Guidelines for Ffowcs Williams-Hawkings Modeling

Use the following guidelines with the Ffowcs Williams-Hawkings models.

• Use a mesh fine enough to resolve the noise sources and the acoustic waves. 20 cells per wavelength is best. See Automobile Aerodynamics.
• In cases of quasi-periodic flow, such as a fan blade in a wind tunnel, use spanwise periodic boundary conditions and set a span dimension for them. No value gives a perfect result because the true situation is not 2D or periodic. To get reasonably satisfactory results, make the depth of the computational domain large enough. In the cases of unsteady flow simulations (RANS, DES, or LES) and of noise prediction using the FW-H models, make the depth of the domain greater than or equal to the acoustic correlation length. This depth is not necessarily the same as the depth required for LES and DES simulation. See The Ffowcs Williams-Hawkings Models.
• Use compressible ideal gas LES or DES modeling, coupled with an FW-H model. The compressible ideal gas model correctly accounts for compressible gas effects and sound wave speed in Aeroacoustic simulations.
• For the far-field broadband component, use LES and DES modeling to resolve accurately all turbulent scales that are needed for sound generation.
• For noise sources and propagation in near- to far-field, use high-order discretization schemes, such as Bounded Central-Differencing, Hybrid 3rd Order MUSCL/CD, or other low-dissipation convection schemes.
• Use the Unsteady Flux Dissipation Corrections property for the Segregated Flow model, especially if there are abrupt changes in mesh size such as adapted trimmed mesh.

  Note

  This property adds numerical dissipation to prevent spurious oscillations at mesh interfaces. Do not apply corrections inside the region, where noise sources are present and where noise is transmitted to the permeable FW-H surfaces. You can specify the Limiting Acoustic-CFL property as a constant, field function, table, or user code. If you use non-constant values for Limiting Acoustic-CFL, make sure that these values vary smoothly in space.

• Use the Min-Mod limiter (Eqn. (916)) as a less dissipative gradient limiting scheme. For slightly imperfect meshes, use the Modified Venkatakrishnan limiter (Eqn. (917)).
• Use a time-step small enough to resolve the frequencies being used. Make sure that the Courant number is less than 1 throughout all, or almost all, of the domain.
• Use these guidelines to minimize spurious acoustic reflections when specifying far-field boundary conditions:
  • Set non-reflecting boundary conditions on the outer boundaries of the domain, to allow outgoing disturbances to exit the domain without spurious reflections.
  • Use the Acoustic Suppression Zone model to improve the effect of the freestream boundary conditions. Such boundary conditions are normally used for open domains.
  • To dissipate the vortical structures, stretch the mesh downstream with an acoustic suppression zone.
  • To avoid spurious acoustic reflections, use the correct free-stream boundary together with the Acoustic Suppression Zone model in addition to the mesh stretching.
• To tell if any visible pressure fluctuations are originating at mesh interfaces or numeric boundaries:
  1. Allow sufficient simulation time to compute a mean pressure field $p_{mean}$ .
  2. Subtract the mean pressure field from the instantaneous pressure field $p\left(t\right)$ , to get the pressure fluctuations $p^{\prime }=p\left(t\right)-p_{mean}$ .
  3. Perform surface spectral analysis on the pressure field (Fft:Pressure), based on the stored pressure field $p\left(t\right)$ on derived parts or sections through the computational domain (saved in .simh file format). Use a few fixed frequencies (such as 2000 Hz, 3000 Hz, and 5000 Hz) and a sufficiently long physical time (usually more than 0.1 s).
• To reach a statistically steady transient simulation, use long simulation times (3 to 4 times the flow-through time), so that first the initial transients can be eliminated. This also compensates for the pruning of exported data and so avoids having insufficient acoustic data. See Automatic Signal Pruning.
• Use a constant time-step, with no changes in mesh or physics settings, to eliminate transients. The constant FW-H solver time-step coincides with this time-step, so that the sound pressure data from both have equal time-steps; this allows them to undergo the spectral analysis by FFT.
• Activate the unsteady FW-H models in the unsteady simulation.
• Run the On-The-Fly or Post FW-H simulation to have sufficient far-field pressure data for FFT and correct frequency resolution.
• If the On-the-Fly FW-H Receiver or Post FW-H Receiver node has the Acoustic Data Source property set to Flow or Flow+APE, set the permeable FW-H surface to be open downstream, to avoid the crossing of the wake through the integration surface. When you select the internal interface boundary for the permeable FW-H surface, make it surround all the turbulent noise sources, wrapping around both the body and the most energetic vortical structures of turbulence.

  If the Acoustic Data Source property is set to APE, some large vortical structures can pass through the permeable FW-H surface. The acoustic wave equation model predicts the acoustic signal at the permeable FW-H surface, then FW-H model extrapolates the purely acoustic signal from the permeable FW-H surface to the far-field, ignoring the hydrodynamic pressure contribution to the far-field sound pressure. This splitting method [52][53][87] can obtain accurate far-field noise predictions for applications where the acoustic variables are the same order of magnitude as the flow variables, such as a flow-acoustic feedback coupling (e.g. cavity noise) or duct acoustics, and when a vortical flow passes through the permeable FW-H Surface.