Stability of swirl tube flow

Abstract

This work focuses on detailed investigation of the flow phenomena and flow stability in swirl tubes. In general, a swirl tube is a tube with one or more tangential inlets generating complex swirling flow. This leads to large tangential velocities near the wall and to enhanced turbulent mixing in the tube, which results in a positive influence on the convective heat transfer in the tube. In the present work, a formulation of a condition to investigate stability of a flow is provided. This formulation reflects the definition of the second law of thermodynamics, i.e. the balance of entropy, and also the balance of the total enthalpy. So, the derived condition may serve as a criterion to investigate processes in general flows, for which an incompressible fluid via the Cauchy stress tensor is approximated. The experimental and numerical analysis of flow fields conducted for different Reynolds numbers show an axial backflow region in the tube centre determining possible vortex breakdown. For the lowest Reynolds number, an axial backflow region, in contrast to the higher Reynolds numbers, is observable up to the middle of the tube length. Thus, there is a region where the flow is characterised by no vortex breakdown. Moreover, similar behaviour is observed for the intermediate Reynolds number near the tube outlet. Nevertheless, for strong swirling flows, a possible vortex breakdown may be expected for a Rossby number lower than 0.65. Furthermore, the ratio between the local tangential and axial Reynolds numbers reveals that a vortex breakdown may occur in regions where this ratio is greater than 1. In addition, a connection between the derived stability criterion and the vortex breakdown confirms that the redistribution of flow fields is, due to the highest swirl strength, dominant at the beginning of the tube. Moreover, it is shown that vortex breakdown is accompanied by processes causing flow stabilisation.