Supersonic Boundary Layer Research Articles

On the stability of supersonic boundary layer in interaction with weak shock waves

Numerical simulation of the problem of interaction of the supersonic (M∞=2) boundary layer on the plate with weak shock waves was performed. The shock wave was generated using a wedge located above the plate. The problem was solved using the computational technology, combining the ANSYS Fluent gasdynamic package, which calculates the main flow, and the LOTRAN 3.0 software package, which calculates not only the stability of no-break flow, but also the laminar flow failure. The intensity of the incident shock wave was varied by varying the wedge inclination angle. The N-factor envelopes of the Tollmien-Schlichting wave instability for different wedge tilt angles, including those in the local breakaway zones, were obtained. It is demonstrated that the proposed approach using the ANSYS Fluent and LOTRAN 3.0 combination computational technology allows one to calculate the stability of flows with the shockwave, including the presence of local breakaway zones.

Turbulence amplification in the shock wave/turbulent boundary layer interaction over compression ramp by the flux reconstruction method

Wall-resolved large eddy simulation on a supersonic turbulent boundary layer over a 24° compression ramp is performed under the framework of high order discontinuous methods for a free-stream Mach number M∞=2.9 and Reynolds number Re∞=5.966×106. The turbulent flow is resolved by the high order flux reconstruction method, and the shock is captured by a high-resolution, but stable weighted essentially non-oscillation limiter. The solver used in this paper is validated by the double Mach reflection case and the Taylor–Green vortex case. The results of shock wave/turbulent boundary layer interaction at the ramp corner are validated by the numerical simulations and the experimental data in the literature. The analysis of the physics behind the turbulence amplification at around the ramp corner is presented. The shear effects and the flow deceleration/acceleration are the main reasons of the turbulence amplification.

Wall pressure fluctuations in supersonic boundary layers over compression ramps with different turning angles

In the present study, we investigate influences of shock intensity on wall pressure fluctuations by performing direct numerical simulations of supersonic turbulence boundary layers over compression ramps with different turning angles. We found that as the turning angle increases, low-frequency motions of the separation shock are enhanced, accompanied by enlarged energetic pressure structures with lower convection velocities. By inspecting wavenumber-frequency spectra under the assumption of streamwise homogeneity, we further identified two energetic modes convected at different velocities. The one with the lower convection velocity, namely, the “slow mode,” inherited from the upstream pressure fluctuations of the turbulent boundary layer, is decelerated when passing through the oblique shock, during which the “rapid mode” with pressure fluctuations convected at higher speeds are generated. The increasing turning angle decelerates the slow mode and intensifies the fast mode. The reconstruction of the flow field suggests that the rapid mode is associated with the shear layer generated adjacent to the interaction zone, while the slow mode is associated with the Görtler vortices on the ramp.

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.

Effective aero-optical suppression by steady wall blowing and wall suction schemes for supersonic turbulent boundary layer

AbstractAs a basic flow model for engineering applications, wall-bounded turbulent flow has been widely studied in the field of aero-optics, but the flow control methods that could effectively suppress aero-optical effects are relatively rare. As an urgent requirement in engineering application, the concept of the steady wall blowing and suction is proposed by the author. Firstly, the author briefly described the flow model and physical method. Secondly, the choice of disturbance type is given. Then, the results of wall blowing-suction, suction and blowing ways based on steady and unsteady disturbance are compared. Finally, it is concluded that employing the high steady wall blowing disturbance (A = 0.2) could realise aero-optical suppression by around 20%. Besides, the steady wall suction scheme contributes to about 70%–80% reduction effect within a wide amplitude range (A = 0.2–1.0), which suppresses this effect by maintaining laminar state downstream contrasted by the baseline case.

Time-resolved visualization of coherent structures during supersonic boundary layer transition

The coherent structures arising during flat-plate boundary layer transition at Mach number 3.4 are investigated using a custom-built hyper-rate imaging system. The evolution of transitional structures is investigated in the Eulerian and Lagrangian reference frames. The upstream evolution of transition is dominated by the generation of new hairpin structures, while the interaction among multiple structural types dominates the evolution downstream. The breakdown of the existing structure, which may be caused by interactions among multiple types of structures with similar scales, is also visualized.

Wall-attached temperature structures in supersonic turbulent boundary layers

It is well known that low- and high-speed velocity streaks are statistically asymmetric. However, it is unclear how different the low- and high-temperature structures (T-structures) are even though they are strongly coupled with the streamwise velocity. Therefore, this paper identifies three-dimensional wall-attached temperature structures in supersonic turbulent boundary layers over cooled and heated walls (coming from direct numerical simulations) and separates them into positive and negative families. Wall-attached T-structures are self-similar; especially, the length and width of the positive family are linear functions of the height. The superposed temperature variance in both positive and negative families exhibits a logarithmic decay with the wall distance, while the superposed intensity of the wall-normal heat flux in the negative family shows a logarithmic growth. The modified strong Reynolds analogy proposed by Huang, Coleman, and Bradshaw [“Compressible turbulent channel flows: DNS results and modelling,” J. Fluid Mech. 305, 185–218 (1995)] is still valid in the negative family. The relative position between T-structures of opposite signs depends on the wall temperature and that in the cooled-wall case differs significantly from the relative position between low- and high-speed streaks, especially those tall ones. In the cooled-wall case, although positive temperature fluctuations below and above the maximum of the mean temperature can cluster to large-scale wall-attached structures, they are very likely dynamically unrelated.

Experimental investigation on evolution characteristics of high- and low-speed streaks in supersonic turbulent boundary layer

High-speed and low-speed streak structures in the near wall region of a turbulent boundary layer with a Mach number of 3 are experimentally examined by employing the spatiotemporally resolved nanoparticle plane laser scattering technique. The time evolution characteristics of the high-speed and low-speed streaks in the supersonic turbulent boundary layer are systematically investigated through the speed field sequence results at various time intervals. The obtained results reveal that the dynamic behavior of the bands is chiefly represented by the translation along the flow direction. The process of dissipation of the existing streaks and the formation of a new streak is also observed and analyzed. The duration values of the high-speed and low-speed streak structures are assessed by utilizing the time-resolved characteristics of the speed field, and the predicted duration of the streak structure and the maximum flow length exceed 306 µs and 23.6 times the thickness of the boundary layers, respectively. Finally, the merging phenomenon of medium and low-speed streaks in the turbulent boundary layer is carefully scrutinized. The merging of low-speed streaks observed under supersonic conditions is consistent with the vortex packet merging model proposed by Tomkins and Adrian.

A modified wall-adapting local eddy-viscosity model for large-eddy simulation of compressible wall-bounded flow

The wall-adapting local eddy-viscosity (WALE) model in large-eddy simulation can well predict wall-bounded flows but it is also well known for excessive dissipation. In this study, we apply the minimum-dissipation model to constrain the WALE model in compressible flows and obtain the coefficient of the WALE model. Through this process, the dissipation of WALE model can be lower while it still maintains strong stability. In the modified WALE model, the isotropic part of the subgrid-scale (SGS) stress is also reconstructed. In the filtered total energy equation, all of the extra SGS unclosed terms (besides SGS stress and SGS heat flux) are modeled instead of neglecting some SGS terms, such as the SGS viscous diffusion. The modified WALE model is tested in a compressible turbulent channel flow and a supersonic turbulent boundary layer over a compression corner. The new model can well predict the mean velocity, the mean temperature, the Reynolds stress, and the separation bubble.

Revisit of the oblique-breakdown regime in supersonic boundary layers and mechanism of the extra amplification of streak modes

In the low-Mach-number supersonic boundary layers, the oblique-breakdown regime may be the most efficient route to trigger the laminar–turbulent transition, because the most unstable Mack first mode always appears as an oblique wave. In this paper, we revisit this issue by use of the nonlinear parabolized stability equation (NPSE) approach and particularly focus on the extra amplification of the streak mode generated by the direct interaction of the introduced oblique modes. This mechanism is then well explained based on the weakly nonlinear analysis, and its predictions on the evolution of the streak mode and the two-dimensional traveling-wave mode are quantitatively confirmed by the NPSE calculations. Additionally, the important role of the streak mode, leading to the secondary instability, on triggering the transition onset is identified.

Effect of expansion on the wall heat flux in a supersonic turbulent boundary layer

Direct numerical simulation of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.25 and a friction Reynolds number of Reτ = 769 subjected to an expansion corner with a deflection angle of 12° is performed to investigate the effect of expansion on the characteristics of the wall heat flux (WHF). The effect of expansion on the statistical and structural properties of the fluctuating WHF is analyzed systematically in terms of probability density function, frequency spectra, and space-time correlations. Normalization using the local root mean square value yields good collapse of the probability density function curves. Unlike with wall pressure frequency spectra, it is found that expansion has little influence on the low-frequency components of the WHF spectrum. The correlation results show that the main effect of expansion is to increase the characteristic length scales and convection velocity of the WHF fluctuation in the post-expansion region. Furthermore, a direct comparison between the conditionally averaged flow fields and those presented in the authors' previous work [Tong et al., Phys. Fluids 34, 015127 (2022)] is performed to uncover the effect of expansion on the flow structures associated with extreme positive and negative WHF fluctuation events. We highlight that the extreme positive event emerges below a small hot spot under the action of a strong Q4 event, whereas the extreme negative event is relatively insensitive to expansion and still occurs between a pair of strong oblique vortices. In addition, we decompose the mean WHF into seven physics-informed contributions and quantify the effect of expansion on the dominating components with the aid of the bidimensional empirical mode decomposition method. The scale-decomposed results demonstrate quantitatively that expansion decreases the contribution of the large-scale structures in the outer region but the small-scale structures in the near-wall region contribute heavily to the mean WHF generation in the downstream region.

Investigation of the secondary flow by convergent–divergent riblets in a supersonic turbulent boundary layer over a compression ramp

In this paper, the effect of the secondary flow induced by convergent–divergent riblets in supersonic turbulent boundary layers over a 24° compression ramp at Mach number 2.9 is studied via direct numerical simulation. Two riblet cases with the wavelength Λ being 1.1δ and 1.65δ (δ is the boundary layer thickness) are conducted to examine their impact on the secondary rolling motion, momentum transfer, turbulent fluctuations, flow separation, and unsteady shock motion. As the flow develops over the riblet section, both the size and intensity of the secondary rolling motion tend to increase. For the riblet case with Λ/δ=1.1, a single rolling mode is observed within a half wavelength, while a pair of co-rotating vortical structures is obtained for Λ/δ=1.65. Both rolling patterns lead to an apparent spanwise variation of the flow field. The results reveal that the secondary flow contributes to the increase of both the mean momentum flux and turbulent fluctuations. By using the spanwise averaging, the mean momentum flux contributed from the dispersive stress and compressible effect caused by the secondary flow is identified. Both components appear to enhance the near-wall momentum mixing, and a larger enhancement is observed for Λ/δ=1.1, where the intensity of the secondary flow is stronger. Compared to the baseline case, the area of the separation zone at Λ/δ=1.1 and Λ/δ=1.65 is decreased by 56% and 38%, respectively. For all the cases, the low-frequency motion near the foot of the shock is observed. In comparison, the frequency of the low-frequency motion for the riblet case is two times higher than that in the baseline case, owing to the reduction of the separation area and length.

Control of oblique breakdown in a supersonic boundary layer employing a local cooling strip

Oblique breakdown in a Mach 2.0 supersonic boundary layer controlled by a local cooling strip with a temperature jump is investigated using direct numerical simulations and linear stability theory. The effect of temperature on the stability of the fundamental oblique waves is first studied by linear stability theory. It is shown that the growth rate of fundamental oblique waves will decrease monotonically as the temperature decreases. However, the results of the direct numerical simulations indicate that transition reversal will occur as the growth rate of the fundamental oblique waves of cooled case becomes faster compared with that of baseline case downstream of the cooling strip. When the cooling strip is in the linear region, the transition is delayed due to the suppression effect of the cooling strip on the fundamental oblique waves. When the cooling strip is located in the early nonlinear region, the fundamental oblique waves will be suppressed by higher spanwise wavenumber steady modes generated by the mutual and self-interaction between the fundamental oblique waves and harmonic modes, which is first called the self-suppression effect (SSE) in the present study. Further research indicated that the meanflow distortion generated by steady modes plays an important role in the SSE. Compared with the stabilization effect of the cooling strip, the SSE is more effective. Moreover, the SSE might provide a new idea on the instability control, as it is observed that the SSE works three times leading to the growth rate of fundamental oblique waves slowing down at three different regions, respectively.

Effect of injection of gas with high specific heat capacity on supersonic boundary-layer stability to controlled disturbances

A study of the effect of distributed gas with high specific heat capacity blowing into the supersonic boundary layer on its stability to artificial disturbances was conducted. It is shown that the injection of gas with high heat capacity Cp at certain flow values can lead to the stabilization of the supersonic boundary layer.

Influence of jet spacing in spanwise-inclined jet injection in supersonic crossflow

In separation control with air-jet vortex generators in supersonic flow, the spacing of the jets in a row array has a crucial effect on the control effectiveness. Previous experimental studies have revealed the overall influence of jet spacing on air-jet vortex generator controlled shock-induced separation zones, focusing mostly on the separation regions. There is, however, a gap in knowledge regarding the mechanisms leading to these changes in control effectiveness, particularly on the interaction between multiple jets and the details of downstream flow evolution. Therefore, the objective of the current study is to provide detailed information on the underlying flow dynamics associated with the injection of a row of spanwise-inclined jets into a supersonic turbulent boundary layer – and in particular the effects of different jet spacings. Four different spacings were studied with large-eddy simulations. In addition, we performed oil-flow and schlieren visualizations of separation control in a 24$^\circ$compression–ramp interaction with different jet-spacing configurations to validate and discuss our conclusions regarding the effects of jet/jet interactions on the separation-control effectiveness. We analyse the influence of jet spacing on the flow topology, induced vortical structures, and boundary-layer statistics. The jet-induced major vortex pair is the dominant flow structure energizing the near-wall boundary layer. The paper details how interactions amongst adjacent vortex pairs differ for varying jet spacings, thus influencing the momentum transfer and eventually the control efficiency. The dynamic behaviour of the flow was analysed using a three-dimensional dynamic mode decomposition. The resulting insights are key to the development of efficient control set-ups.

Linking supersonic boundary layer separation to structural deformation using the Kármán–Pohlhausen momentum-integral equation

A first-order link between local separation of supersonic turbulent boundary layer flow and structural deformation is established. First, mathematical analysis of the Kármán–Pohlhausen momentum integral equation is carried out with the assumption of spatially varying surface topology in order to identify fluid-centric representations of structural deformation. Next, a data-driven approach is used to identify the dominant fluid-centric parameters. This ultimately yields a simple linear correlation between local skin friction coefficient and surface curvature, which is the unifying parameter relating deformation and separation. This link represents a key step toward deep understanding of the nuanced interplay between turbulent boundary layers and structural deformation and significantly improves fundamental understanding of fluid-structure interaction problems with prominent turbulent boundary layer dynamics.

Positive and negative pairs of fluctuating wall shear stress and heat flux in supersonic turbulent boundary layers

The negative and positive fluctuations of wall shear stress τ′x and wall heat flux q′w can be related to the wall-attached paired up large-scale velocity and temperature streaks. It is justifiable to infer the spatially paired-up coexistence of those wall flow quantities. The present study aims at testifying this hypothesis. We establish such relations between the negative and positive wall shear stress by exploiting a direct numerical simulation database over heated and cooled walls at the friction Reynolds number of 800 and the Mach number of 2.25. The clustering method is adopted for the search of the in-pair structures. It is found that the τx- and qw-structures are less self-similar for flows over cold walls. As they become wider, the τx-structures are increasingly more streamwise stretched, while the trend is reversed for qw-structures. τx-structures of opposite signs are paired up and aligned in the spanwise directions as the wall-attached streamwise velocity, and are left behind by streamwise rollers. The relative position between qw-structures of opposite signs, on the other hand, is sensitive to the wall temperature. Scrutinizing the statistical structures, we elucidate that such spatial coherence is determined by the meandering of velocity streaks that yields strong streamwise gradients of the streamwise velocity.

Direct numerical simulation of shock-wave/boundary layer interaction controlled with convergent–divergent riblets

In this paper, a section of convergent–divergent (C–D) riblets is applied upstream of a compression ramp in a supersonic turbulent boundary layer in a Mach 2.9 flow with a Reynolds number of Reθ=2240. Direct numerical simulations are undertaken to examine the impact of C–D riblets on the shock wave/boundary layer interaction and the feasibility of using them to mitigate flow separation. Over the riblet section, a large-scale secondary roll mode is produced by C–D riblets with the downwelling motion occurring around the diverging region and upwelling motion near the converging region. This consequently leads to a spanwise heterogeneity in mean quantities and turbulent structures over the riblet section and also in the interaction zone. Compared with the baseline case, the area of the separation zone for the riblet case experiences a dramatic local reduction of 92% in the diverging region, owing to the downwelling motion that injects the high-momentum fluid toward the wall and the near-wall spanwise velocity that transports the low-momentum fluid away. The enhanced upwelling motion around the converging region induced by C–D riblets, on the one hand, contributes to the decrease of the near-wall momentum and subsequently the increase of the local separation area. On the other hand, the upwelling motion effectively reduces the incoming Mach number upstream of the compression corner. This appears to reduce the strength of the separation shock, leading to a more gradual compression of the incoming flow that helps ease the enlargement of the separation area nearby. Overall, the area of the mean flow separation is reduced by 56%, indicating an effective flow separation control by the C–D riblets.

Direct numerical simulation of supersonic and hypersonic turbulent boundary layers at moderate-high Reynolds numbers and isothermal wall condition

We study the structure of high-speed zero-pressure-gradient turbulent boundary layers up to friction Reynolds number $Re_{\tau } \approx 2000$ using direct numerical simulation of the Navier–Stokes equations. Both supersonic and hypersonic conditions with nominal free-stream Mach numbers $M_{\infty }=2$ , $M_{\infty }=5.86$ and heat transfer at the wall are considered. The present simulations extend the database currently available for wall-bounded flows, enabling us to explore high-Reynolds-number effects even in the hypersonic regime. We first analyse the instantaneous fields to characterize the structure of both velocity and temperature fluctuations. In all cases elongated strips of uniform velocity and temperature (superstructures) are observed in the outer portion of the boundary layer, characterized by a clear association between low-/high-speed momentum and high/low temperature streaks. The results highlight important deviations from the typical organization observed in the inner region of adiabatic boundary layers, revealing that the near-wall temperature streaks disappear in strongly non-adiabatic flow cases. We also focus on the structural properties of regions of uniform streamwise momentum (De Silva, Hutchins & Marusic, J. Fluid Mech., vol. 786, 2016, pp. 309–331) observed in turbulent boundary layers, confirming the presence of such zones in the high-speed regime at high Reynolds number and revealing the existence of similar regions for the temperature field. The accuracy of different compressibility transformations and temperature–velocity relations is assessed extending their range of validation to moderate/high Reynolds numbers. Spanwise spectral densities of the velocity and temperature fluctuations at various wall distances have been calculated revealing the energy content and the size of the turbulent eddies across the boundary layer. Finally, we propose a revised scaling for the characteristic length scales, that is based on the local mean shear computed according to the recent theory by Griffin, Fu & Moin [Proc. Natl Acad. Sci. USA, vol. 118 (34)].

Stochastic receptivity of laminar compressible boundary layers: An input-output analysis

In this study, a receptivity analysis of streaks, oblique and two-dimensional flow structures is presented with a stochastic receptivity framework for different inputs for supersonic adiabatic boundary layer flows. In particular, an active role of temperature fluctuation is identified for the amplification of oblique patterns, while a passive role is observed for the onset of streaks and two-dimensional flow structures. From a practical point of view, this study can help to improve the effectiveness of actuators aiming at a particular response in supersonic boundary layer flows.