10.1063/1.4906219.3

Abstract

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 rocket walls, leading to the shear layer instability process to be amplified. The induced velocity fluctuations in the wake and the ultimately resulting pressure perturbations on the after-body feature three global characteristic frequency ranges, depending on the streamwise position inside the cavity. The most dominant peaks are detected at SrD r3 = 0.85 ± 0.075 near the nozzle exit, while the lower frequency peaks, in the range of SrD r2 = 0.55 ± 0.05 and SrD r1 = 0.25 ± 0.05, are found to be dominant closer to the rocket’s base. A sparse promoting DMD algorithm is applied to the time-resolved velocity field to clarify the origin of the detected peaks. This analysis extracts three low-frequency spatial modes at SrD = 0.27, 0.56, and 0.85. From the three-dimensional shape of the DMD modes and the reconstructed modulation of the mean flow in time, it is deduced that the detected most dominant peaks of SrD r3 ≈ 0.85 are caused by the radial flapping motion of the shear layer, while the middle-frequency range of SrD r2 ≈ 0.55 is found to be associated with its swinging motion. The less intensive peaks of SrD r1 ≈ 0.25 pronounced on the base wall are caused by the low-frequency longitudinal pumping of the two toroidal large-scale vortices inside the cavity.