On the Stability of Axial Flow in an Annulus

Abstract

A theoretical study of the stability of fully-developed axial flow in a concentric annulus is presented. The coupled, linear, ordinary differential equations governing the propagation of the infinitesimal disturbance through the fluid are solved numerically for the complex eigenvalues, each of which defines a mode of propagation. The integration starts at the outer wall by means of a series solution and is continued to the inner wall by the fourth order Runge-Kutta method. An eigenvalue search technique is used to ascertain the number of eigenvalues within a closed region of the complex eigenvalue plane. It is found that the axial flow in the annulus is spatially stable to infinitesimal axisymmetric disturbances upto a modified Reynolds number of 10,000.