A mapping method based on Gaussian quadrature: Application to viscous mixing

In this work, a novel mapping method based on distributed Gaussian quadrature is proposed to analyze viscous distributive mixing criteria when considering geometry and/or time periodic laminar flows. It avoids the recourse to the mesh tracking procedure that is hard to manage. In addition, its extension to 3D is straightforward. The appeal of the mapping technique is that it is independent from initial feeding conditions of the passive phase (e.g. pigments or additives). The mapping matrix is calculated once over a single hydrodynamic period. Then, successive mixing patterns are recovered by multiplying, as much as needed, the mapping matrix by the chosen feeding conditions. The behavior of this new method is verified on academic test cases to determine its accuracy. It is found that by increasing the number of Gauss points per element, the accuracy of predicted concentration patterns improves. Finally, the new mapping method is applied on twin-screw extruders and a Kenics static mixer. The predicted concentration patterns are found to be in good agreement in regards to available experimental and computational data. Also, it is found that improved spatial discretization helps to recover high accuracy mixing patterns resulting from repeated mapping steps.