An Immersed Boundary Method for Polymeric Continuous Mixing

TL;DR

The paper addresses simulating temperature-dependent non-Newtonian polymer flows in complex moving geometries, characterized by viscosity $mu(dot_gamma, T)$. It introduces a finite-volume Immersed Boundary Method implemented in OpenFOAM and integrates it with the PIMPLE solver to enforce boundary conditions on non-conforming meshes via an interpolation operator $S_{IB}$ leading to corrected states $U^{corr}$. The rheology uses a generalized Newtonian model with a power-law viscosity $mu(dot_gamma, T) = H(T) K (dot_gamma)^{n-1}$ and Arrhenius temperature dependence $ln H(T) = alpha (1/T - 1/T_r)$, capturing shear thinning and viscous heating. Validation on SSE, TSE, and PRE demonstrates robustness, accuracy, and scalability, enabling predictive analyses and design optimization for industrial polymer mixing.

Abstract

We introduce a new implementation of the Immersed Boundary method in the finite-volume library OpenFOAM. The implementation is tailored to the simulation of temperature-dependent non-Newtonian polymeric flows in complex moving geometries, such as those characterizing the most popular polymeric mixing technologies.

Figures (11)

• Figure 1: Representation of point-to-cell stencil of level 2 (left) and schematics of IBM mesh elements (right).
• Figure 2: Extended stencil of an IB cell (left), points cap criterion on anisotropic meshes (right): the closest 8 cells are hatched using standard Euclidean distance (top) and anisotropic distance (bottom).
• Figure 3: Strong scalability test on a SSE test case, with around 4 million cells (cf. Section \ref{['sec:ibm:numer']}).
• Figure 4: Representation of the meshes employed to perform simulations. Left: uniform non-conforming mesh. Right: conforming mesh.
• Figure 5: Evaluation of various quantities on the screw surface for different discretization methods.

Theorems & Definitions (3)

• remark 1: Parallelization of IBM for large scale problems
• remark 2: Enriched stencils
• remark 3: Diffuse Interface Method