Validation Case: Butterfly Valve with Subsonic solver

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“$^1$.

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Geometry

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

butterfly valve at 20 degrees inside pipe — Figure 1: Pipe model with butterfly valve inside the opening at 20° angle

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

Table 1: Pipe and valve dimension

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

Analysis Type and Mesh

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

Mesh and Element Types: The mesh was created with SimScale’s Subsonic mesh type.

Mesh Sensitivity

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

Table 2: Mesh data for butterfly valve validation case

Mesh Valve opening angle 50 deg cutting plane butterfly valve subsonic — Figure 2: Mesh within the flow domain with fineness level 8

Mesh Valve opening angle 50 deg ISO butterfly valve subsonic — Figure 3: Subsonic meshing performed on the valve with refinement around the edge of the valve

Simulation Setup

Fluid:

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

Boundary Conditions:

boundary condition overview butterfly valve subsonic — Figure 4: Boundary condition overview where the flow goes from left to right

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

Table 3: Boundary conditions for pipe and valve

Reference Solution

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

Flow coefficient:

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

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 $(in)$

Result Comparison

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

Valve validation Flow Coefficient _ Valve Opening Angle -Subsonic — Figure 5: Flow coefficient comparison between reference results and SimScale

Deviation to Reference

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]