# A Performance Prediction Model for Pumps as Turbines (PATs)

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{p}and the ratio efficiency in pump and turbine mode. Barbarelli et al. [34] developed an operative procedure for optimal PAT selection composed of four phases tested for six pumps with specific speed between 9 and 65. As an alternative to laboratory experiments, Computational Fluid Dynamics (CDF) methods have been used to forecast PAT performance, trying to overcome the difficulties due to the time-consuming and expensive laboratory activities. Of course, the CFD approach introduces additional difficulties, due to the credibility of the mathematical model and of the numerical approach used [25,35,36].

## 2. Data Available

## 3. Performance Prediction of a PAT

#### 3.1. Specific Speed

_{b}(m) and Q

_{b}(m

^{3}/s) are the head and the discharge at the BEP point, while N(rpm) is the rotational speed. For the Redawn database, the pump mode specific number NS

_{p}ranges between 6 and 80, while the turbine mode specific number NS

_{t}ranges between 5 and 86.

_{t}and NS

_{p}(see Figure 1). This relationship is approximately linear, and is expressed as

_{t}= 0.8793 NS

_{p}

#### 3.2. BEP Performance

_{tb}/Q

_{pb}and the ratio N

_{t}/N

_{p}is shown in Figure 2, where Q

_{tb}(L/s) and Q

_{pb}(L/s) are the bQBEP turbine mode and pump mode discharges, respectively, while N

_{t}(rpm) and N

_{p}(rpm) are the corresponding rotational speeds. It is evident that this relationship is linear with good approximation, supplying

_{t}/N

_{p}< 1.2828, given the data available from the Redawn database. Expectedly, the ratio between the BEP discharges in pump and reverse modes mainly depends on the motor features and on the presence of an inverter drive.

_{tb}(m) and H

_{pb}(m) are the bQBEP turbine- and pump-mode heads, respectively. Equation (4), which is valid in the same range of Equation (3), is represented in Figure 3, where the experimental data are also reported. The good agreement between Equation (4) and the experimental data confirms that the BEP hydraulic characteristics in turbine-mode are strongly dependent on the motor features.

_{tb}/P

_{pb}on the cube of the ratio N

_{t}/N

_{p}. This relationship is elucidated in Figure 4, and the interpolation supplies

_{tb}.

#### 3.3. Characteristic Curves

_{t}, head H

_{t}, and discharge Q

_{t}for a given rotational speed N

_{t}and for functioning conditions different from the BEP. Of course, the dependence on N

_{t}is conveniently eliminated by considering the dependence of the dimensionless variables P

_{t}/P

_{tb}and H

_{t}/H

_{tb}on Q

_{t}/Q

_{tb}. For this reason, the database Redawn is investigated in order to find suitable turbine mode characteristic curves in dimensionless form. Interestingly, the MSS device available in the database has a behavior significantly different from that of the other devices, and must be treated separately.

_{t}/Q

_{tb}, H

_{t}/H

_{tb}) experimental points are reported with blue dots for the ESOB, MSO, and MSV pumps, while the MSS data are plotted with red dots. The inspection of the panel shows that ESOB, MSO, and MSV data are nicely aligned without regard to the rotational speed Nt, while the MSS data constitute a separate family. The same can be observed in Figure 5, lower panel, where the (P

_{t}/P

_{tb}, H

_{t}/H

_{tb}) experimental points are plotted.

_{t}/H

_{tb}= 1 when Q

_{t}/Q

_{tb}= 1, and that P

_{t}/P

_{tb}≈ 0 when Q

_{t}/Q

_{tb}= 0, while P

_{t}/P

_{tb}= 1 when Q

_{t}/Q

_{tb}= 1. The corresponding efficiency curves can be obtained from Equations (7) and (8) (ESOB, MSO, and MSV pumps) or from Equations (9) and (10) using the definition

_{t}/η

_{tb}= 1 for Q

_{t}/Q

_{tb}= 1 is nicely satisfied.

#### 3.4. Comparison with Methods Available in the Literature

_{t}/Q

_{tb}< 3, but departs from the experimental data for higher values of the discharge, which seems to highlight the limited range of flow rates considered.

_{t}/Q

_{tb}> 2. Actually, Equation (14) by Derakhshan and Nourbakhsh [27] exhibits a maximum around Q

_{t}/Q

_{tb}= 4.5, implying that the power predicted in turbine-mode decreases for Q

_{t}/Q

_{tb}> 4.5, which is unphysical and not confirmed by experimental data. The decreasing behavior is immediately understood considering that the power-discharge model by Derakhshan and Nourbakhsh [27] exhibits a negative coefficient that is multiplied by the cube of Q

_{t}/Q

_{tb}, producing a concave plot for higher values of Q

_{t}/Q

_{tb}. An additional minor incongruence is evident, that is the value 0.0452 of the intercept in the power-discharge Derakhshan and Nourbakhsh [27] model, implying that power is produced also for null discharge.

## 4. Application

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Comparison of all available experimental points in the literature and the experimental data of database Redawn.

**Figure 2.**Correlation between $\raisebox{1ex}{${\mathrm{Q}}_{\mathrm{tb}}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{Q}}_{\mathrm{pb}}$}\right.$ and $\raisebox{1ex}{${\mathrm{N}}_{\mathrm{t}}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{N}}_{\mathrm{p}}$}\right.$.

**Figure 3.**Correlation between $\raisebox{1ex}{${\mathrm{H}}_{\mathrm{tb}}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{H}}_{\mathrm{pb}}$}\right.$ and the square of $\raisebox{1ex}{${\mathrm{N}}_{\mathrm{t}}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{N}}_{\mathrm{p}}$}\right.$.

**Figure 5.**Redawn database: head-discharge (

**upper**panel) and power-discharge (

**lower**panel) dimensionless characteristic curves.

**Figure 6.**Comparison of efficiency curves evaluated using Relationship (11) for the ESOB, MSV, and MSO model with the MSS ones.

**Figure 7.**Comparison of Redawn database (ESOB, MSO, MSV, MSS) with efficiency-discharge evaluated using Relationship (11).

**Figure 8.**Comparison between the Redawn experimental data and the Derakhshan and Nourbakhsh [27] model in terms of; head-discharge (

**upper**panel), power-discharge (

**central**panel) and efficiency-discharge (

**lower**panel).

**Figure 9.**Characteristic curves for the 92SV2G150T_IE3 MSV pump. Experimental data (dots), proposed model (blue dashed line), and Derakhshan and Nourbakhsh [27] model (black dashed line): head-discharge (

**upper**panel), power-discharge (

**central**panel), and efficiency-discharge (

**lower**panel).

**Figure 10.**Characteristic curves for the ’P(E18S64)/1A’ MSS pump. Experimental data (dots), proposed model (blue dashed line), and Derakhshan and Nourbakhsh [27] model (black dashed line): head-discharge (

**upper**panel), power-discharge (

**central**panel), and efficiency-discharge (

**lower**panel).

Device Code | Manufacturer | Type | K |
---|---|---|---|

‘Etanorm 32-125’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 50-160’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘FHE80-200’ | Lowara (Vicenza, Italy) | ESOB | 2 |

‘Etanorm 150-200’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 100-315’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 50-315?’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 65-125’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 65-160’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 65-200’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 65-250’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 65-315’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 80-200’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 80-250’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 80-315’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 80-400’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 100-200’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 100-315’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 100-400’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 125-400’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘Etanorm 150-250’ | KSB (Frankenthal, Germany) | ESOB | 1 |

‘P(E18S64)/1A’ | Caprari (Modena, Italy) | MSS | 3 |

‘P14C/1G’ | Caprari (Modena, Italy) | MSV | 3 |

‘P14C/1A’ | Caprari (Modena, Italy) | MSV | 3 |

‘P14C/1C’ | Caprari (Modena, Italy) | MSV | 3 |

‘P16D/1B’ | Caprari (Modena, Italy) | MSV | 3 |

‘P16C/1A’ | Caprari (Modena, Italy) | MSV | 3 |

‘P18C/1A’ | Caprari (Modena, Italy) | MSV | 2 |

‘92SV2G150T_IE3’ | Lowara (Vicenza, Italy) | MSV | 4 |

‘PM50/3’ | Caprari (Modena, Italy) | MSO | 1 |

‘PM50/4’ | Caprari (Modena, Italy) | MSO | 1 |

‘HMU40-2/2’ | Caprari (Modena, Italy) | MSO | 1 |

‘HMU50-1/2’ | Caprari (Modena, Italy) | MSO | 1 |

‘HMU50-2/2’ | Caprari (Modena, Italy) | MSO | 1 |

‘MEC-MR80-3/2A’ | Caprari (Modena, Italy) | MSO | 2 |

Q_{tb} | H_{tb} | P_{tb} | η_{tb} | |
---|---|---|---|---|

Proposed model | 0.48% | 1.03% | 2.00% | 4.48% |

Derakhshan & Nourbakhsh [27] | 1.6% | 20.0% | 30.0% | 4.5% |

Tan et Engeda [33] | 1.2% | 38.0% | 86.0% | 14.0% |

Devices | Manufacturer | Q_{pb} (m³/s) | H_{pb} (m) | P_{pb} (KW) | η_{pb} | N_{p} (rpm) |
---|---|---|---|---|---|---|

ESOB, Etanorm 100-400 | KSB (Frankenthal, Germany) | 0.052673 | 49.37302837 | 33.95912663 | 0.750954 | 1450 |

MSO, MEC-MR80-3/2A | Caprari (Modena, Italy) | 0.042037 | 130.9518891 | 69.89042498 | 0.772358 | 2900 |

MSV, 92SV2G150T_IE3 | Lowara (Vicenza, Italy) | 0.025474 | 42.28917636 | 13.42392097 | 0.786942 | 2900 |

MSS, ’P(E18S64)/1A’ | Caprari (Modena, Italy) | 0.1964461 | 48.9573971 | 114.3579978 | 0.8246829 | 2935 |

Device | Manufacturer | Q_{tb} (m³/s) | H_{tb} (m) | P_{tb} (KW) | η_{tb} | N_{t} (rpm) |
---|---|---|---|---|---|---|

ESOB, Etanorm 100-400 | KSB (Frankenthal, Germany) | 0.072615 | 77.57348 | 41.93998986 | 0.759266 | 1520 |

MSO, MEC-MR80-3/2A | Caprari (Modena, Italy) | 0.030197 | 51.0721 | 10.41159796 | 0.68847 | 1570 |

MSV, 92SV2G150T_IE3 | Lowara (Vicenza, Italy) | 0.026722 | 44.25196 | 8.521971903 | 0.734943 | 2400 |

MSS, ’P(E18S64)/1A’ | Caprari (Modena, Italy) | 0.1447000 | 19.5269 | 18.7352210 | 0.6761843 | 1550 |

Devices | Qtb_{EV} (m³/s) | E_{Qtb} | Htb_{EV} (m) | E_{Htb} | Ptb_{EV} (KW) | E_{Pt} | ηt_{EV} | E_{ηt} |
---|---|---|---|---|---|---|---|---|

ESOB, Etanorm 100-400 | 0.0750659 | −3.37% | 79.03889 | −1.89% | 40.6951 | 2.97% | 0.6992 | 7.91% |

MSO, MEC-MR80-3/2A | 0.0309395 | −2.46% | 55.91328 | −9.48% | 11.5367 | −10.81% | 0.6798 | 1.26% |

MSV, 92SV2G150T_IE3 | 0.0286611 | −7.26% | 42.19448 | 4.65% | 7.9155 | 7.12% | 0.6672 | 9.22% |

MSS, ’P(E18S64)/1A’ | 0.1410412 | 2.53% | 19.89140 | −1.87% | 17.5225 | 6.47% | 0.6367 | 5.84% |

**Table 6.**PAT performance at BEP, evaluated using Derakhshan and Nourbakhsh [27].

Devices | Qtb_{D} (m³/s) | E_{Qtb} | Htb_{D} (m) | E_{Htb} | Ptb_{D} (KW) | E_{Pt} | ηt_{D} | E_{ηt} |
---|---|---|---|---|---|---|---|---|

ESOB, Etanorm 100-400 | 0.083529 | −15.03% | 104.217 | −34.35% | 53.33965 | −27.18% | 0.62486 | 17.70% |

MSO, MEC-MR80-3/2A | 0.0331197 | −9.68% | 75.92709 | −48.67% | 12.72625 | −22.23% | 0.51609 | 25.04% |

MSV, 92SV2G150T_IE3 | 0.0319179 | −19.45% | 49.65282 | −12.20% | 11.65847 | −36.80% | 0.75019 | −2.07% |

MSS, ’P(E18S64)/1A’ | 0.099137 | 31.49% | 15.3896 | 21.19% | 13.134578 | 29.89% | 0.87793 | −29.84% |

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**MDPI and ACS Style**

Fontanella, S.; Fecarotta, O.; Molino, B.; Cozzolino, L.; Della Morte, R.
A Performance Prediction Model for Pumps as Turbines (PATs). *Water* **2020**, *12*, 1175.
https://doi.org/10.3390/w12041175

**AMA Style**

Fontanella S, Fecarotta O, Molino B, Cozzolino L, Della Morte R.
A Performance Prediction Model for Pumps as Turbines (PATs). *Water*. 2020; 12(4):1175.
https://doi.org/10.3390/w12041175

**Chicago/Turabian Style**

Fontanella, Stefania, Oreste Fecarotta, Bruno Molino, Luca Cozzolino, and Renata Della Morte.
2020. "A Performance Prediction Model for Pumps as Turbines (PATs)" *Water* 12, no. 4: 1175.
https://doi.org/10.3390/w12041175