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The influence of thermal nonequilibrium on the laminar–turbulent transition is studied with the use of the $$\mathrm{e}^N$$ -method for two widespread flow regimes in a supersonic boundary layer at the Mach number $$\textrm{M}=4.5$$ . The set of the actual frequencies of spatial disturbances is determined on the basis of the neutral curves for temporal disturbances. Families of the curves of $$N$$ -factors are calculated for selected frequencies. Then, based on the envelopes of these curves, the transition Reynolds number $$\mbox{Re}_{\delta T}$$ for a given transition factor $$N_T$$ is determined. The calculations show that the transition region in the case with $$N_T=8$$ and vibrational excitation level below the dissociation limit is located 12–14% downstream as compared to the transition region in a perfect gas.

The interaction of a laminar boundary layer with a shock wave at a Mach number M = 1.43 is studied by numerical simulation. The results obtained by direct numerical simulation are compared with the results of calculations using the Reynolds-averaged Navier–Stokes (RANS) equations supplemented with different turbulence models describing laminar–turbulent transition. The possibility of determining the position of the flow turbulence zone based on linear stability theory and the $$\mathrm{e}^{N}$$ -method is estimated. Comparison of the numerical simulation with experimental data shows that engineering RANS methods can be used to study supersonic flows in which transition to turbulence occurs in regions of shock wave–boundary layer interaction.

Flight experiments aimed at studying the transition from the laminar to turbulent flow in the boundary layer on the glider wing at different levels of atmospheric turbulence performed in the 1980s are reviewed. The results are obtained by means of hot-wire measurements and visualization of the flow on the wing surface by the method of sublimating coatings. The transition is found to proceed in several stages: emergence, evolution, and failure of a discrete packet of instability waves in the region of the adverse pressure gradient. The data obtained in the study are compared with the results of similar investigations carried out in a large wind tunnel on the same real glider wing at realistic Reynolds numbers.

A new experimental method for panoramic contactless determination of the laminar-turbulent transition position in a three-dimensional boundary layer is described. It is demonstrated that this method allows accurate determination of the transition region boundaries at both low and enhanced levels of free-stream turbulence.

Results of direct numerical simulations of the roughness-induced development of instability and transition to turbulence in a supersonic boundary layer on a blunted cone for the free-stream Mach number M∞ = 5.95 are presented. The flow parameters and model geometry are consistent with the conditions of the experiments performed in the study. The following roughness types are considered: random distributed roughness, isolated roughness elements of different shapes, and a group of regularly arranged roughness elements. The processes of the instability development and transition for different roughness types are compared, and possible mechanisms of the roughness influence on the stability of boundary layers on blunt bodies are discussed.

The influence of the molecular structure of gas flows on the characteristics of turbulent flows and the influence of the properties of molecules on turbulent processes have been studied. A review of the results of studies of turbulent processes is presented. Data on flows at the boundary of a supersonic jet and in a pipe with a divergent inlet section, and Hagen–Poiseuille flow are given. Experimental study of Hagen–Poiseuille flow has shown that the molecular properties of the medium have an effect on the critical Reynolds number. It is shown that in comparing the critical Reynolds numbers for flows of different gases at different pressures, the common determining parameter is the second virial coefficient.

Stability of plane and cylindrical Poiseuille flows of nanofluids to comparatively small perturbations is studied. Ethylene glycol-based nanofluids with silicon dioxide particles are considered. The volume fraction of nanoparticles is varied from 0 to 10%, and the particle size is varied from 10 to 210 nm. Neutral stability curves are constructed, and the most unstable modes of disturbances are found. It is demonstrated that nanofluids are less stable than base fluids; the presence of particles leads to additional destabilization of the flow. The greater the volume fraction of nanoparticles and the smaller the particle size, the greater the degree of this additional destabilization. In this case, the critical Reynolds number significantly decreases, and the spectrum of unstable disturbances becomes different; in particular, even for the volume fraction of particles equal to 5%, the wave length of the most unstable disturbances of the nanofluid with particles approximately 20 nm in size decreases almost by a factor of 4.

Direct numerical simulations of instability development and transition to turbulence in a supersonic boundary layer on a flat plate are performed. The computations are carried out for moderate supersonic (free-stream Mach number M = 2) and hypersonic (M = 6) velocities. The boundary layer development is simulated, which includes the stages of linear growth of disturbances, their nonlinear interaction, stochastization, and turbulent flow formation. A laminar–turbulent transition initiated by distributed roughness of the plate surface at the Mach number M = 2 is also considered.

The influence of a cylinder-shaped single roughness element on the laminar–turbulent transition in the presence of an entropy layer is experimentally studied. The experiments are performed on a blunted cone model at the Mach number M = 5. The roughness element is located on the blunted tip of the model. Information about the mean and fluctuating parameters of the boundary layer in the wake behind the roughness element is obtained by using hot-wire anemometry. It is shown that flow turbulization behind the roughness elements occurs at the local Reynolds number calculated on the basis of the roughness element height and equal to 400–500. It is found that the presence of the roughness element exerts a significant effect on the unsteady characteristics of the boundary layer if the roughness element height is smaller than the effective value.

Results of an experimental study of the laminar-turbulent transition in a hypersonic flow around cones with different bluntness radii at a zero angle of attack, free-stream Mach number M ∞ = 6, and unit Reynolds number in the interval Re ∞,1 = 5.79 · 106–5.66 · 107 m−1 are presented. Flow regimes in which a reverse of the laminar-turbulent transition (decrease in the length of the laminar segment with increasing bluntness radius) are studied. Heat flux distributions over the model surface are obtained with the use of temperature-sensitive paints. Lines of the beginning of the transition in the boundary layer are analyzed by using heat flux fields. The critical Reynolds number Re ∞,R ≈ 1.3 · 105 beginning from which the laminar-turbulent transition substantially depends on uncontrolled disturbances, such as the model tip roughness, is found. In supercritical regimes, the line of the transition beginning is shifted in most cases toward the model tip (reverse of the transition). The results obtained are compared with available experimental data.

A method of statistical modeling the flow in the boundary-layer transition region is proposed on the basis of experimental data on kinematics and dynamics of turbulent spots (Emmons spots) on a flat plate in an incompressible fluid. This method allows one to determine the intermittency with allowance for overlapping of the spots, the forces on the plate surface, and the flow field in the vicinity of the transition region if the field of the streamwise component of the mean velocity in the developed turbulent boundary layer is known as a function of the Reynolds number. In contrast to multi-parameter models of the transition, this approach makes it possible to avoid the use of physically meaningless parameter values.

An energy functional leading to a resolvable variational problem for determining the critical Reynolds number of laminar-turbulent transition Re cr is constructed within the framework of the nonlinear energy stability theory of compressible flows. Asymptotic estimates containing the characteristic dependence $$\operatorname{Re} _{cr} \sim \sqrt {\alpha + 4/3} (\alpha = \eta _b /\eta )$$ in the main order are obtained for the stability of various modes of Couette compressible gas flow. The asymptotics considered are long-wave approximations. This suggests that the obtained dependence describes the effect of bulk viscosity on the large-scale vortex structures characteristic of Kelvin-Helmholtz instability.

Stability of compressible three-dimensional boundary layers on a swept wing model is studied within the framework of the linear theory. The analysis based on the approximation of local self-similarity of the mean flow was performed within the Falkner-Skan-Cooke solution extended to compressible flows. The calculated characteristics of stability for a subsonic boundary layer are found to agree well with the measured results. In the case of a supersonic boundary layer, the results calculated for a Mach number M = 2 are also in good agreement with the measured spanwise scales of nonstationary vortices of the secondary flow. The calculated growth rates of disturbances, however, are substantially different from the measured values. This difference can be attributed to a high initial amplitude of disturbances generated in the experiment, which does not allow the linear stability theory to be applied. The evolution of natural disturbances with moderate amplitudes is fairly well predicted by the theory. The effect of compressibility on crossflow instability modes is demonstrated to be insignificant.

The laminar-turbulent transition is experimentally studied in boundary-layer flows on cones with a rectangular axisymmetric step in the base part of the cone and without the step. The experiments are performed in an A-1 two-step piston-driven gas-dynamic facility with adiabatic compression of the working gas with Mach numbers at the nozzle exit M ∞ = 12–14 and pressures in the settling chamber P0 = 60–600 MPa. These values of parameters allow obtaining Reynolds numbers per meter near the cone surface equal to Re 1e = (53–200) · 106 m −1. The transition occurs at Reynolds numbers Re tr = (2.3–5.7) · 106.

The possibility of controlling the laminar-turbulent transition in hypersonic shock layers by means of porous coatings is considered. The linear stability of the shock layer to acoustic disturbances is analyzed. A dispersion relation is derived in an analytical form and analyzed for different characteristic values of porosity of the wall, which allows one to study the spectrum of acoustic disturbances in the shock layer. Analytical expressions for the growth rate of instability of acoustic disturbances are presented as functions of the reflection factor. Their structure indicates that the porous coating effectively decreases acoustic instability of the shock layer.

The influence of ultrasound‐absorbing coatings on stability of hypersonic boundary layers is considered. Two types of coatings were used in experiments: felt‐metal with a random porous microstructure and a sheet perforated by blind cylindrical microchannels. The experiments were performed in a wind tunnel at a Mach number M = 5.95 on sharp cones with a 7° apex half‐angle. Evolution of natural disturbances and artificially induced wave packets in the boundary layer was studied with the help of hot‐wire anemometry. Spatial characteristics of artificial disturbances were obtained. It is demonstrated that such coatings exert a stabilizing effect on second‐mode disturbances.

Weakly nonlinear development of waves in an axisymmetric hypersonic boundary layer is studied by the method of bispectral analysis. The type of nonlinear interaction that was not observed previously in such flows is found. The possibility of subharmonic resonance of the second mode at the nonlinear stage of transition is demonstrated. The previously discovered nonlinear generation of the harmonic of the fundamental wave of the second mode of disturbances is observed.