# Velocities in a Centrifugal PAT Operation: Experiments and CFD Analyses

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}/h and a water head of 30 m, reach 100 kW using PATs [4,5]. In Germany, eight parallel PATs with a total installation capacity of 300 kW were used in a WSS for pressure control and electricity generation in pipelines, where the generated electricity fed into local grid [6]. Others case studies were enumerated by [7]; these cases showed the advantages of these machines in order to improve the efficiency and sustainability of the water distribution systems.

## 2. Experimental Setup

#### 2.1. Lab Facility Description

#### 2.2. Experimental Tests

## 3. Numerical Simulations

#### 3.1. Model Description

- ▪
- Values of the characteristic parameters of the BEP of the PAT, supplied by the manufacturer and presented in Table 1.
- ▪
- Longitudinal and transversal sections of the PAT device, supplied by the manufacturer.

#### 3.2. Mesh

- ▪
- If ${C}_{split}>{\epsilon}_{split}$, the cell has to be subdivided. The value of indicator ${C}_{split}$ (i.e., refinement indicator value) is calculated individually for each cell according to an algorithm that controls the type of refinement. The value of ${\epsilon}_{split}$ is a constant, defined automatically and represents the refinement threshold value. Setting refinement levels individually for each criterion makes it possible to influence the total number of cells that will be generated [15].

#### 3.3. Computational Fluid Dynamics (CFD) Results

## 4. Experimental and Computational Fluid Dynamics (CFD) Comparisons

#### 4.1. Velocity Profiles

#### 4.2. Triangle of Velocities

_{1}and (exit impeller radius) r

_{2}, respectively the [26]:

#### 4.3. Dissipative Effects

## 5. Characteristic Curves

^{3}/s), P (kW) and D (m) are the head, rotational speed, flow rate, power, and impeller diameter respectively.

^{3}/s) or 51 rpm (m, kW), with a nominal rotation speed of 1020 rpm, a comparison is made with the available Ns curves of available PATs. The maximum efficiency obtained for the PAT at IST and by the CFD model was below than 70%, due to the additional turbulence between rotor and stator edges inducing small leaks, and due to the micro scale of the small PAT turn this effects predominant, reducing the efficiency of the machine. Figure 12b,c present comparisons between CFD, experimental for the tested PAT and with the Ns available curve in (a).

## 6. Conclusions

^{3}/s). For the velocity profiles analysis, a UDV 3000 series technique was performed. Despite the difficulty of the probe access and the complexity of the instrumentation adjustment, the flow field in the region of the PAT was characterized. The obtained experimental data and CFD results allowed to understand the flow behavior along the PAT, inside the volute, crossing the impeller, in the draft tube, and, most interesting, was the analysis of the velocity vectors along the blades for different operating conditions associated to each flow discharge, head and rotational speed. The obtained data provides a good base for better characterizations the best flow conditions, the main loss mechanisms through the velocity fields between the rotating and static parts of a runner. The analysis to the velocity fields of the flow in the radial PAT impeller allowed the characterization of the triangle of velocity components (i.e., V, W, C) at each particle position at inlet and outlet of the impeller. From the CFD simulation and for different rotational speeds, the velocity profiles were obtained in different measured points of the PAT. The velocity profiles from CFD simulations show a trend of the velocity variation similar to the one observed with the UDV in the experimental facility. Since the variation of the physical parameters that characterizes the hydrodynamic of the flow inside any hydraulic turbo-machine, adequate shape of the impeller was then imposed.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Velocity profiles along the pipe diameter measure with Ultrasonic doppler velocimetry (UDV), expressed as the distance between the UDV probe and faraway pipe wall in the radial direction: (

**a**) N = 520 rpm; (

**b**) N = 600 rpm; (

**c**) N = 680 rpm; (

**d**) N = 780 rpm; (

**e**) N = 850 rpm; (

**f**) N = 880 rpm; (

**g**) N = 880 rpm; (

**h**) N = 1140 rpm.

**Figure 4.**Geometric model for computational fluid dynamics (CFD) analyses: (

**a**) pump as turbine (PAT) impeller; (

**b**) PAT volute.

**Figure 5.**Velocity values for different rotational speeds (m/s): Streamlines (on the left); velocities field in the PAT (on the right). (

**a**) N = 600 rpm; (

**b**) N = 780 rpm; (

**c**) N = 880 rpm; (

**d**) N = 1020 rpm; (

**e**) N = 1140 rpm; (

**f**) N = 1250 rpm; (

**g**) N = 1500 rpm.

**Figure 6.**Velocity profiles (m/s) obtained in experimental tests and CFD simulations: (

**a**) N = 520 rpm; (

**b**) N = 600 rpm; (

**c**) N = 680 rpm; (

**d**) N = 780 rpm.

**Figure 7.**Velocity profiles (m/s) obtained through experimental tests and CFD simulations: (

**a**) N = 850 rpm; (

**b**) N = 880 rpm; (

**c**) N = 880 rpm; (

**d**) N = 1140 rpm.

**Figure 10.**Velocity triangles obtained by CFD simulation for the best efficiency point (BEP): (

**a**) Absolute fluid path; (

**b**) relative fluid path; (

**c**) triangle of velocities at inlet and outlet of the impeller.

**Figure 11.**Values of velocity, shear stress and turbulence in several parts of the PAT: (

**a**) N = 810 rpm and Q = 2.9 L/s; (

**b**) N = 1500 rpm and Q = 4.6 L/s.

**Figure 12.**Performance curves and selection of a PAT. (

**a**) Characteristic curves for different Ns [19]; (

**b**) comparison between CFD, experimental for the tested PAT and Ns curve: Variation of the efficiency and head number with the discharge number; (

**c**) dimensionless head and flow characteristic curves. Reproduced with permission from [19].

Best Efficiency Point | |
---|---|

Discharge | 3.36 L/s |

Head | 4 m |

Efficiency | 60% |

Power | 0.08 kW |

Rotational speed | 1020 rpm |

Specific speed | 51 rpm (m, kW) |

**Table 2.**Experiments in the pump as turbine (PAT) for different rotational speeds with ultrasonic doppler velocimetry (UDV) data acquisition from S1 to S4 points.

Section | Q_{A} (L/s) | N (rpm) | H_{A} (m) | H_{B} (m) | ∆H (m) | Ph (W) | Torque (N·m) | Pm (W) | η (%) |
---|---|---|---|---|---|---|---|---|---|

S3 | 2.40 | 520 | 4.29 | 2.24 | 2.04 | 47.98 | 0.33 | 18.01 | 38 |

S4 | 2.35 | 600 | 4.19 | 2.17 | 2.02 | 46.52 | 0.32 | 20.11 | 43 |

S2 | 2.46 | 680 | 4.68 | 2.33 | 2.35 | 56.65 | 0.34 | 24.21 | 43 |

S1 | 2.40 | 780 | 4.71 | 1.74 | 2.98 | 70.09 | 0.35 | 28.18 | 40 |

S3 | 2.80 | 850 | 6.11 | 2.77 | 3.34 | 91.65 | 0.21 | 19.09 | 21 |

S2 | 2.80 | 880 | 6.15 | 2.7 | 3.44 | 94.39 | 0.37 | 34.10 | 36 |

S4 | |||||||||

S1 | 2.70 | 1140 | 7.03 | 1.98 | 5.05 | 133.62 | 0.51 | 60.88 | 46 |

Mesh | Number of Fluid Mesh Cells | Number of Solid Mesh Cells | H_{B} (m) | Error (%) | Duration |
---|---|---|---|---|---|

Mesh 1 | 25,668 | 15,400 | 5.10 | 0.15 h | |

Mesh 2 | 50,381 | 30,229 | 2.30 | 55% | 0.29 h |

Mesh 3 | 100,691 | 60,088 | 1.42 | 38% | 1.23 h |

Mesh 4 | 101,936 | 61,162 | 1.73 | 22% | 1.52 h |

Mesh 5 | 102,152 | 61,291 | 1.68 | 3% | 2.28 h |

Mesh 6 | 102,274 | 61,364 | 1.67 | 1% | 2.33 h |

Q (L/s) | N (rpm) | H_{A} (m) | H_{B} (m) | ∆H (m) | Torque (N·m) | w (rad/s) | Ph (W) | Pm (W) | η (%) |
---|---|---|---|---|---|---|---|---|---|

2.40 | 520 | 4.80 | 2.33 | 2.47 | 0.39 | 54.45 | 58.13 | 21.24 | 37 |

2.35 | 600 | 4.41 | 2.57 | 1.83 | 0.28 | 62.83 | 42.24 | 17.59 | 42 |

2.46 | 680 | 4.76 | 2.37 | 2.39 | 0.35 | 71.21 | 57.55 | 24.92 | 43 |

2.40 | 780 | 4.92 | 1.85 | 3.07 | 0.36 | 81.68 | 72.10 | 29.41 | 41 |

2.80 | 850 | 6.71 | 3.18 | 3.53 | 0.35 | 89.01 | 96.83 | 31.15 | 32 |

2.80 | 880 | 7.85 | 2.88 | 4.97 | 0.62 | 92.15 | 136.46 | 57.14 | 42 |

3.36 | 1020 | 6.83 | 1.67 | 5.06 | 1.13 | 97.39 | 185.56 | 110.05 | 60 |

2.70 | 1140 | 7.34 | 2.12 | 5.22 | 0.55 | 119.38 | 138.05 | 65.66 | 48 |

4.17 | 1275 | 9.61 | 1.69 | 7.76 | 0.86 | 133.52 | 317.21 | 114.83 | 36 |

4.91 | 1500 | 15.29 | 3.82 | 11.24 | 1.30 | 157.08 | 540.79 | 204.20 | 38 |

N (rpm) | Q (L/s) | EXP | CFD | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

∆h (m) | Ph (W) | Pm (W) | Torque (N·m) | η (%) | ∆h (m) | Ph (W) | Pm (W) | Torque (N·m) | η (%) | ||

520 | 2.40 | 2.04 | 47.98 | 18.01 | 0.33 | 38 | 2.47 | 58.13 | 21.24 | 0.39 | 37 |

600 | 2.35 | 2.02 | 46.52 | 20.11 | 0.32 | 43 | 1.83 | 42.24 | 17.59 | 0.28 | 42 |

680 | 2.46 | 2.35 | 56.65 | 24.21 | 0.34 | 43 | 2.39 | 57.55 | 24.92 | 0.35 | 43 |

780 | 2.40 | 2.98 | 70.09 | 28.18 | 0.35 | 40 | 3.07 | 72.10 | 29.41 | 0.36 | 41 |

850 | 2.80 | 3.34 | 91.65 | 19.09 | 0.21 | 21 | 3.53 | 96.83 | 31.15 | 0.35 | 32 |

880 | 2.80 | 3.44 | 94.39 | 34.10 | 0.37 | 36 | 4.97 | 136.46 | 57.14 | 0.62 | 42 |

1020 | 3.36 | 6.30 | 218.00 | 104.00 | 1.21 | 60 | 5.06 | 185.56 | 110.05 | 1.13 | 60 |

1140 | 2.70 | 5.05 | 133.62 | 60.88 | 0.51 | 46 | 5.22 | 138.05 | 65.66 | 0.55 | 48 |

1275 | 4.17 | 7.06 | 292.42 | 112.00 | 0.84 | 38 | 7.76 | 317.21 | 114.83 | 0.86 | 36 |

1500 | 4.91 | 10.23 | 498.84 | 181.00 | 1.15 | 36 | 11.24 | 540.79 | 204.20 | 1.30 | 38 |

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## Share and Cite

**MDPI and ACS Style**

Simão, M.; Pérez-Sánchez, M.; Carravetta, A.; López-Jiménez, P.; Ramos, H.M.
Velocities in a Centrifugal PAT Operation: Experiments and CFD Analyses. *Fluids* **2018**, *3*, 3.
https://doi.org/10.3390/fluids3010003

**AMA Style**

Simão M, Pérez-Sánchez M, Carravetta A, López-Jiménez P, Ramos HM.
Velocities in a Centrifugal PAT Operation: Experiments and CFD Analyses. *Fluids*. 2018; 3(1):3.
https://doi.org/10.3390/fluids3010003

**Chicago/Turabian Style**

Simão, Mariana, Modesto Pérez-Sánchez, Armando Carravetta, Petra López-Jiménez, and Helena M. Ramos.
2018. "Velocities in a Centrifugal PAT Operation: Experiments and CFD Analyses" *Fluids* 3, no. 1: 3.
https://doi.org/10.3390/fluids3010003