Three-dimensional Temporal Instability of Unsteady Pipe Flow

In this paper, 3-dimensional linear instability analysis has been carried out for unsteady pipe flow. An inflectional velocity profile from [2] has been considered and the stability analysis of it has been carried out for (axisymmetric mode) and 0 = n 2 & 1 = n . It was revealed that the profile is unstable for both axisymmetric and non-axisymmetric modes. The mode 1 = n was observed to be most unstable for this particular case considered. Both upstream and downstream moving disturbances have been observed as reverse flow exists in this flow. The vector plot of the disturbances showed the full shape and nature of the disturbances in the flow field. The predicted instability characteristics could explain the exact nature of visualized results of [2]. Wavelength of unstable disturbance from stability analysis and experimental observation of [2] matched well. The 3-D instability shows the observed helical nature of the flow.