Stability of developing pipe flow subjected to non-axisymmetric disturbances

Abstract

The linear stability of the developing flow of an incompressible fluid in the entrance region of a circular tube is investigated. The case of non-axisymmetric small disturbances is considered in the analysis. The main-flow velocity distribution used in the stability calculations is that from the solution of the linearized momentum equation. The eigenvalue problem consisting of the disturbance equations and the boundary conditions is solved by a direct numerical integration scheme along with an iteration procedure. An orthonormalization method is employed to remove the ‘parasitic errors’ inherent in the numerical integration of the coupled disturbance equations. The flow is found to be unstable to non-axisymmetric disturbances with an azimuthal wavenumber of one. Neutral-stability curves and critical Reynolds numbers at various axial locations are presented. A comparison of these results is made with those for axisymmetric disturbances reported by Huang & Chen. It is found that the first instability of the flow is due to non-axisymmetric disturbances and occurs in the entrance region of the pipe with a minimum critical Reynolds number of 19 780.