Problem description
In the case of separated flows, like the flow past a bluff body, there are instabilities that immediately trigger the transition to turbulence. In attached or mildly separated flows no geometrical induced disturbances exists and turbulent fluctuations or the turbulent spectra must be generated artificially.
Different approaches exists like the “recycling” of downstream turbulence, but this is limited to simple flows or academic cases. Here a flexible and high-quality method is implemented, the synthetic generation of turbulence based on a series of Fourier modes. For further details of the method see the theory manual or the reference section.
This validation case is the flat plate turbulent flow with synthetic turbulence generation. The Mach number of the flow is Ma 0.1, the Reynolds number based on the friction velocity is Reτ = 1000 and Reτ = 10000.
Software
OpenCruncher, version 5.2
Hardware
NVIDIA GeForce RTX A4000 (2x)
Synthetic turbulence interface
Interface with steady RANS (left) – WMLES (right)
Results
This zero pressure gradient boundary layer simulation was performed with two different momentum thickness Reynolds numbers, Reτ = 1000 and Reτ = 10000. The inflow boundary condition is a profile with a turbulent boundary layer calculated in a precursor RANS simulation.
Wall modeled large eddy simulation
It is very expensive to resolve all turbulent near wall structures and eddies (WRLES) for high Reynolds number cases. Here we have used a high aspect ratio grid and model the turbulence or turbulent eddy viscosity in the boundary layer with the WMLES approach.
There is a good agreement with the theory and the wall law, and there is also an agreement with a commercial solver. Both solvers run with the same mesh and the with identical boundary conditions but with a different numeric.
Wall function large eddy simulation
For an LES with the WALE model a almost uniform grid with ∆x ≈ ∆y ≈ ∆z has to be used. All turbulent scales need to be resolved. With wall functions the resolution requirements for the smallest scales near the wall can be reduced.
The picture shows the normalized boundary layer velocity profile compared with the analytical law of the wall.
Velocity spectra
Finally the Kolmogorov energy spectra was evaluated at a monitor point located inside the boundary layer.
The “natural” spectrum of turbulence and the velocity fluctuations arises quickly, the decay follows the “-5/3” law (orange line).
References
W. Bechara, C. Bailly, P. Lafon and S. Candel, “Stochastic approach to noise modeling for free turbulent
flows”, AIAA Journal, vol. 32, pp. 455-463, 1994
M. L. Shur, P. R. Spalart, M. K. Strelets and A. K. Travin, “Synthetic Turbulence Generators for RANS-LES Interfaces in Zonal Simulations of Aerodynamic and Aeroacoustic Problems”, Flow Turbulence Combust, vol. 93, pp. 63-92, 2014