## Fluids

#### Wave propagation in an elastic tube with incompressible fluid 2way FSI

• shehab Gamrah
Subscriber

Dear all,

I hope everyone is safe and sound during these harsh times.

I am trying to carry out a 2 way FSI simulation using ansys fluent and transient mechanical with system coupling to model wave propagation in an elastic tube(mimicking blood flow in an artery)

My geometrical model is a tube of length 25cm and diameter 25mm (L/D = 10). The tube thickness for the solid domain is 2mm. The tube material model is linear elastic isotropic with a Young's modulus 1 MPa, density 1000 kg/m3, and poisson ratio 0.49 (aortic tissue)

The fluid is incompressible with density 1060 kg/m3 and viscosity 0.0034 Pa.s (blood fluid).

The inlet boundary condition is a pulsatile velocity wave and the outlet is a 0 Pa pressure outlet.

The fluid and solid meshes are both structured using ansys meshing.

Usually the solution of this problem is exactly like this youtube video so long as the fluid is elastic and no matter the fluid compressibility:

Simply put, a wave should propagate from the inlet to the outlet then reflect back thus creating a lag between fluid solution values (velocity) from the upstream to the downstream of the pipe (known as pulse wave velocity)

The pulse wave velocity according to the above mentioned inputs is 8.48  m/s which is in the same ball park as real aortas.

My problems are the following:

1- I can't workout how to estimate a time step dt to give a stable solution for the 2 way FSI problem. The ansys documentation once mentioned dt should be 1/20f where f is the highest frequency being modeled whatever in the world that even means. Another documentation says you should work out the FEM solution and calculate dv = maximum solid deformation/simulation time then calculate dt as dx/dv where dx now is the minimum fluid mesh length scale.

When I tried to run this problem the only time step that worked was 2.5e-3 s using the coupled solver (non of the other coupling algorithms worked at all) and I had to use the first order implicit time scheme (second order which should be more accurate and efficient never works). I also had to underrelax the pressure values in fluent to 0.3 instead of the default 0.7 and use solution stabilisation in the dynamic mesh settings. When I decrease the time step nothing works, when I increase it the simulation works but the solution gets further away from what I should be seeing. Bearing in mind I always have difficulties converging the continuity equation and in some time steps it never converges.

Some documentations mention the Courant number for the CFD time step guess but that can never make sense since fluent is implicit which is unconditionally stable.

2- My second problem is that I can't see any wave propagation whatsoever! The tube just expands everywhere with the same dilatation then recoils and that's it.

I have a feeling the settings to solve this problem are much simpler than this maze I have been running through for the past year and I am missing something very simple.

I have no idea what to do and I am miserably in a very bad position as this is part of my PhD. I also tried to read all the ansys workshops and FSI related material but it led me to complete abyss. I am suffering daily and may get demoted where I work due to this unresolved issue.

This forum is my last option and I will be forever grateful if any one is willing to help me. If anyone can just go through how to set up this problem from estimating a good time step to choosing appropriate coupling and fluent settings that would definitely seal the deal.

Thank you to everyone in advance and I wish you never go through what I am going through at the moment.

• Rob
Ansys Employee

The Courant Number comments refer to the time it takes the flow to pass through a cell.  That helps stabilse the transient solution, aim for a time step size so the flow takes around 10 steps to cross a cell: it's a rough value so don't get too worried about calculating to umpteen decimal places.

Re the tube deformation, what's holding the tube in?

• Azdine
Subscriber
Hi Gamrah! I have read your post about the PWV. I am developing the same simulation and unluckily encountering the same problems as you perhaps. Did you manage to solve it and getting any results? I either bump into the excessive distortion/negative cell volume or I just get an inflating tube at the inlet, even though in order to make it converge I had to make the tube long just 15mm and I would need a 200mm tube.nThank you!n
• Stephen Orlando
Ansys Employee
Hi ArraynPlease provide some further information with screenshots about your setup including boundary conditions for both Fluent and Mechanical, and Dynamic Mesh settings. Also, I recommend reviewing the following:nGoing over this tutorial in the Ansys documentation that shows a 2-way FSI simulation with Fluent and Mechanical. https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v202/en/sysc_tut/sysc_tut_oscplate_wb_fluent.htmlnSystem Coupling Tutorials \\ Tutorials with Workbench-Setup Workflows \\ Tutorials with Workbench Setup and Execution \\ Oscillating Plate FSI with Fluent and MechanicalnnYou can also look at the following for the same tutorial but run with the System Coupling GUI or Command Line Interface that is run outside of Workbench. The new System Coupling GUI (run outside of Workbench) is available by searching for System Coupling 2019R3 (or newer) in the Start menu. https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v202/en/sysc_tut/sysc_tut_oscplate_cli_fluent.htmlnSystem Coupling Tutorials \\ Tutorials with Command-Line Interface (CLI) Workflows \\ Oscillating Plate FSI with Fluent and MechanicalnnFSI simulations with very soft materials or membranes are prone to numerical instabilities. In 2020R1 we have introduced a stabilization method in System Coupling called the Quasi-Newton Stabilization Algorithm. Note that this has to be used with the new System Coupling GUI or Command Line Interface that is run outside of Workbench. More information here: https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v202/en/sysc_ug/sysc_gen_scservice_dt_supplemental_iqnils.htmlnSystem Coupling User's Guide \\ System Coupling Data Transfers \\ Supplemental Processing Algorithms \\ Quasi-Newton Stabilization AlgorithmnnIt is very important to build up the FSI simulation in stages as opposed to setting up the 2-way FSI right at the start. This document Best Practices for Coupled Fluid-Structure Interaction (FSI) describes this process and is available here: https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v202/en/sysc_ug/sysc_bestpractices_fsi.htmlnSystem Coupling User's Guide \\ Best Practices for System Coupling \\ Best Practices for Coupled Fluid-Structure Interaction (FSI)n
• Ahmed_Aissa
Subscriber
For incompressible fluids, you need either a very small relaxation factor which may lead your simulation to become ridiculously slow. Or you may solve this using the IQN-LS stabilization method. It is not well documented within Ansys documentation so I suggest you read about it before applying it.n