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Turbulent boundary layers (TBLs) over surface perturbations like bumps with roughness – notably altering heat and mass transfer, drag, etc. – are prevalent in nature (mountains, dunes, etc.) and technology. We study a channel flow with a transverse bump on one wall superimposed with small-scale longitudinal grooves via direct numerical simulation (DNS) of incompressible flow. Turbulence statistics and dynamics are compared between grooved wall (GW) and smooth wall (SW) bumps. Streamwise spinning jets emanating from the crests’ corners alter the flow structure within the separation bubble (SB), extending the SB length by 30 % over that for SW, and have lingering effects far downstream. Grooves decrease skin friction but increase the bump's form drag by 25 %. In GW, the peaks of turbulence intensity and production decrease by 20 % and shift downstream, compared with SW. Three regions of negative production, found upstream as well as downstream of the bump, are explained in terms of two separate mechanisms: normal and shear productions. Separation upstream of the bump occurs always for GW, but intermittently for SW. Within the downstream SB, counter-rotating minibubbles form intermittently for SW but always for GW. Interestingly, a minibubble causes streamwise vorticity reversal of the upstream moving secondary flow around each crest corner. The wall pressure in GW is invariant in the spanwise direction and is explained in terms of its non-local nature and its connection with outer structures. The grooved bump unearths rich TBL flow physics – upstream separation, dynamics of the downstream minibubble, altered reattachment dynamics and negative production.

A study on the generation and development of high-amplitude steady streamwise streaks in a flat-plate boundary layer is presented. High-amplitude streamwise streaks are naturally present in many bypass transition scenarios, where they play a fundamental role in the breakdown to turbulence process. On the other hand, recent experiments and numerical simulations have shown that stable laminar streamwise streaks of alternating low and high speed are also capable of stabilizing the growth of Tollmien–Schlichting waves as well as localized disturbances and to delay transition. The larger the streak amplitude is, for a prescribed spanwise periodicity of the streaks, the stronger is the stabilizing mechanism. Previous experiments have shown that streaks of amplitudes up to 12 % of the free stream velocity can be generated by means of cylindrical roughness elements. Here we explore the possibility of generating streaks of much larger amplitude by using a row of miniature vortex generators (MVGs) similar to those used in the past to delay or even prevent boundary layer separation. In particular, we present a boundary layer experiment where streak amplitudes exceeding 30 % have been produced without having any secondary instability acting on them. Furthermore, the associated drag with the streaky base flow is quantified, and it is demonstrated that the streaks can be reinforced by placing a second array of MVGs downstream of the first one. In this way it is possible to make the control more persistent in the downstream direction. It must be pointed out that the use of MVGs opens also the possibility to set up a control method that acts twofold in the sense that both transition and separation are delayed or even prevented.

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.

Suitable slot structure of the compressor blade can generate high-momentum jet flow through pressure difference between the pressure and suction surface, it has been proved that the slot jet flow can reenergize the local low-momentum fluid to effectively suppress the flow separation on the suction surface. In order to explore a slotted method for better comprehensive suppressing effects on the boundary layer separation near blade midspan and the three-dimensional corner separation, a diffusion stator cascade with large camber angle is selected as the research object. Firstly, the Slotted_1 and Slotted_2 whole-span slotted schemes are set up, then the Slotted_3 scheme with whole-span slot and blade-end slots is proposed, finally the performance of original cascade and slotted cascades is computed under a wide range of incidence angles at the Mach number of 0.7. The results show that: in the full range of incidence angles, compared with the whole-span slotted cascades, the development of the endwall secondary flow on the suction surface of Slotted_3 cascade is effectively suppressed, the degree of the mutual interference between the secondary flow and the main flow is reduced. Besides, on the suction surface of Slotted_3 cascade, the boundary layer separation near blade midspan and the corner separation are basically eliminated. As a result, compared with those of original cascade, the total pressure losses of Slotted_3 cascade are reduced in the full range of incidence angles, and its operating range of incidence angles is broadened. Moreover, compared with the whole-span slotted schemes, Slotted_3 scheme has a better adaptability to wide range of incidence angles.

Experiments were conducted to study the transition and flow development in a laminar separation bubble (LSB) formed on an aerofoil. The effects of a wide range of free-stream turbulence intensity ($0.15\\,\\%< Tu<6.26\\,\\%$) and streamwise integral length scale ($4.6\\ {\\rm mm}<\\varLambda _{u}<17.2\\ {\\rm mm}$) are considered. The co-existence of modal instability due to the LSB and non-modal instability caused by streaks generated by free-stream turbulence is observed. The flow field is measured using hot-wire anemometry, which showed that the presence of streaks in the boundary layer modifies the mean-flow topology of the bubble. These changes in the mean flow field result in the modification of the convective disturbance growth, where an increase in turbulence intensity is found to dampen the growth of the modal instability. For a relatively fixed level of $Tu$, the variation of $\\varLambda _{u}$ has modest effects. However, a slight advancement of the nonlinear growth of disturbances and eventual breakdown with the decrease in $\\varLambda _{u}$ is observed. The data show that the streamwise growth of the disturbance energy is exponential for the lowest levels of free-stream turbulence and gradually becomes algebraic as the level of free-stream turbulence increases. Once a critical turbulence intensity is reached, there is enough energy in the boundary layer to suppress the laminar separation bubble, resulting in the non-modal instability taking over the transition process. Linear stability analysis is conducted in the fore position of the LSB. It accurately models incipient disturbance growth, unstable frequencies and eigenfunctions for configurations subjected to turbulence intensity levels up to 3 %, showing that the mean-flow modification due to the non-modal instability dampens the modal instability.

Resolvent analysis is used to study the low-frequency behaviour of the laminar oblique shock wave/boundary layer interaction (SWBLI). It is shown that the computed optimal gain, which can be seen as a transfer function of the system, follows a first-order low-pass filter equation, recovering the results of Touber & Sandham (J. Fluid Mech., vol. 671, 2011, pp. 417–465). This behaviour is understood as proceeding from the excitation of a single stable, steady global mode whose damping rate sets the time scale of the filter. Different Mach and Reynolds numbers are studied, covering different recirculation lengths $L$. This damping rate is found to scale as $1/L$, leading to a constant Strouhal number $St_{L}$ as observed in the literature. It is associated with a breathing motion of the recirculation bubble. This analysis furthermore supports the idea that the low-frequency dynamics of the SWBLI is a forced dynamics, in which background perturbations continuously excite the flow. The investigation is then carried out for three-dimensional perturbations for which two regimes are identified. At low wavenumbers of the order of $L$, a modal mechanism similar to that of two-dimensional perturbations is found and exhibits larger values of the optimal gain. At larger wavenumbers, of the order of the boundary layer thickness, the growth of streaks, which results from a non-modal mechanism, is detected. No interaction with the recirculation region is observed. Based on these results, the potential prevalence of three-dimensional effects in the low-frequency dynamics of the SWBLI is discussed.

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.

This experimental work explores the flow field around a three-dimensional expansion–compression geometry on a slender cone at Mach 8 using high-frequency pressure sensors, high-frame-rate schlieren, temperature-sensitive paint, shear-stress measurements and oil-flow visualizations. The $7^\\circ$ cone geometry has a hyperbolic slice which acts as an expansion corner and suppresses the disturbances present in the upstream boundary layer. Downstream of the cone-slice corner, high-frequency boundary-layer disturbances attenuate in all cases. Under laminar conditions, second-mode instabilities from the cone diminish and lower-frequency second-mode waves develop on the slice at a frequency commensurate with the increased boundary layer thickness. For fully turbulent cases, the boundary layer over the slice shows evidence of a two-layered nature with a turbulent outer region and a near-wall region with strong attenuation of high-frequency disturbances and reappearance of lower-frequency instability waves. When a downstream compression ramp is added to the slice, the expanded boundary layer shows enhanced susceptibility to separation such that separation is observed at a $10^{\\circ }$ deflection, which is smaller than expected for turbulent conditions. For a $30^{\\circ }$ ramp, boundary-layer separation occurs further upstream where the heat flux contours show a decrease in heating that is characteristic of a transitional separation. These results demonstrate the effect of relaminarization caused by an upstream expansion on a subsequent shock-wave/boundary-layer interaction.

Experiments of transitional shock wave–boundary layer interactions (SBLIs) over 6$^\\circ$ and 10$^\\circ$ compression ramps were performed at Mach number 1.65. The unit Reynolds number was varied by a factor of two between 5.6 million per metre and 11 million per metre. Schlieren flow visualization was performed, and mean flow measurements were made using Pitot probes. Free interaction theory was verified from pressure measurements for all operating conditions. A new non-dimensional parameter was developed for scaling the strength of the imposed shock, which was based on the pressure required to separate a boundary layer. The validity of this new scaling was supported by the reconciliation of large discrepancies in a diverse collection of experimental results on the length scales of transitional interactions. This non-dimensional scaling was also applied to turbulent interactions, where different models were used to determine the pressure required to separate a turbulent boundary layer. Finally, a direct comparison between transitional and turbulent SBLIs was made, which revealed new insights into the evolution of length scales based on the state of the boundary layer.

Supersonic internal flows often exhibit multiple reflected shocks within a limited distance. These shocks can interact with each other in a complex manner due to the characteristics of the shock wave–turbulent boundary layer interaction (STBLI), including flow distortion and the relaxing boundary layer. This study aims to characterise this type of interaction and to clarify its fluid physics. A separated STBLI zone was established either upstream or downstream, and another weaker STBLI was established in the opposing position to serve as a perturbation. Time-resolved measurements were employed to characterise the mean separation and unsteadiness as the two regions approached each other, as well as their relationship. The experimental results indicated that the STBLI could affect the separation and reattachment of the other STBLI through either the decelerated or relaxing boundary layer. Despite a small deflection angle, the incident shock can amplify the low-frequency oscillations in the downstream STBLI region. Additionally, the interaction in the downstream region can be influenced by both low- and high-frequency oscillations associated with the upstream STBLI through a relaxing boundary layer. Despite the limited correlation observed between the low-frequency fluctuations in the downstream region and the boundary layer flow not far upstream, there still exists some degree of correlation between the low-frequency shock motions even when they are widely separated. Both the ‘upstream mechanism’ and ‘downstream mechanism’ have been observed, and the significance of low-frequency dynamics in the separated flow, relative to that of the upstream flow, is closely associated with interaction intensity.