A novel passive flow-control method for shock-wave/turbulent boundary-layer interactions (STBLI) is investigated. The method relies on a structured roughness pattern constituted by streamwise-aligned ridges. Its effectiveness is assessed with wall-resolved large-eddy simulations of the interaction of a Mach 2 turbulent boundary layer flow with an oblique impinging shock with shock angle 40^∘. The structured roughness pattern, which is fully resolved by a cut-cell based immersed boundary method, covers the entire computational domain. Results show that this rough surface induces large-scale secondary streamwise vortices, which energize the boundary layer by transporting high-speed fluid closer to the wall. A parametric study is performed to investigate the effect of the spacing between the ridges. This investigation is further substantiated through spectral analysis and sparsity-promoting dynamic mode decomposition. We find that ridges with small spacing effectively mitigate the low-frequency unsteadiness of STBLI and slightly reduce total-pressure loss.

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We investigate Reynolds number effects in strong shock-wave/turbulent boundary-layer interactions (STBLI) by leveraging a new database of wall-resolved and long-integrated large-eddy simulations. The database encompasses STBLI with massive boundary-layer separation at Mach 2.0, impinging-shock angle 40^◦ and friction Reynolds numbers Re_τ 355, 1226 and 5118. Our analysis shows that the shape of the reverse-flow bubble is notably different at low and high Reynolds number, while the mean-flow separation length, separation-shock angle and incipient plateau pressure are rather insensitive to Reynolds number variations. Velocity statistics reveal a shift in the peak location of the streamwise Reynolds stress from the separation-shock foot to the core of the detached shear layer at high Reynolds number, which we attribute to increased pressure transport in the separation-shock excursion domain. Additionally, in the high Reynolds case, the separation shock originates deep within the turbulent boundary, resulting in intensified wall-pressure fluctuations and spanwise variations associated with the passage of coherent velocity structures. Temporal spectra of various signals show energetic low-frequency content in all cases, along with a distinct peak in the bubble-volume spectra at a separation-length-based Strouhal number St_Lsep ≈ 0.1. The separation shock is also found to lag behind bubble-volume variations, consistent with the acoustic propagation time from reattachment to separation and a downstream mechanism driving the shock motion. Finally, dynamic mode decomposition of three-dimensional fields suggests a Reynolds-independent statistical link among separation-shock excursions, velocity streaks and large-scale vortices at low frequencies.

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The dynamic coupling between a Mach 2.0 shock-wave/turbulent boundary-layer interaction (STBLI) and a flexible panel is investigated. Wall-resolved large-eddy simulations are performed for a baseline interaction over a flat-rigid wall, a coupled interaction with a flexible panel, and a third interaction over a rigid surface that is shaped according to the mean panel deflection of the coupled case. Results show that the flexible panel exhibits self-sustained oscillatory behavior over a broad frequency range, confirming the strong and complex fluid-structure interaction (FSI). The first three bending modes of the panel oscillation are found to contribute most to the unsteady panel response, at frequencies in close agreement with natural frequencies of the mean deformed panel rather than those for the unloaded flat panel. This highlights the importance of the mean panel deformation and the corresponding stiffening in the FSI dynamics. The time-averaged flow shows an enlarged reverse-flow region in the presence of mean surface deformations. The separation-shock unsteadiness is enhanced due to the panel motion, leading to higher wall-pressure fluctuations in the coupled interaction. Spectral analysis of the separation-shock location and bubble-volume signals shows that the STBLI flow strongly couples with the first bending mode of the panel oscillation. This is further confirmed by dynamic mode decomposition of the flow and displacement data, which reveals variations in the reverse-flow region that follow the panel bending motion and appear to drive the separation-shock unsteadiness. Low-frequency modes that are not associated with the fluid-structure coupling, in turn, are qualitatively similar to those obtained for the rigid-wall interactions, indicating that the characteristic low-frequency unsteadiness of STBLI coexists with the dynamics emerging from the fluid-structure coupling. Based on the present results, unsteady FSIs involving STBLIs and flexible panels are likely to accentuate rather than mitigate the undesirable features of STBLIs.

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We revisit the origin of low-frequency unsteadiness in turbulent recirculation bubbles (TRBs), and, in particular, the hypothesis of a dynamic feedback mechanism between unconstrained separation and reattachment locations. To this end, we conduct wall-resolved large-eddy simulations of a novel experimental configuration where a shock-induced TRB forms over a backward-facing step that is intended to intercept the hypothesized dynamic feedback. Our results demonstrate, for the first time, effective suppression of the low-frequency characteristics of the TRB without reducing its size, strongly supporting our hypothesis.

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We propose several enhancements to improve the accuracy and performance of the digital filter turbulent inflow generation technique and assess their efficacy in the context of wall-resolved large-eddy simulations of a compressible turbulent boundary layer. Improvements of accuracy include a more realistic correlation function for the transversal directions, target length scales that vary with wall-distance, and a counter-intuitive approach that involves the suppression of streamwise velocity fluctuations at the inflow. For improving the computational performance, we propose to generate the inflow data in parallel in single precision and at a prescribed time interval based on the turbulence time scale, and not at every time-step of the simulation. Based on the results of 7 wall-resolved large-eddy simulations, we find that the new correlation functions and the considered performance improvements are beneficial and therefore desired. Suppressing streamwise velocity fluctuations at the inflow leads to the fastest relaxation of the pressure fluctuations; however, this approach increases the adaptation length defined in terms of compliance with the von Kármán integral equation. The adaptation length can be shortened by artificially increasing the wall-normal Reynolds stresses, thereby preserving the desired turbulence kinetic energy level. A detailed inspection of the Reynolds stress transport budgets reveals that the observed spurious spatial transients are largely driven by pressure-related terms. For instance, increased values of u^′p^′¯ are found throughout the computational domain when a physical Reynolds stress distribution is prescribed at the inflow. Therefore, efforts to enhance digital filter techniques should aim at modeling pressure fluctuations as well as their correlation with the velocity components.

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Wall-resolved large-eddy simulations (LES) are performed to investigate Reynolds number effects in supersonic turbulent boundary layers (TBLs) at Mach 2.0. The resulting database covers more than a decade of friction Reynolds number Re_τ, from 242 to 5554, which considerably extends the parameter range of current high-fidelity numerical studies. Reynolds number trends are identified on a variety of statistics for skin-friction, velocity and thermodynamic variables. The efficacy of recent scaling laws as well as compressibility effects are also assessed. In particular, we observe the breakdown of Morkovin's hypothesis for third-order velocity statistics, in agreement with previous observations for variable-property flows at low Mach number. Special attention is also placed on the size and topology of the turbulent structures populating the TBL, with an emphasis on the outer-layer motions at high Reynolds number. The corresponding streamwise spectra of streamwise velocity fluctuations show a clear separation between inner and outer scales, where energetic peaks are found at streamwise wavelengths of λ_x⁺≈700 and λ_x/δ₀≈6. The spanwise spacing of the outer-layer structures, in turn, is found to be insensitive to the Reynolds number and equal to ∼0.7δ₀. It is also found that the integral length-scales in spanwise direction for the temperature, streamwise and spanwise velocity fields appear to progressively collapse with increasing Reynolds number. The modulating influence that the outer-layer structures exert on the near-wall turbulence is also clearly visible in many of the metrics discussed. In addition, the present LES data is further exploited to assess the Re_τ-sensitivity of uniform momentum regions in the flow. We find that the resulting probability density function of the number of zones as well as its evolution with Re_τ agrees well with incompressible data. This suggests that uniform zones, which have been associated with outer-layer dynamics, are not strongly influenced by compressibility at the considered Mach number.

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Wall-resolved large-eddy simulations (LES) are carried out to investigate the aeroelastic coupling between a Mach 2.0 impinging shock-wave/turbulent boundary-layer interaction (STBLI) and a flexible thin-panel. After the initial transient, the panel exhibits self-sustained oscillatory behavior with varying oscillation amplitude, confirming the strong and complex dynamic coupling over a broad frequency range. The first three bending modes of the panel oscillation are found to contribute most to the unsteady panel response. The observed modal frequencies are in close agreement with natural frequencies of the pre-stressed panel, which differ significantly from the natural frequencies of the unloaded flat panel. This highlights the importance of the mean panel deformation and the corresponding stiffening in the fluid-structure interaction (FSI) dynamics. Mean-flow shows an enlarged reverse-flow region compared to a flat rigid-wall STBLI at the same flow conditions. The separation shock is also located further upstream in the coupled case, and wall-pressure fluctuations have a higher peak at the separation-shock foot. Spectral analysis of wall-pressure, separation-shock location and bubble-volume signals indicates that the STBLI flow resonates with the panel oscillation, primarily at the first bending frequency. This is further confirmed by sparsity-promoting dynamic mode decomposition of the flow and displacement data, which identifies this frequency as the most dominant and successfully isolates the associated FSI dynamics. Based on present results, it is clear that dynamic FSI involving STBLI and flexible panels accentuates the undesirable features of STBLI.@en

We investigate Reynolds number effects in shockwave/turbulent boundary-layer interactions (STBLI) with strong mean flow separation. Three wall-resolved large-eddy simulations (LES) are performed for this purpose, with different Reynolds number but otherwise equal flow parameters and simulation setup. The resulting LES data covers more than a decade of friction Reynolds number. The high-Reynolds case, with friction Reynolds number Re_τ = 5118 and momentum Reynolds number Re_θ = 26438 at the virtual impingement point without the shock, features a turbulent boundary layer with clear inner and outer scale separation. All STBLI simulations exhibit substantial flow reversal and have been integrated for a very long time (90 flow-through times of the full domain length) to properly resolve low-frequency dynamics. Instantaneous and mean flow as well as spectral features are described in detail, together with a modal analysis of the three-dimensional streamwise velocity, streamwise vorticity and pressure fields.

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Experiments on shock–shock interactions were conducted in a transonic–supersonic wind tunnel with variable free-stream Mach number functionality. Transition between the regular interaction (RI) and the Mach interaction (MI) was induced by variation of the free-steam Mach number for a fixed interaction geometry, as opposed to most previous studies where the shock generator angles are varied at constant Mach number. In this paper, we present a systematic flow-based post-processing methodology of schlieren data that enables an accurate tracking of the evolving shock system including the precise and reproducible detection of RI⇄ MI transition. In line with previous experimental studies dealing with noisy free-stream environments, transition hysteresis was not observed. However, we show that establishing accurate values of the flow deflections besides the Mach number is crucial to achieve experimental agreement with the von Neumann criterion, since measured flow deflections deviated significantly, up to 1. 2 ^∘, from nominal wedge angles. We also report a study conducted with a focusing schlieren system with variable focal plane that supported the image processing by providing insights into the three-dimensional side-wall effects integrated in the schlieren images.

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The response of asymmetric and planar shock interactions to a continuous excitation of the lower incident shock is investigated numerically. Incident shock waves and centred expansion fans are generated by two wedges asymmetrically deflecting the inviscid free stream flow at Mach 3. The excitations mechanisms considered are (i)Â pitching of the lower wedge traversing the steady-state dual-solution domain (DSD) of regular interaction (RI) and Mach interaction (MI), (ii) a periodic (sinusoidal) oscillation of the lower wedge deflection with a mean value both within and outside of the steady-state DSD and (iii) a periodic (sinusoidal) streamwise oscillation of the lower wedge location with fixed wedge deflection. A detailed analysis of characteristic unsteady flow features, including the Mach stem growth, pressure evolution across the shock system and corresponding flow deflections and entropy rise, is presented with a focus on the bi-directional RIMI transition process. For fast pitching conditions, the MI pattern is maintained far inside the steady-state RI domain. The observed transition limit as the rotational velocity decreases does not fully match steady-state theory, however. This is attributed to geometry-related effects. In the opposite case, transition, good agreement with steady-state theoretical predictions is obtained for slow rotations, and a shock polar analysis applied in the (moving) frame of reference of the shock interaction location improves the agreement with fast pitching numerical data significantly. Furthermore, the MI pattern is found to be more robust against periodic perturbations than the corresponding RI configuration for mean flow conditions inside the steady-state DSD, which appears to be a consequence of the dynamics of the Mach stem during a period of excitation. This is not the case for mean flow conditions outside the steady-state DSD in the RI domain for which a periodic alternation occurs instead.

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An experimental investigation of shock-shock interactions has been conducted with the aim of studying the transition between Regular (RI) and Mach (MI) interactions induced by a variation of the inflow Mach number. The experiments were conducted in the TST-27 wind tunnel at Delft University of Technology. For all cases, the wind tunnel runs were initialized in the RI domain after which the Mach number was slowly decreased to the MI domain, thereby traversing the whole dual solution domain. The process was then inverted to reach again the RI domain in order to investigate a possible transition hysteresis. Both conventional Schlieren and Focusing Schlieren systems were used to visualize the shock wave patterns. The recorded Schlieren images allow accurate transition detection together with quantitative measurements of the Mach Stem Heigth (MSH). The results show no hysteresis effects. All transitions are recorded to occur at the von Neuman line, for both RI to MI and MI to RI cases. @en

The dynamic interaction of two planar and asymmetric shock waves at a free-stream Mach number M¥ = 3 is studied numerically in order to characterize the transition between the regular (RI) and Mach (MI) interaction patterns. Shock deflection disturbances are independently introduced in the form of a sinusoidal oscillation of the shock generator. Selected amplitudes of oscillations ensure that both boundaries of the theoretical dual solution domain (DSD) are crossed every period. The range of angular frequencies investigated resembles the dynamics of the separation shock in shock-wave/turbulent boundarylayer interactions. Computational results show that the MI unambiguously prevails regardless of the initial wave pattern disturbed, provided that the oscillation frequency is not too large. This holds for mean conditions embedded inside the DSD. For those outside, a RI_MI alternation is observed when the initial wave pattern is a RI, and no single event of a RI interaction occurs when the initial patter is a MI. @en