Tube case with OpenFOAM3D and Abaqus3D

This example calculates the flow inside and the deformation and stresses of a straight flexible tube, where a pressure pulse is applied at the inlet. This done by using OpenFOAM and Abaqus, both with a fully 3D case.

Coupling algorithm

The coupling technique used is the interface quasi-Newton algorithm with an approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS).

Predictor

The initial guess in every time step is done using the linear predictor.

Convergence criterion

Two convergence criteria have been specified:

• The number of iterations in every time step is larger than 20.
• The residual norm on the displacement is a factor $10^{-3}$ lower than the initial value.

When either criterion is satisfied the simulation stops.

Solvers

The flow solver is OpenFoam, used to solve a fully 3D tube, with 48 cells on the fluid-structure interface in the length direction and 8 in the circumferential direction. When setting up the case, the mesh is build based on the file blockMeshDict. The displacements are applied in the nodes. In contrast, the loads (pressure and traction) are calculated in the cell centers. The axial direction is along the x-axis. When setting up the case using the setup.sh script, the solver coconut_pimpleFoam is compiled automatically.

The structural solver is Abaqus, used to solve a fully 3D tube, with 12 elements on the fluid-structure interface in the length direction and 8 in the circumferential direction. The Abaqus case is built when setting up the case starting from the file mesh_tube3d.inp containing nodes and elements. This is done by running Abaqus with the make_inp.py Python script to set all parameters, such as surface definitions, material parameters, boundary conditions and time step information. The result of the setup is a completed input file case_tube3d.inp. The Abaqus element type used is S8R. These are 8-node shell elements. The R refers to reduced integration. See the Abaqus documentation for more information. The loads are applied on the faces in 9 points per element, which means on 864 load points in total. The displacement is calculated in the nodes. There are 304 nodes on the fluid-structure interface. The axial direction is along the x-axis.

The coordinate frames of both solvers are the same so there is no need for a permutation mapper. In contrast, the difference of the points where loads and displacements are applied or calculated, require the use of interpolation mappers. Therefore, a radial basis mapper is introduced in the structural solver to interpolate in the x-, y- and z-direction.