EllipsoidalFiberFoam, a novel Eulerian-Lagrangian solver for resolving translational and rotational motion dynamics of ellipsoidal fibers

Abstract

A novel Eulerian-Lagrangian MPI parallelized solver is developed to resolve the dynamics of ellipsoidal fibers in the OpenFOAM platform. Due to the nonspherical shape of the ellipsoidal fibers and the dependence of the drag force on the orientation of the fiber, the solver solves the full conservation of linear and angular momentum equations, in addition to the time evolution equation for Euler's parameters, quaternions. To this end, a new parcel type is introduced to represent ellipsoidal fibers with several new properties, including Euler's parameters, angular velocity, and torque class. Finally, new member functions are defined to solve angular momentum and Euler's parameters time evolution equations. The solver is the first publicly available, robust and reliable computational framework for the numerical analysis of ellipsoidal fibers motion. It promotes the capability of the standard Lagrangian OpenFOAM solvers and libraries to capture the orientation and rotational dynamics of nonspherical particles. As validation cases, the solver was applied to four benchmarks: three-dimensional rotation of an ellipsoid in linear shear flow, two-dimensional rotation of a magnetic ellipsoid in linear shear flow subjected to a uniform magnetic field, motion of an ellipsoid in pipe flow, and ellipsoids deposition in three-dimensional bifurcation flow. Comparison of the results with analytical solutions, experimental data and in-silico results indicates close agreements and high accuracy of the developed numerical model for single- and multi-physics test cases.

Program summary

Program title: EllipsoidalFiberFoam

CPC Library link to program files: https://doi.org/10.17632/nf35zjvmr2.1

Licensing provisions: GNU General Public License Version 3

Programming language: C++

Nature of problem: The developed Eulerian-Lagrangian solver introduces the Euler's parameters, angular velocity and hydrodynamic and magnetic torques of ellipsoidal fibers and it solves the equations of conservation of angular momentum and Euler's parameters time evolution to describe the fiber orientation fully. The orientation-dependent drag force and the fiber trajectory are calculated afterward by solving the equations of conservation of linear momentum.

Solution method: Fluid phase velocity and pressure are obtained through the PIMPLE algorithm. For the particulate phase, a new parcel type owning Euler's parameters and angular velocity accompanied by new classes for hydrodynamic and magnetic torques and orientation-based drag force represents an ellipsoidal fiber, and the Lagrangian cloud of the parcel is evolved through the integration of the equations of translational and rotational motion.

Additional comments, including restrictions and unusual features: The current version of the solver is based on creeping flow conditions and one-way interaction regime. These limitations will be relaxed in the near future by incorporating two- and four-way interaction regimes.