# Periodic turbulent channel flow

The periodic turbulent channel flow is a well-known benchmark in CFD, to study wall-bounded turbulence. It is attractive as a test case due to its simple setup, and it is well documented in the literature with plenty of database available.

## DNS Reτ= 180

Have a look at the following video to see how to run a turbulent channel flow simulation with Xcompact3d and post-process the data with Py4Incompact3d.

In the video, it is shown how to perform a Direct Numerical Simulation of the turbulent channel flow case with a Reynolds number equal to 180. The simulation should take few hours on a dozen of CPU cores to collect converged statistics. The idea is to reproduce figure 4 of *Bartholomew, P., Deskos, G., Frantz, R. A., Schuch, F. N., Lamballais, E., & Laizet, S. (2020).* **Xcompact3D: An open-source framework for solving turbulence problems on a Cartesian mesh.** *SoftwareX, 12, 100550.*, web link, but with a lower spatial resolution.

You will see how to use **Paraview** to visualise the snapshots and **Py4Incompact3d** to generate the statistics (mean streamwise velocity profiles and rms of the velocity fields). The key parameters in the input file are also discussed.

For this case, `input_DNS_Re180_LR_explicittime.i3d`

from the `examples/Channel-Flow`

directory is used. Information is also provided on how to use the small Fortran file `stretching_parameter_channel.f90`

which can be use for: (i) determine the stretching intensity close to the wall via the `beta`

parameters (see *Laizet, S., & Lamballais, E. (2009)* **High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy.** *Journal of Computational Physics, 228(16), 5989-6015*, web link); (ii) determine the input Reynolds number of the simulation (the Reynolds number in the input file in Xcompact3d is based on the centreline velocity of a Poisseuille profile and half the height of the channel flow).

The statistics generated with **Py4Incompact3d** are compared with two sets of reference data (available in ``examples/Channel-Flow` directory of **Py4Incompact3d**):

1-*Lee, M., & Moser, R. D. (2015).* **Direct numerical simulation of turbulent channel flow up to Reτ=5,200.** *Journal of fluid mechanics, 774, 395-415.*

2-*Vreman, A. W., & Kuerten, J. G. (2014).* **Comparison of direct numerical simulation databases of turbulent channel flow at Reτ= 180.** *Physics of Fluids, 26(1), 015102.*