Suitable time step for Ffowcs Williams and Hawkings
 

Hi all,

I have a question on the selection of the proper time step when performing an aeroacoustic calculation with the Ffowcs Williams and Hawkings (FW-H) model.

The case is a low-speed propeller (5 blades, maximum Mach number is 0.2) with air at 20 degrees.

Additional details of my setup are:

• On-the-Fly FW-H (impermeable formulation with propeller blades set as solid surface)
• SST-IDDES
• Compressible flow formulation

I have some noise experimental data at disposal in the range [10-10000] Hz, and the main contribution to the sound power level is up to 5000 Hz: hence, for the purpose of this investigation (and to avoid the cell count to skyrocket), I have generated a mesh with a cell size corresponding to 15 points per wavelength at 5000 Hz.
Considering the maximum frequency of 10000 Hz and the Nyquist theorem, I set a time step of 0.00005 s (i.e. the inverse of the sampling frequency).
This time step guarantees the physical CFL to be < 1, and I am running the case for enough rotations in order to have a frequency resolution of 2-3 Hz.

Additionally, the IDDES blending function contour results to be correct and the mesh has a y+ < 1.

However, it is not fully clear to me if the approach I have followed to select the time step is correct to have an accurate aeroacoustic simulation or if I should further refine it ?

I have checked the STAR-CCM+ theory and tutorial for the FW-H model (cylinder crossflow): they describe different ways of selecting the time step for the FW-H model (some seem somehow related to the use of the perturbed convective wave equation, which is not my case), but I could not find an answer that clarifies my question/doubt.


Can you please provide a feedback ?

Thanks !