## 3 Results and Discussion
### Scenario II: Longitudinal Distance between Two Valves L = 3D (6 m)  
Using the Solid Works 2020 design tool, the pipeline was re-prepared and executed for each of the geometric conditions of the location of the butterfly valve from the Howell-Bunger numerical model. In addition, the hydraulic conditions of the flow in the pipeline for a distance of 6 m (3D) were investigated. It is noteworthy that the increase in the distance between the butterfly valve and the Howell-Bunger valve was created in a pipe with a diameter of 2 m. Actually, the contraction did not change from 2.5 m to 2 m in diameter, and this increase was applied between the contraction and the Howell-Bunger valve. Velocity profiles in the area between the butterfly valve and the Howell-Bunger valve were extracted, as shown in Figure 8. Figure 8 velocity profiles revealed that by increasing the distance between the butterfly valve and the Howell-Bunger valve from 4 m to 6 m more conditions were offered for the development of flow in the pipe after passing the butterfly valve. A comparison of the velocity distribution at this point in 2D and 3D showed that by increasing the distance between the butterfly valve and the Howell-Bunger valve, it can result in the better formation of velocity profiles before the butterfly valve. However, it seems that the flow conditions for the complete stability of the velocity distribution cannot be formed at the inlet section of the Howell-Bunger valve, thus, it could be more feasible researchers to consider the numerical model in terms of 4D and 5D conditions.  
Figure 8: The Sectional view of velocity magnitude contours for the longitudinal distance between two valves = 3D.  
Figure 7: (a) sectional view of turbulent energy contours for the longitudinal distance between two valves = 2D; and (b) vorticity contours.  
Another parameter of research interest was to determine the ways under which the turbulence kinetic energy changes between the two valves. As previously noted, sudden and cross-sectional changes in this parameter indicate that flow expansion cannot occur in the enclosed and pressurized pipes and can induce unfavorable hydraulic conditions. Moreover, utilizing the numerical model results it can be a precise and comprehensive understanding of how the turbulence kinetic energy parameter changes in the areas between the butterfly valve and the Howell-Bunger valve for 3D conditions (Figure 9a). Figure 9 disclosed that the perturbation energy continued to the areas close to the Howell-Bunger valve due to the presence of a butterfly valve in the pipe downstream of the valve. Moreover, this energy was dissipated during contractions. According to the numerical model results, distance increased between the butterfly valve and the Howell-Bunger valve from 2D to 3D, and was essential in order to completely dissipate the turbulence energy. Figure 9b further showed that the vorticity profile changes at a distance of 6 m, which can be interpreted since, as the flow ran through the cross-section of the butterfly valve, then the vorticity created by the butterfly valve it continued in the 6 m long pipe to the location of the valve. However, the formation of vorticity in 3D conditions was reduced compared to 2D conditions, thus, supporting a more regular distribution pattern. However, depending on the other conditions, this distance can also be checked to ensure proper duct function for 4D and 5D conditions.