Verification & Validation

Verification

The first two thing we check for verification are the mass conservation and inlet boundary conditions. We check the inlet boundary conditions to ensure that the UDF is doing what we expected it to perform. Then, we do a mesh refinement and use a smaller time-step to check whether the results are consistent with the original calculation. By using a finer mesh and a smaller time-step, we investigate the effects of truncation error caused by spatial discretization and temporal discretization. Then we will do a case comparison for the results obtained after spatial and temporal refinement.

Mass conservation & Inlet boundary conditions

To check whether mass is conserved in this calculation, open up solutions. Go to Reports -> Fluxes and then under options, check "Mass flow rate". Then select the one inlet and two outlets. We would expect the mass flux to sum up to zero (or extremely small).

As we can see from the window above, the mass fluxes add up to -2.624226e-07, which is very close to zero.

Inlet boundary conditions are checked during the calculations. As long as the surface monitor for average velocity has been turned on, the velocity at the inlet will be plotted. Below is the velocity profile at the inlet plotted during the calculation.

The profile matches our mathematical function for inlet velocity perfectly.

Mesh Refinement & Smaller Time-step

In the original calculation, a body sizing of 1e-3 is applied, hence the total number of cells in that mesh is 145082. However, in the refined mesh, a body sizing of 5e-4, which is half of the original size, is applied, and resultantly the total number of cells in the refined mesh is 217475. Ideally it is also good to refine the inflation mesh by choosing a smaller inflation thickness. In this tutorial, this has not been done, but readers are encouraged to do this step.

In the original calculation, the time-step that was used was 0.01s. For verification, a smaller time-step of 0.005s is used.

Case Comparison

After recalculating the cases, a case comparison is made to check the differences. First, wall shear on the artery wall is plotted for comparison.

From the graph above, we can tell that the wall shear distribution is almost identical throughout all three cases. But in order to make a more mathematically rigorous comparison, we need to extract some numerical data from the cases for comparison. The function calculator can be used to extract numerical information from the cases.

Here as an example, the maximum pressure on the wall in the three cases is calculated. By comparing the values, we can see that the difference between the original case and the refined cases are only 0.02% and 0.001%. This shows that pressure value is consistent in all cases. Thus based on these results from case comparisons, it is safe to say that the results obtained in the original case is verified.

Validation

In this blood flow in 3D bifurcating artery simulation, we have included most of the physical properties in this problem, such as non-newtonian fluid properties and pulsatile flow. However, in order to perform a simulation closer to the real scenario, elastic wall features should be included. This can be done by coupling the solution from FEA simulation and CFD simulation in ANSYS workbench. It is also always good to compare the results obtained from simulations with experimental results. In this case however, we do not have experimental data based on the exact same geometry.

References:

[1] Cutnell, John & Johnson, Kenneth. Physics, Fourth Edition. Wiley, 1998: 308.
[2] Siebert, Mark W. & Fodor, Petru S. Newtonian and Non-Newtonian Blood Flow over a Backward- Facing Step – A Case Study. Excerpt from the Proceedings of the COMSOL Conference 2009 Boston 2009.
[3] SINNOTT, Matthew. CLEARY, Paul W. & PRAKASH, Mahesh. An investigation of pulsatile blood flow in a bifurcating artery using a grid-free method. Fifth International Conference on CFD in the Process Industries CSIRO, Melbourne, Australia 2006

Acknowledgement:

This tutorial is made under great help and support from Dr. Rajash Bhaskaran, Cornell University.

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