# Scalability of Mach Number Effects on Noise Emitted by Side-by-Side Propellers
## 1 Introduction  
The constant growth of urban overcrowding and pollution has made the individuation of alternative and environmentally sustainable solutions to the standard urban mobility a crucial issue. This has led to an ever-growing interest towards Urban Air Mobility (UAM), which represents an interesting solution for the infrastructure congestion, overcoming the limited capacity of ground transport. At the same time, the need to enhance the sustainability of conventional aircraft (namely for regional, continental and intercontinental transport) is also mandatory, in the perspective of a low impact next generation aviation. These two different applications share the common target to develop eco-friendly vehicles, in terms of both chemical and acoustic pollution, in response to the increasingly demanding requirements and certification rules. Focusing on the latter application, a great effort has been made to find new solutions to reduce the environmental impact of conventional, currently-employed aircraft. This approach has led to remarkable improvements but, in order to meet the targets in terms of performance and acoustic emissions set in [1], disruptive layouts and technologies have to be adopted. In this scenario, the interest of manufacturers and researchers highly focused on the concept of Distributed Propulsion (DP) and, more specifically, Distributed Electric Propulsion (DEP). In these propulsive systems the thrust is delivered by multiple and decoupled propulsive devices [2]. Thanks to this peculiarity and the flexibility in the operating method of each device, this propulsive system is a viable green alternative to the traditional single/twin engine propulsive systems, mainly when electric-powered devices are exploited. Furthermore, this propulsive configuration lends itself well to be installedon aircraft wing, usually resulting in an improvement of the system aerodynamics due to the lift increase produced by the propeller wakes/wing interactions [3; 4]. Several research activities have been performed in this field and a lot of literature on this topic is already available, well testifying the growing interest in DEP layouts design. However, most of the existing literature mainly focuses on preliminary aircraft and propulsive system design or, at most, investigates aerodynamic issues [2; 5; 6; 7; 8]. Nevertheless, there are few studies aimed at assessing the aeroacoustic behaviour of such concepts (see, for instance [9; 10]). A key point in DEP configurations design is the difficulty of accurately predicting the aeroacoustic effects due to the aerodynamic interactions occurring with other aircraft components, which may significantly modify both the aerodynamic performance and emitted noise of the system [11]. Focusing on aerodynamic interactions occurring between adjacent propellers a great amount of literature is already present, as for instance in [12] for tilt-rotor configurations and in [13; 14; 15; 16] for drones. Furthermore, in [13], a numerical investigation of a quadcopter in hovering condition is proposed to examine the aeroacoustic effect of the rotors interactions, through a nonlinear vortex-lattice/vortex-particle method coupled with [PERSON]'s formulation 1A. A similar investigation is presented in [14], where the effect of the relative position on the aerodynamics and acoustics of two side-by-side propellers has been investigated. In [17] a numerical/experimental investigation on the effect of hub separation distance, propeller tilting and blade phasing, for a two two-bladed co-rotating/counter-rotating propellers, has been presented. However, the available literature mainly concerns hovering conditions, whereas the aeroacoustic interaction effects in forward-flight remains relatively unexplored. Besides, although isolated multi-propeller systems or wing-mounted single rotors have been extensively investigated [18; 19; 20; 21; 22], installation effects on multi-rotor configurations have not been deeply examined so far.