Simulating Interaction of Liquid Steel with Gate Wall at Harmonic Motion

The problem of determining the forces of interaction of a viscous fluid with the cylindrical pipe wall is considered. It is assumed that near the pipe wall, the fluid motion is completely determined by viscous forces. The pipe moves along the streamline. The annular fluid element motion law is a special case of the Navier–Stokes equation in a cylindrical coordinate system. The equation is solved by the Fourier method in Bessel functions. Considering the orthogonality of the eigenfunctions, an equation for the squared norm is found. As an example, the case is considered when the pipe is subjected to vibration. Equations have been obtained for the velocities and viscous friction forces in the laminar sublayer. It has been found that when the pipe moves harmonically, the velocities and shear stresses at the pipe wall do not reach their maximum synchronously. The distribution of velocities and stresses in the section of the steel-pouring ladle gate channel has been considered for three vibration modes. The solution provided can be, in particular, used to determine the fluid–pipe wall interaction forces when the pipe is technologically affected by vibration, impulse, etc., as well as study moving joints such as piston, plunger, etc.