# 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

- Kougias, I.; Patsialis, T.; Zafirakou, A.; Theodossiou, N. Exploring the potential of energy recovery using micro hydropower systems in water supply systems. Water Util. J.
**2014**, 7, 25–33. [Google Scholar] - Nogueira, M.; Perrella, J. Energy and hydraulic efficiency in conventional water supply systems. Renew. Sustain. Energy Rev.
**2014**, 30, 701–714. [Google Scholar] [CrossRef] - Moreno, M.; Córcoles, J.; Tarjuelo, J.; Ortega, J. Energy efficiency of pressurised irrigation networks managed on-demand and under a rotation schedule. Biosyst. Eng.
**2010**, 107, 349–363. [Google Scholar] [CrossRef] - Jiménez-Bello, M.A.; Royuela, A.; Manzano, J.; Prats, A.G.; Martínez-Alzamora, F. Methodology to improve water and energy use by proper irrigation scheduling in pressurised networks. Agric. Water Manag.
**2015**, 149, 91–101. [Google Scholar] [CrossRef] - Cabrera, E.; Cabrera, E., Jr.; Cobacho, R.; Soriano, J. Towards an Energy Labelling of Pressurized Water Networks. Procedia Eng.
**2014**, 70, 209–217. [Google Scholar] [CrossRef] - Carravetta, A.; Houreh, S.D.; Ramos, H.M. Pumps as Turbines: Fundamentals and Applications; Springer International Publishing: Cham, Switzerland, 2018; p. 218. ISBN 978-3-319-67507-7. [Google Scholar]
- Abbott, M.; Cohen, B. Productivity and efficiency in the water industry. Util. Policy
**2009**, 17, 233–244. [Google Scholar] [CrossRef] - Araujo, L.; Ramos, H.; Coelho, S. Pressure Control for Leakage Minimisation in Water Distribution Systems Management. Water Resour. Manag.
**2006**, 20, 133–149. [Google Scholar] [CrossRef] - Dannier, A.; Del Pizzo, A.; Giugni, M.; Fontana, N.; Marini, G.; Proto, D. Efficiency evaluation of a micro-generation system for energy recovery in water distribution networks. In Proceedings of the 2015 International Conference on Clean Electrical Power (ICCEP), Taormina, Italy, 16–18 June 2015; pp. 689–694. [Google Scholar]
- Giugni, M.; Fontana, N.; Ranucci, A. Optimal Location of PRVs and Turbines in Water Distribution Systems. J. Water Resour. Plan. Manag.
**2014**, 140, 06014004. [Google Scholar] [CrossRef] - Ramos, H.; Borga, A. Pumps as turbines: An unconventional solution to energy production. Urban Water
**1999**, 1, 261–263. [Google Scholar] [CrossRef] - Pérez-Sánchez, M.; Sánchez-Romero, F.; Ramos, H.; López-Jiménez, P.A. Energy Recovery in Existing Water Networks: Towards Greater Sustainability. Water
**2017**, 9, 97. [Google Scholar] [CrossRef] - Senior, J.; Saenger, N.; Müller, G. New hydropower converters for very low-head differences. J. Hydraul. Res.
**2010**, 48, 703–714. [Google Scholar] [CrossRef] - Razan, J.I.; Islam, R.S.; Hasan, R.; Hasan, S.; Islam, F. A Comprehensive Study of Micro-Hydropower Plant and Its Potential in Bangladesh. ISRN Renew. Energy
**2012**, 2012, 635396. [Google Scholar] [CrossRef] - Elbatran, A.H.; Yaakob, O.B.; Ahmed, Y.M.; Shabara, H.M. Operation, performance and economic analysis of low head micro-hydropower turbines for rural and remote areas: A review. Renew. Sustain. Energy Rev.
**2015**, 43, 40–50. [Google Scholar] [CrossRef] - Nourbakhsh, A.; Jahangiri, G. Inexpensive small hydropower stations for small areas of developing countries. In Proceedings of the Conference on Advanced in Planning-Design and Management of Irrigation Systems as Related to Sustainable Land Use, Louvain, Belgium, 14–17 September 1992; pp. 313–319. [Google Scholar]
- Simão, M.; Ramos, H.M. Hydrodynamic and performance of low power turbines: Conception, modelling and experimental tests. Int. J. Energy Environ.
**2010**, 1, 431–444. [Google Scholar] - Arriaga, M. Pump as turbine—A pico-hydro alternative in Lao People’s Democratic Republic. Renew. Energy
**2010**, 35, 1109–1115. [Google Scholar] [CrossRef] - Pérez-Sánchez, M.; López Jiménez, P.A.; Ramos, H.M. Modified Affinity Laws in Hydraulic Machines towards the Best Efficiency Line. Water Resour. Manag.
**2018**, 3, 829–844. [Google Scholar] [CrossRef] - Ramos, H.M.; Borga, A.; Simão, M. New design solutions for low-power energy production in water pipe systems. Water Sci. Eng.
**2009**, 2, 69–84. [Google Scholar] - Carravetta, A.; Del Giudice, G.; Fecarotta, O.; Ramos, H.M. Energy Recovery in Water Systems by PATs: A Comparisons among the Different Installation Schemes. Procedia Eng.
**2014**, 70, 275–284. [Google Scholar] [CrossRef] - Caxaria, G.; de Mesquita e Sousa, D.; Ramos, H.M. Small Scale Hydropower: Generator Analysis and Optimization for Water Supply Systems. 2011, p. 1386. Available online: http://www.ep.liu.se/ecp_article/index.en.aspx?issue=57;vol=6;article=2 (accessed on 12 March 2017).
- Butera, I.; Balestra, R. Estimation of the hydropower potential of irrigation networks. Renew. Sustain. Energy Rev.
**2015**, 48, 140–151. [Google Scholar] [CrossRef] - Carravetta, A.; Fecarotta, O.; Del Giudice, G.; Ramos, H. PAT Design Strategy for Energy Recovery in Water Distribution Networks by Electrical Regulation. Energies
**2013**, 6, 411–424. [Google Scholar] [CrossRef] - Fecarotta, O.; Aricò, C.; Carravetta, A.; Martino, R.; Ramos, H.M. Hydropower Potential in Water Distribution Networks: Pressure Control by PATs. Water Resour. Manag.
**2014**, 29, 699–714. [Google Scholar] [CrossRef][Green Version] - Fecarotta, O.; Carravetta, A.; Ramos, H.M.; Martino, R. An improved affinity model to enhance variable operating strategy for pumps used as turbines. J. Hydraul. Res.
**2016**, 54, 332–341. [Google Scholar] [CrossRef] - Sitzenfrei, R.; Berger, D.; Rauch, W. Design and optimization of small hydropower systems in water distribution networks under consideration of rehabilitation measures. Urban Water J.
**2015**, 12, 1–9. [Google Scholar] [CrossRef] - De Marchis, M.; Milici, B.; Volpe, R.; Messineo, A. Energy Saving in Water Distribution Network through Pump as Turbine Generators: Economic and Environmental Analysis. Energies
**2016**, 9, 877. [Google Scholar] [CrossRef] - Samora, I.; Manso, P.; Franca, M.; Schleiss, A.; Ramos, H. Energy Recovery Using Micro-Hydropower Technology in Water Supply Systems: The Case Study of the City of Fribourg. Water
**2016**, 8, 344. [Google Scholar] [CrossRef] - Pérez-Sánchez, M.; Sánchez-Romero, F.; Ramos, H.; López-Jiménez, P.A. Modeling Irrigation Networks for the Quantification of Potential Energy Recovering: A Case Study. Water
**2016**, 8, 234. [Google Scholar] [CrossRef] - Corcoran, L.; McNabola, A.; Coughlan, P. Predicting and quantifying the effect of variations in long-term water demand on micro-hydropower energy recovery in water supply networks. Urban Water J.
**2016**, 9, 1–9. [Google Scholar] [CrossRef] - Pérez-Sánchez, M.; Sánchez-Romero, F.J.; Ramos, H.M.; López Jiménez, P.A. Optimization Strategy for Improving the Energy Efficiency of Irrigation Systems by Micro Hydropower: Practical Application. Water
**2017**, 9, 799. [Google Scholar] [CrossRef] - Imbernón, J.A.; Usquin, B. Sistemas de generación hidráulica. Una nueva forma de entender la energía. In Proceedings of the II Congreso Smart Grid, Madrid, Spain, 27–28 October 2014. [Google Scholar]
- McNabola, A.; Coughlan, P.; Corcoran, L.; Power, C.; Prysor, A.; Harris, I.; Gallagher, J.; Styles, D. Energy recovery in the water industry using micro-hydropower: An opportunity to improve sustainability. Water Policy
**2014**, 16, 168–183. [Google Scholar] [CrossRef] - Ramos, H. Simulation and Control of Hydrotransients at Small Hydroelectric Power Plants. Ph.D. Thesis, IST, Lisbon, Portugal, December 1995. [Google Scholar]
- White, F.M. Fluid Mechanics, 6th ed.; McGrau-Hill: New York, NY, USA, 2008. [Google Scholar]
- Wylie, E.B.; Streeter, V.L. Fluid Transients in Systems; Prentice Hall: Englewood Cliffs, NI, USA, 1993. [Google Scholar]
- Almeida, A.B.; Koelle, E. Fluid Transients in Pipe Networks; Computational Mechanics Publications, Elsevier Applied Science: Amsterdam, The Netherlands, 1992. [Google Scholar]
- Chaudhry, M. Applied Hydraulic Transients, 2nd ed.; Springer-Verlag: New York, NY, USA, 1987. [Google Scholar]
- Abreu, J.; Guarga, R.; Izquierdo, J. Transitorios y Oscilaciones en Sistemas Hidráulicos a Presión; Abreu, J., Guarga, R., Izquierdo, J., Eds.; U.D. Mecánica de Fluidos, Universidad Politécnica de Valencia: Valencia, Spain, 1995. [Google Scholar]
- Iglesias-Rey, P.; Izquierdo, J.; Fuertes, V.; Martínez-Solano, F. Modelación de Transitorios Hidráulicos Mediante Ordenador; Grupo Mult.; Universidad Politécnica de Valencia: Valencia, Spain, 2004. [Google Scholar]
- Subani, N.; Amin, N. Analysis of Water Hammer with Different Closing Valve Laws on Transient Flow of Hydrogen-Natural Gas Mixture. Abstr. Appl. Anal.
**2015**, 2, 12–19. [Google Scholar] [CrossRef] - Ramos, H.M.; Covas, D.; Borga, A.; Loureiro, D. Surge damping analysis in pipe systems: Modelling and experiments. J. Hydraul. Res.
**2004**, 42, 413–425. [Google Scholar] [CrossRef] - Ramos, H. Design concerns in pipe systems for safe operation. Dam Eng.
**2003**, 14, 5–30. [Google Scholar] - Ramos, H. Guidelines for Design of Small Hydropower Plants; Western Regional Energy Agency & Network (WREAN); Department of Economic Development (DED): Belfast, UK, 2000. [Google Scholar]
- Ramos, H.; Almeida, A.B. Dynamic orifice model on water hammer analysis of high or medium heads of small hydropower schemes. J. Hydraul. Res.
**2001**, 39, 429–436. [Google Scholar] [CrossRef] - Ramos, H.; Almeida, A.B. Parametric Analysis of Water-Hammer Effects in Small Hydro Schemes. J. Hydraul. Eng.
**2002**, 128, 689–696. [Google Scholar] [CrossRef] - Ramos, H.M.; Simão, M.; Borga, A. Experiments and CFD Analyses for a New Reaction Microhydro Propeller with Five Blades. J. Energy Eng.
**2013**, 139, 109–117. [Google Scholar] [CrossRef] - Mataix, C. Turbomáquinas Hidráulicas; Universidad Pontificia Comillas: Madrid, Spain, 2009. [Google Scholar]
- De Marchis, M.; Fontanazza, C.M.; Freni, G.; Messineo, A.; Milici, B.; Napoli, E.; Notaro, V.; Puleo, V.; Scopa, A. Energy recovery in water distribution networks. Implementation of pumps as turbine in a dynamic numerical model. Procedia Eng.
**2014**, 70, 439–448. [Google Scholar] [CrossRef] - ITA. Allievi, 2010. Available online: www.allievi.net (accessed on 17 July 2017).

**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