# PATs Operating in Water Networks under Unsteady Flow Conditions: Control Valve Manoeuvre and Overspeed Effect

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Basic Hydraulic Modelling of the Transient Conditions

^{2}; A is the inner area of the pipe in m

^{2}; $Q$ is the flow in m

^{3}/s; x is the coordinate along the pipeline axis; ${\tau}_{w}$ is the shear stress at the pipe wall in N/m

^{2}; $\rho $ is the density of the fluid in kg/m

^{3}; and $D$ is the inner diameter of the pipe in m.

^{2}; E is the Young’s modulus of elasticity of the pipe in N/m

^{2}; and $\u0471$ is the dimensionless parameter that takes into account the cross-section parameter of the pipe and supports constraint.

- The flow is homogenous and compressible;
- The changes of density and temperature in the fluid are considered negligible when these are compared to pressure and flow variations;
- The velocity profile is considered pseudo-uniform in each section, assuming the values of momentum and Coriolis coefficients constant are equal to one;
- The behaviour of the pipe material is considered linear elastic;
- Head-losses are calculated by uniform flow friction formula, which is used in steady flow.

_{r}= 1) (6):

#### 2.2. Control Valves

_{ef}) is the real time of valve closure (shorter than the total time (T

_{C})), which can induce high discharge reduction, responsible for the extreme water hammer phenomenon (as presented in Figure 2). Equation (10) mathematically defines the effective time closure based on the tangent to the point of the curvature in which dq/dt is highest:

#### 2.3. Damping Effects

^{2}(due to almost exclusively friction effects). Based on the well-known upsurge given by the Joukowsky formulation through Equation (11):

^{3}/s; g is gravity constant in m/s

^{2}and S is the section of the pipeline (m

^{2}), the time head variation ($h=\frac{H}{\Delta {H}_{j}}$) can be obtained according to Equation (12):

_{0}the dimensionless head at initial time, ${\tau}_{0}=\frac{{t}_{0}}{\raisebox{1ex}{$2L$}\!\left/ \!\raisebox{-1ex}{$c$}\right.}$, and ${t}_{0}$ the time for the first pressure peak where the head is maximum.

_{plas}and K

_{elas}are decay coefficients for the plastic and elastic effects, respectively.

#### 2.4. Runaway Conditions

_{s}) given by Equation (15):

_{RW}) and the discharge for initial conditions ($Q$

_{0}), which lean towards a linear increase with the rise of the specific speed (Figure 4) [6,35,45].

_{BEP}for constant values of h (H/H

_{BEP}) are shown in Figure 5 for radial and axial conventional turbines. $Q$/$Q$

_{BEP}are based on Suter parameters which are in accordance with the dynamic behaviour associated with the runner shape [35].

## 3. Results and Discussion

#### 3.1. Experiments and Simulations

^{3}capacity; an electromagnetic flowmeter; one hundred meters of high density polyethylene (HDPE) pipe, with 50 mm nominal diameter; a PAT which is connected downstream of the HDPE loop pipe; and a ball valve located downstream of the PAT.

^{3}), an electromagnetic flowmeter to measure the flow and the axial machine, which is followed by a butterfly valve to isolate the facility. The pump and the air vessel were joined by a steel pipe with a length of 3.50 m and diameter of 80 mm. The axial machine and the butterfly valve were connected by a pipe, which is composed of PVC (4.90 m and 110 mm of diameter) and a steel pipe (4.50 m and 80 mm of diameter). The butterfly valve and the reservoir were connected by a steel pipe, 2 m long, with a diameter equal to 80 mm. Two pressure sensors were installed upstream and downstream of the axial machine.

#### 3.2. Control Valve Closure and PAT Trip-Off

#### 3.3. Control Valve Opening and PAT Start-Up

#### 3.4. Overspeed Effect in PATs

_{0}, H

_{0}, N

_{0}). Furthermore, the experimental results can be associated with the values of the best efficiency point of the machine in turbine mode ($Q$

_{BEP}, H

_{BEP}, N

_{BEP}). These variations are shown in Figure 14. If $Q$

_{RW}/$Q$

_{0}versus N

_{RW}/N

_{0}(the subscripts ‘RW’ indicates runaway conditions) is observed, the values were almost constant for all experimental data denoting a typical characteristic of the radial machine. In this case, the ratio $Q$

_{RW}/$Q$

_{0}is near 0.514; therefore, there was a flow reduction of around 50%. This value is close to the presented value in Figure 4 that shows the characteristic of the radial machine under the overspeed effect. Similar conclusions can be obtained if the upstream and downstream pressures are analysed in the axial machine. In this case, the values were near 1.40 and 0.85, inducing an upsurge and a downsurge upstream and downstream, respectively, of the machine. If the values are compared with the best efficiency point of the radial machine, under the overspeed effect, the flow decreased for a constant value of h (h = H/H

_{BEP}).

_{0}, H

_{0}, N

_{0}) during the overspeed conditions of the axial machine. In this case, the ratio $Q$

_{RW}/$Q$

_{0}showed an increase in flow. This value is higher than the obtained value using Figure 4, for n

_{s}of 280 rpm (in m, kW).

_{BEP}, H

_{BEP}, N

_{BEP}). The results contrasted with those obtained for the radial machine. Under a constant value of h (h = H/H

_{BEP}), the flow increased when the rotational speed increased. Figure 16 shows all analysed cases considering a constant h value and they present the same tendency.

## 4. Conclusions

- the characteristics of the pipe system to be protected; in fact, these characteristics based on the head loss and inertia of the water column can adversely modify the system behaviour and the same valve closure time can induce a slow or a rapid flow change;
- the intrinsic characteristics of the valve: a butterfly valve (e.g., for medium heads) and a spherical valve (e.g., for high heads) have different effects on the dynamic flow response for the same closure law;
- since PATs have no guide vane, the flow control is made through valves where the closure and opening laws are crucial in the safety system conditions, such as the type of the valve actuator;
- based on the characteristics of the pump such as turbine machine (i.e., radial or axial), different dynamic behaviour will be associated with:
- ○
- the small inertia of the rotating masses induces a fast overspeed effect under runaway conditions imposed by a full load rejection.
- ○
- the overspeed effects provoke flow variations (i.e., flow reduction in low n
_{s}machines and flow increasing in the high n_{s}machines) and pressure variations that can propagate upsurges upstream of a radial machine and downsurges downstream of it, in contrast to axial machines (downsurges upstream and upsurges downstream).

_{BEP}, with the rotating speed, N/N

_{BEP}(Figure 14 and Figure 16, for radial and axial machines, respectively). This procedure facilitates understanding of the dynamic pump as turbine behaviour under unsteady conditions.

_{s}) [35,45,47,51] apart from the associated scale effects.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Valves manoeuvres. (

**a**) type of loss coefficients and (

**b**) opening cross area depending on the type of valve and the opening degree.

**Figure 2.**Comparison between effective closure and total closure of a ball valve: H/H

_{0}(upstream and downstream) variation and $Q$/${Q}_{0}$. (

**a**) turbulent flow (Re = 100,000) and (

**b**) laminar flow (Re = 1000).

**Figure 7.**Experimental Head and Efficiency curves of axial (N

_{0}= 750 rpm) and radial (N

_{0}= 1020 rpm) machines.

**Figure 9.**Experimental data recorded for the fast closure of the downstream control valve in radial and axial turbine machines. (

**a**) flow for radial machine (

**b**) rotational speed for radial machine (

**c**) flow for axial machine (

**d**) rotational speed for axial machine.

**Figure 10.**Experimental and simulated pressure values along time in a fast closure manoeuvre (t = 2 s): (

**a**) radial and (

**b**) axial machine.

**Figure 11.**Experimental data recorded flow and rotational speed for the fast opening of the downstream control valve in turbine machines. (

**a**) flow for radial machine (

**b**) rotational speed for radial machine (

**c**) flow for axial machine (

**d**) rotational speed for axial machine.

**Figure 12.**Experimental data and simulation for pressure variation due to a fast opening downstream control valve of (

**a**) radial and (

**b**) axial machine.

**Figure 13.**Experimental data of flow, rotational speed, and upstream and downstream head in the radial machine under the overspeed effect. (

**a**) flow for radial machine (

**b**) rotational speed for radial machine (

**c**) flow for axial machine (

**d**) rotational speed for axial machine.

**Figure 14.**(

**a**) Q

_{RW}/$Q$

_{0}and H

_{RW}/H

_{0}as a function of N

_{RW}/N

_{0}and (

**b**) $Q$/$Q$

_{BEP}as a function of N/N

_{BEP}and H/H

_{BEP}for the radial machine.

**Figure 15.**Experimental data of (

**a**) flow, (

**b**) rotational speed, and (

**c**) the upstream and (

**d**) downstream head in the axial machine under the overspeed effect.

**Figure 16.**(

**a**) $Q$

_{RW}/$Q$

_{0}and H

_{RW}/H

_{0}as a function of N

_{RW}/N

_{0}and (

**b**) $Q$/$Q$

_{BEP}as a function of N/N

_{BEP}and h = H/H

_{BEP}for the axial machine.

Material | Inner Diameter (m) | Roughness (mm) | Wave Speed (m/s) |
---|---|---|---|

HDPE | 0.044 | 0.2 | 280 |

PVC | 0.110 | 1.2 | 385 |

Rigid PVC | 0.047 | 0.2 | 527 |

Steel | 0.068 | 2 | 1345 |

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**MDPI and ACS Style**

Pérez-Sánchez, M.; López-Jiménez, P.A.; Ramos, H.M.
PATs Operating in Water Networks under Unsteady Flow Conditions: Control Valve Manoeuvre and Overspeed Effect. *Water* **2018**, *10*, 529.
https://doi.org/10.3390/w10040529

**AMA Style**

Pérez-Sánchez M, López-Jiménez PA, Ramos HM.
PATs Operating in Water Networks under Unsteady Flow Conditions: Control Valve Manoeuvre and Overspeed Effect. *Water*. 2018; 10(4):529.
https://doi.org/10.3390/w10040529

**Chicago/Turabian Style**

Pérez-Sánchez, Modesto, P. Amparo López-Jiménez, and Helena M. Ramos.
2018. "PATs Operating in Water Networks under Unsteady Flow Conditions: Control Valve Manoeuvre and Overspeed Effect" *Water* 10, no. 4: 529.
https://doi.org/10.3390/w10040529