# Analysis of Flow Characteristics and Effects of Turbulence Models for the Butterfly Valve
## 4 Results and Discussion
### Flow Behavior  
Figure 4 shows the velocity contour and profile for the DN 80, DN 262, and DN 400 valves under different disc opening percentages with two-equation \(k-\varepsilon\), \(k-\omega\), and SST turbulence models. The flow behavior and turbulence characteristics were observed with velocity profiles in two characteristic locations: 5 x/Y and 10 x/Y with the developing and the developed flow region, respectively, where x is the distance from the valve and Y is the nominal valve size. Velocity profile was presented with the ratio of velocity of cross section to the initial velocity at two characteristic locations. The fully developed region,  
Figure 3: Discrepancies of flow coefficient results for the different turbulence models with different-sized valves and opening percentage: (**a**) DN 80 valves, (**b**) DN 262 valves, (**c**) DN 400 valves. development length was shown for the effective flow region. Flow analysis was conducted with different valve disc configuration in CFD model for each case. Figure 4: _Cont._  
For the small disc opening of 20% at location 5 x/Y, wake region containing vortices induced were generated from the upper side direction behind the valve disc owing to the high disturbance of the flow. The higher turbulence owing to vortices was observed for the \(k-\omega\) model expressed with higher turbulence kinetic energy as shown in Figure 5. With flow passing through the gap between the disc and pipe wall, the increased reattachment point toward the downstream direction for the \(k-\omega\) model was observed. Flow mixing with vortices is seen to be developed with wake and recirculation regions for the SST model. Meanwhile, smaller turbulence kinetic energy and wake region were expressed by the \(k-\varepsilon\) model. With increasing valve size in the case of DN 400, the tendency that less velocity changes through the valve disc was expressed with smaller vortex regions in the stream-wise direction, compared to larger changes in the case of the DN 80 valve. With developed flow at location 10 x/Y, each flow passing through the gap was mixed. With increasing valve size, flow mixing was seen to develop in the upper side. This is due to relatively larger flow in the gap between the disc and wall of the valve. Figure 4: Velocity contour and profile with different opening for the \(k-\varepsilon\), \(k-\omega\), and SST turbulence models: (**A**) DN 80, (**B**) DN 262, (**C**) DN 400. Figure 5: Turbulence kinetic energy profile with 20% opening for the DN 80 (**a**) and 50% opening for the DN 262 (**b**), with different turbulence model of \(k-\varepsilon\), \(k-\omega\) and SST. At 50% disc opening percentage as shown in Figure 4, flow recirculation and secondary flow developed near the valve disc in the form of vortex mixing. With increasing opening percentage, larger flow passing through the gap between the disc and pipe wall resulted in a circulation region that moved closer to the disc. [PERSON] et al. [8] and [PERSON] [4] reported similar results for turbulent and vortex behavior. At location 5 x/Y, flow disturbances due to vortices were expressed by the \(k-\omega\) model, representing higher turbulence kinetic energy, followed by the SST and \(k-\varepsilon\) models for the DN 80 valve. At location 10 x/Y, the velocity profile was shown to be twisted toward the downstream direction. Flow disturbance, mixing, and secondary flow due to vortices were seen to develop for the \(k-\omega\) model, and followed by SST model. At location 10 x/Y, as valve size increased, the twisted velocity profile changed more uniformly in cross section, and there was little change in velocity profile between the turbulence models. With large opening of 80% as shown in Figure 4, due to the large flow area between the disc and the pipe wall, the amount of recirculation and vortex behind the valve disc was reduced. Two stream-wise secondary flows were developed and separated after passing through the valve disc. Vortex regions were rapidly dissipated along the downstream due to large currents.