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.

旋流广泛用于增强能量转换装置中的传热和传质，预测旋流衰减率在一些应用中很重要。本研究调查了直环形管内的涡流衰减率及其主要参数。推导出旋流数的一维模型。我们通过考虑方位角速度剖面和两壁之间的壁剪应力差异来修正经验壁剪应力模型。模型给出的涡流数与模拟结果显示出更好的一致性。该模型具有影响旋流衰减率的三个主要参数：入口雷诺数、内外半径之比（即伽马）和旋流强度。使用基于常微分方程 (ODE) 的模型，显示了旋流衰减率的参数图。尽管文献中主要参数对旋流衰减率的影响大多得到证实，但伽马的几何参数显示出与其他参数不同的影响。存在最小化涡流衰减率或角动量损失的伽马值。发现最佳伽马值来自壁面剪切应力和径向湍流应力之间的平衡。随着涡流强度或雷诺数的增加，最佳伽马值会略有增加。使用 ODE 分量和横流速度的流场进行物理分析。伽马的几何参数显示出与其他参数不同的效果。存在最小化涡流衰减率或角动量损失的伽马值。发现最佳伽马值来自壁面剪切应力和径向湍流应力之间的平衡。随着涡流强度或雷诺数的增加，最佳伽马值会略有增加。使用 ODE 分量和横流速度的流场进行物理分析。伽马的几何参数显示出与其他参数不同的效果。存在最小化涡流衰减率或角动量损失的伽马值。发现最佳伽马值来自壁面剪切应力和径向湍流应力之间的平衡。随着涡流强度或雷诺数的增加，最佳伽马值会略有增加。使用 ODE 分量和横流速度的流场进行物理分析。