I opened this topics in 2015, in the frame of the Master 2 Thesis of Matthieu Gisselbrecht.
High Reynolds number K - ε
model of turbulent pipe flows with standard wall laws:
first quantitative results.
M. Gisselbrecht and E. Plaut.
Communication 67210 at 22d Congrès Français de Mécanique, Lyon 2015.
We study turbulent pipe flow with the high-Reynolds number K- ε model, using wall laws as boundary conditions. The differential system obtained is discretised with a spectral method. We estimate all the spectral coefficients and the pressure gradient thanks to a Newton - Raphson method. The results are relevant physically, e.g., the friction factors found are close to the Blasius correlation. These results constitute a landmark that could be used to validate `industrial' codes. An asymptotic regime is found at large Reynolds number. We also propose a slight possible optimization of the model to better describe intermediate Reynolds number cases.
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