# Numerical and Experimental Characterization of a Coanda-Type Industrial Air Amplifier
## 5 Results
### Numerical Characterization
#### 5.3.3 Geometry Sensitivity Study  
For certain applications, it could be interesting to increase the amount of secondary mass flow. It can be magnified not only by increasing the high pressure value, \(p_{c}\), but also by scaling the entrainment area. Fixing the clearance gap, \(\delta\), and modifying other geometrical parameters allows us to explore the effects of scaling the air amplifier device. This study was conducted by employing axisymetric numerical simulations, as enunciated in Section 4.3. Comparing both the three-dimensional and the axisymmetric setup, the observed asymmetric behavior of the flow is lost in the axisymmetric simulations. However, the velocity profile recovered for the simplified model reproduces a similar trend and scaling compared to the 3D model, as shown in Figure 27 with \(p_{c}=0.45\) MPa and \(\delta=0.23\) mm. In Figure 27(left), Mach number contours are shown for a transversal slice (\(Z=0\) m) of the 3D numerical simulation and compared with those obtained with the simplified axisymmetric one. Despite the loss in the slight asymmetric behavior, both show an excellent agreement. In Figure 27(right), velocity profiles measured at 3.5 diameters downstream from the air amplifier outlet are depicted, and experimental results are compared with numerical data for both the 3D and the simplified simulation. The variation in the results, which eliminate the non-symmetry, lands within the confidence interval defined by the standard deviation of the experimental measurements. To complete the analysis of different geometric parameters to evaluate the technical feasibility of the air amplifier to achieve a higher entrained flow, we therefore use the axisymmetric numerical setup to improve the computational cost. Considering a fixed value of \(\delta=0.23\) mm, three different values of the inlet total pressure, \(p_{c}\), and the amplifier inner diameter, \(D_{m}\), were considered. The set of studied cases is gathered in Table 3, with the first line being the original dimensions of the air amplifier. While increasing these geometrical or flow parameters leads to an increment in the injected and entrained mass flows, a saturation value of the amplification factor is eventually reached. For an scaled inner diameter, successive increments of the inlet total pressure do indeed produce larger entrained mass flows, but this does not translate into a better performance of the air amplifier. Comparing the nondimensional parameters in Table 3, however, may suggest a linear relationship between the aspect ratio defined by the internal diameter and the clearance gap, \(D_{m}/\delta\), and the amplification factor, \(Q_{o}/Q_{c}\). Exploring larger values of \(D_{m}/\delta\) for different \(\delta\) values offers a consistent behavior. A growing linear trend eventually reaches a clear maximum, with a later saturation of the amplification factor that rapidly decays. The maximum occurs for aspect ratio values between 1800 and 2000, independently of the gap size, which afterward shows a decreasing trend. These results are collected in Table 4. The air amplifier performance is based on its  
Figure 27: Comparison of the numerical results obtained for a 3D and an axisymmetric simulation with \(p_{c}=0.45\) MPa and \(\delta=0.23\) mm. Contours of flow Mach number are shown in the **left image** for both cases, together with streamwise velocity distributions in the **right image**. The experimental data include the standard deviation of the measured values. entrainment capability, which is related to the dragging effect of the pressure driven flow created by the annular jet. Thus, as the nozzle moves away from the axis of symmetry, the perturbation effects decay. Interestingly, this relationship depends on the fixed gap size. Larger gaps present a maximum value of the total (injected+entrained) mass flow for aspect ratio values smaller than those observed for thinner gaps. This has been reflected in Figure 28, where gaps of \(\delta=0.23\) mm and \(\delta=0.08\) mm are compared.