Inertia Effects in Fully Developed Axisymmetric Laminar Flow

Abstract

The three components of the Navier-Stokes equation are solved here simultaneously in their nonlinear form for axisymmetric radial inward and outward flow cases between two parallel rotating walls. Examples of application in rotating machinery are close clearance face seals, thrust bearings, high speed thrust device, rotating disk, narrow gap between centrifugal impeller and housing, etc. The differential equations of motion with the proper boundary conditions were converted into integral equations of the “Fredholm second kind” type and solutions have been obtained for the nonlinear cases. The use of integral equations greatly enhanced the advantage of the numerical solution developed here. The results are compared to simplified solutions and to solutions considering some of the nonlinear members. The effects of the inertia forces are especially emphasized and discussed in detail. The inclusion of these terms significantly affected the velocity field in the area discussed here. It is shown here that for low inward or outward flows the centrifugal force, and for high flows the convective acceleration terms have the main controlling influence on the radical velocity component.