## 3 Validation Examples  
### Example 1  
For validation purposes, a simulation model was developed and its findings were cross-validated against the experimental results of [PERSON] et al. [25]. The geometry of the validation model is a 6 m vertical pipe with a 0.050 m diameter. First, similar geometry and boundary conditions were applied during simulation. Boundary conditions were  
Figure 4: Boundary conditions. **(a)** Cross section of the water and air inlet. **(b)** Working medium physical properties (at 20 \({}^{\circ}\)C). **(c)** Air and water superficial velocity graph at the inlet for slug flow. **(d)** Superficial velocities used for simulation [34].  
adjusted to simulate slug flow using water superficial velocity, \(U_{SL}=1.4\) m/s, and air superficial velocity \(U_{SG}=0.5\) m/s. A similar procedure of obtaining pressure readings was used; readings were obtained at 14 different locations for a total duration of 10 s at every 0.001 s interval. [PERSON] et al. [25] analyzed their pressure data from experiments and defined four parameters to identify the associated flow regimes. These four parameters are: (i) slope of total and inlet pressure drop \((\Delta p_{T})\), (ii) pressure drop variation \((\delta)\), (iii) pressure amplitude \((\gamma)\), and (iv) ratio of the pressure amplitude to the average pressure \((\lambda)\). \(\Delta p_{T}\) shows the pressure drop through the entire pipe length, which is caused by friction due to fluid flow. Pressure drop variation, \(\delta\), shows the effect of inlet pressure drop in total pressure drop. Pressure amplitude, \(\gamma\), is defined as the pressure difference between highest and lowest readings divided by 2, for a particular measurement point. Every flow regime can be recognized using at least one of these parameters. For validation purposes, these parameters were calculated using the present numerical model and compared with experimental results [25] in Table 2. The difference between the findings is very small, except for \(\delta\), which can be contributed to the fact that for simulation of slug flow, phase introduction at the inlet is not the same in the experimental and numerical method.  
The second parameter used for comparison purposes is the acquired dominant frequency of slug flow determined by [PERSON] et al. [25] using FFT. Figure 5 shows a comparison on the pressure frequency spectrum between the present model and the published work. In case of slug flow [25], the reported dominant frequency range was 3-5.5 Hz, whereas the present model was from 2.6 to 5.4 Hz. The highest peak reported by [25] was 3.00 Hz, while in the present finding it is 2.62 Hz.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{3}{c}{**Slug Flow**} \\ \cline{2-4}  & **[PERSON] et al. [25]** & **Present Study** & **Percentage Error** \\ \hline \(\gamma\) (bar) & 0.092 \(\pm\) 0.01 & 0.091 & 1.08\% \\ \hline \(\lambda\) & 0.724 \(\pm\) 0.10 & 0.753 & 3.85\% \\ \hline \(\Delta p_{T}\) & \(-\)0.056 \(\pm\) 0.003 & \(-\)0.057 & 1.75\% \\ \hline \(\delta\) & \(-\)0.796 \(\pm\) 0.15 & \(-\)0.656 & 17.50\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of present model and [PERSON] et al. [25] for various pressure parameters.  
Figure 5: Comparison on frequency spectrum of pressure signals for slug flow between published data and the findings from the present study.