Sergey Karskanov

The results of the theoretical solution of the problem of braking a supersonic flow in a round pipe based on direct numerical simulation by integrating the Navier – Stokes equations without the use of additional models and empirical constants are shown. Shaded maps of density distribution depending on flow parameters are presented. The flow consists of successive rhombus-shaped shock waves distributed along the entire length of the channel. It is determined that the size of x-shaped structures depends on the flow parameters. At a lower Mach number, the rhombuses have a smaller size and, accordingly, their number increases along the length of the channel. The Reynolds number also affects the size of structures, however, it is less pronounced. With a lower Reynolds number, x-shaped structures have a smaller size. It is shown that over time the flow tends to a stationary state.

The results of the theoretical solution of aerodynamic problems based on direct numerical simulation by integrating the Navier – Stokes equations without involving additional models and empirical constants are shown. Modern approaches to the theoretical study of high-speed flows are determined. The advantages, problems, development trends and scientific directions of research on various approaches are revealed. The advantages and disadvantages of the direct numerical simulation are analyzed. The velocity vectors of laminar and transient flows in a rectangular channel with a sudden expansion at the inlet are presented in different planes. The convergence of the method is studied when the computational domain is quantized in space. It is discovered that fast relaminarization is characteristic of transitional flows. A mathematical model for calculating bottom drag is presented. The numerical results are compared with the data of physical experiments and the results of other methods. It is shown that the results of simulation based on DNS are not inferior in accuracy to RANS and LES results. The results of a parametric study of a transonic flow around a profile are presented. The high-speed buffet onset is investigated. The distribution surfaces of the velocity pulsation energy generation are shown. The frequency of self-oscillations is determined on the basis of spectral analysis.