Incompressible 𝜇(I) rheology for OpenFOAM

this is a viscosity module for OpenFOAM with a focus on granular flow. Currently I work on implementing:

• a standard 𝜇(I) rheology for incompressible solvers (e.g. interFoam)
• a regularized 𝜇(I) rheology for incompressible solvers

as a scientific basis for this work I follow the following papers:

• Barker, T., & Gray, J. (2017). Partial regularisation of the incompressible 𝜇(I)-rheology for granular flow. Journal of Fluid Mechanics, 828, 5-32.
• Barker, T., Rauter, M., Maguire, E., Johnson, C., & Gray, J. (2021). Coupling rheology and segregation in granular flows. Journal of Fluid Mechanics, 909, A22.

Citing the code

If you use this OpenFOAM-muI module in your work/research/simulations, please cite the code in your publications by using the dedicated DOI number for a given code version:

The DOI number displayed here always refers to the latest release of OpenFOAM-muI. If you require a DOI for an older release, please refer to the Zenodo homepage of this code (by clicking the DOI badge above) and find a list of all DOI's for all code releases.

Installation

Current development on the main branch is for OpenFOAM version 9. After having installed OpenFOAM version 9 on your system, clone this git repository to a directory on your system:

git clone https://github.com/alexjarosch/OpenFOAM-muI.git

now change into the folder just created and compile the code

cd OpenFOAM-muI
wmake libso

If you want to clean the build, use

wclean

Usage

The viscosity library will be placed into $FOAM_USER_LIBBIN and is called libviscositymuI.so. To make use of the library with a solver place the following code at the bottom of system/controlDict:

libs
(
    "libviscositymuI.so"
);

Parameters of the regularized 𝜇(I) rheology are defined in constant/transportProperties:

    transportModel muIreg;
    muIregCoeffs
    {
        mus      0.342;
        mud      0.557;
        muInf    0.05;
        alphaReg 1.9;
        I0       0.069;
        dg       5.0e-4;
        rhog     2500;
        nuMax    1e3;
        nuMin    1e-5;
        pMin     10.0;
    }
    rho          2500;

For an explanation what the parameters mean and recommended values for a given granular medium, please consult the published 𝜇(I) rheology literature.

Examples

In the tutorials directory you can find two tutorial cases, which are modified version of the OpenFOAM interFoam tutorial case "damBreak" and are inspired by the benchmark of Balmforth, N. J., & Kerswell, R. R. (2005). Granular collapse in two dimensions. Journal of Fluid Mechanics, 538, 399-428.. You can run a regularized and a non-regularized version of the examples.

Note: To reproduce the actual benchmark data of Balmforth and Kerswell, a more advanced configuration of the example cases is required.

Which Implementation

Two versions of a 𝜇(I) rheology are implemented:

• muI follows the classical, unregularized 𝜇(I) rheology, implemented in accordance with equation 2.21 in Barker & Gray 2017.
• muIreg is the regularized version of a 𝜇(I) rheology, implemented accordance equation 6.3 in Barker & Gray 2017.

Regularized 𝜇(I) Python utility

In the 'utils' directory there is a Python script which you can use to estimate the I threshold for the 𝜇(I) regularization. It is the same algorithm the muIreg viscosity module uses.

Acknowledgements

OpenFOAM is a free, open-source software for computational fluid dynamics (CFD). The development is primarily done by CFD Direct on behalf of the OpenFOAM Foundation.

Disclaimer

This code is under development and not yet fully benchmarked against known granular flow examples. Use at your own risk!