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

Published online by Cambridge University Press:  22 June 2017

Vito Pasquariello Open the ORCID record for Vito Pasquariello [Opens in a new window] ,
Stefan Hickel Open the ORCID record for Stefan Hickel [Opens in a new window]  and
Nikolaus A. Adams
Vito Pasquariello*
Affiliation:
Technical University of Munich, Department of Mechanical Engineering, Chair of Aerodynamics and Fluid Mechanics, Boltzmannstr. 15, D-85748 Garching bei München, Germany
Stefan Hickel
Affiliation:
Technische Universiteit Delft, Faculty of Aerospace Engineering, P.O. Box 5058, 2600 GB Delft, The Netherlands
Nikolaus A. Adams
Affiliation:
Technical University of Munich, Department of Mechanical Engineering, Chair of Aerodynamics and Fluid Mechanics, Boltzmannstr. 15, D-85748 Garching bei München, Germany
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Boundary Layers: Boundary layer separation Turbulent Flows: Compressible turbulence Compressible Flows: Shock waves
Type
Papers
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Journal of Fluid Mechanics , Volume 823 , 25 July 2017 , pp. 617 - 657
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© 2017 Cambridge University Press 

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Pasquariello et al. supplementary movie

DMD analysis of spanwise-averaged snapshots. Flow modulation by means of mode Φ1. The animation shows contours of the pressure gradient magnitude in the range │∇p│δ0/p∞ = [0,10] at 8 equally spaced phase angles. The mean shock system together with the instantaneous separation bubble are highlighted by black solid lines.

Download Pasquariello et al. supplementary movie(Video)
Video 1.2 MB

Pasquariello et al. supplementary movie

DMD analysis of spanwise-averaged snapshots. Flow modulation by means of mode Φ2. The animation shows contours of the pressure gradient magnitude in the range │∇p│δ0/p∞ = [0,10] at 8 equally spaced phase angles. The mean shock system together with the instantaneous separation bubble are highlighted by black solid lines.

Download Pasquariello et al. supplementary movie(Video)
Video 1.1 MB

Pasquariello et al. supplementary movie

DMD analysis of spanwise-averaged snapshots. Flow modulation by means of mode Φ3. The animation shows contours of the pressure gradient magnitude in the range │∇p│δ0/p∞ = [0,10] at 8 equally spaced phase angles. The mean shock system together with the instantaneous separation bubble are highlighted by black solid lines.

Download Pasquariello et al. supplementary movie(Video)
Video 864.2 KB

Pasquariello et al. supplementary movie

MDMD analysis of spanwise-averaged snapshots. Flow modulation by means of mode Φ4. The animation shows contours of the pressure gradient magnitude in the range │∇p│δ0/p∞ = [0,10] at 8 equally spaced phase angles. The mean shock system together with the instantaneous separation bubble are highlighted by black solid lines.

Download Pasquariello et al. supplementary movie(Video)
Video 796.4 KB

Pasquariello et al. supplementary movie

DMD analysis of wall-plane snapshots. Flow modulation by means of mode Φ1. The animation shows contours of the two-dimensional skin-friction coefficient at 8 equally spaced phase angles. The instantaneous separation and reattachment locations are highlighted by black solid lines.

Download Pasquariello et al. supplementary movie(Video)
Video 2.5 MB

Pasquariello et al. supplementary movie

DMD analysis of wall-plane snapshots. Flow modulation by means of mode Φ2. The animation shows contours of the two-dimensional skin-friction coefficient at 8 equally spaced phase angles. The instantaneous separation and reattachment locations are highlighted by black solid lines.

Download Pasquariello et al. supplementary movie(Video)
Video 2.3 MB

Pasquariello et al. supplementary movie

DMD analysis of wall-plane snapshots. Flow modulation by means of mode Φ3. The animation shows contours of the two-dimensional skin-friction coefficient at 8 equally spaced phase angles. The instantaneous separation and reattachment locations are highlighted by black solid lines.

Download Pasquariello et al. supplementary movie(Video)
Video 1.6 MB

Pasquariello et al. supplementary movie

DMD analysis of wall-plane snapshots. Flow modulation by means of mode Φ3. The animation shows contours of the two-dimensional skin-friction coefficient at 8 equally spaced phase angles. The instantaneous separation and reattachment locations are highlighted by black solid lines.

Download Pasquariello et al. supplementary movie(Video)
Video 1.6 MB