Investigations of Unsteady Transonic and Supersonic Wake Flow of Generic Space Launcher Configurations Using Zonal RANS/LES and Dynamic Mode Decomposition

Dynamic mode decomposition (DMD) is applied to time-resolved results of zonal RANS/LES computations of three different axisymmetric generic space launcher configurations having freestream Mach numbers of 0. 7 and 6. 0. Two different after-body geometries consisting of an attached sting support mimicking an endless nozzle extension and an attached cylindrical after-expanding nozzle are considered. The distinguishing feature of the investigated configurations is the presence of a separation bubble in the wake region. The dynamics of the bubble and the dominant frequencies are analyzed using DMD. The results are then compared to the findings of spectral analysis and temporal filtering techniques. The transonic case displays distinct peaks in the Fourier transform spectra. We illustrate a close agreement between the frequencies of the DMD modes and the aforementioned peaks. From the shape of the DMD modes, it is deduced that most of the peaks are related to the dynamics of the separation bubble and the corresponding shear layer. The same geometry with higher Mach number shows the existence of two distinct DMD modes of axisymmetric and helical nature, respectively. The presence of the helical mode is illustrated through composite DMD of the cylindrical velocity components. Finally, when considering the free-flight configuration we were able to identify DMD modes with frequency Sr D ≈ 1 which results in the flapping motion of the shear layer and a mode of a lower frequency which causes the breathing of the recirculation bubble.