*2.3. Boundary Conditions and Solver Settings*

The calculations started by simulating free flow, i.e., forced only by a rotating impeller at 3000 r·min−<sup>1</sup> around the X axis. For this purpose, boundary conditions of 0 Pa corresponding to atmospheric pressure were applied at the inlet and outlet, respectively. To reduce calculation time, the strategy involves running the simulation at a steady state (MRF) for about 500 iterations until the solution converges below 10−<sup>4</sup> and then take the

results as initial conditions for the unsteady simulation (sliding mesh) with a time step of 5.5 · <sup>10</sup>−<sup>5</sup> s, which corresponds to 360 time steps per rotation of the rotor. Since the Mach number value was approximately 0.1, the flow was assumed to be incompressible, reducing the computational resources required and the computation time. The calculation used the FW-H equation implemented in Ansys Fluent based on Lighthill's acoustic analogy. The rotor and the pipeline walls are indicated as sources of sound (control surface). As receivers, 510 points were selected and placed on a sphere with a radius of 3 m where the acoustic pressure was computed (Figure 4).

**Figure 4.** Receivers distribution.

The resulting sound pressure obtained in the time domain was subjected to Fourier analysis. The boundary conditions are shown in Table 2.

**Table 2.** Boundary Conditions.


To obtain the fan characteristics, calculations were performed for 20 various volume flow rate values in the range of 0.0997 ÷ 0.1994 m3·s−1, of which the points marked 1 ÷ <sup>4</sup> turned out to be a stall range, while the range 5 ÷ 20 determined the operating range of the fan. In order to improve the readability of the presented graphs, we decided not to include characteristic points from the stall range on the graphs. Table 3 shows the calculation points and the corresponding percentage of unthrottled flow.


**Table 3.** Measurement points.

A pressure-based coupled algorithm was used to perform the calculations. The pressure-based solver uses an algorithm called the projection method, which solves the continuity and momentum equations [36]. The equation of momentum is calculated by the second-order upwind scheme [37].
