Stability of steady flow through an axially corrugated pipe

The linear stability of steady flow in pipes with circular cross-section and sinusoidal axial variation in diameter is studied by finding global eigenmodes with axial wavelength commensurate with that of the wall corrugation, chosen to be equal to one pipe mean radius. The maximum peak-to-peak height of corrugation considered is approximately 8% of the mean diameter. At low corrugation amplitude and at low Reynolds numbers, the base flow remains attached to the wall, while at larger amplitudes and Reynolds numbers, an axisymmetric separation bubble forms within the corrugation. For all Reynolds numbers considered, flows remain stable to axisymmetric perturbations, but become unstable to standing-wave modes of low azimuthal wavenumber, with critical Reynolds number first falling, then increasing with increasing corrugation height. Both attached and separated flows exhibit similar types of instability modes, which in the case of separated flow are most energetic near the reattachment line of the base flow. The leading instability modes consist of counter-rotating vortices situated near the pipe wall. VC 2011 American Institute of Physics. [doi:10.1063/1.3660522]