Part one: Test Fluent, comparison with Matlab results:



3.6: Part one: Test Fluent, comparison with Matlab results:

Fluent and Matlab can be used to analyse fluid flows. However the process is quite different. When the first one use numerical way to obtain solutions (create a geometry – mesh – solve), the second one use theoretical and analytical way: solve equations of motions and Navier Stokes equations by using boundary conditions and then obtain an analytical expression for the velocity (depending on the time and the radius).

Finally, to compare solutions I will have to export Fluent results on Matlab.

As I already made in the fifth part, I had changed my initial Matlab unsteady code in a steady state one. This operation just needed little modifications and I found the following equation for the steady state velocity:

XXX-relation vitesse-XXX

By plotting it, we obtain the shape of the theoretical velocity profile for various Womersley number and internal radius

With Gambit, I first created and meshed a simple annular geometry similar to the case studied on the part 5. Naturally I used here a structured mesh with a bi-exponent law to catch boundary layers. The objective here was to obtain, with as less as possible cell’s number (to reduce the calculation’s time), a convergent solution.

After that I still had to define inflow and outflow conditions. I chose to use a given velocity inlet and a simple outflow relation. I could have used others parameters too (pressure inlet or pressure outlet for example).

Considering the flow rate as a constant and using Loth’s article, we can define an average velocity inlet. For that I used the relation

XXX-relations debit-XXX

Now I know each parameters I can start using Fluent.

To compare those numerical results to the theoretical ones, I had to convert it in a special format, reading with Matlab. For that, I used the export Fluent’s function and inserted the appropriate parameters.

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