Tube case with Fluent2D and Abaqus2D

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 Fluent and Abaqus, both on an axisymmetric 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 10.
• The residual norm on the displacement is a factor $10^{-4}$ lower than the initial value.

When either criterion is satisfied the simulation stops.

Solvers

The flow solver is Fluent, used to solve an axisymmetric representation of the tube, with 100 cells on the fluid-structure interface. When setting up the case, the mesh is build based on the file mesh.jou using Gambit. The displacements are applied in the nodes, of which there are 101. In contrast, the loads (pressure and traction) are calculated in the cell centers, of which there are 100. The axial direction is along the x-axis, the radial direction along the y-axis. The setup script runs Fluent with the case.jou journal file to set up the case parameters, starting from the mesh file mesh_tube2d.msh. This case is written to the case_tube2d.cas file, which serves as input for CoCoNuT. Additionally, a folder create_mesh is provided containing a script to create the mesh in Gambit using a journal file. The mesh can be created by running the script create_mesh.sh, given that Gambit v2.4.6 is available.

The structural solver is Abaqus, used to solve an axisymmetric representation of the tube, with 50 elements on the fluid-structure interface. The Abaqus case is built when setting up the case starting from the file mesh_tube2d.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_tube2d.inp. The Abaqus element type used is CAX8RH. These are continuum elements for axisymmetric calculations, for stress and displacement without twist. They are: 8-node biquadratic, reduced integration, hybrid with linear pressure. See the Abaqus documentation for more information. The loads are applied on the faces in three points per element, which means on 150 load points in total. The displacement is calculated in the nodes. There are 101 nodes on the fluid-structure interface. The axial direction is along the y-axis, the radial direction along the x-axis.

The difference in reference frames and number of cells on the fluid-structure interface requires the use of mappers. In the structural solver wrapper, a permutation mapper is introduced to match the coordinate frames, flipping the x- and y-axis of the input. Thereafter, a linear interpolation mapper is used to interpolate in the x- and y-direction from the 100 cell centers of Fluent to the 150 load points in Abaqus. For the output the same is done in the opposite order: first interpolating and then flipping the axes.