Velocity Field Computation in Plastic Flow in Non-Circular Tubes Using Natural Coordinates

A numerical method to determine the velocity field, and related variables, in plastic flow in non-circular straight ducts is presented. The method is an extension of previous work of the senior author related to modeling laminar flow in pipes of arbitrary cross-sectional contours using natural coordinates. In this case the concept of "natural coordinates" is applied to the system of orthogonal curves determined by the plane isovels and their normal counterparts. The momentum equation for the axial velocity is expressed in natural coordinates in which one relevant variable is the radius of curvature of isovels. The method is applied to a selected set of shapes when the fluid is a Bingham plastic. Isovels and plug zones are determined drawing on the properties of the isolvels and normal curves. Computations start at the pipe perimeter and advance toward the center. Copyright © 2012 by ASME.