On the interaction of moving liquid media with streamlined surfaces

Abstract

The interaction of liquid or gaseous media with streamlined surfaces is primarily determined by the «sticking» hypothesis, according to which in all cases (excluding discharged media), their velocity on solid surfaces is always zero. The consequence of this boundary condition is the obvious fact that any streamlined surface introduces a strong disturbance into the moving liquid medium, characterized by a surface friction stress τw. In turn this value is determined by the transverse velocity gradient that occurs at the wall dudy|y=0 to some extent n, depending on the nature of the flow in the wall area. The force interaction of real moving media is primarily determined by the shape of the velocity profile and the value of its transverse gradient on the streamlined surface. If the specified value can be determined as a result of theoretical calculations for the laminar flow regime, then for the turbulent flow it is necessary to use some semi-empirical dependencies. It is on the basis of this dependence that L. Prandtl obtained the logarithmic velocity profile, which is still the basis of the physical picture of the interaction of moving media with streamlined surfaces. The presented materials show that this profile does not satisfy any of the three natural boundary conditions, and the result of matching the calculated data obtained from it with the experimental results is the result of using special "floating" coordinates. At the same time, the physical validity of the introduction of the concept of the existence of a laminar sublayer near the wall, which contacts the streamlined surface, is considered in detail when deducing the logarithmic velocity profile. As an alternative solution, we consider a fixed logarithmic profile that satisfies all three boundary conditions arising from the definition of the boundary layer, without using the hypothesis of the existence of a logarithmic sublayer.