Abstract
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.
Highlights
In fluid processes, such as transport, mixing, reaction, and heat transfer, flow pattern is of essential importance to the process performance
In real flow of interest, local flow pattern changes from one spatial point to another, and is not well-defined rheometic flows such as simple shear or simple elongation used in rheological characterization of fluid
Local flow pattern or topology is determined by the deformation-rate tensor; the problem of flow field classification can be analyzed by eigenanalysis of the deformation-rate tensor (Tanner and Huilgol, 1975; Chong et al, 1990)
Summary
In fluid processes, such as transport, mixing, reaction, and heat transfer, flow pattern is of essential importance to the process performance. In real flow of interest, local flow pattern changes from one spatial point to another, and is not well-defined rheometic flows such as simple shear or simple elongation used in rheological characterization of fluid In such situations, flow classification scheme of non-rheometric flow is required. Local flow pattern or topology is determined by the deformation-rate tensor; the problem of flow field classification can be analyzed by eigenanalysis of the deformation-rate tensor (Tanner and Huilgol, 1975; Chong et al, 1990) Such analysis technique have not been commonly applied in fluid processing, partly because since this analysis involves the flow topology, intensity, and directions, physical interpretation is not straightforward in real flow fields. Application of our flow field classification to flow of a non-Newtonian fluid in melt-mixing in twin-screw extrusion demonstrates that the difference in the channel geometry highly affects the distribution of elongational flow (diverging and bifurcating flows)
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