Three-dimensional finite element method for rotating disk flows

Abstract

This paper deals with the numerical simulation of rotating disk flow, coupling the hydrodynamic field to the transport of a chemical species generated in electrochemical cells by the dissolution of an iron electrode in a 1M H2SO4 electrolyte. The time asymptotic steady-state solution of rotating disk flow obtained in this work by numerical integration of the incompressible Navier--Stokes equations through the finite element method (FEM) with the appropriate boundary conditions is consistent with the generalized von Kármán's similarity solution. This paper reviews the main features of generalized von Kármán's flow, the adopted FEM scheme, a discussion of implementation of the boundary conditions, validation of the code and the results. In particular, the results confirm the assumption that the non-dimensional velocity and concentration profiles do not depend on the coordinate along the radial direction.