# An Experimental Analysis of Gas Reduction in Multiphase Flow with a KMS Helical Static Mixer
## 4 Validation Studies of the KMS Cyclonic Effect
### Numerical Validation for a Single Phase  
Thickness \(\delta\) is aimed to be reproduced in a CFD simulation platform, which must serve as a baseline to analyze the KMS effect and predict the performance with different fluid properties. The CFD code was analyzed according to the effect of parameters such as as the drag and lift forces, bubble size, and turbulence; moreover, the coalescence and rupture of the surface are important factors to be considered in the numerical configuration [22]. Based on the ALS where the liquid fluid is a continuous flow carrying dispersed gas bubbles along the pipe in a lower volume of the fraction, the CFD code was developed in Ansys CFX@to perform numerical experiments with an Eulerian-Eulerian multiphase model approach that ensures that the turbulence effect does not affect the continuity equation, considering it as a turbulent dispersion force in the momentum equation [23]; instead, the Lagrangian available solver is used, where the flow was considered as tracking particles. In addition, transient state simulations were developed to verify the time behavior of the flow. On the other hand, a sensitivity mesh analysis to define a suitable discretization of the computational domain to capture the pressure drop at the walls and the turbulence dynamics includes 6 different meshes differing by the number of nodes and elements and the skewness metric, resulting in a configuration of 2.9 million nodes for more than 6 million hexahedric elements and a skewness metric of 0.79 to better reproduce the phenomenon. To reproduce the experimental performance of Figure 3, Table 1 depicts the evaluated parameters from which the best of the 54 configurations results in the SST model of turbulence with a bubble size in the dispersion phase of 2 mm without drag and lift forces being considered and the bound conditions are defined by different controlled velocities at the incoming stream, while at the output, the pressure condition is set at the reservoir with no slipping on the walls. It has been shown that the \(k-e\) is a fast model; however, it is not necessarily the most accurate for multiphase flows and transient state simulations. The BLS model, in comparison, produces good results, but the eddies at the end of the KMS are not appreciated as in the SST model. Figure 3: Experimental thickness \(\delta\) for water. The performance is described from the fitting curve to develop CFD codes along the distance \(d_{l}\) where the cyclonic phenomenon remains. Figure 4 shows the numerical performance of this configuration on water/air for the thickness \(\delta\) on the transversal section along the distance \(d_{l}\). The sections are defined as S1 at \(d_{l}=-110\) mm, S2 at \(d_{l}=0\) mm, and S3 at \(d_{l}=50\) mm, showing a non-homogeneous distribution of the fluid at the wall, so thickness \(\delta\) is not possible to determine in this transient regimen. However, Sections S4-S6, at \(d_{l}=120\) mm, \(d_{l}=150\) mm, and \(d_{l}=180\) mm, respectively, exhibit a rotational dynamics with an easy thickness identification, suggesting a mean inner diameter \(d_{i}\) of gas for the casing and deviation tube. Discrete samples from multiple transversal sections along \(d_{l}\) construct a numerical curve that fits with the experimental one with an \(RMSE=10.8\%\) in the domain of \(d_{l}\), as depicted in Figure 5, where it can be seen how the cyclone becomes stable about \(d_{l}=120\) mm and remaining with the profile at least to \(d_{l}=200\) mm. \begin{table}
\begin{tabular}{c c c} \hline
**Turbulence Model** & **Bubble Size** & **Non-Drag Forces** \\ \hline \multirow{3}{*}{k-\(\epsilon\), SST, BSL} & \multirow{3}{*}{0.5, 1.0, 1.5, **2.0**, 4.0, 5.0 (mm)} & Lift force (Tomiyama model), virtual mass force (CVM = 0.5), wall lubrication (Tomiyama model), _non-drag forces omitted_ \\ \hline \end{tabular}
\end{table} 
Table 1: Configuration parameters for CFD code definition. The final parameters are identified in bold font. SST: shear stress transport, BSL: baseline.