We have performed direct numerical simulations of compressible turbulent channel flow using R-134a as a working fluid in transcritical temperature ranges ( $\unicode[STIX]{x0394}T=5$ , 10 and 20 K, where $\unicode[STIX]{x0394}T$ is top-to-bottom temperature difference) at supercritical pressure. At these conditions, a pseudophase change occurs at various wall-normal locations within the turbulent channel from $y_{pb}/h=-0.23$ ( $\unicode[STIX]{x0394}T=5$ K) to 0.89 ( $\unicode[STIX]{x0394}T=20$ K), where $h$ is the channel half-height and $y=0$ the centreplane position. Increase in $\unicode[STIX]{x0394}T$ also results in increasing wall-normal gradients in the semi-local friction Reynolds number. Classical, compressible scaling laws of the mean velocity profile are unable to fully collapse real fluid effects in this flow. The proximity to the pseudotransitioning layer inhibits turbulent velocity fluctuations, while locally enhancing the temperature and density fluctuation intensities. Probability distribution analysis reveals that the sheet of fluid undergoing pseudophase change is characterized by a dramatic reduction in the kurtosis of density fluctuations, hence becoming thinner as $\unicode[STIX]{x0394}T$ is increased. Instantaneous visualizations show dense fluid ejections from the pseudoliquid viscous sublayer, some reaching the channel core, causing positive values of density skewness in the respective buffer layer region (vice versa for the top wall) and an impoverishment of the turbulent flow structure population near pseudotransitioning conditions.

A novel approach to identify internal interfacial layers, or IILs, in wall-bounded turbulent flows is proposed. Using a fuzzy cluster method (FCM) on the streamwise velocity component, a unique and unambiguous grouping of the uniform momentum zones (UMZs) is achieved, thus allowing the identification of the IILs. The approach overcomes some of the key limitations of the histogram-based IIL identification methods. The method is insensitive to the streamwise domain length, can be used on inhomogeneous grids, uses all the available flow field data, is trivially extended to three dimensions and does not need user-defined parameters (e.g. number of bins) other than the number of zones. The number of zones for a given snapshot can be automatically determined by an a priori algorithm based on a kernel density estimation algorithm, or KDE. This automated approach is applied to compute the average number of UMZs as a function of Reynolds number $Re_{\unicode[STIX]{x1D70F}}$ in turbulent channel flows in several numerical simulations. This systematic approach reveals a dependence of the Reynolds number on the average number of UMZs in the channel flow; this supports previously reported observations in the boundary layer. The fuzzy clustering approach is applied to the turbulent boundary layer (experimental, planar particle image velocimetry) and channel flow (numerical, direct numerical simulation) at varying Reynolds numbers. The interfacial layers are characterized by a strong concentration of spanwise vorticity, with the outer-most layer located at the upper edge of the log layer. The three-dimensional interface identification reveals a streak-like organization. The large-scale motion (LSM) at the outer region of the channel flow boundary layer modulates the outer IIL. The corrugations of the outer IIL are aligned with the LSM and the conditional correlation of the inner and outer IIL height shows that extreme near-wall events leave their mark on the outer IIL corrugations.

Hypersonic flow conditions pose exceptional challenges for Reynolds-averaged Navier–Stokes (RANS) turbulence modeling. Critical phenomena include compressibility effects, shock/turbulent boundary layer interactions, turbulence–chemistry interaction in thermo-chemical non-equilibrium, and ablation-induced surface roughness and blowing effects. This comprehensive review synthesizes recent developments in adapting turbulence models to hypersonic applications, examining approaches ranging from empirical modifications to physics-based reformulations and novel data-driven methodologies. We provide a systematic evaluation of current RANS-based turbulence modeling capabilities, comparing eddy viscosity and Reynolds stress transport formulations in their ability to predict engineering quantities of interest such as separation characteristics and wall heat transfer. Our analysis encompasses the latest experimental and direct numerical simulation datasets for validation, specifically addressing two- and three-dimensional equilibrium turbulent boundary layers and shock/turbulent boundary layer interactions across both smooth and rough surfaces. Key multi-physics considerations including catalysis and ablation phenomena along with the integration of conjugate heat transfer into a RANS solver for efficient design of a thermal protection system are also discussed. We conclude by identifying the critical gaps in the available validation databases and limitations of the existing turbulence models and suggest potential areas for future research to improve the fidelity of turbulence modeling in the hypersonic regime.

We study the boundary-layer turbulence and freestream turbulence interface (BTFTI), the turbulent spot and freestream turbulence interface (TSFTI), and the laminar boundary-layer and freestream turbulence interface (LBFTI) using direct simulation. Grid spacings in the freestream are less than 1 Kolmogorov length scale during transition. Probability density functions of temperature and its derivatives are used to select the interface identification threshold, corroborated by a vorticity-based method. The interfaces so detected are confirmed to be physical a posteriori by the distinctive quasi-step-jump behavior in the swirling strength and temperature statistics along traverses normal to the BTFTI and TSFTI. No interface-normal inflection is detected across the LBFTI for either swirling strength, temperature, vorticity magnitude, Reynolds shear stress, streamwise velocity, normal velocity, or turbulence kinetic energy. The present direct numerical simulation data thus cast serious doubts on the shear-sheltering hypothesis/theory, which asserts that a subset of freestream fluctuations is blocked by the LBFTI. In the early stage of transition, quasi-spanwise structures exist on the LBFTI. The TSFTI shape is dominated by head prints of concentrated hairpin vortices. Further downstream, the BTFTI geometry is strongly modulated by groves of hairpin vortices (the boundary layer large-scale motions) with a distinct streamwise preferential orientation. Streamwise velocity and turbulence kinetic energy only exhibit minor plateaus (rather than quasi-step-jump) across the BTFTI and the TSFTI. We emphasize that it is more meaningful and important to acquire reproducible and reliable interface-normal statistics prior to considering any plausible substructures and elusive transient dynamics of the BTFTI, TSFTI, and LBFTI.