Instability and low-frequency unsteadiness in a shock-induced laminar separation bubble

Three-dimensional direct numerical simulations (DNS) of a shock-induced laminar separation bubble are carried out to investigate the flow instability and origin of any low frequency unsteadiness. A laminar boundary-layer interacting with an oblique shock-wave at M = 1:5 is forced at the inlet with a pair of monochromatic oblique unstable modes, selected according to local linear stability theory (LST) performed within the separation bubble. Linear stability analysis is applied to cases with marginal and large separation, and compared to DNS. While the parabolized stability equations approach accurately reproduces the growth of unstable modes, LST performs less well for strong interactions. When the modes predicted by LST are used to force the separated boundary-layer, transition to deterministic turbulence occurs near the reattachment point via an oblique-mode breakdown. Despite the clean upstream condition, broadband low-frequency unsteadiness is found near the separation point with a peak at a Strouhal number of 0:04, based on the separation bubble length. The appearance of the low-frequency unsteadiness is found to be due to the breakdown of the deterministic turbulence, filling up the spectrum and leading to broadband disturbances that travel upstream in the subsonic region of the boundary-layer, with a strong response near the separation point. The existence of the unsteadiness is supported by sensitivity studies on grid resolution and domain size that also identify the region of deterministic breakdown as the source of white noise disturbances. The present contribution confirms the presence of low-frequency response for laminar flows, similarly to that found in fully turbulent interactions

Three-dimensional instability of a ow past a sphere: Mach evolution of the regular and Hopf bifurcations

A fully three-dimensional linear stability analysis is carried out to investigate the unstable bifurcations of a compressible viscous fluid past a sphere. A time-stepper technique is used to compute both equilibrium states and leading eigenmodes. In agreement with previous studies, the numerical results reveal a regular bifurcation under the action of a steady mode and a supercritical Hopf bifurcation that causes the onset of unsteadiness but also illustrate the limitations of previous linear approaches, based on parallel and axisymmetric base flow assumptions, or weakly nonlinear theories. The evolution of the unstable bifurcations is investigated up to low-supersonic speeds. For increasing Mach numbers, the thresholds move towards higher Reynolds numbers. The unsteady fluctuations are weakened and an axisymmetrization of the base flow occurs. For a sufficiently high Reynolds number, the regular bifurcation disappears and the flow directly passes from an unsteady planar-symmetric solution to a stationary axisymmetric stable one when the Mach number is increased. A stability map is drawn by tracking the bifurcation boundaries for different Reynolds and Mach numbers. When supersonic conditions are reached, the flow becomes globally stable and switches to a noise-amplifier system. A continuous Gaussian white noise forcing is applied in front of the shock to examine the convective nature of the flow. A Fourier analysis and a dynamic mode decomposition show a modal response that recalls that of the incompressible unsteady cases. Although transition in the wake does not occur for the chosen Reynolds number and forcing amplitude, this suggests a link between subsonic and supersonic dynamics

System Identification of Two-Dimensional Transonic Buffet

When modeled within the unsteady Reynolds-Averaged Navier-Stokes framework, the shock-wave dynamics on a two-dimensional aerofoil at transonic buffet conditions is char- acterized by time-periodic oscillations. Given the time series of the lift coefficient at different angles of attack for the OAT15A supercritical profile, the sparse identification of nonlinear dy- namics (SINDy) technique is used to extract a parametrized, interpretable and minimal-order description of this dynamics. For all of the operating conditions considered, SINDy infers that the dynamics in the lift coefficient time series can be modeled by a simple parametrized Stuart-Landau oscillator, reducing the computation time from hundreds of core hours to sec- onds. The identified models are then supplemented with equally parametrized measurement equations and low-rank DMD representation of the instantaneous state vector to reconstruct the true lift signal and enable real-time estimation of the whole flow field. Simplicity, accuracy and interpretability make the identified model a very attractive tool towards the construction of real-time systems to be used during the design, certification and operational phases of the aircraft life cycle

Stability and unsteadiness of transitional shock-wave/boundary-layer interactions in supersonic flows

The aim of this research is to study the effect of transition location on the interaction between an oblique shock-wave and a boundary-layer. A large set of direct and large eddy simulations are performed with an in-house high-order fully-parallelised finite difference compressible Navier-Stokes solver to study the inherent instability and unsteady behaviour of laminar, transitional and turbulent interactions. The numerical simulations are compared with the experiments conducted at the Novosibirsk State University as part of the EU-FP7 TFAST project, providing a better understanding of the fundamental mechanisms of the shock-wave/boundary-layer interaction (SWBLI). As well as the characteristics of the interactions, interest is also focused on methods to control the transition location. Three distinct forcing techniques are used to obtain different transition scenarios for a laminar SWBLI at free-stream Mach number of 1.5. An oblique mode breakdown caused by forcing the most unstable eigenmodes, predicted by the local linear stability theory, is compared with a bypass-like transition due to high-amplitude free-stream acoustic disturbances. A non-thermal plasma flow actuation device is also used, however showing a low applicability to supersonic flows due to the high electric power required to trigger transition. Attention is also focused on the response of a laminar shock-induced separation bubble. For both 2D and 3D configurations, a low-frequency response is found for the first time in a laminar SWBLI, even when the separation bubble is only forced internally, therefore supporting the idea that the separated region is influenced by internal mechanisms. The SWBLI is further analysed via linear and nonlinear stability approaches, including local stability theory or parabolised stability equations based tools. The response of the separated region for increasing shock intensities is studied and the stability based tools provide satisfactory results even for largely separated boundary-layer

Transition location effect on oblique shock-wave/boundary-layer Interaction at M=1.5

The effect of transition location on the interaction between an oblique shock-wave and a boundary-layer at M=1.5 on a flat plate is investigated via direct numerical simulations. It is shown that the shock trips transition at the impingement location and the effect of the impingement location on the separation is studied for laminar, transitional and turbulent interactions. Qualitative agreement is obtained with the experiments, as part of the European FP7-2012 TFAST project

Effect of the Mach number on the instabilities of flow around a sphere

International audienc

Three-Dimensional Instability of Shock-Wave/Boundary-Layer Interaction for Rocket Engine Nozzle Applications

International audienceA fully three-dimensional analysis is carried out on an over-expanded rocket enginenozzle configuration in order to investigate the role of the internal shock-induced separationon the mechanism of generation of side loads during start-up and shut-down transients. Ahybrid URANS/LES approach based on the delayed detached eddy simulations turbulencemodel is used. Reasonable good agreement is obtained between numerical and experimentalresults. The wall-pressure spectrum shows a narrow peak at f≈2000 Hz and a dynamic modedecomposition reveals this to be associated to a mode whose characteristics resemble theexperimental azimuthal mode believed to be the cause of the generation of side loads