Song L. Modeling and calculation of processes of flow around spatial bodies with complex surface geometry

The dissertation is devoted to the study of incompressible and slightly compressible fluid flow in the boundary layer, which is formed near the surface of a body during its motion in a still fluid. By theoretical means of physics and mathematics new models of incompressible and slightly compressible fluid flow in the boundary layer were obtained. On the basis of these models, relevant problems were formulated and their solutions were found. First chapter includes critical analysis of scientific researches on the dissertation topic. In second chapter, an original approach that takes into account the spatial variability of the molecular viscosity in the boundary layer region, and the solution of the problem is based on the use of the extreme for the fluid flow functional. Spatial variability of molecular viscosity in the boundary layer, by analogy with the theory of thermal conductivity, is based on the absence of spatial isotropy of the medium. If the flow is unsteady and non-gradient or steady and gradient, then two forces act on both of these flows. In such flows, the molecular viscosity can be a constant value. The obtained exponential law is consistent with experimental data. Two approaches to describing the laminar unsteady flow of an incompressible fluid in the boundary layer are given. As a result, as before for the steady case, solutions describing both non-gradient and gradient flows of incompressible fluid in the boundary layer are obtained. The asymptotic analysis of the transition to the steady flow testifies to the consistency of these solutions. For the case of non-gradient flow, a comparison of the classical solution with the solution corresponding to the extreme of fluid rate carried by the moving surface is made. It is shown that according to the solution obtained on the basis of the calculus of variation approach, the shear stress on the surface does not disappear anywhere after the motion is established, but as expected, acquires a constant value. In the third chapter, flow development region problem is considered. It is about the fluid boundary layer in the region of flow development in the problem of the motion of a semi-infinite plane, where the pressure gradient is zero. It is proposed, as it was done before for the problem of steady motion of a plane and the problem of acceleration of a plane, to depart from the false statement about the constancy of molecular viscosity in the non-gradient boundary layer of an incompressible and slightly compressible flow and consider the molecular viscosity in boundary layer as a function of spatial coordinates. Since the use of the incompressible fluid flow model is restricted by the Mach number, to further expand the speed range, the problem of the of slightly compressible fluid flow development region in the boundary layer was considered. It is analytically proven that all considerations regarding the impossibility of complete non-slip in the flow development region can be applied to a slightly compressible flow. Slight compressibility at the same time means the subsonic nature of the flow and the neglect of temperature effects due to friction. In fourth chapter, a number of models of vortex flows that are generated by aircraft flight, are considered. In particular, this applies to the turbulent vortex flow during the formation of a vortex sheet, compact analogues of the Burgers-Rott vortex - both the classical one corresponding to laminar motion and the one consisting of a laminar flow in the core and a turbulent flow on the periphery of the vortex.