Flow Classification and Its Application to Fluid Processing

Mathematically, the problem of flow field classification can be analyzed by the eigenanalysis of the deformation-rate tensor; however, such analysis technique have not been commonly applied in fluid processing. We derive a simplified objective flow classification scheme based on the invariants of the strain-rate tensor and the vorticity tensor. Multiaxiality of flow, which is related to the type of elongation, and converging/bifurcating flow, is characterized by the strain-rate tensor, while rotation contribution that protects fluid element from stretching is characterized by the relative intensity of an objective vorticity to the strain-rate. The spatial distributions of flow classification quantities offer an essential tool in understanding the flow pattern structure, and therefore can be useful to get insights into the connection between the geometry and the process performance.