# Scalability of Mach Number Effects on Noise Emitted by Side-by-Side Propellers
## 1 Introduction
In particular, some studies regarding the aerodynamics of these configurations are available in the literature [3], whereas their acoustics remains relatively unexplored. Moreover, due to the novelty of this concepts, semi-empirical computationally efficient models are not present in literature and approximate solutions, as for instance, scattering models [23; 24] are no longer applicable. Driven by all these considerations, many European projects have started in the framework of Horizon 2020, among which VENUS (inVestigation of distributEd propulsion Noise and its mitigation through wind tUnnel experiments and numerical Simulations), which led to the present research, focused on the analysis of DEP systems aeroacoustics, through both numerical simulations and experimental activities. Regarding the latter, one issue to be carefully approached, is the sizing of the scaled model to be experimentally tested. To this purpose, some constraints have to be considered, as the wind tunnel geometrical characteristics, the power required to move the propeller and the permitted upper limit for the angular velocity to maintain an accurate control of the propeller blade shift. All these constraints limit the allowable experimental tip Mach number, which is significantly lower than that of the real model. Thus, the present paper provides an assessment of the tip Mach number effects on the aeroacoustic emissions, with the objective of defining general guidelines to suitably scale the model to be used in the experimental campaign. Specifically, the numerical analysis investigates the combined effects of the propeller tip Mach number, distance between hubs, direction of rotation and azimuth shift angle between blades. The ultimate goal is to assess the possibility of predicting the influence of the design parameters considered on the real configuration noise emission, starting from the experimental data related to the scaled model. As a by-product, the proposed analysis provides a systematic investigation of the combined effects of the blade tip Mach number and of the aforementioned geometrical/kinematic parameters on the noise emitted by multi-propeller configurations in forward flight, which, to the authors' knowledge, is not available in the current literature. The numerical investigation exploits for the aerodynamic analysis a velocity-potential based zeroth-order boundary element method that accounts for the effect of wake/body interaction [25] and, for the aeroacoustic one, an acoustic-pressure based zeroth-order boundary element method, which solves the Fowcs [PERSON] and Hawkings equation [26]. The paper is structured as follows: first, in Section 2 the numerical solvers herein applied are briefly described, with Sections 2.1 and 2.2 outlining the aerodynamic and acoustic formulations, respectively. Then, Section 3 discuss the numerical investigation of a multi-rotor configuration to assess the effects of the propeller tip Mach number on system noise emissions when the rotor hubs distance, the azimuth phasing angles between the blades of adjacent propellers, and the direction of rotation change. Finally, Section 4 summarizes the main outcomes of the numerical analysis.