Analysis of the dynamic characteristics in the supersonic wake using dynamic mode decomposition

Numerical research is carried out to investigate the dynamics of the wake behind a wedge in the supersonic flow. Large eddy simulation (LES) is employed to acquire the flow field parameters in a period, then Dynamic mode decomposition (DMD) is employed to analyze the LES data. First DMD is used to analysis the whole wake area. A single peak can be found in the DMD spectrum, corresponding to the Strouhal (St) number of 0.395. The x-component of the mode corresponding to this frequency shows an asymmetric pattern, while the y-component is of symmetric pattern. To examine the development process of the dynamics in the wake area, the wake area is divided into five sub-areas. Local peaks corresponding to approximately the same value in different sub-areas are examined together. The DMD modes corresponding to these frequencies of different sub-areas are found to represent the same characteristics develop along the flow direction. Three main characteristics can be identified in the wake area. The first one is a three-dimensional structure with a spanwise wave length of about 1.2d. This three-dimensional structure is identified as the same structure appears in low Re flows name Mode B, and the frequency is nearly half of the primary karman vortex shedding. The second one is a two-dimensional structure which represents the karman vortex, which has the same frequency with that of the whole wake area DMD analysis, corresponding to st = 0.395. The third structure also displays a three-dimensional structure, in which the wave convects downstream inclined to the spanwise direction. The frequency of these structures corresponds to st = 0.40, which is slightly higher than the parallel shedding. Coexistence of the three-dimensional characteristics, identified as Mode B and oblique shedding, with the two-dimensional parallel shedding is also confirmed in the supersonic wake flow. However, the three-dimensional characteristics gradually diminish as a result of the unstable nature, whereas the two-dimensional characteristics are amplified along the wake.