Mean Skin Friction Research Articles

Direct Numerical Simulation of High-Enthalpy Turbulent Boundary-Layer Flow with Light Gas Injections

Two light gases (He and H2) are, respectively, introduced upstream of a high-enthalpy turbulent flat-plate flow with a boundary-layer edge Mach number of Maδ=2.25 and temperature of Tδ=1800 K. The flow condition refers to the after-shock wave flow on a blunt-body hypersonic vehicle (Duan and Martín, AIAA Journal, Vol. 49, No. 1, 2011, pp. 172–184). Direct numerical simulation results show that the injection of these light gases has little effect on the mean velocity profiles but significantly reduces the near-wall density and skin friction. The separation and fragmentation of near-wall vortical structures are restrained, and the Reynolds shear stress decreases. The injection of inert He inhibits the dissociation reaction of O2 and weakens the chemical nonequilibrium effect, resulting in enhanced mean and fluctuating temperatures. The injection of active H2 promotes the reaction between H2 and O2, which increases the mean temperature but inhibits its fluctuation. After decomposing the mean skin friction into physics-informed contributions, both injections largely reduce the turbulent kinetic energy production term Cf,T and the spatial growth term of the flow, Cf,G, through lowering the near-wall density and reducing vortices.

Decomposition of mean skin friction in incident shock wave/turbulent boundary layer interaction flows at Mach 2.25

The evolution characteristics of the mean skin friction beneath the supersonic turbulent boundary layer that interacts with incident shock waves at Mach 2.25 are analyzed using Direct Numerical Simulation (DNS). The separated and attached boundary layers in the interaction region that respectively correspond to 33.2° and 28° incident shock angles are considered. The mean skin friction recovery rate for the separated boundary layer is much gentler and distinctly less than that for the attached case where the skin friction completes its recovery within one boundary layer thickness. The novel mean skin friction decomposition method for compressible flows proposed by the recent research is applied in the interaction region to investigate the internal evolution characteristics quantitatively. The results reveal that the three decomposition components are distinctly unequal between the two cases. The contributions of the turbulent motions at different scales to the associated term are focused on using empirical mode decomposition technology. It indicates that the outer large-scale structures dominate separation and reattachment regions, while contributions from inner small-scale structures are limited. In contrast, contributions from the outer large-scale structures are dramatically reduced in the attached case, which results in the outer large-scale and inner small-scale motions being of equal importance.

Evolution of Air Plastron Thickness and Slip Length over Superhydrophobic Surfaces in Taylor Couette Flows

Drag reduction (DR) using superhydrophobic surfaces (SHSs) has received intensive interest due to the emergence of SH coating technology. The air layer (plastron “δ”) trapped between the SHS and the water controls the flow slip over the SHSs. We demonstrate slippage over three fabricated SHSs in laminar and low turbulent Taylor–Couette flows. We experimentally investigate how the slip length increases with a higher Reynolds number (Re) over the tested SHSs; simultaneously, the air plastron thickness investigates using a viscous model. The mean skin friction coefficient (Cf) can be fitted to a modified semi-empirical logarithmic law expressed in the Prandtl–von Kármán coordinate. An effective slip length is estimated in the 35–41 µm range with an achieved 7–11% DR for the tested surfaces. Statistical analysis is used to develop a regression model from the experimental data. The model shows an R2 of 0.87 and good agreement with the experimental data. This shows the relation between the dimensionless slip length (b+), the dimensionless plastron thickness (δ+), and the Reynolds number, which is directly proportional. The regression model shows that b+ and Reynolds numbers have a higher impact on the δ+ than the surface wettability, which attribute to the small difference in the wetting degree between the three tested surfaces. The practical importance of the work lies in its ability to provide a deep understanding of the reduction in viscous drag in numerous industrial applications. Furthermore, this research serves as a groundwork for future studies on hydrophobic applications in internal flows.

An integral method to determine mean skin friction in turbulent boundary layers

This study is concerned with accurately determining the mean skin friction in a zero-pressure-gradient turbulent boundary layer. By assuming a linear relation for the weighted total shear stress in the near-wall region, an integral method to evaluate the skin friction is proposed. The method requires the wall-normal profiles of the mean streamwise velocity and Reynolds shear stress within the range of y/δ≤0.4 at only one streamwise location, where δ is the boundary layer thickness. A number of direct numerical simulation and experimental data available in the literature are employed to validate the accuracy of the method over a wide range of Reynolds numbers. The skin friction coefficient obtained using the proposed method is found to be within ±4% in agreement with the published values in both the smooth- and rough-wall turbulent boundary layers. A comparison of the present approach with several existing methods is presented, showing that the proposed skin friction relation is robust and accurate.

Large-eddy simulation of a hypersonic turbulent boundary layer over a compression corner

In this paper, large-eddy simulation of the interaction between a shock wave and the hypersonic turbulent boundary layer in a compression corner with a fixed 34° deflection angle at Ma = 6 for different Reynolds number cases is conducted. For investigating the effects of the Reynolds number for hypersonic cases, three cases where the free-stream Reynolds numbers are 14000, 20000, and 30000/mm are selected. The averaged statistics, such as the mean velocity, the skin friction, the heat flux, and the wall pressure, are used in this paper. The flow structures in the compression ramp including the shock wave and interaction region are discussed. The decomposition of the mean skin-friction drag for the flat flow is extended to be used in the compression corner. In addition, the turbulent kinetic energy is studied through the decomposition of the mean skin-friction drag for the flat-plate region and the corner region. It is found that higher Reynolds numbers would increase the turbulent kinetic energy by turbulent dissipation at the interaction region, while higher Reynolds numbers would decrease the turbulent kinetic energy by turbulent dissipation after reattachment. In addition, it is also found that the turbulent kinetic energy is larger with a higher Reynolds number and higher turbulent kinetic energy inhibits the movement from the separation point to the inflection point (x = 0 mm), which deduces larger separation bubbles.

Experimental Characterization of an Axisymmetric Transonic Separated Flow for Computational Fluid Dynamics Validation

An experimental characterization of transonic, turbulent, separated flow generated by an axisymmetric model is presented, with intent for use as a computational validation case. The model is a scaled version of a geometry inspired by Bachalo and Johnson (“Transonic, Turbulent Boundary-Layer Separation Generated on an Axisymmetric Flow Model,” AIAA Journal, Vol. 24, No. 3, 1986, pp. 437–442), consisting of a circular bump on a constant-diameter cylinder aligned with the flow. The Mach 0.875 flow is turbulent approaching the bump and becomes locally supersonic at the apex. This leads to a shock-wave/boundary-layer interaction, a separation bubble, and unsteady flow reattachment downstream. Tunnel boundary conditions are characterized, and mean surface pressure, mean skin friction, and both mean and fluctuating velocity fields are measured throughout the interaction region. Uncertainty estimates are provided for all measurements. The degree of flow axisymmetry and evidence of relaminarization are discussed, and a comparison is made to historical data.

Numerical simulation of turbulent, plane parallel Couette–Poiseuille flow

We present numerical simulation and mean-flow modelling of statistically stationary plane Couette–Poiseuille flow in a parameter space $(Re,\theta )$ with $Re=\sqrt {Re_c^2+Re_M^2}$ and $\theta =\arctan (Re_M/Re_c)$ , where $Re_c,Re_M$ are independent Reynolds numbers based on the plate speed $U_c$ and the volume flow rate per unit span, respectively. The database comprises direct numerical simulations (DNS) at $Re=4000,6000$ , wall-resolved large-eddy simulations at $Re = 10\,000, 20\,000$ , and some wall-modelled large-eddy simulations (WMLES) up to $Re=10^{10}$ . Attention is focused on the transition (from Couette-type to Poiseuille-type flow), defined as where the mean skin-friction Reynolds number on the bottom wall $Re_{\tau,b}$ changes sign at $\theta =\theta _c(Re)$ . The mean flow in the $(Re,\theta )$ plane is modelled with combinations of patched classical log-wake profiles. Several model versions with different structures are constructed in both the Couette-type and Poiseuille-type flow regions. Model calculations of $Re_{\tau,b}(Re,\theta )$ , $Re_{\tau,t}(Re,\theta )$ (the skin-friction Reynolds number on the top wall) and $\theta _c$ show general agreement with both DNS and large-eddy simulations. Both model and simulation indicate that, as $\theta$ is increased at fixed $Re$ , $Re_{\tau,t}$ passes through a peak at approximately $\theta = 45^{\circ }$ , while $Re_{\tau,b}$ increases monotonically. Near the bottom wall, the flow laminarizes as $\theta$ passes through $\theta _c$ and then re-transitions to turbulence. As $Re$ increases, $\theta _c$ increases monotonically. The transition from Couette-type to Poiseuille-type flow is accompanied by the rapid attenuation of streamwise rolls observed in pure Couette flow. A subclass of flows with $Re_{\tau,b}=0$ is investigated. Combined WMLES with modelling for these flows enables exploration of the $Re\to \infty$ limit, giving $\theta _c \to 45^\circ$ as $Re\to \infty$ .

Wall-Modeled Large-Eddy Simulation with Second-Order-Accurate Upwind Scheme

In aircraft aerodynamic design, it is essential for certification by analysis to estimate aircraft aerodynamic characteristics with high fidelity across the full flight envelope using computational fluid dynamics. Improving accuracy of the simulation of unsteady flows such as transonic buffet is one of the problems. Wall-modeled large-eddy simulation (WMLES) is expected to improve the accuracy. In this study, three quantitative requirements for the matching points, where LES feeds the wall model with flow variables, are proposed to ensure the accuracy of the WMLES with a second-order-accurate upwind scheme that is often used for engineering codes. These requirements are related to 1) matching point height, 2) the number of cells below the matching point, and 3) grid resolution at the matching point. The proposed requirements are assessed on a flat-plate turbulent boundary layer and a shock/turbulent boundary-layer interaction flow. As a result, it is clarified that all of the requirements are necessary to ensure the accuracy in terms of mean velocity, Reynolds stresses, and skin friction.

Effect of interaction strength on recovery downstream of incident shock interactions

Direct numerical simulations of a supersonic turbulent boundary layer on a flat plate interacting with an impinging shock wave are carried out with two different incident shock angles at Mach 2.25. The effect of the interaction strength on the recovery process in the downstream region is systematically studied, including the turbulence evolution, the statistical and structural properties of wall pressure fluctuations, and the generation of mean skin friction and wall heat flux. The variations of the Reynolds stress components, the anisotropy tensor, and the turbulent kinetic energy budget in the two flow cases highlight a slow reversal tendency and an increasingly pronounced importance of the outer-layer large-scale structures in the relaxation region of the strong interaction. We find that the effect of increasing the interaction strength on the fluctuating wall pressure is reflected by a decrease in the characteristic frequencies, an increase in the spatial extent, and a decrease in the convection velocity. We decompose the mean skin friction and wall heat flux into different physically informed contributions and reveal that the mean wall heat flux generation is the same regardless of the interaction strength; in contrast, the generation mechanism of mean skin friction is found to be fundamentally changed. A novel scale-decomposition method is used to quantify the effect of the increased interaction strength on the leading components, and it is demonstrated that the energetic outer-layer large-scale structures are the dominant contributor in the recovery process as the interaction strength is increased.

Skin-friction drag reduction by local porous uniform blowing in spatially developing compressible turbulent boundary layers

This paper investigates the effects of local porous uniform blowing on the skin-friction drag reduction in the spatially developing compressible turbulent boundary layers through direct numerical simulations. Under the influence of uniform blowing, the skin-friction drag decreases drastically within the controlled regions, and the effect extends downstream. The drag reduction rate exceeds 10% for the uniform blowing velocities considered herein. The intrinsic mechanism of decreased skin-friction drag is further explored, in terms of the various contributions to this quantity, the Reynolds shear stress budget, and the multi-scale distributions and transfer of enhanced turbulent motions. The numerical results for the identity of Renard and Deck [“A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer,” J. Fluid Mech. 790, 339–367 (2016)] indicate that the decreased skin-friction drag is reflected in a negative contribution in the streamwise developing direction. The enhanced turbulent motion is investigated through the Reynolds shear stress budget, and uniform blowing is found to strengthen the magnitudes of all budget terms. We conclude that uniform blowing promotes the energy cascade process in the near-wall region, promoting the appearance of smaller turbulent structures and the formation of large outer scales. Similar skin-friction drag reduction in the subsonic case is also observed in a supersonic case. The upstream transition process is delayed, which leads to a relatively larger skin-friction drag reduction rate in a supersonic case. Finally, we investigate the porosity effects on the skin-friction drag and conclude that the blowing flux is a decisive factor.

Direct numerical simulation of supersonic bump flow with shock impingement

Direct numerical simulations are carried out to identify the effects of shock impingement on the behavior of bump flow at freestream Mach number of 2.25. Two cosine-shaped bump cases, with and without an impinging oblique shock at an angle of 33.2°, are compared. The shock impingement exhibits a remarkable influence on the pattern of the shock system and on the size of the separation region. A spectral analysis finds that low-frequency unsteadiness is significantly enhanced by the impingement interaction, and the proper orthogonal decomposition highlights the low-frequency breathing motion of the separation bubble, which is accurately reconstructed using only the first ten low-order modes. Downstream of the bump, both the Reynolds stress components and the turbulence kinetic energy exhibit a general amplification, with the peaks reoccurring at outer wall-normal locations. A turbulent kinetic energy budget analysis shows the greatly increased production in the outer layer which is balanced by turbulent transport and dissipation. An anisotropy-invariant map analysis identifies enhanced isotropic turbulence in the vicinity of the bump, which is qualitatively modified into a two-component axisymmetric state around the reattachment point. In addition, the mean skin friction decomposition suggests that the shock impingement has little influence on the predominant contribution of turbulence kinetic energy production, apart from the spatial growth dominance at the bump summit in the absence of the impinging shock. Interestingly, a scale-decomposed analysis quantitatively demonstrates that the contributions of small-scale structures are attenuated, but those of large-scale ones are relatively increased, with a contribution of more than 80% with shock impingement.

Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element

Global stability analysis and direct numerical simulation (DNS) are used to study boundary layer flows with an isolated roughness element. The aspect ratio of the element ( $\eta$ ) is small, while the ratio of element height to displacement boundary layer thickness ( $h/\delta ^{*}$ ) is large. Both steady base flows and time-averaged mean flows are able to capture the frequencies of the primary vortical structures and mode shapes. Global stability results highlight that although the varicose instability is dominant for large $h/\delta ^{*}$ , sinuous instability becomes more pronounced as $Re_h$ increases for the thin geometry ( $\eta =0.5$ ), due to increased spanwise shear in the near-wake region. Wavemaker results indicate that $\eta$ affects the convective nature of the shear layer more than the type of instability. DNS results show that different instability mechanisms lead to different development and evolution of vortical structures in the transition process. For $\eta =1$ , the varicose instability is associated with the periodic shedding of hairpin vortices, and its stronger spatial transient growth indicated by wavemaker results aids the formation of hairpin vortices farther downstream. In contrast, for $\eta =0.5$ , the interplay between varicose and sinuous instabilities results in a broader-banded energy spectrum and leads to the sinuous wiggling of hairpin vortices in the near wake when $Re_h$ is sufficiently high. A sinuous mode with a lower frequency captured by dynamic mode decomposition analysis, and associated with the ‘wiggling’ of streaks, persists far downstream and promotes transition to turbulence. A new regime map is developed to classify and predict instability mechanisms based on $Re_{hh}^{1/2}$ and $d/\delta ^{*}$ using a logistic regression model. Although the mean skin friction demonstrates different evolutions for the two geometries, both of them efficiently trip the flow to turbulence at $Re_h=1100$ . An earlier location of a fully-developed turbulent state is established for $\eta =1$ at $x \approx 110h$ .

Hypersonic shock wave and turbulent boundary layer interaction in a sharp cone/flare model

A direct numerical simulation of hypersonic Shock wave and Turbulent Boundary Layer Interaction(STBLI) at Mach 6.0 on a sharp 7° half-angle circular cone/flare configuration at zero angle of attack is performed. The flare angle is 34° and the momentum thickness Reynolds number based on the incoming turbulent boundary layer on the sharp circular cone is Reθ = 2506. It is found that the mean flow is separated and the separation bubble occurring near the corner exhibits unsteadiness. The Reynolds analogy factor changes dramatically across the interaction, and varies between 1.06 and 1.27 in the downstream region, while the QP85 scaling factor has a nearly constant value of 0.5 across the interaction. The evolution of the reattached boundary layer is characterized in terms of the mean profiles, the Reynolds stress components, the anisotropy tensor and the turbulence kinetic energy. It is argued that the recovery is incomplete and the near-wall asymptotic behavior does not occur for the hypersonic interaction. In addition, mean skin friction decomposition in an axisymmetric turbulent boundary layer is carried out for the first time. Downstream of the interaction, the contributions of transverse curvature and body divergence are negligible, whereas the positive contribution associated with the turbulence kinetic energy production and the negative spatial-growth contribution are dominant. Based on scale decomposition, the positive contribution is further divided into terms with different spanwise length scales. The negative contribution is analyzed by comparing the convective term, the streamwise-heterogeneity term and the pressure gradient term.

A Comparative Study of Thermoconvective Flows of a Newtonian Fluid Over Three Horizontal Undulated Surfaces in a Porous Medium

Abstract This paper presents a comparison between the results of three thermoconvective flows of a Newtonian fluid over uniformly heated, undulated horizontal surfaces in a porous medium against the background of the results of a flat plate. The undulations are assumed to have sinusoidal, sawtooth, and triangular waveforms. A system of nonlinear coupled partial differential equations arising in the study is solved using the Keller–Box method. Streamlines and isotherms have been plotted and analyzed to examine the effect of parameters on the fluid dynamics and heat transfer. At large surface amplitudes, secondary flow is observed in the cases of sinusoidal and triangular waveforms, but not in the cases of a sawtooth surface and a flat plate. The magnitude of the slip velocity at the horizontal surface is greatest for the sine waveform, while it is least in the case of triangular. The flat plate does not support slip in the velocity to the extent seen in the case of undulated surfaces. The variation of the mean Nusselt number and mean skin friction with surface amplitude and the Rayleigh number indicate that heat transfer and viscous friction at the boundary increase with individual and collective increases in the values of the amplitude and the Rayleigh number. Further, the mean Nusselt number and mean skin friction are found to be maximum for the sinusoidal surface and minimum for the triangular one. The heat transfer and skin friction by the flat surface are much less than that of all three undulated surfaces.

Universal scaling of mean skin friction in turbulent boundary layers and fully developed pipe and channel flows

A dynamically consistent scaling of mean skin friction in zero-pressure-gradient turbulent boundary layers and fully developed pipe and channel flows, is derived. Theoretical arguments are based on transfer of kinetic energy from mean flow to large eddies of turbulence. A single new velocity scale $M/\nu$ is shown to be dynamically relevant for scaling skin friction in all flows; $M$ is the planar kinematic momentum rate of the shear flow and $\nu$ is fluid kinematic viscosity. An asymptotic $-1/2$ power scaling law (in $M$ – $\nu$ scaling) is shown to be universally applicable. It is observed that the semi-empirical finite- $Re$ skin friction model, resulting from the asymptotic scaling law, applies well to individual flows, but fails to describe all flows in a universal fashion. This non-universality could be due to the differences in flow boundary conditions at finite Reynolds numbers and flow geometry, that affect the outer-layer structures in these flows. It is argued that these differences may be simply absorbed by considering differences in the shapes of mean velocity profiles amongst these flows. An empirical correction to $M$ – $\nu$ scaling is proposed based on Clauser's shape factor $G$ . It is demonstrated that data from all flows in this new, semi-empirical $M$ – $\nu$ – $G$ scaling collapse remarkably well onto a single universal curve. The corresponding universal finite- $Re$ model in $M$ – $\nu$ – $G$ scaling is shown to describe this curve to an excellent accuracy. These results underscore the importance of a dynamically consistent approach towards revealing universality of skin friction scaling in wall turbulence.

Effect of MHD on Unsteady Oscillatory Couette Flow Through Porous Media

This paper describes the effects of a magnetic field on unsteady free convection oscillatory systems. When temperature and species concentration fluctuate with time around a non-zero constant, “Couette flow” across a porous medium occurs. The system of non-linear ODEs that governs the flow is solved analytically using the perturbation approach because the amplitude of fluctuations is very tiny. Mean flow and transient velocity, transient concentration, transient temperature, heat transfer, mean skin friction and phase and amplitude of skin friction. All have approximate solutions. The influence of different parameters on flow characteristics has been specified and discussed.

Comparison of the mean skin friction with the heat transfer and the flow development in turbulent planar wall-attaching jet flows.

Measurements of the mean skin friction below turbulent planar wall-attaching offset jet flows were performed using oil-film interferometry for jets initially offset (Hs) 0.2 to 1 times the jet height (Hj) from the wall. The results were compared with turbulent flow field measurements and with previous heat transfer measurements. The profiles of the mean skin friction coefficient below the offset or preattachment region were similar when compared relative to the distance to the reattachment location (Xr). The initial recovery length of the mean skin friction downstream of the reattachment location was proportional to the reattachment length similar to the decrease in the wall pressure fluctuations in this region. The longer recovery and initial decay of the mean skin friction coefficient appeared to collapse in terms of (x-Xr)/Hj; as did the initial change in the mean static pressure, the measures of the mean flow development, and the Stanton number downstream of the reattachment point. The decay in the maximum of the turbulent stresses associated with the attached shear layer also collapsed in terms of (x-Xr)/Hj, unlike the fluctuating pressure and initial recovery of the mean skin friction. The change in the location of the minimum and zero in the turbulent shear stress as the flows transitioned to the wall jet region collapse in terms of x-Xr/Hj similar to the longer recovery and initial decay of the mean skin friction. The mean skin friction for flows with Hs of Hj and jet Reynolds numbers (Rej) of 21800 to 54500, varied as Rej-0.2 below the attaching jet, in the reattachment region, and in the downstream wall jet region.

Stable channel flow with spanwise heterogeneous surface temperature

Recent studies have demonstrated that large secondary motions are excited by surface roughness with dominant spanwise length scales of the order of the flow's outer length scale. Inspired by this, we explore the effect of spanwise heterogeneous surface temperature in weakly to strongly stratified closed channel flow (at$Ri_\tau =120$, 960;$Re_\tau = 180$, 550) with direct numerical simulations. The configuration consists of equally sized strips of high and low temperature at the lower and upper boundaries, while an overall stable stratification is induced by imposing an average temperature difference between the top and bottom. We consider the influence of the width of the strips (${\rm \pi} /8 \leq \lambda /h \leq 4{\rm \pi} $), Reynolds number, stability and upper boundary condition on the mean flow structure, skin friction and heat transfer. Results indicate that secondary flows are excited, with alternating high- and low-momentum pathways and vortices, similar to the patterns induced by spanwise heterogeneous surface roughness. We find that the impact of the surface heterogeneity on the outer layer depends strongly on the spanwise heterogeneity length scale of the surface temperature. Comparison to stable channel flow with uniform temperature reveals that the heterogeneous surface temperature increases the global friction coefficient and reduces the global Nusselt number in most cases. However, for the high-Reynolds cases with$\lambda /h \geq {\rm \pi} /2$, we find a reduction of the friction coefficient. At stronger stability, the vertical extent of the vortices is reduced and the impact of the heterogeneous temperature on momentum and heat transfer is smaller.

Characteristics of reattached boundary layer in shock wave and turbulent boundary layer interaction

The reattached boundary layer in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer at Mach number 2.25 is studied by means of Direct Numerical Simulation (DNS). The numerical results are carefully compared with available experimental and DNS data in terms of turbulence statistics, wall pressure and skin friction. The coherent vortex structures are significantly enhanced due to the shock interaction, and the reattached boundary layer is characterized by large-scale structures in the outer region. The space-time correlation of fluctuating wall shear stress and streamwise velocity fluctuation reveals that the structural inclination angle exhibits a gradual decrease during the recovery process. The scale interactions are analyzed by using a two-point amplitude modulation correlation. A possible mechanism is proposed to account for the strong amplitude modulation in the downstream region. Moreover, the mean skin-friction is decomposed to understand the physically informed contributions. Unlike the upstream Turbulent Boundary Layer (TBL), the contribution associated with the Turbulence Kinetic Energy (TKE) production is greatly amplified, while the spatial growth contribution induced by the pressure gradient largely inhibits skin-friction generation. Based on bidimensional empirical mode decomposition, the turbulence kinetic energy production contribution is further split into different terms with specific spanwise length scales.

Direct numerical simulation of supersonic turbulent expansion corner with shock impingement

This study conducted a direct numerical simulation of an incident shock wave impinging at an angle of 33.2° on a 12° supersonic turbulent expansion corner at Mach 2.25 to determine the influence of expansion on the physics of interaction. The point of nominal impingement was located at the tip of the expansion corner. This scenario was compared in detail with interactions in the case of a flat plate under the same inflow conditions. The expansion led to a significant reduction in the wall pressure and the size of the separation bubble. The pre-multiplied spectra of the fluctuating wall pressure indicated that the motion induced by the low-frequency shock was strongly inhibited by the presence of an expansion corner. The root mean-squared wall pressure declined rapidly downstream of the corner, and relaxed at a nearly constant level very close to its upstream value. The evolution of the reattached boundary layer was analyzed in terms of its velocity profile, map of anisotropic invariance, and turbulent kinetic energy, and a quick recovery process was clearly identified. Moreover, the analysis of decomposition of the mean skin friction revealed the dominant contribution of the turbulent kinetic energy regardless of the effect of expansion. Unlike in the case of flat-plate interaction, the component of negative spatial growth became positive owing to large positive streamwise heterogeneity, and could be neglected. Bidimensional empirical-mode decomposition was used to decompose the fluctuations into four modes with specific spanwise length scales, and the primary mechanism for the generation of skin friction was linked to small-scale structures in the near-wall region.