Periodic channel

Problem description

A Large Eddy Simulation (LES) of a turbulent channel flow is performed. The computational domain is rectangular, with two no-slip walls oriented normal to the y-axis, the remaining boundaries are connected using periodic boundary conditions in order to approximate an infinite channel. The Reynolds number based on the friction velocity is Reτ = 395, Reτ = 2400 and Reτ = 18000.

To maintain the friction Reynolds numbers Reτ, a body force is applied which is proportional to the pressure gradient. This gradient is taken into account via a source term in the momentum equations to drive the flow through the channel. It is important to notice that the bulk velocity ub is not specified and is therefore part of the solution.

Software

OpenCruncher, version 5.2

Hardware

NVIDIA GeForce RTX 2080 SUPER (2x)

Vorticity, Reτ = 2400

Results

The computational domain is a box with dimensions of 8δ x 2δ x 3δ in streamwise, wall-normal and spanwise direction. The grid contains hexahedral cells, we compare against the analytical solution, the law of the wall and against Prandtl’s assumption for the turbulent viscosity (µt+ = κ y+).

Wall modeled large eddy simulation

When simulating the channel flow the same high aspect ratio mesh spacing in x- and z-direction is always used. In y-direction, the wall normal direction, the grid is becoming more and more coarse. Due to the high aspect ratio cells next to the wall the turbulent viscosity will be modeled with the WMLES approach. For high y+ values a wall function approach is used.

WMLES at Reτ = 2400, 4 grids with different wall y+

Wall function large eddy simulation

The wall function approach combines the WALE model with a wall function. It is important to understand that the near wall resolution of wall function LES (WFLES) requires a near wall resolution of ∆x ≈ ∆y ≈ ∆z.

The WALE model does not add eddy viscosity to near wall cells to model the boundary layer. The turbulent structures must be resolved by the grid, but the size of the turbulent eddies scales linearly with the wall distance. This approach works well, but is very expensive for high Reynolds number cases combined with low y+ values.

WALE model at Reτ = 2400, 4 grids with different wall y+

Velocity spectra

To check the Kolmogorov energy spectra and the turbulent kinetic energy energy dissipation the velocity at a monitor point location was evaluated.

Monitor point location (green), vorticity, WMLES at Reτ = 18000
Spectra, WMLES at Reτ = 18000

References

F. Nicoud and F. Ducros, “Subgrid-scale stress modelling based on the square of the velocity gradient tensor” Flow, Turbulence and Combustion, vol. 62, pp. 183–200, 1999

P. Sagaut, “Large Eddy Simulation for Incompressible Flows”, Springer, 2002

M. L. Shur, P. R. Spalart, M. K. Strelets and A. K. Travin, “A hybrid rans-les approach with delayed-des and wall-modelled les capabilities”, International Journal of Heat and Fluid Flow, vol. 29, pp. 1638–1649, 2008