## 2 Materials and Methods
### CFD Analysis
#### 2.3.1 Governing Equations and Turbulence Model  
Mass and momentum conservation Equations (4) and (5) are solved for all flows analyzed in ANSYS Fluent [30]. The additional equation of energy conservation is solved for analysis involving heat transfer or fluid compressibility. Because neither of these effects were present in our analysis, the energy equation was not included.  
\[\frac{\partial\rho}{\partial t}+\
abla\times\left(\rho\overrightarrow{v} \right)=\mathrm{S}_{m} \tag{4}\]  
\[\frac{\partial}{\partial t}\left(\rho\overrightarrow{v}\right)+\overrightarrow {v}\times\
abla\left(\rho\overrightarrow{v}\right)=-\
abla p+\
abla\times \left(\bar{\tau}\right)+\rho\overrightarrow{g}+\overrightarrow{F} \tag{5}\]  
where \(\rho\)--the fluid density; \(\
abla\)--Nabla operator; \(\overrightarrow{v}\)--velocity vector; \(S_{m}\)--mass from the dispersed phase, e.g., from the evaporation of liquid droplets, added to the continuous phase; \(p\)--the static pressure; \(\rho\overrightarrow{g}\)--the gravitational body force; \(\overrightarrow{F}\)--body force; \(\bar{\tau}\) --stress tensor given by Equation (6).  
\[\bar{\tau}=\mu\left[\left(\
abla\overrightarrow{v}+\
abla\overrightarrow{v} ^{T}\right)-\frac{2}{3}\
abla\times\overrightarrow{v}I\right] \tag{6}\]  
where \(\mu\)--molecular viscosity; \(I\)--unit tensor.  
The shear stress transport model (k-\(\omega\) SST) was used in the calculations. This two-equation turbulence model was developed by [PERSON] [31, 32] to effectively blend the k-\(\omega\)  
Figure 11: Diagram of the measurement system.  
Wilcox model [33] near walls and standard k-\(\varepsilon\) model [34] in the fare field. The blending functions were developed to activate particular model depending on flow regions. This makes the k-\(\omega\) SST model more accurate and reliable for a wide range of flows than standard k-\(\omega\) or k-\(\varepsilon\) models [35]. The k-\(\omega\) SST model is widely used in the analysis of airfoils or wind turbine blades [36; 37; 38]. The turbulence kinetic energy \(k\) and the specific dissipation rate \(\omega\) are obtained from the transport Equations (7) and (8).  
\[\frac{\partial}{\partial t}(\rho k)+\frac{\partial}{\partial x_{i}}(\rho ku_{ i})=\frac{\partial}{\partial x_{i}}\left(\Gamma_{k}\frac{\partial k}{\partial x_{j}} \right)+\widetilde{G}_{k}-Y_{k}+S_{k} \tag{7}\]  
\[\frac{\partial}{\partial t}(\rho\omega)+\frac{\partial}{\partial x_{j}}(\rho \omega u_{i})=\frac{\partial}{\partial x_{j}}\left(\Gamma_{\omega}\frac{ \partial\omega}{\partial x_{j}}\right)+G_{\omega}-Y_{\omega}+D_{\omega}+S_{\omega} \tag{8}\]  
where \(\widetilde{G}_{k}\)--the turbulence kinetic energy generation caused by the average velocity gradients; \(G_{\omega}\)--the generation of \(\omega\); \(Y_{k}\) and \(Y_{\omega}\)--the dissipation of \(k\) and \(\omega\) due to turbulence; \(D_{\omega}\)--the cross-diffusion term; \(S_{k}\) and \(S_{\omega}\)--user-define source terms; \(\Gamma_{k}\) and \(\Gamma_{\omega}\)--the effective diffusivity of \(k\) and \(\omega\) given by Equations (9) and (10).  
\[\Gamma_{k}=\mu+\frac{\mu_{t}}{\sigma_{k}} \tag{9}\]  
\[\Gamma_{\omega}=\mu+\frac{\mu_{t}}{\sigma_{\omega}} \tag{10}\]  
where \(\mu_{t}\)--the turbulent viscosity given by Equation (11), whereas \(\sigma_{k}\) and \(\sigma_{\omega