# Numerical and Experimental Characterization of a Coanda-Type Industrial Air Amplifier
## 2 Air Amplifier Setup  
The industrial air amplifier considered here is the EXAIR Super Air Amplifier 120024, hereinafter referred to as ESAA. The ESAA is made up of two separate body parts that, when assembled, create a cylindrical duct. The first, on which the external fittings are mounted, contains the inlet section of the duct and a screwed intake for the pressurized flow, connected to an annular stagnation chamber that ends in an annular slot. The second part is screwed into the first one, allowing for an adjustment in the aperture of the aforementioned slot (see Figure 1). The following sub-indexes are used to identify the different sections: \(S_{i}\) is the inlet amplifier section, \(S_{o}\) is the outlet amplifier section, and \(S_{c}\) is the compressed air inlet section. The reference frame is mounted on the axisymmetric axis of the circular section of the secondary flow of the amplifier. As sketched in Figure 1, two inflow sections and one outflow section are identified. A primary pressurized flow characterized by its volumetric flow rate and static pressure (\(Q_{c}\) and \(p_{c}\), respectively) is first introduced into an annular chamber through the compressed air inlet section, \(S_{c}\), with an inner diameter \(D_{c}\). This primary flow is then accelerated through a thin ring nozzle, the aperture of which is defined by the gap parameter \(\delta\). The flow is tangentially ejected, remaining attached along the intake thanks to a Coanda profile, which directs the flow to the outlet, preventing boundary layer separation. Transfer of momentum from the primary jet flow towards the axis of symmetry occurs through viscous effects, and a low-pressure area is created at the center line of the inlet section \(S_{i}\), with diameter \(D_{i}\). This pressure drop produces an entrainment of induced flow rate, \(Q_{i}\). The combination of the two incoming flows results in the formation of the secondary flow, which is expelled through the outlet section \(S_{o}\), with diameter \(D_{o}\), at a flow rate of \(Q_{o}\). Downstream from the outlet section, secondary and primary flows are mixed due to the persistence of a high turbulent intensity. The clearance distance that defines the Coanda nozzle gap, \(\delta\), is one of the critical parameters in the geometry of the air amplifier (see Figure 2), as it can limit the injected mass flow due to blockage effects (this is elaborated in Section 5.3.1). Main dimensions are depicted in Figure 2. Axis \(X\) is aligned with the axis of symmetry and the main direction of the flow, and \(Y\) and \(Z\) define the main azimuthal plane. Two additional parameters are defined to characterize the air amplifier: the minimum diameter of the section in the secondary flow area, \(D_{m}\), and the diameter of the section where the Coanda nozzle is located, \(D_{g}\), with this last one being used to compute the non-dimensional mass flow. The main dimensions of the air amplifier model used are listed in Table 1.  
The performance of an air amplifier is usually measured by the volumetric flow rate (or amplification factor) as \(Q_{o}/Q_{c}\). The amplification factor reflects the impact of the primary flow on the entrainment of the secondary flow and can be complemented by the mass flow rate measured in the outlet section or the outflow mass flow rate \(\dot{m}\) as follows:  
\[\dot{m}=\rho_{0}Q_{o}=\rho_{c}Q_{c}+\rho_{i}Q_{i}, \tag{1}\]  
where \(\rho\) is the air density in the respective section indicated by the subscript. The flow regime remains defined by the Reynolds and Prantdl numbers. The local Reynolds number in a characteristic section may be defined by the passing massflow, \(\dot{m}\), and the section diameter, \(D\):  
\[\text{Re}_{\text{D}}=\frac{4\dot{m}}{\pi D\mu}, \tag{2}\]  
where \(\mu\) is the fluid viscosity. The Prandtl number is defined as follows:  
\[\text{Pr}=\frac{C_{p}\mu}{k}, \tag{3}\]  
where \(C_{p}\) is the specific heat capacity at constant pressure and \(k\) is the air thermal conductivity computed through the [PERSON]'s law.