Maintaining the Appropriate Acoustic CFL in the Wave Equation

To maintain the accuracy of acoustic predictions, apply criteria for points per wavelength (PPW) and the Acoustic CFL. This section outlines the requirements and calculations for this case.

The mesh size in the acoustic zone affects two criteria that are important for accurate acoustic predictions: the Acoustic CFL and the points per wavelength (PPW). The appropriate calculations for this tutorial are shown below.

Points Per Wavelength (PPW)

The recommended PPW for an acoustic calculation is PPW ≥ 30-40, maintained throughout the undamped zone. You can calculate the expected wavelength for this simulation from the vortex shedding frequency across the cylinder. This frequency is calculated from the Strouhal number:

S t = f D v
(5266)

where f is the vortex shedding frequency, D is the diameter of the cylinder, and v is the air velocity.

The settings given in this tutorial are representative for a typical industrial application, where flow is turbulent.

The Reynolds number for this tutorial is Re=6.38104, which is within the sub-critical range 300<Re1.5105. To obtain the correct vortex shedding frequency it would be necessary to use the Laminar model instead, according to the flow regime that the cylinder experiences.

The expected Strouhal number for this regime is St=0.2, which corresponds to a frequency of:

f=StvD=0.250/0.02=500Hz

The wavelength in turn is calculated as:

λ=c/f

where c=340m/s is the speed of sound. As PPW=(c/f)/Δx, the required mesh size for PPW of 40 is:

Δx=340ms/5001s40=0.017m

Acoustic CFL

For the recommended PPW of 40, aim to have Acoustic CFL ≤ 4 in the zone of interest. Acoustic CFL is defined as:

Acoustic CFL=cΔtΔx
(5267)

Rearranging and inserting a time-step Δt of 2.5105s gives a candidate mesh size of:

Δx=340ms(2.5105s)/4=0.002125m

Overall Mesh Size

Taking the lower computed amount of 0.002125 m and rounding down gives a final target mesh size of 0.002 m in the acoustic zone.