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We use the Reynolds-averaged Navier–Stokes (RANS) equations with a full Reynolds stress model (RSM) to study the effect of the corner angle in supersonic corner flow. RANS data are compared to reference direct numerical simulation of fully developed a square duct flow, which support predictive capability of secondary flows from Stress-ω RSM. We then carry out a parametric study by changing the corner angle in the range θ = 45 °– 135 °, focusing on the effect on the mean streamwise and secondary flow. The maximum strength of the secondary flows of about 0.015 u ∞ occurs for θ = 90 °, which is similar to what is found in fully developed square ducts. Secondary eddies have approximately unit aspect ratio, and they maintain their shape for different corner angles by translating in the direction parallel to the closest wall. As a result, the position of the vortex center can be described by a simple geometrical transformation of the wall-parallel coordinate. We find that small corner angles are responsible for locally relaminarization flow at the corner, but otherwise the mean streamwise velocity profiles transformed according to van Driest following the canonical law-of-the-wall.

Fin-generated swept shock wave/turbulent boundary layer interactions were experimentally investigated via nanoparticle-based planar laser scattering method, surface oil flow visualizations, surface pressure measurements, and particle image velocimetry. Surface plateau pressure is also theoretically predicted. The plateau pressure of present quasi-conical swept shock interaction is dependent on the local skin friction coefficient and normal Mach number component, and can be predicted per a criterion deduced from free interaction theory. Visualizations and surface pressure measurements confirm that the surface plateau pressure data are equal to the pressure downstream of the separation shock; the upstream influence line is parallel to the impingement line of the separation shock on the flat plate. These observations support the free interaction theory as-applied to quasi-conical swept shock interactions.

By employing a nanoparticle-based planar laser scattering technique, with inflow Mach number of 2.95, boundary layers formed over two concave walls with respective curvature radii of 113 and 908 mm are visualized. The formation and the breakup process of the Gortler vortices have been clearly captured, which has seldom been done before under the supersonic condition. Different from the incompressible case, the breakup of the Gortler vortices in the supersonic boundary layer is found to be mainly attributed to the varicose mode instability. The Gortler vortices are not stationary, instead they are moving in the spanwise direction.

Direct numerical simulation is conducted to uncover the response of a supersonic turbulent boundary layer to streamwise concave curvature and the related physical mechanisms at a Mach number of 2.95. Streamwise variations of mean flow properties, turbulence statistics and turbulent structures are analysed. A method to define the boundary layer thickness based on the principal strain rate is proposed, which is applicable for boundary layers subjected to wall-normal pressure and velocity gradients. While the wall friction grows with the wall turning, the friction velocity decreases. A logarithmic region with constant slope exists in the concave boundary layer. However, with smaller slope, it is located lower than that of the flat boundary layer. Streamwise varying trends of the velocity and the principal strain rate within different wall-normal regions are different. The turbulence level is promoted by the concave curvature. Due to the increased turbulence generation in the outer layer, secondary bumps are noted in the profiles of streamwise and spanwise turbulence intensity. Peak positions in profiles of wall-normal turbulence intensity and Reynolds shear stress are pushed outward because of the same reason. Attributed to the Görtler instability, the streamwise extended vortices within the hairpin packets are intensified and more vortices are generated. Through accumulations of these vortices with a similar sense of rotation, large-scale streamwise roll cells are formed. Originated from the very large-scale motions and by promoting the ejection, sweep and spanwise events, the formation of large-scale streamwise roll cells is the physical cause of the alterations of the mean properties and turbulence statistics. The roll cells further give rise to the vortex generation. The large number of hairpin vortices formed in the near-wall region lead to the improved wall-normal correlation of turbulence in the concave boundary layer.

The separation length of shock wave/boundary layer interaction (SWBLI) was studied by a numerical method, which was validated by experimental results. The computational domain was two-dimensional (2-D). The flow field was an incident oblique shock interacting with a turbulent boundary layer on a flat adiabatic plate. According to the simulation data, the dependency of the separation length on the relevant flow parameters, such as the incident shock strength, Reynolds number, and Mach number, was analyzed in the range of 2≤M≤7. Based on the relations with the flow parameters, two models of the separation length at low and high Mach numbers were proposed, respectively, which can be used to predict the extent of the separation in the SWBLI.

The structural properties and the phase transition for scandium carbide (ScC) have been studied in NaCl (B1), CsCl (B2), ZB (B3), WZ (B4), NiAs (B81), WC (B h ), and Pmmn structures by using the pseudopotential plane-wave method in the framework of the density functional theory. Our theoretical results show that the most stable structure is the B1 phase, contrary to the result of Rahim et al. The phase transitions B1 → Pmmn and Pmmn → B2 are predicted at 83.7 and 109.7 GPa, respectively. At the same time, we find that the B3, B4, B81, and B h phases are not stable over the whole pressure range considered. In particular, the elastic constants of Pmmn-ScC under high pressure are obtained successfully. The effects of pressure on the elastic properties of B1-ScC and Pmmn-ScC are also predicted. The Debye temperatures Θ and the sound velocities of these two structures are estimated from the elastic constants, and by analyzing G/B, the brittle-ductile behavior of ScC is assessed. In addition, the density of states of B1-ScC at high pressures is also discussed.

The structure of ZrB2 under high-pressure was predicted by Particle Swarm Optimization method (CALYPSO). We investigated the structure stability, phonon dispersion curve, elasticity, electronic structure and thermodynamic properties of ZrB2 under high-pressure and high-temperature via first-principles calculations. It maintained the hexagonal structure when the pressure lowers below 600 GPa at 0 K, which is confirmed by the calculated phonon dispersion curve. Studies indicate that the elastic modulus and Poisson’s ratio increase monotonically with pressure, as supported by some theoretical and experimental evidences. Calculated anisotropic factors demonstrate that compression and shear isotropy of ZrB2 weakens as the pressure increases. Using the quasi-harmonic approximation Debye model, the Debye temperature, sound velocity, expansion coefficient, thermal capacity under the high-temperature and pressure were also predicted.

With an inflow Mach number of 2.95, the isolated impacts of the convex curvature and the streamwise favorable pressure gradient on the supersonic turbulent boundary layer are experimentally investigated by employing particle image velocimetry. An experiment on the convex turbulent boundary layer with a zero streamwise pressure gradient is carefully arranged to investigate the impact of the streamline curvature. The results are compared with the favorable-pressure-gradient case (with pressure gradient parameter β = −0.60). For both of the zero-pressure-gradient and the favorable-pressure-gradient convex boundary layers, the log law is found to be well preserved in the streamwise velocity profile with inner scaling. The streamline convex curvature and the streamwise favorable pressure gradient are found to have similar impacts on the distribution of mean streamwise velocity. They both weaken the boundary layer’s wake strength, as well as the principal strain rate in the near wall region. While both of the convex streamline curvature and the favorable pressure gradient are observed to dampen the streamwise turbulent fluctuation, their effects on the normal fluctuation are opposite. The convex curvature reinforces the normal fluctuation, and its strengthening effect is much stronger than the relaxation effect of the favorable pressure gradient. Retrograde vortices are notably weakened by the favorable pressure gradient, which contributes to the relaxation of turbulence. The impacts of the streamline convex curvature and the streamwise favorable pressure gradient are more notable in the outer layer, while in the near wall region their contributions are weakened.

For a better understanding of the local unstart of supersonic/hypersonic inlet, a series of experiments has been conducted to investigate the shock-induced boundary layer separation extended to the leading edge. Using the nanoparticle-based planar laser scattering, we recorded the fine structures of these interactions under different conditions and paid more attention to their structural characteristics. According to their features, these interactions could be divided into four types. Specifically, Type A wave pattern is similar to the classic shock wave/turbulent boundary layer interaction, and Type B wave configuration consists of an overall Mach reflection above the large scale separation bubble. Due to the gradual decrease in the size of the separation bubble, the separation bubble was replaced by several vortices (Type C wave pattern). Besides, for Type D wave configuration which exists in the local unstart inlet, there appears to be some flow spillage around the leading edge.

By employing the particle image velocimetry, the mean and turbulent characteristics of a Mach 2.95 turbulent boundary layer are experimentally investigated without the impact of curvature. The physical mechanism with which the streamwise adverse pressure gradient affects the supersonic boundary layer is revealed. The data are compared to that of the concave boundary layer with similar streamwise distributions of wall static pressure to clarify the separate impacts of the adverse pressure gradient and the concave curvature. The logarithmic law is observed to be well preserved for both of the cases. The dip below the logarithmic law is not observed in present investigation. Theoretical analysis indicates that it could be the result of compromise between the opposite impacts of the compression wave and the increased turbulent intensity. Compared to the zero pressure gradient boundary layer, the principal strain rate and the turbulent intensities are increased by the adverse pressure gradient. The shear layer formed due the hairpin packets could be sharpened by the compression wave, which leads to higher principal strain rate and the associated turbulent level. Due to the additional impact of the centrifugal instability brought by the concave wall, even higher turbulent intensities than that of the adverse pressure gradient case are introduced. The existence of velocity modes within the zero pressure gradient boundary layer suggests that the large scale motions are statistically well organized. The generation of new velocity modes due to the adverse pressure gradient indicates that the turbulent structure is changed by the adverse pressure gradient, through which more turbulence production that cannot be effectively predicted by the Reynolds-stress transport equations could be brought.

Structural responses of the supersonic turbulent boundary layer to the expansions induced by a convex wall and a ramp are experimentally investigated. Relaminarization of part of the turbulent boundary layer in the near wall region is clearly visualized, which has been seldom presented before. The relaminarized layers formed over two test models are different. While a thicker relaminarized layer is observed for the ramp, a longer lasting layer is noticed for the convex wall. The structure angle is found to be increased by the expansions. Increases of turbulence scale and boundary layer thickness are observed. The contribution of the bulk dilatation to the boundary layer growth is stronger than that of the centrifugal force.

By employing particle image velocimetry, the response of a Mach 2.95 turbulent boundary layer to the concave curvature is experimentally investigated. The radius of the concave wall is 350 mm, and the turning angle is 20∘. Logarithmic law is well preserved in the profile of streamwise velocity at all streamwise positions despite the impact of curvature. The varying trend of principal strain rate is found to be different at different heights within the boundary layer, which cannot be explained by the suggestion given by former researchers. Based on the three-layer model proposed in this paper, distribution of the principal strain rate is carefully analyzed. The streamwise increase of wall friction is suggested to be brought by the increase of velocity gradient in the thin subsonic layer. Increases of the static temperature and the related sound speed are responsible for that. Larger correlated turbulent motions could be introduced by the concave curvature. The probability density histograms of streamwise velocity reveal that the large scale hairpin packets are statistically well organized. The concave curvature is found to have the potential of reinforcing the organization, which explains the increase of turbulent level in the supersonic concave boundary layer.