# A Performance Prediction Method for Pumps as Turbines (PAT) Using a Computational Fluid Dynamics (CFD) Modeling Approach

^{*}

## Abstract

**:**

## 1. Introduction

^{®}, developed by Simerics Inc.

^{®}(1750 112th Ave NE, Ste C250, Bellevue, WA, USA). In the fourth section, the test bench layout is shown with all the transducers’ characteristics.

## 2. Literature Overview on Prediction Methods

## 3. Simulation Model

^{3}/s) to have different geometries and operating conditions to better test the prediction method.

_{S}= 37.6 is shown. This pump is a shrouded one with one- channel impeller and six blades and is called Pump 1. Starting from the real geometry in a .step format, the fluid volume has been extracted. In Figure 1, the fluid-volume is colored in green while the solid impeller is in blue and the solid rotor in red. In the same way, fluid volumes of others two pumps have been extracted and then modelled using a 3D-CFD approach.

^{®}. PumpLinx

^{®}is a three-dimensional CFD software developed by Simerics Inc. (1750 112th Ave NE, Ste C250, Bellevue, WA 98004, USA) [25,26,27,28,29]. It numerically solves the fundamental conservation equations of mass, momentum and energy and includes robust models of turbulence and cavitation.

^{®}grid generator using a body-fitted binary tree approach. These grids have been demonstrated to be extremely accurate and efficient [25,26,27,28,29]. In fact, the parent-child tree architecture allows for an expandable data structure with reduced memory storage, the binary refinement is optimal for transitioning between different length scales and resolutions within the model, the majority of cells are cubes, and, since the grid is created from a volume, it can tolerate inaccurate CAD surfaces with small gaps and overlaps. It is important to underline that, cells are hexagonal not deformed therefore the skewness is zero [30].

- PUMP 1 (N
_{S}= 37.6): - Total number of cells: 851.673Total number of faces: 3.383.745Total simulation time: 8.9 h as Pump, 9 h as PAT
- PUMP 2 (N
_{S}= 20.5): - Total number of cells: 1.039.450Total number of faces: 3.926.412Total simulation time: 4.2 h as Pump, 4.8 h as PAT
- PUMP 3 (N
_{S}= 64): - Total number of cells: 324.596Total number of faces: 3.348.318Total simulation time: 4.5 h as Pump, 4.8 h as PAT

_{1}= 1.44, c

_{2}= 1.92, σ

_{k}= 1, σ

_{ε}= 1.3, where σ

_{k}and σ

_{ε}are the turbulent kinetic energy and the turbulent kinetic energy dissipation rate Prandtl numbers.

_{i}’ (i = 1, 2, 3) being components of v’.

_{t}is calculated by [16,23,24,32,33]:

_{μ}= 0.09.

_{t}can be expressed as a function of velocity and the shear stress tensor as [16,23,24]:

_{S}= 20.5) and pump 3 (N

_{S}= 64) at 2900 rpm.

^{3}/h, the head varies from 47 m to 3 m. In the plots in Figure 5, the model results are shown in red. The comparison in Figure 5 demonstrates the accuracy of the adopted methodology; in fact, the percentage error is always less than 4% while for many points the error is near zero.

## 4. Ns 37.6 Pump Model Validation with Experimental Data

_{1}and P

_{2}(Burkert

^{®}model 8314), and a flow meter Q (Siemens

^{®}mag 500) have been installed. All test bench data have been acquired by a homemade acquisition system. Furthermore, a 360-tooth encoder has been installed on the electrical motor to acquire the shaft speed.

- Ceramic technology
- 0–10 bar pressure range
- ±0.25% accuracy
- 2 ms response time

## 5. Model Results

^{3}/s), and P (W) are the head, flow rate and power, respectively. The rotational speed is n (RPS) and D (m) is the impeller diameter. In the reverse mode simulation, the boundary conditions in pump and PAT mode were the same (declared data in pump mode). The boundary conditions in reverse mode are summarized in Table 2.

## 6. Comparison of Prediction Methods

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

PRV | Pressure Reducing Valve |

PAT | Pump as Turbine |

CFD | Computational Fluid Dynamic |

BEP | Best Efficiency Point |

H_{p} | Pump head |

Q_{p} | Pump flow rate |

P_{p} | Pump power |

η_{p} | Pump overall efficiency |

H_{t} | Turbine head |

Q_{t} | Turbine flow rate |

P_{t} | Turbine power |

η_{t} | Turbine overall efficiency |

ψ | Specific head |

ϕ | Specific capacity |

π | Specific power |

η | Efficiency |

N_{s} | Pump specific speed |

N_{st} | Turbine specific speed |

z | Impeller’s blade number |

P_{it} | Power losses due to leakage |

P_{vt} | Volute power losses |

P_{et} | Kinetic energy losses |

P_{nt} | Turbine net power |

P_{it} | Hydraulic losses of the impeller in turbine mode |

n | Surface normal |

k | Turbulence kinetic energy |

p | Pressure (Pa) |

Q | Flow rate (m^{3}/h) |

rpm | Revolution per minute |

U | Initial velocity |

u | Velocity component (m/s) |

u′ | Component of v’ |

v | Velocity vector |

v′ | Turbulent fluctuation velocity |

μ | Fluid viscosity (Pa-s) |

ρ | Fluid density (kg/m^{3}) |

$\tilde{\mathsf{\tau}}$ | Shear stress tensor |

c_{1}, c_{2} | Constant |

σ_{k} | Turbulent kinetic energy |

σ_{ε} | Turbulent kinetic energy dissipation |

S’_{ij} | Strain tensor |

μ_{t} | Turbulent viscosity |

G_{t} | Turbulent generation |

τ_{ij} | Turbulent Reynolds stress |

ε | Turbulence dissipation |

Ω | Control volume |

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**Figure 3.**Model results for Pump 1 (Ns = 37.6) at 2900 rpm. (

**a**) Pressure distribution; (

**b**) velocity vectors.

**Figure 4.**Pressure distribution in the fluid volume of pumps 2 and 3 at 2900 rpm. (

**a**) Ns = 20.5; (

**b**) Ns = 64.

**Figure 6.**Test bench—water grid of the Department of Civil Construction and Environmental Engineering of the University of Naples Federico II.

Impeller Diameter (mm) | Delivery Outlet Diameter (mm) | H_{bep} (m) | Q_{bep} (m^{3}/h) | |
---|---|---|---|---|

(Ns 37.6) | 190 | 80 | 39 | 148 |

(Ns 20.5) | 200 | 70 | 60 | 45.4 |

(Ns 64.0) | 120 | 80 | 3.9 | 54 |

Boundary Conditions | Pump 1 | Pump 2 | Pump 3 |
---|---|---|---|

Outlet pressure | 1.9 bar | 1.9 bar | 1.9 bar |

Inlet Volumetric Flow | 90/210 m^{3}/h | 30/85 m^{3}/h | 48/90 m^{3}/h |

T_{in} | 293.15 K | 293.15 K | 293.15 K |

P_{sat} | 2886 Pa | 2886 Pa | 2886 Pa |

Boundary Conditions | Pump 1 | Pump 2 | Pump 3 | |||
---|---|---|---|---|---|---|

Direct Mode | Reverse Mode | Direct Mode | Reverse Mode | Direct Mode | Reverse Mode | |

Head (m) | 39 | 61 | 45.4 | 67 | 3.9 | 4.6 |

Capacity (m^{3}/s) | 0.041 | 0.05 | 0.017 | 0.021 | 0.015 | 0.022 |

Power (kW) | 20.5 | 19.98 | 10.01 | 10.24 | 1.05 | 0.75 |

Efficiency | 0.787 | 0.663 | 0.743 | 0.741 | 0.543 | 0.487 |

Methods | H (m) | Q (m^{3}/s) | P (kW) | η |
---|---|---|---|---|

Model results | 61.42 | 0.05 | 19.98 | 0.663 |

Stepanoff | 49.55 | 0.0463 | 22.5 | 0.787 |

Alatorre-Frenk | 42.79 | 0.091 | 28.92 | 0.757 |

Sharma | 51.99 | 0.0498 | 20.5 | 0.807 |

Schmiedl | 43.94 | 0.0514 | 16.82 | 0.759 |

Grover | 78.59 | 0.0657 | 36.92 | 0.729 |

Hergt | 41.90 | 0.0508 | - | - |

Childs | 49.55 | 0.0522 | 19.96 | 0.787 |

D&N | 58.56 | 0.0411 | 18.17 | 0.769 |

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**MDPI and ACS Style**

Frosina, E.; Buono, D.; Senatore, A.
A Performance Prediction Method for Pumps as Turbines (PAT) Using a Computational Fluid Dynamics (CFD) Modeling Approach. *Energies* **2017**, *10*, 103.
https://doi.org/10.3390/en10010103

**AMA Style**

Frosina E, Buono D, Senatore A.
A Performance Prediction Method for Pumps as Turbines (PAT) Using a Computational Fluid Dynamics (CFD) Modeling Approach. *Energies*. 2017; 10(1):103.
https://doi.org/10.3390/en10010103

**Chicago/Turabian Style**

Frosina, Emma, Dario Buono, and Adolfo Senatore.
2017. "A Performance Prediction Method for Pumps as Turbines (PAT) Using a Computational Fluid Dynamics (CFD) Modeling Approach" *Energies* 10, no. 1: 103.
https://doi.org/10.3390/en10010103