THE EFFECT OF PARTIAL SLIP ON THE SURFACE PRESSURE DISTRIBUTION IN A SLIGHTLY COMPRESIBLE FLOW DEVELOPMENT REGION IN THE BOUNDARY LAYER

Abstract

The study of laminar incompressible fluid flow in the boundary layer revealed, even earlier, that the condition of complete adhesion of fluid particles to the surface (non-slip condition) of the moving body (half-plane) is not met in the flow development (formation) region. The assumption of constancy of the fluid velocity on the surface of a moving body, hence non-slip, leads, in the flow development region, to the complete absence of the normal component of the velocity field. And this contradicts the very concept of the flow development region, where there should be two velocity components - longitudinal (primary) and normal (secondary) ones. In the previous works of the authors, analytical solutions were obtained for the velocity field in the region of development of incompressible fluid flow in the boundary layer. 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. On the basis of a critical analysis of the existing approaches, which consider the flow of a fluid around a immobile plate in the framework of non-gradient flow (which is just impossible due to the lack of a mechanism for creating the motion of the fluid), it is shown that the system of equations is actually non-closed. For the region of flow development, where the longitudinal pressure gradient is not a constant value, one equation is missing. This equation, as in previous works, is obtained from the necessary condition for the extreme of the fluid rate functional. And although the complete solution for the longitudinal component of the velocity contains four constants of integration, to obtain the asymptotics near the solid surface it is sufficient to know only two quantities - the velocity and its first derivative (gradient). These values, as it turns out from the asymptotic solution, coincide with the case of incompressible flow, which allows us to expand the scope of the previously obtained results for a wider domain of Mach numbers, for example . And such values already correspond to the speeds of modern civil aircraft. The dimensionless distribution of pressure in the slightly compressible flow development region is presented and its significant heterogeneity is shown, which, in turn, indicates the importance of the obtained results.