# Analysis of Flow Characteristics and Effects of Turbulence Models for the Butterfly Valve
## 6 Concluding Remarks  
The flow behavior through a butterfly valve for three different-sized valves of DN 80 (76.2 mm), DN 262 (254 mm), and DN 400 (406 mm) was analyzed under various flow configurations and disc opening percentages. Two-equation \(k-\varepsilon\), \(k-\omega\), and SST turbulence models were assessed to determine the accuracy of numerical solutions and turbulence model effects on the valve flow coefficient were compared with experimental values. Sensitivity analysis of flow properties was conducted to determine the sensitivity of the constants used in the two-equation turbulence model. The main conclusions are as follows:  
* With different-sized valves, discrepancies between numerical and experimental results for the flow coefficient were observed with different disc openings. The discrepancies increased with increasing valve size, and different degrees of discrepancy were observed with disc opening percentage for each valve size.
* Higher turbulence due to vortices was observed for the \(k-\omega\) model expressed with higher turbulence kinetic energy, followed by the SST and \(k-\varepsilon\) models. The difference between the results of turbulence models increased with decreasing valve size and disc opening. This can be attributed to the increasing turbulence effect which could  
Figure 7: Extreme value of the sensitivity coefficients with respect to the constants for the \(k-\omega\) turbulence model: (**a**) 20% opening, (**b**) 50% opening, (**c**) 80% opening case.  
cause lots of discrepancies between turbulence models, especially in areas with large pressure drop and sharp velocity increase.
* \(\omega\) turbulence model.
* For the \(k-\omega\) turbulence model, relatively smaller value of sensitivity with different locations and openings were observed compared to the \(k-\varepsilon\) turbulence model. From sensitivity analysis results, it can be suggested that turbulence constant adoptability in numerical calculations should be checked when using each turbulence model.
* For the numerical calculations, currently three turbulence models were the most frequently used turbulent models. These models were advantageous over other turbulence models because the computational conditions could be easily implemented. Therefore, the investigated analysis will be helpful to current users of turbulence models. The results of this research could also be widely applied to engineering design using the various valve systems.
* The numerical approach presented in this paper can be effectively used in future research on various valve flow analyses especially for the cavitation phenomenon.  
Conceptualization, S.-W.C. and H.-S.K.; methodology, S.-W.C. and H.-S.K.; resources, H.-S.S.; data curation, H.-S.S.; writing--original draft preparation, S.-W.C.; writing--review and editing, S.-W.C. and H.-S.K.; visualization, H.-S.S.; supervision, S.-W.C. All authors have read and agreed to the published version of the manuscript. Authorship must be limited to those who have contributed substantially to the work reported.  
This research received no external funding.  
Not applicable.  
This research was supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP; Ministry of Science, ICT & Future Planning) (No. NRF-2018R1C1B5086170), and in part by the Gachon University research fund of 2020 (GCU-202002430001).  
The authors declare that they have no conflict of interest.