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.

Experimental Investigation on the Time–Space Evolution of a Laminar Separation Bubble by Proper Orthogonal Decomposition and Dynamic Mode Decomposition

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
D. Lengani ◽  
D. Simoni ◽  
M. Ubaldi ◽  
P. Zunino ◽  
F. Bertini
Keyword(s):  
Separation Bubble ◽  
Low Frequency ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Laminar Separation Bubble ◽  
Laminar Separation ◽  
Time Space ◽  
Mode Decomposition ◽  
Low Frequency Motion ◽  
Proper Orthogonal

A time-resolved particle image velocimetry (TR-PIV) system has been employed to investigate a laminar separation bubble which is induced by a strong adverse pressure gradient typical of ultrahigh-lift low-pressure turbine (LPT) blades. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are described and applied within this paper. These techniques allow reducing the degrees-of-freedom of complex systems producing a low-order model ranked by the energy content (POD) or by the modal contribution to the dynamics of the system itself (DMD), useful to highlight the dominant dynamics. The time–space evolution of the laminar separation bubble is characterized by rollup vortices shed in the surrounding of the bubble maximum displacement as a consequence of the Kelvin–Helmholtz (KH) instability process as well as by a low-frequency motion of the separated shear layer. The decomposition techniques proposed allow the identification of these coherent structures and the characterization of their modal properties (e.g., temporal frequency, spatial wavelength, and growth rate). The POD separates the different dynamics that induce velocity fluctuations at different frequencies and wavelength looking at their contribution to the overall kinetic energy. The DMD provides complementary information: the unstable spatial frequencies are identified with their growth (or decay) rates. DMD modes associated with the Kelvin–Helmholtz instability and the corresponding vortex shedding phenomenon clearly dominate the unsteady behavior of the laminar separation bubble, being characterized by the highest growth rate. Modes with longer wavelength describe the low-frequency motion of the laminar separation bubble and are neutrally stable. Results reported in this paper prove the ability of the present methods in extracting the dominant dynamics from a large dataset, providing robust and rapid tools for the in depth analysis of transition and separation processes.

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.

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 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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