Kinetic energy flux (KEF) is an important physical quantity that characterizes cascades of kinetic energy in turbulent flows. In large-eddy simulation (LES), it is crucial for the subgrid-scale (SGS) model to accurately predict the KEF in turbulence. In this paper, we propose a new eddy-viscosity SGS model constrained by the properly modelled KEF for LES of compressible wall-bounded turbulence. The new methodology has the advantages of both accurate prediction of the KEF and strong numerical stability in LES. We can obtain an approximate KEF by the tensor-diffusivity model, which has a high correlation with the real value. Then, using the artificial neural network method, the local ratios between the real KEF and the approximate KEF are accurately modelled. Consequently, the SGS model can be improved by the product of that ratio and the approximate KEF. In LES of compressible turbulent channel flow, the new model can accurately predict mean velocity profile, turbulence intensities, Reynolds stress, temperature–velocity correlation, etc. Additionally, for the case of a compressible flat-plate boundary layer, the new model can accurately predict some key quantities, including the onset of transitions and transition peaks, the skin-friction coefficient, the mean velocity in the turbulence region, etc., and it can also predict the energy backscatters in turbulence. Furthermore, the proposed model also shows more advantages for coarser grids.

Direct numerical simulation (DNS) of transition over a hypersonic lifting body model HyTRV developed by China Aerodynamics Research and Development Center is performed. The free-stream parameters are: the free-stream Mach number is 6, the unit Reynolds number is 10000/mm, the free-stream temperature is 79 K, the angle of attack is 0, and the wall temperature is 300 K. Weak random blowing-and-suction perturbations in the leading range are used to trigger the transition. A high order finite-difference code OpenCFD developed by the authors is used for the simulation, and grid convergence test shows that the transition locations are grid-convergence. DNS results show that transition occurs in central area of the lower surface and the concaved region of the upper surface, and the transition regions are also the streamline convergence regions. The transition mechanisms in different regions are investigated by using the spectrum and POD analysis.