## 4 Aeroacoustic Results
### Engine Noise Source Term  
Figure 7a (left) illustrates the investigated geometry: the fan stage consists of a rotor with 16 blades and a stator with 38 vanes. With a rotor tip radius of \(R_{tip}=0.89\) m and a rotor hub radius of \(R_{hub}=0.56\) m, a hub-to-tip ratio \(\eta=0.63\) is achieved. For the noise prediction, a symmetric flow in circumferential direction is assumed. The impact of the tail fin structure, shown in Figure 1, is neglected. In this case, no tonal boundary layer rotor interaction noise can be excited at the BPF and its harmonics. However, due to the different noise mechanism, tonal RSI noise is still excited and altered depending on the presence or absence of the inflow distortion. The investigated operating point of the propulsor is given in Table 1. Note that this operating point is the design point of the fan stage. Due to the circumferential symmetry of the geometry and flow conditions shown in Figure 7a, a periodic boundary condition, completing the domain in azimuthal direction, can be used for the CFD, and the computation of a single rotor-stator passage is sufficient to represent the investigated problem. The resulting computational domain drastically reduces the numerical costs and is exemplary illustrated in Figure 7b. The domain is  
Figure 6: Sound Exposure Level (SEL) calculation procedure from the Overall Sound Pressure Level (OASPL) time history. discretized by approximately 4 mio. cells. Particular attention is paid to ensure that the rotor wake region is meshed in high quality to adequately resolve the rotor wakes causing the RSI noise mechanism. In addition, a non-dimensional wall distance of \(y^{+}<1\) is ensured everywhere at the rotor blade and stator vane wall. These walls are modeled as viscid walls. Thus, a no wall-function is used to model the mean velocity gradient within the blade and vane boundary layer. For simplicity, the tip and hub wall of the fan stage are modeled by inviscid walls. In addition, the total temperature \(T_{t}\) and total pressure \(p_{t}\) have to be given at the inlet plane. The mass-flow is used as boundary condition at the outlet plane. Finally, the rotor block group is assumed to move around the engine axis by the given engine rotational speed \(\Omega\), while the stator block group is fixed. The turbulence is modeled by the Menter SST 2003 \(k-\omega\) model. A second-order Fromm scheme is used for the spatial solution of the equations. The time integration is performed by a second-order backward Euler scheme, using the predictor-corrector method. Figure 8a is an exemplary illustration of the inflow distortion entering the Aft-Propulsor (blue) in comparison with the Clean inflow configuration (red). Note that the boundary layer thickness \(\delta_{99}\) slightly exceeds the tip radius [32; 33]. Thus, a strong inflow distortion of a boundary layer thickness exceeding 2.5 of the hub-to-tip gap at the rotor is considered. Only the normalized mean velocity profile part of the unhatched region is considered and entering the propulsor. Note that in both cases the same massflow, given in Table 1, is ensured to maintain the operating point of the fan stage. As aforementioned, the total pressure has to be defined at the inlet plane of the rotor block group. The radial varying inflow distortion is defined by the total pressure distortion shown in Figure 8 and used as a radial resolved boundary condition for the CFD computation. The detailed process of defining the boundary layer profile for the considered aircraft configuration is given by [PERSON] et al. [32; 33]. For the Clean configuration, the total pressure is assumed to be constant for all radial positions. Figure 7: Illustration of investigated Aft-Propulsor and CFD domain. (**a**) Exemplary shape of the inflow distortion of Aft-Propulsor configuration. Source: [31], reproduced with permission. (**b**) Exemplary illustration of single-passage computation domain for CFD. Source: [12], reproduced with permission.