## 3 Results and Discussion  
### Scenario I: Longitudinal Distance between Two Valves L = 2D (4 m)  
Based on the numerical model results it was reported that the flow conditions in the area between the butterfly valve and the Howell-Bunger valve (contractions with a length of 4 m from a diameter of 2.5 to 2 m) were investigated. For this purpose, the numerical model outputs -being based on the distribution of velocity values in the cross-section-they must be firstly considered. Besides, a velocity distribution was extracted for the mentioned region, as it is shown in Figure 6a. According to Figure 6, the presence of a \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Hydrodynamic Parameters** & **V (m/s)** & **Pressure (Pa)** & **Q (m\({}^{3}\)/s)** \\ \hline Experimental Modeling & 17.8 & 24,571 & 56.25 \\ Numerical Modeling & 16.74 & 25,837 & 54.83 \\ Error \% & 5.95 & 5.15 & 2.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of validation and accuracy results and numerical model calibration for hydrodynamic parameters. Figure 5: Comparison of the flow rates between inflow and outflow from Flow3D numerical model. butterfly valve in the pipeline as well as the presence of a contraction downstream they caused sudden changes in velocity, and velocity profiles showed that these immediately observed changes were intensified at the Howell-Bunger valve and do not create suitable conditions at this point for fluid flow. The short distance between the butterfly valve and the Howell-Bunger valve prevented the flow from developing upstream of the Howell-Bunger, which was inappropriate for the bottom outlet system. Figure 6b shows the stream-wise velocity component in the section before the flow entered the valves and downstream of the butterfly valve, the intensive turbulence of the flow, and the formation of cross flows in this area. Another significant parameter considers the effect of the presence of a butterfly valve at close distances to the Howell-Bunger valve in the studied model, as well as the changing ways of the turbulence kinetic energy. Sudden and cross-sectional changes in this parameter can lead to unfavorable hydraulic conditions. Based on the numerical model results, the changes in the turbulence kinetic energy parameter in the area between the butterfly valve and the Howell-Bunger valve were investigated and presented in Figure 7a. As shown in Figure 7, the presence of a butterfly valve and a contraction in the upstream area created the conditions for increased turbulence kinetic energy until the inlet flow to the Howell-Bunger valve. Due to the short distance between these two valves, the turbulence kinetic energy created in this path was not dissipated and penetrated the Howell-Bunger valve. Another examining parameter of the numerical model is related to the determination of the hydraulic conditions of the flow between the butterfly valve area and the Howell banger is how the vorticity changes after the flow passes through the butterfly valve (Figure 7b). According to Figure 7b, the vorticity flow due to velocity changes can be amplified after the current passes through the butterfly valve and then it can be transferred to the Howell-Bunger valve. The vorticity flow formed in the cross-section before the current can enter and then it flowed in the contraction region, at the direction of the current into the Howell-Bunger valve, which can cause adverse effects on the system. Considering the evaluation of the numerical model results, and taking into consideration some of the most important hydraulic parameters, including velocity profiles, turbulence kinetic energy, and vortex or vorticity formation, it can be concluded that the proposed distance of 4 m (2D) with one contraction was not desirable; therefore it should be supplemented with numerical studies. Based on these results, flow patterns can be examined based on the longitudinal distance of three to five times the pipe's diameter.