An experimental investigation of separation bubble shaped control bumps for oblique shock wave–boundary-layer interactions was performed in two supersonic wind tunnel facilities at Mach 2.5 and 2, with incident shock deflection angles of 8° and 12°, respectively, and momentum thickness Reynolds numbers of approximately 1.5 × 10⁴. Shock control bumps were designed to replicate the time-averaged separation bubble shape, and were placed onto the floor in the separation location. This resulted in almost complete elimination of flow separation. There was also a marked improvement in the downstream boundary-layer state. A low-frequency bubble breathing oscillation was identified in the baseline interaction using high-speed shadowgraphy and particle image velocimetry measurements. This oscillation was strongly suppressed in the controlled interactions. Velocity fluctuations in the downstream boundary layer were also significantly reduced. We propose that the key mechanism by which flow separation is eliminated is by breaking down the overall pressure rise into smaller steps, each of which is below the separation threshold. A key feature is the bump crest expansion fan, located near to where the incident shock terminates, which negates the shock induced pressure jump. Thus, the precise bump geometry is critical for control efficacy and should be designed to manage these pressure rise steps as well as the expansion fan strength and location with respect to the incident shock wave. The length of the bump faces must also be sufficiently long for the boundary layer to recover between successive adverse pressure jumps.

In this study, plume experiments were conducted to mimic the thermodynamic conditions on Saturn's moon, Enceladus. The icy moon's subsurface ocean and cracks in the surface have been simulated using a liquid water reservoir and a narrow channel, while the low-pressure environment at Enceladus’ surface was achieved with a vacuum chamber. We aimed to examine how channel temperature affected the plume's temperature, solid fraction and velocity, testing two models with differing wall temperatures: room temperature and near 0 °C. The colder setup better replicated Enceladus’ plume, producing a saturated flow in which nucleation of icy particles is possible. A conservative 1.5%–3% minimum solid fraction is estimated from measurements and modelling. Pitot-tube measurements indicated velocities around 400–500 m/s at the channel outlet. Flow temperature and velocity are closely correlated with wall temperature, indicating effective heat transfer. With a plume model based on the energy conservation law, we concluded that supersonic plume velocities observed on Enceladus cannot be achieved with straight channels, i.e. without requiring extreme expansion ratios. Additionally, the research provides evidence of the relationship between the crevasse's expansion ratio and the temperatures of flow and crevasse walls.

Unsteady pressure fluctuations in transonic launcher configurations represent a major challenge, driven by shock oscillations, flow separation, and compressibility effects. To address these phenomena, this work presents and validates a methodology for reconstructing instantaneous pressure fields from planar (2D2C) and stereo particle image velocimetry (2D3C PIV) data using Taylor’s hypothesis. The approach is first assessed using a simulated PIV dataset of an axisymmetric backward-facing step, representing a launcher base flow configuration. In this case, the Taylor-based pressure reconstruction is validated against reference data and compared with results from a hypothetical time-resolved pressure reconstruction, demonstrating the accuracy of the method. The methodology is then applied to wind tunnel PIV data of a VEGA-like hammerhead launcher model at Mach 0.8 and zero angle of attack. Hammerhead configurations, characterized by payload fairings with a larger diameter than the main body, are particularly prone to separation and intense pressure fluctuations in the transonic ascent phase. The reconstructed pressure fields are analyzed together with unsteady transducer data, providing a general characterization of the flow features (oscillating shock, separation, and reattachment) and showing very good agreement for instantaneous, mean, and fluctuating components (ΔC_{p avg} ~ 0.01–0.02; ΔC_{p std} ~ 0.02). Finally, the analysis highlights the impact of neglecting out-of-plane velocity components, which introduces noticeable discrepancies in separated regions.

The design of transonic compressors increasingly focuses on higher blade loading, sparking interest in shock oscillation mechanisms in highly loaded transonic fans operating at cruise altitude. At such conditions, low chord Reynolds numbers (1.4 Mio.) may sustain a laminar boundary layer on the suction side of the blade up to the shock-wave/boundary-layer interaction (SBLI). The resulting interaction with large separation (pre-shock Mach number of 1.6) cause shock oscillations and structural excitation. In this study, we demonstrate that a canonical research configuration enables the experimental investigation of a specific shock oscillation mechanism relevant to transonic fans at altitude, providing a basis for validation. Using Large Eddy Simulations and experimental data, we show that the oscillation mechanism depends on the conditions at the SBLI rather than the geometry. The oscillation arises from the growth and self-suppression of the upstream laminar section of the separation bubble. Periodic collapse of this laminar section generates turbulence that entrains the separation bubble, influencing the dynamics of the reflected shock. The reflected shock movement resembles the cascade passage shock behavior, driven by blockage variations from the separation bubble. Additionally, we examine the numerical requirements to resolve this mechanism. These findings provide insights to advance compressor designs and hypersonic applications featuring similar mechanisms.

Hammerhead launcher configurations, characterized by a larger diameter in the payload fairing than the rest of the launch vehicle, face substantial challenges during transonic operations due to their susceptibility to flow separation. This experimental study investigates the influence of the nose and boat tail geometry on the flow around hammerhead configurations in the transonic regime (Ma = 0.7–0.8) and for various angles of attack (α = 0–4°). To gain a general understanding of the shockwave structures, flow separation and reattachment, oil flow and schlieren visualizations were employed. Schlieren visualizations were also utilized to characterize the level of unsteadiness in these regions. Additionally, particle image velocimetry was employed to quantify variations in the velocity field. The study’s findings reveal an optimization of flow performance in the presence of a bi-conic nose, attributed to the creation of two-shockwave structures with relatively low intensity. This is in contrast to the ogive and conic noses, which exhibit a single, more detrimental shockwave structure. The investigation into different boat tail angles indicates that adopting low-angle boat tails (5° and 15° compared to 34°) leads to a noticeable reduction in the separated area, albeit associated with an increase in the range of oscillation of the shockwave structures.

Reynolds numbers at cruise altitude can be such that a laminar boundary layer persists on the suction side of a transonic fan blade up to the shock-wave/boundary-layer interaction (SBLI). In a transitional SBLI which exhibits sufficiently large shock-induced separation, a shock oscillation mechanism characterized by growth and natural suppression of the upstream laminar section of the separation bubble occurs. To validate the shock oscillation mechanism observed in large eddy simulations (LES), the shock oscillation mechanism is studied experimentally using high-speed Schlieren and spark-light shadowgraphy. A characteristic length based on the distance of laminar separation shock travel is proposed. Strouhal numbers from LES and the experiment collapse at around 0.075. A strong dependency of the oscillation mechanism on free-stream turbulence and boundary-layer state is shown. Dominant oscillation frequencies are an order of magnitude lower for the turbulent interaction as opposed to the laminar case. For the laminar case, dynamic mode decomposition showed a strong relationship of the laminar separation shock with the separation bubble and reflected shock movement. The turbulent interaction shows a significantly lower reflected shock travel distance. The findings experimentally confirm that stabilization of the shock is achieved by tripping the boundary layer.

The jet-in-coflow is a two-stream configuration having engineering applications in combustors and gas turbine engine exhausts. In practical systems, the coflow generates a boundary layer of the outer wall of the jet pipe and may also have a certain level of turbulence. In the current work, the evolution of this flow configuration is studied using an air-air turbulent jet in a low turbulence coflow (turbulence intensity < 6%), and the 2D velocity field is measured by planar particle image velocimetry. Cases of varying coflow ratio (ratio of coflow velocity to jet velocity) of 0 (turbulent free jet), 0.09, 0.15, and 0.33 are generated by keeping a constant velocity jet (Re = 14000) and varying the coflow velocity. The trends of jet centerline properties such as velocity decay, jet spread, and jet momentum of jet-in-coflow cases, scaled to represent an equivalent free jet, show deviations from that of the turbulent free jet. The radial profile of mean velocity shows a region of velocity deficit, compared to a turbulent free jet, on the coflow side in the jet-in-coflow cases. In contrast, the turbulence intensity and Reynolds shear stress profiles show an enhanced peak near the interface for the jet-in-coflow cases. Further, conditional statistics were extracted by detecting the interface between the jet and the surroundings, wherein the same trends are observed. The low turbulence levels of the coflow have little effect on the jet/coflow interface, as seen by the conditional enstrophy diffusion and tortuosity compared to a turbulent free jet. The differences at the jet/coflow interface of a jet-in-coflow with respect to a turbulent free jet are attributed to the boundary layer initially developed by the turbulent coflow over the pipe generating the jet, and these are seen throughout the near-to-intermediate field (0≤x/D≤40).

For the largest wind turbines currently being designed, operation close to cut-out conditions can lead to the tip airfoil experiencing transonic flow conditions. To date, this phenomenon has been explored primarily through numerical simulations, but modelling uncertainties limit the reliability of these predictions. In response to this challenge, our study marks the first experimental investigation of a wind turbine airfoil under transonic conditions, for which we selected the FFA-W3-211 airfoil. Measurements were carried out in the high-subsonic range (Mach 0.5 and 0.6), utilizing schlieren visualization and particle image velocimetry (PIV) to characterize the airfoil across a range of angles of attack (AoAs) expected to be close to the boundary of transonic flow occurrence. Unsteady shock wave formation was observed for the higher Mach number, with the shock oscillation range increasing with steeper angles of attack. In addition, it was confirmed that the presence of a local supersonic flow region does not necessarily result in a shock wave. For cases with shock waves and trailing-edge separation, a buffet cycle was identified that is similar to, but distinct from, those seen in aviation applications. Our findings highlight the need for unsteady analyses even in steady operating conditions and call for dedicated research on wind turbine tip airfoils in transonic flow.

Low emissions and fuel flexibility are two important criteria required for gas turbine combustors to facilitate the energy transition to low-carbon fuels for propulsion and power applications. A jet-stabilized combustor, having both these characteristics, was operated with CH ₄–H ₂ fuel mixtures with H ₂ varying from 0 to 100 % and with varying equivalence ratios (ϕ). Comprehensive measurements were carried out of the velocity field using Particle Image Velocimetry (PIV), temperature and gas composition by traversing probes in the chamber, and flame topology using chemiluminescence imaging. The flow field in this combustor consists of a jet that undergoes recirculation, generating Central and Peripheral Recirculation Zones (CRZ and PRZ). The recirculation ratio in the PRZ is found to be twice that of the CRZ. Increasing H ₂ % for the same ϕ leads to higher NO _x. Ultra-low ϕ flames could be stabilized only at H ₂≥50 %, which in turn leads to low NO _x due to low adiabatic flame temperatures. The combination of temperature, gas composition (CO/NO), and chemiluminescence images is used to identify the extent and location of the reaction zone. Distributed reaction zones, stabilizing at around 30 % of the length of the chamber, are achieved at lean conditions, whereas an increase in H ₂ % makes the reaction zone more compact and shifts upstream towards the burner head. Flame kernels are extracted from the instantaneous chemiluminescence images, and probability distribution functions for their aspect ratio and axial location are constructed. It is seen that reducing ϕ leads to low aspect ratio kernels that tend to occur further downstream, whereas increasing H ₂ % leads to higher aspect ratio kernels, stabilizing upstream. These flame kernel statistics are also used to identify ignition modes (autoignition/flame propagation) for varying fuel H ₂ % and inlet ϕ based on a hypothesis of flame stabilization mechanisms.

This study investigates the spatial evolution of a zero pressure gradient turbulent boundary layer (TBL) imposed by a square-wave (SqW) of steady spanwise wall-forcing, which varies along the streamwise direction (x). The SqW wall-forcing is imposed experimentally via a series of streamwise periodic belts running in opposite spanwise directions, following the methodology of Knoop et al. [Exp. Fluids 65, 65 (2024)]0723-486410.1007/s00348-024-03799-9, with the streamwise extent increased to beyond ∼11 times the boundary layer thickness (δo) in the present study. This unique setup is leveraged to investigate the influence of viscous-scaled wavelength of SqW wall-forcing on the turbulent drag reduction efficacy for λx+=471 (suboptimal), 942 (near-optimal), and 1884 (postoptimal conditions), at fixed viscous-scaled wall-forcing amplitude, A+=12, and friction Reynolds number, Reτ=960. The TBL's response to this wall-forcing is elucidated by drawing inspiration from established knowledge on traditionally studied sinusoidal forcing, based on analysis of the streamwise-phase variation of the Stokes strain rate (SSR). The analysis reveals the SqW forcing to be characterized by a combination of two markedly different SSR regimes whose influence on the overlying turbulence is found to depend on the forcing waveform: subphase I of local and strong impulses of SSR downstream of the half- (λx/2) and full-phase (λx) locations, associated with a reversal in spanwise forcing directions, leading to significant turbulence attenuation, and subphase II of near-zero SSR over the remainder of forcing phase that enables turbulence recovery (when wall-forcing magnitudes and direction remain constant). Upon the initial imposition of the SqW forcing, the Reynolds stresses are strongly attenuated over the short streamwise extent of x/δ0<0.5 for all wavelengths, whereas the skin-friction transient is more gradual. Thereafter, once the forcing is ultimately established, the suboptimum and optimum wavelength regimes display no distinctive responses to the individual SSR subphases; rather, the drag-reduced TBL response is quasi-streamwise homogeneous. In contrast, an SSR-related phenomenology establishes itself clearly for the postoptimal case, in which a local attenuation of near-wall turbulence characterizes subphase I, while the turbulent energy recovers in subphase II owing to the extended region of near-zero SSR.

In this paper, a non-intrusive pressure measurement scheme based on particle image velocimetry (PIV) is presented for the complex supersonic flows with intense shock systems, by elaborately combining the MacCormack method, the streamline-based method, and the spatial integration in conservative form. According to the detailed analyses of flow structures, the pressure fields are well reconstructed by the proposed scheme for the two typical shock-wave/boundary-layer interactions containing regular and Mach reflections, which are induced by the relatively strong oblique shock waves generated by the wedges of 21° and 17° in the freestreams of Mach 2.5 and 2.0, respectively. Based on the theoretical solutions by oblique shock relationship, free interaction theory, and shock polar analysis, this pressure reconstruction scheme is completely validated to effectively suppress the propagation of PIV velocity error to the pressure field and the accumulation of reconstructed pressure error behind the strong shock wave. Compared with the literature presently, this work would be the most challenging application of PIV-based pressure measurement to such complex supersonic flows with intense shock reflections, large oscillations, wide speed ranges, and various compressible flow structures. These good results could confirm the feasibility and high accuracy of the proposed reconstruction scheme and may greatly promote its applications in academic research and engineering test for supersonic flows in the future.

For the largest wind turbines currently designed, when operating at rated power and at high wind speeds, the tip airfoils can experience large negative angles of attack. For these conditions and in combination with turbulence, the airfoils are at risk of reaching locally supersonic flow, even at low free-stream Mach numbers. The possibility of shock wave formation and its consequences endangers the lifetime of these largest rotating machines ever built. So far only numerical analyses of this challenge have been attempted with significant modelling uncertainty. Here, for the first time, a wind turbine airfoil (the FFA-W3-211, used at the blade tip of the IEA 15MW reference wind turbine) is studied under transonic conditions using experimental techniques. Schlieren visualization and Particle Image Velocimetry were employed for free-stream Mach numbers of 0.5 and 0.6 and various angles of attack. It was shown that calculations based on isentropic flow theory and compressibility corrections were able to predict the situations where supersonic flow occurred. However, they could not predict the frequency of occurrence and whether shock waves were formed. In conclusion, an unsteady characterization of such airfoil behavior in transonic flow seems to be warranted.

We present an experimental realisation of spatial spanwise forcing in a turbulent boundary layer flow, aimed at reducing the frictional drag. The forcing is achieved by a series of spanwise running belts, running in alternating spanwise direction, thereby generating a steady spatial square-wave forcing. Stereoscopic particle image velocimetry in the streamwise–wall-normal plane is used to investigate the impact of actuation on the flow in terms of turbulence statistics, drag performance characteristics, and spanwise velocity profiles, for a non-dimensional wavelength of λ_x⁺=397. In line with reported numerical studies, we confirm that a significant flow control effect can be realised with this type of forcing. The scalar fields of the higher-order turbulence statistics show a strong attenuation of stresses and production of turbulence kinetic energy over the first belt already, followed by a more gradual decrease to a steady-state energy response over the second belt. The streamwise velocity in the near-wall region is reduced, indicative of a drag-reduced flow state. The profiles of the higher-order turbulence statistics are attenuated up to a wall-normal height of y⁺≈100, with a maximum streamwise stress reduction of 45% and a reduction of integral turbulence kinetic energy production of 39%, for a non-dimensional actuation amplitude of A⁺=12.7. An extension of the classical laminar Stokes layer theory is introduced, based on the linear superposition of Fourier modes, to describe the non-sinusoidal boundary condition that corresponds to the current case. The experimentally obtained spanwise velocity profiles show good agreement with this extended theoretical model. The drag reduction was estimated from a linear fit in the viscous sublayer in the range 2≤y⁺≤5. The results are found to be in good qualitative agreement with the numerical implementations of Viotti et al. (Phys Fluids 21, 2009), matching the drag reduction trend with A⁺, and reaching a maximum of 20%. Graphical abstract: (Figure presented.)

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.

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.

Recent numerical studies have suggested the potential of substrates with streamwise-preferential permeability to reduce drag in turbulent boundary layers. Such a substrate is theorized to facilitate relaxation of the no-slip condition and thereby reduce the skin friction. So far, these beneficial effects have not been demonstrated experimentally yet and therefore the scope of this work is to present this concept in air flow where the substrate geometry satisfies the theoretical permeability requirements for an expected reduction in drag. For this, a three-dimensional-printed structure with anisotropic permeability (φxz=2.7, φxy=3.9) and small pores (s≈250μm), akin to an acoustic liner, was developed. The substrate was investigated using direct force measurements and 2D-2C PIV in the range of U∞≈5-35 ms-1, corresponding to frictional Reynolds numbers of Reτ≈430-1960. Results show an increase in drag of 0%<ΔCD<8% and, while contrasting the model predictions, this agrees with DNS data on structures with similar geometric properties when using the inverse wall-normal Forchheimer coefficient, or inertial permeability, as the equivalent roughness parameter. Hence the present results constitute the first experimental evidence that this is the governing property for the drag behavior of acoustic liners. The absence of the predicted beneficial flow modulation effects is attributed to the investigated substrate not strictly satisfying the theoretical framework assumptions on characteristic length scales. However, to expand beyond this structural limitation, we analytically derive that, for realistic, geometrically resolved cases, this length scale mismatch is unavoidable and thereby render it unfeasible to model the substrate as a continuum for the virtual-origin approach. We expect that translating the abstraction of substrates with streamwise-preferential permeability into physical realisations relevant for practical applications would result in structures very similar to riblets.

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.