Kinematic waves and collision effects in dense fluid–particle flow during hydraulic conveying

The effects of fluid–particle and particle–particle interactions on the kinematic waves and particle dynamics in a vertical pipe with continuous upward fluid flow are investigated. The unresolved computational fluid dynamics-discrete element method, in which fluid flow field is modeled using large eddy simulation with dynamic Smagorinsky model for the eddy viscosity, is used to simulate the conveying process for particle Reynolds numbers within 8000 and 40000. The results imply that it can show kinematic waves and determine wave velocity based on the wave frequency and wave number relationships, which is also found to closely agree with the theory of kinematic waves based on the Richardson-Zaki relation. One feature is that the kinematic wave velocity in hydraulic conveying manifests itself in relation to the upward fluid velocity. In addition, two different flow regimes are found in the simulation. For relative low particle Reynolds numbers (8000