# Mass Flow Scaling of Gas-Assisted Coaxial Atomizers
## 4 Results and Discussion
### Evaluation of the Relevant Measurement Position for Coaxial Nozzles  
To estimate the ideal measurement position for droplet size detection, primary breakup was investigated using high-speed camera images. When performing droplet size measurements, the measurement plane must fulfill various criteria: (i) the secondary breakup of liquid droplets and fragments must be completed; (ii) droplets must be spherical, which enables the application of quantitative measurement techniques such as PDA; and (iii) droplet number density must be adequate to minimize measurement errors via shading and the Gaussian beam effect from consideration [42]. As shown in Figure 4, these criteria were fulfilled for \(\dot{M}_{liq}~{}=~{}20\) kg\(\cdot\)h\({}^{-1}\) and also for the lowest investigated \(We_{aero}\) at \(z=130\) mm. For increasing \(We_{aero}\) the atomization process was even finished at lower \(z\) values. In contrast to this, the primary breakup of the nozzle N4 at \(\dot{M}_{liq}~{}=~{}500\) kg\(\cdot\)h\({}^{-1}\) and \(We_{aero}~{}=~{}250\) reveals that at \(z=130\) mm, none of the mentioned criteria is achieved, as the primary breakup length in particular significantly increases with increasing liquid mass flow. To guarantee the best possible comparability of the data, the measurement plane was chosen based on the theory of similarity at constant dimensionless ratio \(z/d_{eq}\) based  
Figure 3: Radial distribution of Sauter mean diameter (**left**) and high-speed camera images at \(z=130\) mm (**right**) utilizing nozzle N1 at \(\dot{M}_{gas}~{}=~{}14\) kg\(\cdot\)h\({}^{-1}\), \(We_{aero}~{}=~{}1000\) applying \(\dot{M}_{liq}~{}=~{}20/35/50\) kg\(\cdot\)h\({}^{-1}\).  
on the equivalent diameter \(d_{eq}\) of free jet theory [46]. This method is commonly applied for gas flame length calculation and is based on momentum conservation, as described in further detail in [PERSON] et al. [47]. Here, this concept was utilized for two phase free jets emerging from coaxial atomizers, where the equivalent diameter \(d_{eq}\) was calculated using Equation (8) for each nozzle:  
\[d_{eq}\ =\ \sqrt{\frac{4\cdot A_{gas}}{\pi}} \tag{8}\]  
For nozzle N1 operated at \(\dot{M}_{liq}\ =\ 20\) kg\(\cdot\)h\({}^{-1}\), the measurement plane was set to \(z\) = 130 mm, which represents \(z/d_{eq}\ =\ 26\). The application of nozzles N2-N4, which have higher \(d_{eq}\) values, leads to a constant \(z/d_{eq}\ =\ 26\) in measurement positions of \(z\) = 220/340/930 mm. The verification of this concept was performed with high-speed camera images, which revealed that all of the mentioned criteria for measurement positions were fulfilled for the respective measurement plane. As an example, the measurement plane of nozzle N4 is shown in Figure 4, when applying \(\dot{M}_{liq}\ =\ 500\) kg\(\cdot\)h\({}^{-1}\) at \(We_{zero}\ =\ 250\).  
Following the evaluation of the concrete measurement positions for each nozzle, measurement techniques were applied to detect the resulting droplet sizes as described in Section 4.3.  
Finally, for all liquid mass flows \(\dot{M}_{liq}\) = 20-500 kg\(\cdot\)h\({}^{-1}\) and \(We_{zero}\) = 250 primary breakup is always in fiber type mode (see Figure 4), which is characterized by small liquid fibers that are peeled off the liquid jet, according to [13]. As for further experimental investigation, \(We_{zero}\) was further increased up to 1000, and primary breakup was in fiber type for the whole set of experiments.