501 / 2018-12-31 17:54:55

DMD as a tool for Investigation of the dynamic characteristics in the supersonic wake

dynamic characteristics, DMD, supersonic wake

全体主题 > 数值模拟、建模与CFD

Accompanied with the development of supersonic flight vehicles, the supersonic wake flow had been studied by many researchers for a long time. In order to investigate the spectrum characteristics, dynamic structure and oscillation mechanism, a numerical research is carried out. LES is employed to acquire the flow field parameters in a period of time, and then DMD analysis is performed on those parameters. A single peak is found around 48082 Hz in the DMD spectrum of the velocity field, corresponding to the Strouhal number(St number) of 0.40, based on St=f*d/U∞, in which f is the frequency, d is the base height of the wedge, and U∞ is the velocity of the free stream. St number is an important parameter characterizing the dynamics of the period flow. Behrens reported a St number of 0.42 for the supersonic wake with Re=55700 and M=4. From the St-Re relationship given by Bearman, the St number for the cylinder wake was 0.46 at a similar Re value. While the results from Achenbach show that the St number was 0.5 for Re around 10e6.
The DMD mode corresponding to St=0.4 is also extracted, and the X component and Y component of the DMD mode are analyzed. The contour of the X component of the DMD mode consists of two rows of anti-symmetric two dimensional vortex-like structures. The sizes of the structures are increasing according to the flow direction. The contour of the Y component consists of a single row of symmetric two dimensional vortex-like structures, with the positive and negative part displaying in turn. Similar to the situation of X component, the sizes of these structures increase.
In order to explore the oscillation mechanism of the supersonic wake, the dynamic characteristic of the recirculation area right behind the wedge is investigated. The DMD analysis of the velocity field is performed especially on this area. The DMD spectrum shows a dominate frequency of St=0.2, as well as a second harmonic corresponding to St=0.4 with the magnitude of two order lower. The DMD modes corresponding to St=0.2 and St=0.4 are both three dimensional structures. The instability in the recirculation area corresponding to St=0.2 disturbs the shear layers detached from the trailing edge of the wedge, and eventually lead to the oscillation in the wake area of the wedge.