Mechanism analysis of secondary flow and mechanical energy loss in toroidal flow field

The imbalance between the radial pressure gradient and centrifugal force in curved pipe flow produces a secondary flow, resulting in a non-uniform distribution of streamwise velocity across the pipe cross section. These phenomena are believed to exhibit higher fluid resistance than straight pipes with similar flow rates, thereby motivating research into the mechanical energy losses in curved pipes. First, to ensure the accuracy and efficiency of the calculations, the results of various turbulence models were compared with direct numerical simulation to select the most appropriate turbulence model. Based on the momentum conservation equation, the mechanical influencing factors of secondary flow and streamwise velocity stratification in toroidal flow field were theoretically studied. Computational fluid dynamics method was employed to explore the spatiotemporal evolution characteristics of the mechanics and velocity distribution in transient flow fields to explain the formation mechanism of the secondary flow and the coupling relationship between the streamwise and radial directions. Then, the typical energy components of the toroidal flow field were analyzed using the energy equation, and the energy conservation and distribution characteristics were numerically studied. Furthermore, the influence of typical parameters (Reynolds number and curvature ratio) on the velocity distributions and mechanical properties as well as the percentage and distribution of various energy components were analyzed. Finally, the calculation results were statistically presented to quantify the variation of the energy components with typical parameters.