A hypersonic, spatially evolving turbulent boundary layer at Mach 12.48 with a cooled wall is analysed by means of direct numerical simulations. At the selected conditions, massive kinetic-to-internal energy conversion triggers thermal and chemical non-equilibrium phenomena. Air is assumed to behave as a five-species reacting mixture, and a two-temperature model is adopted to account for vibrational non-equilibrium. Wall cooling partly counteracts the effects of friction heating, and the temperature rise in the boundary layer excites vibrational energy modes while inducing mild chemical dissociation of oxygen. Vibrational non-equilibrium is mostly driven by molecular nitrogen, characterized by slower relaxation rates than the other molecules in the mixture. The results reveal that thermal non-equilibrium is sustained by turbulent mixing: sweep and ejection events efficiently redistribute the gas, contributing to the generation of a vibrationally under-excited state close to the wall, and an over-excited state in the outer region of the boundary layer. The tight coupling between turbulence and thermal effects is quantified by defining an interaction indicator. A modelling strategy for the vibrational energy turbulent flux is proposed, based on the definition of a vibrational turbulent Prandtl number. The validity of the strong Reynolds analogy under thermal non-equilibrium is also evaluated. Strong compressibility effects promote the translational–vibrational energy exchange, but no preferential correlation was detected between expansions/compressions and vibrational over-/under-excitation, as opposed to what has been observed for unconfined turbulent configurations.

The influence of dense-gas effects on compressible wall-bounded turbulence is investigated by means of direct numerical simulations of supersonic turbulent channel flows. Results are obtained for PP11, a heavy fluorocarbon representative of dense gases, the thermophysics properties of which are described by using a fifth-order virial equation of state and advanced models for the transport properties. In the dense-gas regime, the speed of sound varies non-monotonically in small perturbations and the dependency of the transport properties on the fluid density (in addition to the temperature) is no longer negligible. A parametric study is carried out by varying the bulk Mach and Reynolds numbers, and results are compared to those obtained for a perfect gas, namely air. Dense-gas flow exhibits almost negligible friction heating effects, since the high specific heat of the fluids leads to a loose coupling between thermal and kinetic fields, even at high Mach numbers. Despite negligible temperature variations across the channel, the mean viscosity tends to decrease from the channel walls to the centreline (liquid-like behaviour), due to its complex dependency on fluid density. On the other hand, strong density fluctuations are present, but due to the non-standard sound speed variation (opposite to the mean density evolution across the channel), the amplitude is maximal close to the channel wall, i.e. in the viscous sublayer instead of the buffer layer like in perfect gases. As a consequence, these fluctuations do not alter the turbulence structure significantly, and Morkovin’s hypothesis is well respected at any Mach number considered in the study. The preceding features make high Mach wall-bounded flows of dense gases similar to incompressible flows with variable properties, despite the significant fluctuations of density and speed of sound. Indeed, the semi-local scaling of Patelet al.(Phys. Fluids, vol. 27 (9), 2015, 095101) or Trettel & Larsson (Phys. Fluids, vol. 28 (2), 2016, 026102) is shown to be well adapted to compare results from existing surveys and with the well-documented incompressible limit. Additionally, for a dense gas the isothermal channel flow is also almost adiabatic, and the Van Driest transformation also performs reasonably well. The present observations open the way to the development of suitable models for dense-gas turbulent flows.

A numerical investigation of transonic and low-supersonic flows of dense gases of the Bethe–Zel'dovich–Thompson (BZT) type is presented. BZT gases exhibit, in a range of thermodynamic conditions close to the liquid/vapour coexistence curve, negative values of the fundamental derivative of gasdynamics. This can lead, in the transonic and supersonic regime, to non-classical gasdynamic behaviours, such as rarefaction shock waves, mixed shock/fan waves and shock splitting. In the present work, inviscid and viscous flows of a BZT fluid past an airfoil are investigated using accurate thermo-physical models for gases close to saturation conditions and a third-order centred numerical method. The influence of the upstream kinematic and thermodynamic conditions on the flow patterns and the airfoil aerodynamic performance is analysed, and possible advantages deriving from the use of a non-conventional working fluid are pointed out.

The influence of high-enthalpy effects on hypersonic turbulent boundary layers is investigated by means of direct numerical simulations (DNS). A quasiadiabatic flat-plate air flow at free-stream Mach number equal to 10 is simulated up to fully developed turbulent conditions using a five-species, chemically reacting model. A companion DNS based on a frozen-chemistry assumption is also carried out, in order to isolate the effect of finite-rate chemical reactions and assess their influence on turbulent quantities. In order to reduce uncertainties associated with turbulence generation at the inlet of the computational domain, both simulations are initiated in the laminar flow region and the flow is let to evolve up to the fully turbulent regime. Modal forcing by means of localized suction and blowing is used to trigger laminar-to-turbulent transition. The high temperatures reached in the near-wall region including the viscous and buffer sublayers activate significant dissociation of both oxygen and nitrogen. This modifies in turn the thermodynamic and transport properties of the reacting mixture, affecting the first-order statistics of thermodynamic quantities. Due to the endothermic nature of the chemical reactions in the forward direction, temperature and density fluctuations in the reacting layer are smaller than in the frozen-chemistry flow. However, the first- and second-order statistics of the velocity field are found to be little affected by the chemical reactions under a scaling that accounts for the modified fluid properties. We also observed that the Strong Reynolds Analogy remains well respected despite the severe hypersonic conditions and that the computed skin friction coefficient distributions match well the results of the Renard-Deck decomposition extended to compressible flows.

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.