V. Statnikov

Analysis of pressure perturbation sources on a generic space launcher after-body in supersonic flow using zonal turbulence modeling and dynamic mode decomposition

A sparsity promoting dynamic mode decomposition (DMD) combined with a classical data-based statistical analysis is applied to the turbulent wake of a generic axisymmetric configuration of an Ariane 5-like launcher at Ma∞ = 6.0 computed via a zonal Reynolds-averaged Navier-Stokes/large-eddy simulation (RANS/LES) method. The objective of this work is to gain a better understanding of the wake flow dynamics of the generic launcher by clarification and visualization of initially unknown pressure perturbation sources on its after-body in coherent flow patterns. The investigated wake topology is characterized by a subsonic cavity region around the cylindrical nozzle extension which is formed due to the displacement effect of the afterexpanding jet plume emanating from the rocket nozzle (Mae = 2.52, pe/p∞ = 100) and the shear layer shedding from the main body. The cavity region contains two toroidal counter-rotating large-scale vortices which extensively interact with the turbulent shear layer, jet plume, and ro...

Analysis of spatio-temporal wake modes of space launchers at transonic flow

To detect characteristic wake flow modes responsible for the buffeting phenomenon of space launchers, an optimized dynamic mode decomposition (DMD) combined with a classical statistical analysis is applied to the turbulent wake flow fields of a planar and an axisymmetric generic configuration of an Ariane 5-like launcher at transonic freestream conditions (Ma∞ = 0.8 and ReD = 6 · 10) computed via a zonal RANS-LES method. The investigated wake topologies are characterized by a highly unsteady behavior of the shear layer shedding from the forebody and subsequently reattaching on the nozzle contour. In both cases, the reattachment position features strong oscillations in the streamwise and the spanwise direction, which leads due to wall pressure oscillations to structural loads. The spectral analysis of pressure perturbations on the after-body near the mean reattachment position reveals one dominant characteristic frequency for each configuration, i.e., SrD ≈ 0.23 in the planar and SrD ≈ 0.17 in the axisymmetric case. Moreover, the instantaneous skin-friction coefficient distributions on the nozzle extensions of both configurations indicate the existence of regular longitudinal wedge-shaped patterns with an approximate spanwise/circumferential wave length of 2h in the planar and 120◦ in the axisymmetric case. To clarify the underlying coherent fluid motion responsible for the detected oscillatory behavior, DMD is applied to the time-resolved three-dimensional velocity field. The frequencies of the extracted DMD modes closely coincide with the characteristic peaks in the wall pressure spectra for both configurations. The analysis of the three-dimensional shape of the DMD modes along with the corresponding mean flow modulation in time reveals that the detected periodic behavior is caused by a coherent longitudinal cross-flapping motion of the free shear layer. In the spanwise/circumferential direction, the identified coherent motion of the free shear layer features the same wavelength of ∼ 2h in the planar and ∼ 120◦ in the axisymmetric case as previously indicated by the skin-friction coefficient distributions.

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.

Numerical Investigation of the Turbulent Wake of Generic Space Launchers

The turbulent wakes of generic space launchers are numerically investigated via a zonal RANS/LES method and optimized dynamic mode decomposition (DMD), to gain insight into characteristic wake flow modes being responsible for asymmetrical loads on the engine extension known as buffet loads. The considered launcher geometries range from planar space launchers up to axisymmetric free flight configurations investigated at varying free stream conditions, i.e. transonic and supersonic. The investigated wake topologies reveal a highly unsteady behavior of the shear layer and the separation region resulting in strongly periodic and antisymmetric wall pressure fluctuations on the nozzle surface. Using conventional spectral analysis and dynamic mode decomposition, several spatio-temporal coherent low frequency modes which are responsible for the detected pressure oscillations are identified. In addition, a passive flow control device consisting of semi-circular lobes integrated at the base shoulder of the planar configuration is investigated. The objective of the concept is to reduce the reattachment length and thus the lever arm of the forces as well as to stabilize the separated shear layer. The results show a significant reduction of the reattachment length by about 75%. In addition, the semi-circular lobes partially reduce undesired low frequency pressure fluctuations on the nozzle surface. However, this reduction is achieved at the expense of an increase of high frequency pressure fluctuations due to intensified small turbulent scales.