent boundary layer interaction happening on the upper surface of the airfoil. Modal results of SPOD near the characteristic frequency show strong discontinuity near the shock wave.