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The first thing we check for verification are the mass conservation. We check the inlet boundary conditions to ensure that the conditions are as we expectis the analytical solution since we have one available. Then, we do a mesh refinement and use a smaller pseudo-time-step to check whether the results are consistent with the original calculation. By using a finer mesh and a smaller smaller pseudo-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

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Analytical Solution

The analytical solution is contained in this csv file that contains the concentration (or equivalently, the temperature) at various radial locations.

In addition, here are the analytical solutions for alpha = 1 and alpha = 3/2.

Mesh Refinement & Smaller Pseudo-timestep

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Validation

It is also always a good habit to check that the mesh is refined enough. For example, you could use an element size that is half of what was used in the videos and compare the results.

When using pseudo-transient, it is important to make sure that you are using a small enough pseudo-time-step. For example, you could use a pseudo-time-step that is half of what is used in the videos and compare the results, or you could also use one that is twice as big as what is used in the videos.

Validation

We do not have any experimental data for this problem. compare the results obtained from simulations with experimental results. In this case however, we do not have experimental data but we do have description of flow in the carotid artery, courtesy of your textbook. We find that the flow in the internal and external carotid arteries should be approximately 70% and 30% of the total flow in the common carotid artery. We can check this in Fluent by using the mass flow rate values we found earlier. 

References:

Under construction

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