## CFD Methodology
### Results and Validation  
To check the validity of the CFD results shown above, several water-level measurements were performed on the prototype of the humidifier presented in this paper. Different tests were carried out at inlet gas velocities around the reference operation point (V_gas_inlet = 0.10 m/s) to obtain the level of the steady water column. Lower gas velocities lead to surge on the compressor that feeds the reactor, while higher gas velocities lead to choke. Figure 11 represents--in dots--the value obtained in the experiments, and the comparison with those results from the CFD calculations, both for the continuous and multi-regime interaction models, respectively. The water level predicted by the Continuous interaction models does not capture properly the behavior of the bubble reactor humidifier prototype in the range of operation. With very low gas velocity (below 0.05 m/s) only, both models provide equivalent results. As the multi-regime interaction model is the one that better fits the experimental data, it is the one that has been used to further the design of the bubble reactor. Figure 12 is showing the results of studying the effect of the air stream velocity and the initial water column height over the increase of the water column height. In Figure 12, different air current velocity have been calculated while keeping a given initial water column height of 0.5 m. Similarly, in Figure 12 different initial water column height have been calculated keeping the same air current velocity of 0.1 m/s. Figure 11: Steady water column height. (Red) Multi-regime interaction model, (Blue) continuous regime interaction model. Figure 12: Variation of water column height. (**a**) Influence of gas velocity. (**b**) Influence of initial column height. For this application has been selected a gas velocity of 0.12 m/s and an initial water column height of 0.5 m.  
As can be seen in Figure 12a, the air stream velocity must be controlled as the water column height increases exponentially when increasing the velocity. This parameter is the deciding factor for the minimum footprint area of the bubble reactor, to keep the air velocity in reasonable values when the maximum mass flow rate specified for the application is passing through the reactor (0.25 kg/s). In the case of the initial water column height, it mainly affects the residence time of the air inside the water causing a direct effect on the final humectant capacity of the installation. Hence, it should be as high as possible, but as shown in Figure 12b, has a direct effect on the final height of the water column, so a compromise solution must be reached. In the case of the application described in this paper, a 2D column simplification is proposed as a first step. Afterwards, the results with different phase models are studied to see the effect on the final water column height of each one. Then, with the help of an experimental facility the models are validated and the one that fits the experimental data better is selected. In the next step, the parametric studies for both the initial water height and air stream velocity are carried out, from which the optimal values for the design to avoid overflowing are 0.12 m/s of air stream velocity and 0.5 m of initial water column height. With these two parameters the final geometry of the bubble reactor is obtained. The minimum footprint is calculated as the minimum area that assures that the air stream velocity at the outlet the bubble reactor does not increase above 0.12 m/s for the design point of the installation. In the case of the study presented in this paper, the footprint obtained was 0.81 m\({}^{2}\) for a design point of 2.4 bar, 50 C and 0.25 kg/s. Also, the reactor height was selected as 1.3 m to consider a security margin of 0.4 m over the nominal stabilized water column height of 0.9 m (initially 0.5 m with an increase of 0.4 m due to the 0.12 m/s of air velocity), in order to avoid overflows due to unexpected perturbances that could increase the bubbles height punctually.