## 5 Conclusions
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline
**Model** & **Advantages** & **Disadvantages** \\ \hline Mathematical model (1D) & Provide accurate and adequate numerical information, where variables such as (i) entrapped air pocket pressure, (ii) water drainage velocity, (iii) water flow rate, (iv) air admission flow rate (in the case of presence of air valves) and (v) temperature can be studied through numerical values that vary as a function of time. & These models do not represent different events that occur during emptying processes, such as (i) backflow air effects, (ii) deformation of the air-water interface and (iii) velocity and temperature gradients. & These models do not represent different events that occur during emptying processes, such as (i) backflow air effects, (ii) deformation of the air-water interface and (iii) velocity and temperature gradients. \\ \hline \multicolumn{2}{p{142.3 pt}}{These models are easy to implement and require fewer computational resources; their results are obtained in a few seconds.} & The water column is considered a rigid uniform column; water velocity is equal at different points in the water column. \\ \hline \multicolumn{2}{p{142.3 pt}}{The modelling equations can be manipulated.} & Two-dimensional solution restricts the possibility to analyse hydraulic parameters such as water and/or air-flow rate (in the case of pipes with air valves). & \\ \hline \multicolumn{2}{p{142.3 pt}}{A 2D CFD model shows the variations in physical quantities (pressure, temperature, velocity) at different points of the hydraulic system by means of contours.} & Contractions and expansions in pipes must be adjusted by geometric aspect ratios to obtain a guarantee of equivalent mass flow [22; 34]. & Contractions and expansions in pipes must be adjusted by geometric aspect ratios to obtain a guarantee of equivalent mass flow [22; 34]. \\ \hline \multicolumn{2}{p{142.3 pt}}{Allows the visualisation of physical phenomena associated with water and air-flows, such as (i) deformation of the air–water interface and (ii) backflow air [7; 20].} & Simulations require more computational resources in comparison with mathematical models. \\ \hline \multicolumn{2}{p{142.3 pt}}{The effect of opening drain valves can be simulated by means of a dynamic mesh [21].} & On multi-core processors, simulation times are significantly reduced. & The definition of mesh quality, boundary conditions and numerical schemes are more difficult to calibrate, and require an independent analysis of the numerical results on the spatial discretisation conditions. \\ \hline \multicolumn{2}{p{142.3 pt}}{3D CFD Model} & In addition to the backflow air and the deformation of the air–water interface, this model allows obtaining new information such as (i) water flow rates, (ii) transient flows in the pipe cross-sectional, (iii) velocity profiles in different planes, (iv) heat transfer between water and air and (v) analysis of flow parameters with contour view in cross-sections [8; 24]. & Simulation times on high-performance processors are on the order of hours or days. \\ \hline \multicolumn{2}{p{142.3 pt}}{The simulation of the drain valve approximates the real conditions in more detail.} & The simulation of the drain valve approximates the real conditions in more detail. & These models require more significant computational resources than the other models. \\ \hline \end{tabular}
\end{table} 
Table 8: Advantages and disadvantages for model development for simulation of emptying processes of pipes with trapped air. has been used to explore and study different hydraulic and thermodynamic phenomena that occur in pipelines during an emptying process with air entrapped. To this end, 2D and 3D CFD models were developed by different authors to represent emptying processes in pressurised pipelines with trapped air.