Setting the Appropriate Cell Size and Time-Step Size for the LES Acoustics Simulation

Based on the RANS simulation results and the frequency of the acoustic waves to be resolved, you determine the cell size and the time-step size for the LES acoustics simulation.

Cell Size

To determine the required cell size, use the following guidelines:

The Taylor microscale $λ$ is an intermediate length scale, which lies at the dissipation region end of the inertial sub-range within the turbulence spectrum. Scales that are smaller than the Taylor microscale are mainly viscous-driven. For an accurate prediction of vortices and noise sources inside the HVAC duct, you limit the cell size $Δ x$ based on the Taylor microscale as:

$Δ x \leq λ$

(5268)
To maintain the accuracy of acoustic predictions throughout the flow domain, you apply a critierion for points per wavelength (PPW).
PPW is defined as:

$P P W = \frac{c / f}{Δ x}$

(5269)

where $c$ is the speed of sound, $f$ is the desired frequency, and $Δ x$ is the cell size.
The recommended PPW for a simulation using the Lighthill Wave model is ≥15 PPW. To resolve waves up to a frequency of 2.5 kHz at a speed of sound of 346.5 m/s, you limit the cell size as:

$Δ x \leq \frac{346.5 \frac{m}{s} / 2500 \frac{1}{s}}{15} \approx 0.01 m$

(5270)

Time-Step Size

To resolve the wave amplitude in a Lighthill Wave simulation, you are advised to use ≥15 time-steps per period.

Therefore, you limit the time-step size as:

$Δ t \leq \frac{T}{P P W} = \frac{1 / 2500 \frac{1}{s}}{15} \approx 3.0 e^{- 5} s$

To set up the mesh:

Analyse the Taylor microscale inside the duct:

Select the Solvers > K-Epsilon Turbulence node and activate Temporary Storage Retained.
Expand the Scenes > RANS node and open the Taylor Micro Scale RANS scene.

Edit the Taylor Micro Scale RANS node and set the following properties:


Node	Property	Setting
Scalar 1
Scalar Field	Function	Taylor Micro Scale
	Max	0.002 m

In the scene display, to determine the Taylor microscale in the bulk region of the duct, hover with the pointer over the plane sections in the duct and press . on your keyboard.

The Taylor Micro Scale is ≈0.00125 m. The maximum cell size in the duct should target this value.

Specify the cell size for the LES simulation:

Select the Automation > Simulation Operations > 02_LES > Operations > Set Base Size LES node and set Value to 10.0 mm.

Expand the Geometry > Operations > Mesh LES > Custom Controls node and set the following properties:


Node	Property	Setting
Duct Refinement	Enable Controls
Values
Custom Size	Percentage of Base	12.5
IntakePlenumRefinement	Enable Controls
Values
Custom Size	Percentage of Base	25.0

To activate the unsteady time-scale and set the time-step size, edit the Automation > Time Scales node and set the following properties:


Node	Property	Setting
Time Scales	Active Time Scale	Implicit Unsteady Time Scale
Implicit Unsteady Time Scale	Time-Step	3.0E-5 s

Save the simulation.