# A Comparison of Different Methods for Modelling Water Hammer Valve Closure with CFD

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## Abstract

**:**

## 1. Introduction

_{f}, A, Δp, Δp

_{f}, and q are the flow rate, length between the measuring cross-sections, density, final limit of integration, cross-section area, differential pressure, pressure losses due to friction, and leakage flow rate after valve closure. Transient viscous losses shall be estimated accurately during the water hammer to calculate the flow rate accurately. The existing evaluation method assumes one-dimensional flow limiting its applicability considerably. There is a need to extend the evaluation method to account for geometry variation as well as for second flows. Thus, 3-dimensional numerical simulations to evaluate the experimental data seem to be the next step for a better overall accuracy of the flow rate estimated.

## 2. Materials and Methods

#### 2.1. Test Case

^{3}/s.

^{3}/s, i.e., a Reynolds number Re = 7 × 10

^{5}.

#### 2.2. Mathematical Modelling

_{i}, and µ are the pressure, fluid density, mean velocity, and fluid dynamic viscosity, respectively. To model the Reynolds shear stress term ($-\rho \overline{{u}_{i}{u}_{j}}$) in the turbulent flow, the low Reynolds k-ω SST model [18] is used. Ref. [12] demonstrated that low-Re SST k-ω turbulence models predict more acceptable results for pressure variation during water hammer than high-Re turbulence models. The k-ε model with wall functions cannot capture the variation of the velocity profile close to the wall. This turbulence model was used in similar studies with satisfactory results [4,10,11,12]. To model the fluid compressibility, Hooke’s law with Equation (4) describing the variation of the density with the pressure [19] is used. The effects of pipe elasticity [11] are accounted in modified bulk modulus ${K}_{f}^{\prime}$, Equation (5), where E, e, and D are the Young’s modulus of elasticity, thickness, and pipe diameter, respectively.

#### 2.3. Valve Closure Modeling

#### 2.3.1. Immersed Solid Method

#### 2.3.2. Dynamic Mesh

#### 2.3.3. Sliding Mesh

#### 2.4. Computational Setup

^{+}< 1 at the wall. Moreover, a finer mesh close to the valve is also used to have better accuracy, see Figure 6.

^{6}, 2.4 × 10

^{6}, and 4.5 × 10

^{6}are made using a time step size of 0.1 ms to study the effect of the mesh on the transient simulation solution. The average aspect ratio is around 1021, and the skewness is 0.13.

^{6}nodes is considered for the simulation.

## 3. Results

#### 3.1. Pressure Variation

#### 3.2. Wall Shear Stress Variation

#### 3.3. 3D Effects

#### 3.4. Computational Cost

## 4. Conclusions and Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The water hammer test rig schematic. Figure courtesy of Sundstrom et al. [17].

**Figure 3.**Overlapping of the fluid zone and immersed solid zone at time t =4 s (close to the end of the valve closure) in the immersed solid method for modelling valve movement.

**Figure 4.**Dynamic mesh method grid cut in half: (

**a**) before valve movement; (

**b**) at t = 4 s close to the end of valve closure.

**Figure 5.**Sliding mesh method grid cut in half: (

**a**) at t = 0 s before valve movement; (

**b**) at t = 4 s close to the end of valve closure.

**Figure 6.**Immersed solid method grid: (

**a**) fine grid near the gate; (

**b**) grid at the pipe cross-section.

**Figure 7.**Average absolute pressure monitoring at section 11 m upstream of valve for three different grids.

**Figure 8.**Average absolute pressure monitoring at section 11 m upstream of valve for four different time steps.

**Figure 9.**The variation of differential pressure with time during the valve closure between two cross-sections 11 m and 15 m upstream of the valve.

**Figure 10.**The deviation of estimated differential pressure by sliding mesh with the experiment between two cross-sections 11 m and 15 m upstream of the valve.

**Figure 11.**The time variation of the magnitude wall shear stress at cross-sections 10 m upstream of the valve.

**Figure 12.**Streamlines and axial velocity contour of the flow inside the pipe at the end of the valve closure: (

**a**) immersed solid method; (

**b**) dynamic mesh; (

**c**) sliding mesh.

**Figure 13.**Streamlines of the flow inside the pipe at the end of the valve closure for the different valve modelling method: (

**a**) immersed solid; (

**b**) dynamic mesh; (

**c**) sliding mesh.

**Figure 14.**Axial velocity profile at the vertical line with distances of: (

**a**) 25cm; (

**b**) 50 cm; (

**c**) 75 cm upstream of the valve at the end of the valve closure.

Method | Number of CPU (2.60 GHz) | App. Time (h) |
---|---|---|

Immersed solid method | 48 | 60 |

Dynamic mesh method | 48 | 170 |

Sliding mesh method | 48 | 65 |

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**MDPI and ACS Style**

Neyestanaki, M.K.; Dunca, G.; Jonsson, P.; Cervantes, M.J.
A Comparison of Different Methods for Modelling Water Hammer Valve Closure with CFD. *Water* **2023**, *15*, 1510.
https://doi.org/10.3390/w15081510

**AMA Style**

Neyestanaki MK, Dunca G, Jonsson P, Cervantes MJ.
A Comparison of Different Methods for Modelling Water Hammer Valve Closure with CFD. *Water*. 2023; 15(8):1510.
https://doi.org/10.3390/w15081510

**Chicago/Turabian Style**

Neyestanaki, Mehrdad Kalantar, Georgiana Dunca, Pontus Jonsson, and Michel J. Cervantes.
2023. "A Comparison of Different Methods for Modelling Water Hammer Valve Closure with CFD" *Water* 15, no. 8: 1510.
https://doi.org/10.3390/w15081510