Primary Parameters of Swirl Decay in Turbulent Swirling Flows Inside Annular Pipes

Swirling flows are widely used to enhance heat and mass transfer in energy conversion devices, and predicting the swirl decay rate is important in several applications. This study investigates the swirl decay rate inside a straight annular pipe and its primary parameters. A one-dimensional model of the swirl number is derived. We revise the empirical wall shear stress model by considering the azimuthal velocity profile and the wall shear stress difference between two walls. The swirl numbers given by the model exhibit improved agreement with simulation results. The model has three primary parameters that affect the swirl decay rate: the inlet Reynolds number, the ratio of the inner and outer radii (i.e., gamma), and the swirl intensity. Using the ordinary differential equation (ODE)-based model, the parametric maps of the swirl decay rate are presented. Although the effects of the primary parameters on the swirl decay rate from the literature are mostly confirmed, the geometric parameter of gamma shows an effect distinguished from the others. There exist gamma values that minimize the swirl decay rate or angular momentum loss. It is found that the optimal gamma values result from a balance between the wall shear stress and turbulent stress in the radial direction. The optimal gamma value increases slightly as the swirl intensity or Reynolds number increases. A physical analysis is presented using the ODE components and the flow fields of the cross-stream velocities.