This study experimentally investigates the effect of three-dimensional shock control bumps (SCBs) on the aerodynamic loads of a supercritical airfoil under transonic buffet conditions. The experiments consisted in planar particle image velocimetry (PIV) measurements and have been carried out in the transonic-supersonic wind tunnel of TU Delft under fully developed buffet conditions (Ma=0.7 and α=3.5∘). The bumps are wedge-shaped and have been placed in the center of the shockwave oscillation range. Shock detection and phase-averaged velocity fields confirm that properly designed and spaced (ΔySCB/c=25%) SCBs reduce the shockwave oscillation range (compared to the clean case). The velocity data have been further used to evaluate the pressure field around the entire airfoil, and afterward, lift and drag coefficients have been retrieved, respectively, from momentum contour and wake integral approaches. Results demonstrate that SCBs have a beneficial effect on the aerodynamic loads with an increase in lift and a decrease in drag under fully developed buffet conditions. More importantly, a strong reduction of the amplitude of oscillations of both lift and drag coefficient, within the different buffet phases, was noted. Tests at multiple spanwise locations revealed relevant differences, with lower drag and higher lift values being achieved in the symmetry plane of a SCB, while a worse performance (with values comparable to the clean case) was achieved in the symmetry plane in between two adjacent bumps.

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.

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.

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.

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.

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.)

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.

Modern launcher configurations, often characterized by a larger diameter in the payload fairing than the rest of the launch vehicle (hammerhead configuration), face significant challenges during transonic operations, given their susceptibility to flow separation and intense pressure fluctuations. This experimental study aims to reconstruct pressure from PIV under transonic conditions using Taylor's hypothesis. The focus is on the ESA VEGA-E hammerhead launcher model, investigated in the transonic regime at Ma=0.8 and at α=0°. Initially, the methodology of the pressure reconstruction algorithm is described and the validity of Taylor's hypothesis is established through validation with numerical data. Subsequently, the experimental data are first used to provide a general characterization of the flow phenomenon, highlighting key features such as an oscillating shockwave, separated and reattached flows. Later, the reconstruction of pressure from velocity data is compared to unsteady pressure transducer data, for instantaneous, average and standard deviation values, obtaining a very good agreement (ΔCpAvg~0.01-0.02 and ΔCpStd~0.02). The experimental set-up is also designed to showcase the impact of neglecting the out-of-plane velocity component on pressure reconstruction, showing comparable data for CpAvg, while larger discrepancies in terms of CpStd in particular in the separated area region.

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.

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.

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.

The effects of the wing skin distortion on the boundary layer of a highly flexible wing are analyzed in a wind tunnel experiment using infrared thermography measurements. Considerable differences in the boundary layer flow are observed when comparing the sections of the wing near the ribs, where the design shape of the wing is preserved, and in between the ribs. At the spanwise locations between the ribs, the sectional wing shape distorts and triggers boundary layer transition close to the leading edge. The differences between the design behavior of the wing and the experimental results of the boundary layer analysis demonstrate the need for considering the skin deformation and its effects on the boundary layer flow when designing highly flexible wings.

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.

In this experimental study, the effect of three-dimensional shock control bumps (SCB) on impinging-reflecting shock wave/boundary layer interactions (SWBLI) is investigated as a passive control method. The aim is to develop an understanding of the influence of such devices on the interaction structure by studying the position of the bump with respect to the shock-impingement location. The experiments were conducted in the ST-15 wind-tunnel at the Delft University of Technology for fully developed turbulent boundary layer conditions with Mach number of 2. The effectiveness was assessed by examining the size of the separated flow region, as well as the downstream boundary layer velocity profile. Stereo-PIV was employed as the main diagnostic method to characterise the three-dimensional flow field. Additionally, the effect of shock impingement location on the unsteady interaction dynamics was examined by analyzing the separation size and reflected shock foot position in the instantaneous flow. The investigation revealed the significance of the shock impingement location in terms of control effectiveness. Nevertheless, placement of the bump in the interaction region substantially decreased the probability of flow separation even in off-design conditions when compared to the uncontrolled interaction.

At cruise altitudes, the Reynolds number may become sufficiently low to allow a laminar boundary layer to persist on the suction side of a transonic fan blade up to the shock-wave/boundary-layer interaction (SBLI). In such a transitional SBLI with sufficiently large shock-induced separation, a shock oscillation mechanism occurs, with the source at the upstream growth (until a critical length) and natural suppression (through shear layer instabilities) of the separation bubble. The oscillation cycle is characterized by a temporarily vanishing upstream laminar part of the separation bubble. The suppression of this laminar part is accompanied by downstream advection of turbulence and subsequent entrainment into the bulk separation bubble, affecting the reflected shock movement. In order to study the spatial behavior of the mechanism, particle image velocimetry of a highly separated transitional oblique SBLI at Mach 2.3 is conducted in the high speed aerodynamics laboratory of Delft University of Technology. Statistical quantities, including root mean square velocity fluctuations, phase averages, and spatial modes from proper orthogonal decomposition, are investigated. The entrainment strength varies depending on the phase of the oscillation, and the turbulent shear layer is not fully developed. The main growth and shrinking mode of the separation bubble were extracted, which affects the slip line region size and shock position. Secondary modes that affect the shear layer undulation and upstream effects were also extracted. The study provides quantitative analyses of an important shock oscillation type, with the focus on capturing the separation bubble size variation and upstream effects.

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 and intense pressure fluctuations. 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 main flow features, such as shockwave formation, separated flow in the boat tail region, and flow 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 (with the conic nose being the least favorable configuration). 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.

This study presents an aeroelastic wind-tunnel experiment to identify the influence of the wing stiffness and hinge release threshold on the gust load alleviation performance of a folding wingtip design. Five models with different stiffness and tailoring properties are tested, and the wing root bending moment at different conditions is compared to the response with the locked-hinge condition to assess the impact on the gust load alleviation capabilities of the folding wingtip. The results show that the structural properties do not have an important impact on the peak load alleviation but the hinge release threshold and timing do. Releasing with the correct timing can reduce significantly the peak loads. However, the dynamics of the system are affected by this release; the flutter speed is decreased, and, although the performance can improve, load oscillations increase, which can be considered detrimental for reasons such as fatigue or passenger comfort.

The aeroelastic response of the Delft-Pazy wing to steady and periodic unsteady inflow conditions is analyzed experimentally. The Delft-Pazy wing is a highly flexible wing model based on the benchmark Pazy wing (Avin, O., Raveh, D. E., Drachinsky, A., Ben-Shmuel, Y., and Tur, M., “Experimental Aeroelastic Benchmark of a Very Flexible Wing,” AIAA Journal, Vol. 60, No. 3, 2022, pp. 1745-1768) and exhibits wingtip displacements of more than 24% of the span in the present study. The nonintrusive measurements are performed with an integrated optical approach that provides combined measurements of the structural response of the wing and the unsteady flowfield around it. The aeroelastic loads acting on the wing are derived using physical models and validated against force balance measurements, showing a good agreement for all considered inflow conditions. The analysis of the aeroelastic response of the wing to the unsteady inflow produced by a gust generator shows that both structural and aerodynamic responses depend strongly on the frequency of the gust. The results of this study provide a characterization of the aeroelastic behavior of the Delft-Pazy wing and can serve as a reference for the development of novel and improved nonlinear aeroelastic simulation models.