scholarly journals Low-frequency dynamics in a shock-induced separated flow

2016 ◽  
Vol 807 ◽  
pp. 441-477 ◽  
Author(s):  
Stephan Priebe ◽  
Jonathan H. Tu ◽  
Clarence W. Rowley ◽  
M. Pino Martín
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Low Frequency ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
High Momentum ◽  
Mean Flow ◽  
Linear Superposition ◽  
Downstream Flow

The low-frequency unsteadiness in the direct numerical simulation of a Mach 2.9 shock wave/turbulent boundary layer interaction with mean flow separation is analysed using dynamic mode decomposition (DMD). The analysis is applied both to three-dimensional and spanwise-averaged snapshots of the flow. The observed low-frequency DMD modes all share a common structure, characterized by perturbations along the shock, together with streamwise-elongated regions of low and high momentum that originate at the shock foot and extend into the downstream flow. A linear superposition of these modes, with dynamics governed by their corresponding DMD eigenvalues, accurately captures the unsteadiness of the shock. In addition, DMD analysis shows that the downstream regions of low and high momentum are unsteady and that their unsteadiness is linked to the unsteadiness of the shock. The observed flow structures in the downstream flow are reminiscent of Görtler-like vortices that are present in this type of flow due to an underlying centrifugal instability, suggesting a possible physical mechanism for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions.

scholarly journals Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction

2012 ◽  
Vol 700 ◽  
pp. 16-28 ◽  
Author(s):  
Muzio Grilli ◽  
Peter J. Schmid ◽  
Stefan Hickel ◽  
Nikolaus A. Adams
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Separation Bubble ◽  
Low Frequency ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Layer Interaction ◽  
Mode Decomposition ◽  
Boundary Layer Interaction ◽  
Low Frequency Motion

AbstractThe unsteady behaviour in shockwave turbulent boundary layer interaction is investigated by analysing results from a large eddy simulation of a supersonic turbulent boundary layer over a compression–expansion ramp. The interaction leads to a very-low-frequency motion near the foot of the shock, with a characteristic frequency that is three orders of magnitude lower than the typical frequency of the incoming boundary layer. Wall pressure data are first analysed by means of Fourier analysis, highlighting the low-frequency phenomenon in the interaction region. Furthermore, the flow dynamics are analysed by a dynamic mode decomposition which shows the presence of a low-frequency mode associated with the pulsation of the separation bubble and accompanied by a forward–backward motion of the shock.

scholarly journals Direct numerical simulation of conical shock wave–turbulent boundary layer interaction

2019 ◽  
Vol 877 ◽  
pp. 167-195 ◽  
Author(s):  
Feng-Yuan Zuo ◽  
Antonio Memmolo ◽  
Guo-ping Huang ◽  
Sergio Pirozzoli
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Shear Stresses ◽  
Mean Flow ◽  
Conical Shock

Direct numerical simulation of the Navier–Stokes equations is carried out to investigate the interaction of a conical shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number $M_{\infty }=2.05$ and Reynolds number $Re_{\unicode[STIX]{x1D703}}\approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $\unicode[STIX]{x1D703}_{c}=25^{\circ }$. As found in experiments, the wall pressure exhibits a distinctive N-wave signature, with a sharp peak right past the precursor shock generated at the cone apex, followed by an extended zone with favourable pressure gradient, and terminated by the trailing shock associated with recompression in the wake of the cone. The boundary layer behaviour is strongly affected by the imposed pressure gradient. Streaks are suppressed in adverse pressure gradient (APG) zones, but re-form rapidly in downstream favourable pressure gradient (FPG) zones. Three-dimensional mean flow separation is only observed in the first APG region associated with the formation of a horseshoe vortex, whereas the second APG region features an incipient detachment state, with scattered spots of instantaneous reversed flow. As found in canonical geometrically two-dimensional wedge-generated shock–boundary layer interactions, different amplification of the turbulent stress components is observed through the interacting shock system, with approach to an isotropic state in APG regions, and to a two-component anisotropic state in FPG. The general adequacy of the Boussinesq hypothesis is found to predict the spatial organization of the turbulent shear stresses, although different eddy viscosities should be used for each component, as in tensor eddy-viscosity models, or in full Reynolds stress closures.

Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number

2017 ◽  
Vol 823 ◽  
pp. 617-657 ◽  
Author(s):  
Vito Pasquariello ◽  
Stefan Hickel ◽  
Nikolaus A. Adams
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
High Reynolds Number ◽  
Separation Bubble ◽  
Low Frequency ◽  
Boundary Layer Interaction ◽  
High Reynolds ◽  
Unsteady Effects

We analyse the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES) reproduces recent experiments for the interaction of a Mach 3 turbulent boundary layer with an impinging shock that nominally deflects the incoming flow by $19.6^{\circ }$. The Reynolds number based on the incoming boundary-layer thickness of $Re_{\unicode[STIX]{x1D6FF}_{0}}\approx 203\times 10^{3}$ is considerably higher than in previous LES studies. The very long integration time of $3805\unicode[STIX]{x1D6FF}_{0}/U_{0}$ allows for an accurate analysis of low-frequency unsteady effects. Experimental wall-pressure measurements are in good agreement with the LES data. Both datasets exhibit the distinct plateau within the separated-flow region of a strong SWBLI. The filtered three-dimensional flow field shows clear evidence of counter-rotating streamwise vortices originating in the proximity of the bubble apex. Contrary to previous numerical results on compression ramp configurations, these Görtler-like vortices are not fixed at a specific spanwise position, but rather undergo a slow motion coupled to the separation-bubble dynamics. Consistent with experimental data, power spectral densities (PSD) of wall-pressure probes exhibit a broadband and very energetic low-frequency component associated with the separation-shock unsteadiness. Sparsity-promoting dynamic mode decompositions (SPDMD) for both spanwise-averaged data and wall-plane snapshots yield a classical and well-known low-frequency breathing mode of the separation bubble, as well as a medium-frequency shedding mode responsible for reflected and reattachment shock corrugation. SPDMD of the two-dimensional skin-friction coefficient further identifies streamwise streaks at low frequencies that cause large-scale flapping of the reattachment line. The PSD and SPDMD results of our impinging SWBLI support the theory that an intrinsic mechanism of the interaction zone is responsible for the low-frequency unsteadiness, in which Görtler-like vortices might be seen as a continuous (coherent) forcing for strong SWBLI.

Experimental study of unsteadiness in supersonic shock-wave/turbulent boundary-layer interactions with separation

2010 ◽  
Vol 114 (1155) ◽  
pp. 299-308 ◽  
Author(s):  
D. Estruch ◽  
D. G. MacManus ◽  
D. P. Richardson ◽  
N. J. Lawson ◽  
K. P. Garry ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
High Speed ◽  
Low Frequency ◽  
Fast Response ◽  
Recirculation Region ◽  
Supersonic Wind Tunnel ◽  
Supersonic Shock ◽  
Fluctuation Energy

AbstractShock-wave/turbulent boundary-layer interactions (SWTBLIs) with separation are known to be inherently unsteady but their physical mechanisms are still not totally understood. An experimental investigation has been performed in a supersonic wind tunnel at a freestream flow Mach number of 2·42. The interaction between a shock wave created by a shock generator (α = 3°, α = 9°, α = 13° and α = 15° deflection angles) and a turbulent boundary layer with thickness δ = 5mm has been studied. High-speed Schlieren visualisations have been obtained and used to measure shock wave unsteadiness by means of digital image processing. In the interactions with separation, the reflected shock’s unsteadiness has been in the order of 102Hz. High-speed wall pressure measurements have also been obtained with fast-response micro-transducers along the interactions. Most of the energy of the incoming turbulent boundary layer is broadband and at high frequencies (>104Hz). An addition of low-frequency (<104Hz) fluctuation energy is found at separation. Along the interaction region, the shock impingement results in an amplification of fluctuation energy due to the increase in pressure. Under the main recirculation region core there is only an increase in high frequency energy (>104Hz). Amplification of lower frequency fluctuation energy (>103Hz) is also observed close to the separation and reattachment regions.

scholarly journals Separated shear layer effect on shock-wave/turbulent-boundary-layer interaction unsteadiness

2018 ◽  
Vol 848 ◽  
pp. 154-192 ◽  
Author(s):  
David Estruch-Samper ◽  
Gaurav Chandola
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Shear Layer ◽  
Low Frequency ◽  
Separated Flow ◽  
Layer Interaction ◽  
Separation Shock ◽  
Separated Shear Layer ◽  
Boundary Layer Interaction

This paper presents an experimental study on shock-wave/turbulent-boundary-layer interaction unsteadiness and delves specifically into the shear layer’s role. A range of axisymmetric step-induced interactions is investigated and the scale of separation is altered by over an order of magnitude – mass in the recirculation by two orders – while subjected to constant separation-shock strength. The effect of the separated shear layer on interaction unsteadiness is thus isolated and its kinematics are characterised. Results point at a mechanism whereby the depletion of separated flow is dictated by the state of the large eddy structures at their departure from the bubble. Low-frequency pulsations are found to adjust in response and sustain a reconciling view of an entrainment–recharge process, with both an inherent effect of the upstream boundary layer on shear layer inception and an increase in the mass locally acquired by eddies as they develop downstream.

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