Integral Method for Calculating the Characteristics of a Turbulent Boundary Layer on a Rotating Disk: Quadratic Approximation of the Tangent of the Flow Swirl Angle

Abstract

An improved approximation of the radial velocity profile observed in a turbulent boundary layer on a rotating disk is proposed on the basis of the assumption that the tangent of the swirl angle of the flow is described by a quadratic function. The integral method based on this assumption provides better agreement between the computational and experimental results for the radial velocity profile, the near-wall value of the tangent of the swirl angle, and the flow rate through the boundary layer. For the coefficient of the frictional moment, the accuracy achieved with the proposed method is the same as that available by the Karman method. The solutions to the equations describing the boundary layer are compared to the computational data reported in the literature for three different cases: a radial air flow around the disk, a rotation of the fluid by the law typical of a solid body, and a medium with the Ekman layers.