Three-Dimensional Flows in a Rotating Cylinder in the Presence of Turbulent Boundary Layers on End Disks

Abstract

An analytical model for calculating a viscous incompressible fluid flow in a rotating cylinder with a braking lid and the formation of turbulent boundary layers on the end surfaces is presented. The analysis is made with account for all nonlinear inertial terms in the equations of motion, within the framework of Loitsyanskii's integral relations. The approximate velocity profiles in the boundary layers are preassigned in accordance with the empirical 1/7 law. The main flow is subdivided into an inviscid quasisolid core and a lateral layer, where almost the entire upward part of a circulatory flow is concentrated. The unknown angular velocity of the core and its radial boundary are evaluated from the balance between the moments of the friction forces acting on the main rotating flow and the continuity condition for the circulatory flow.