This validation case belongs to fluid dynamics and the aim of this case is to validate the following parameters inside a pipe with a butterfly valve:

- Pressure drop using the Subsonic solver in SimScale

The simulation results of SimScale were compared to the results presented in the study done by Song, Xue Guan, and Park, Young Chui with the title “Numerical Analysis of Butterfly Valve – Prediction of Flow Coefficient and Hydrodynamic Torque Coefficient“\(^1\).

The model used in this validation case is a pipe with a discus shaped butterfly valve inside, which can be seen below:

The dimensions of the pipe can be seen in the table below:

Dimension | Value \([m]\) |

Upstream length | 14.4 |

Downstream length | 27 |

Valve & pipe diameter (D) | 1.8 |

Valve maximum thickness | 0.36 |

9 variants of valve opening angles ranging from 20° to 85° were used as a comparison to the reference study.

**Analysis Type**: Steady-state, Subsonic with K-Epsilon turbulence model

**Mesh and Element Types**:

The mesh was created with SimScale’s *Subsonic* mesh type.

The **Subsonic meshing **algorithm with hexahedral cells was used to generate the mesh. For this simulation, refinement level 8 was chosen for the comparison of different valve openings.

Mesh Type | Number of cells | Element Type |

Automatic Level 8 | 99000 | 3D Tetrahedral/Hexahedral |

**Fluid**:

- Water
- Kinematic viscosity \((\nu)\): 9.338e-7 \(m^2/s\)
- Density \((\rho)\): 997.3 \(kg/m^3\)

**Boundary Conditions**:

The boundary conditions are the same for all opening angles and were assigned as shown in Table 3:

Boundary Condition | Value |

Velocity inlet | 3 \(m/s\) |

Pressure outlet | 0 \(Pa\) |

No-slip wall | Pipe walls and valve surface |

The reference solution for the flow coefficient and the torque coefficient is given in the following formulae:

**Flow coefficient**:

$$c_v = \frac{Q}{\sqrt{\Delta P \times S_g}} \tag{1}$$

where:

- \(c_v\): flow coefficient
- \(Q\): flow discharge \((GPM-Gallons\,per\,minute)\)
- \(\Delta P\): pressure drop \((psi)\)
- \(S_g\): specific gravity of water

**Torque coefficient**:

$$c_t = \frac{T(x)}{\Delta P \times d^3} \tag{2}$$

where:

- \(c_t\): torque coefficient
- \(T(x)\): torque in the x-axis \((N.m)\)
- \(\Delta P\): pressure drop \((psi)\)
- \(d\): diameter of pipe \((in)\)

Comparison of the flow coefficient obtained from SimScale against the reference results obtained from [1] is given below:

Deviation of the results gained from SimScale in comparison to the results obtained from [1] can be seen in Figure 6. The deviation gets very close to the reference results for the opening angle from 50-70 degrees. It has to be noted that small valve opening angles are deviating highly, which is expected according to Song, Xue Guan, and Park, Young Chui\(^1\).

However, it must be noticed that at valve opening smaller than 20 degrees, the minimum error between CFX simulation and experimental data reach to 49.27958%.

Song, Xue Guan and Park, Young Chui Reference [1]

The flow contours inside the pipe when the valve is opened at the simulated opening angles as observed in our online post-processor:

Note

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Last updated: March 16th, 2022

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