IMPACT OF SOLID BOUNDARIES AND VISCOSITY OF THE MEDIUM ON THE CONTRIBUTION OF THE INERTIAL AND VORTEX COMPONENTS OF THE NORMAL FORCE OF A ROTATING PLATE. PART 2

Abstract

Within the framework of the improved method of discrete vortices, generalized for viscous media, a method has been developed for determining the contribution of forces of inertial, vortex and circulation nature to the normal force of a plate moving in a stationary viscous boundless medium accord- ing to an arbitrary law, in the presence of a wall and in a channel. The developed method was tested for the case of instantaneous angular start of the plate and subsequent constant angular speed of rotation (Wagner's problem) in a viscous boundless medium, in the presence of a wall and in a channel, in laminar and turbulent modes. The application of approximate analytical formulas for the components of the induced velocity from a discrete vortex in a viscous medium near the wall and in the channel made it possible to obtain velocity fields that visualize two vortices separated from the edges of the plate and the dynamics of their dispersion in laminar and turbulent regimes of rotation of the plate near the wall and in the channel. The inertial- vortical nature of the normal force of the plate (with the dominance of inertial forces) is confirmed, which rotates after an instantaneous start with the separation of the flow from both its edges, regardless of the presence of solid boundaries and laminar or turbulent flow regimes. It was found that in the case of the laminar regime, the effect of the presence of the wall on the reduced inertial component of the normal force of the plate is insignificant, but the influence of the channel leads to a faster departure of the laminar vortex from the moving edge of the plate, which leads to a gradual increase in the contribution of the inertial component of the normal force of the plate up to 100 % and more when turning the plate perpendicular to the channel walls. Approximately the same happens in the case of the absence of solid boundaries, when a turbulent vortex of a larger size and intensity than the corresponding laminar one moves away from the moving edge of the plate.