# Flow Conditions for PATs Operating in Parallel: Experimental and Numerical Analyses

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## Abstract

**:**

## 1. Introduction

## 2. Head Losses within PATs

## 3. Experimental Set-Up

## 4. Numerical Simulations

#### 4.1. EPANET Model

#### 4.2. CFD Model

#### 4.2.1. PAT Geometry and Mesh

^{−4}. The rotating components were computed in the Cartesian system attached to the rotating parts, i.e., the stationary parts must be axisymmetric relative to the rotation axis [16].

#### 4.2.2. Boundary Conditions

## 5. Results and Discussion

#### 5.1. Pressure Variation and Velocity Streamlines Distribution

#### 5.2. Analysis of the Head Losses of the PATs System

#### 5.3. Comparisons

## 6. Conclusions

- (1)
- The characteristic curves were rather different from PAT1 to PAT2 due to different rotational speeds and flow rates, associated to each PAT, even for equal machines working in parallel mode;
- (2)
- During the steady state operating condition, in the parallel configuration, the optimal point was obtained for a total flow of Q =7.50 L/s and H = 4 m; corresponding to Q = 4.00 L/s for PAT1 and Q = 3.53 L/s for PAT2, associated to N1 = 440 rpm and N2 = 735 rpm, respectively;
- (3)
- Although parallel operation increases the total flow rate, it also causes greater head losses, with a reduction in the flow rate in each PAT, and consequentially, alterations in the efficiency of each PAT;
- (4)
- In the CFD model, the head losses can be estimated in accordance with empirical formulations, with acceptable errors, allowing a better comprehension of the flow pattern inside the PAT system;
- (5)
- The benefits of PATs working in parallel are the possibility for covering higher flow range conditions than for a single PAT.
- (6)
- Comparing the CFD model with experimental tests, the optimal point for total flow during numerical simulations was achieved for Q = 7.6 L/s and H = 4 m. Also, the predicted flow rates were in good agreement with the measured data, presenting an average error of 10%.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**PATs’ characteristic operating points when working in parallel and in a single mode: (

**a**) h curve; (

**b**) N curve.

**Figure 4.**Identification of experimental characteristic curves: (

**a**) PATs working in parallel mode (with 270 rpm ≤ PAT1 ≤ 441 rpm and 747 rpm ≤ PAT2 ≤ 800 rpm); (

**b**) one PAT working in single mode (725 rpm ≤ PAT ≤ 1080 rpm).

**Figure 5.**Parallel PATs in operation: (

**a**) global system of two PATs in parallel: scenario 1—total flow range between 5.80 L/s and 6.60 L/s, and scenario 2—total flow range between 6.70 L/s and 7.20 L/s; (

**b**) scenario 1 by each PAT; (

**c**) scenario 2 by each PAT.

**Figure 7.**Schematic of the experimental set-up in EPANET. CV: check valve; FCV: flow control valves; GPV: general purpose valves.

**Figure 9.**Computational fluid dynamics (CFD) model: (

**a**) defined mesh; (

**b**) convergence of maximum static pressure results vs. different number of mesh cells.

**Figure 10.**PAT system set-up: (

**a**) fluid volume in PATs operating in parallel; (

**b**) PAT geometry mesh.

**Figure 12.**Pressure variation of the single PAT2 operation for the best efficiency point (BEP) (

**a**); and for the parallel mode (N1 = 440 rpm and Q1 = 2.93 L/s) for PAT1 and (N2 = 735 rpm and Q2 = 3.77 L/s) for PAT2 (

**b**).

**Figure 13.**Velocity streamlines for: (

**a**) Q = 5.80 L/s with N1 = 400 rpm and N2 = 700 rpm; (

**b**) Q = 6.70 L/s with N1 = 440 rpm and N2 = 735 rpm; (

**c**) Q = 7.20 L/s with N1 = 440 rpm and N2 = 735 rpm (with PAT1 on the left, PAT2 on the right).

**Figure 18.**Head losses determined in parallel mode (

**a**) and in single mode (

**b**). Comparison between experimental results and modeling predictions with the associated errors (

**c**).

Condition | Q_{PAT1} (L/s) | Q_{PAT2} (L/s) | N_{PAT1} (rpm) | N_{PAT2} (rpm) | h _{PAT1} (m) | h _{PAT2} (m) |
---|---|---|---|---|---|---|

PATs in Parallel | 2.66 | 3.94 | 284 | 816 | 1.80 | 5.05 |

2.93 | 3.93 | 427 | 812 | 2.34 | 4.88 | |

2.56 | 3.74 | 300 | 725 | 1.66 | 4.00 | |

2.39 | 4.81 | 250 | 1083 | 1.34 | 7.93 | |

2.93 | 4.07 | 427 | 813 | 2.34 | 5.04 | |

2.39 | 3.81 | 250 | 754 | 1.34 | 4.30 | |

3.07 | 3.93 | 497 | 772 | 2.70 | 4.87 | |

2.93 | 3.77 | 427 | 735 | 2.34 | 4.45 | |

3.07 | 4.13 | 497 | 875 | 2.70 | 5.59 | |

2.87 | 2.93 | 400 | 427 | 2.19 | 2.34 | |

3.40 | 4.20 | 520 | 860 | 2.04 | 4.80 | |

3.00 | 4.10 | 300 | 880 | 1.31 | 4.01 | |

2.80 | 3.46 | 280 | 680 | 1.26 | 2.90 | |

3.40 | 4.50 | 570 | 950 | 1.98 | 4.82 | |

2.50 | 4.20 | 230 | 880 | 1.37 | 4.70 | |

2.75 | 4.00 | 300 | 850 | 1.47 | 4.30 | |

2.10 | 4.03 | 190 | 935 | 1.33 | 4.23 | |

2.50 | 3.42 | 205 | 600 | 1.29 | 4.10 | |

2.95 | 3.35 | 350 | 600 | 2.26 | 3.85 | |

2.05 | 1.14 | 440 | 735 | 1.40 | ||

2.16 | 1.31 | 1.50 | ||||

2.45 | 1.73 | 1.80 | ||||

2.63 | 1.96 | 2.00 | ||||

2.95 | 2.36 | 2.40 | ||||

3.24 | 2.71 | 2.80 | ||||

3.38 | 2.87 | 3.00 | ||||

3.52 | 3.02 | 3.20 | ||||

3.64 | 3.16 | 3.40 | ||||

3.77 | 3.30 | 3.60 | ||||

3.89 | 3.43 | 3.80 | ||||

4.00 | 3.56 | 4.00 | ||||

4.12 | 3.69 | 4.20 | ||||

4.23 | 3.81 | 4.40 | ||||

2.39 | 3.26 | 270 | 830 | 1.34 | 3.90 | |

2.66 | 3.11 | 1.80 | 3.63 | |||

2.56 | 2.78 | 1.66 | 3.14 | |||

2.00 | 2.60 | 1.00 | 2.97 | |||

1.80 | 2.22 | 0.90 | 2.69 | |||

2.00 | 2.90 | 1.05 | 3.29 | |||

2.20 | 2.48 | 1.50 | 2.85 | |||

2.75 | 3.42 | 1.50 | 4.19 | |||

Single PAT | 3.81 | 725 | 4.54 | |||

3.95 | 724 | 4.78 | ||||

4.09 | 725 | 5.03 | ||||

4.23 | 726 | 5.29 | ||||

4.80 | 980 | 7.22 | ||||

4.42 | 980 | 6.82 | ||||

4.80 | 979 | 7.46 | ||||

4.17 | 980 | 6.20 | ||||

4.34 | 1080 | 8.26 | ||||

4.80 | 1080 | 8.38 | ||||

4.76 | 1081 | 7.91 | ||||

4.95 | 1150 | 8.66 | ||||

4.49 | 1079 | 7.19 |

**Table 2.**Formulations to estimate the head of PAT [26].

Ref. | Parameter | Formula | Complement |
---|---|---|---|

[31,32,33,34] | net theoretical head (H_{t}) | ${H}_{theoretical}=\sigma \frac{{U}_{2}^{2}}{g}-\frac{\omega Q}{2\pi g{b}_{2}tg{\beta}_{2}}$ | $\sigma =1-\frac{\sqrt{sen{\beta}_{2}}}{{N}_{a}^{0.7}}$ |

[31,33] | friction loss (h_{f}) | ${h}_{friction}={b}_{2}\frac{\left(2{r}_{2}-2{r}_{1}\right){\left({W}_{1}+{W}_{2}\right)}^{2}}{8gsen{\beta}_{2}{r}_{H}}$ | ${W}_{1}=\frac{Q}{2\pi {r}_{1}{b}_{1}sen{\beta}_{1}},{W}_{2}=\frac{Q}{2\pi {r}_{2}{b}_{2}sen{\beta}_{2}}$ |

[34] | shock loss (h_{s}) | ${h}_{shock}=\frac{{k}_{shock}}{2g}{\left[\frac{\left(Q-{Q}_{BEP}\right)}{{Q}_{BEP}}{U}_{1}\right]}^{2}$ | k_{shock} = 0.2 |

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**MDPI and ACS Style**

Simão, M.; Pérez-Sánchez, M.; Carravetta, A.; Ramos, H.M.
Flow Conditions for PATs Operating in Parallel: Experimental and Numerical Analyses. *Energies* **2019**, *12*, 901.
https://doi.org/10.3390/en12050901

**AMA Style**

Simão M, Pérez-Sánchez M, Carravetta A, Ramos HM.
Flow Conditions for PATs Operating in Parallel: Experimental and Numerical Analyses. *Energies*. 2019; 12(5):901.
https://doi.org/10.3390/en12050901

**Chicago/Turabian Style**

Simão, Mariana, Modesto Pérez-Sánchez, Armando Carravetta, and Helena M. Ramos.
2019. "Flow Conditions for PATs Operating in Parallel: Experimental and Numerical Analyses" *Energies* 12, no. 5: 901.
https://doi.org/10.3390/en12050901