# Scalability of Mach Number Effects on Noise Emitted by Side-by-Side Propellers
## 4 Conclusions  
This paper presents a numerical investigation on the effect of the blade tip Mach number on the noise emitted by two side-by-side propellers, in co-rotating and counter-rotating configurations. In particular, the proposed analyses investigate the influence of the propeller blades' tip Mach number on the emitted noise sensitivity to design parameters like the relative distance and the relative phase angle between the propeller blades. Both near-field and far-field noise propagation are examined. From the numerical investigations discussed some considerations can be drawn:  
* for both co-rotating and counter-rotating propellers, the effects on the emitted noise of the tip-clearance is similar for both tip Mach numbers, with those related to the lower tip Mach number mainly localized near the rotor disk plane;
* for the counter-rotating propellers configuration the relative phase angle alters the noise directivity pattern on the rotor disk plane, generally providing an angular shift of it; however, for specific values of phase angle and tip-clearance, a significant reduction of the emitted noise magnitude is observed for a wide angular range, particularly for the low Mach number flight condition;
* for the co-rotating propellers configuration the relative phase angle produces angular shift of the noise directivity pattern on the rotor disk plane, but slight modifications of the magnitude; anyway, these effects are more evident for the lower tip Mach number;
* the differences between near-field and far-field noise predictions decrease with the tip Mach number, increase with the tip clearance, and are greater for the co-rotating propellers configuration; this occurs because, in this case, the dipole-type propagation is still non-vanishing in the near field (whereas it is almost negligible in the counter-rotating propellers configuration because of a mutual cancellation effect).  
A consequence of the results achieved is that, in the perspective of an experimental investigation, even if a low-Mach-number model is tested for near field noise measurements,  
Figure 11: Co-rotating configuration, comparison between far-field and near-field OASPL directivity patterns; red line near field, black line far-field; \(\mathrm{TC}=0.05d\) (upper), \(\mathrm{TC}=d\) (lower).  
these could be suitably scaled to obtain reliable predictions of the far-field noise propagation of the real, higher-Mach-number configuration.  
Conceptualization, C.P., G.B., M.G. and R.C.; methodology, C.P., G.B. and M.G.; software, C.P., G.B. and M.G.; investigation, C.P.; data curation, C.P.; writing--original draft preparation, C.P. and G.B.; writing--review and editing, C.P., G.B., M.G. and R.C.; visualization, C.P.; supervision, G.B., M.G. and R.C. All authors have read and agreed to the published version of the manuscript.  
This work has been partially supported by the European Union Horizon 2020 research and innovation programme under project VENUS (inVestigation of distributEd propulsion Noise and its mitigation through wind tUnnel experiments and numerical Simulations), grant agreement No 886019.  
The authors declare no conflict of interest.