# CFD Analyses and Experiments in a PAT Modeling: Pressure Variation and System Efficiency

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## Abstract

**:**

## 1. Introduction

## 2. Numerical and Experimental Procedure

#### 2.1. PAT Numerical Model

#### 2.1.1. Model Description and Mesh

^{−4}. The Navier-Stokes equations are supplemented by fluid state equations defining the nature of the fluid, and by empirical dependencies of fluid density and viscosity. FloEFD employs one system of equations to describe both laminar and turbulent flows. The rotating parts were computed in coordinate systems attached to the models rotating parts, i.e., the models’ stationary parts must be axisymmetric with respect to the rotation axis.

#### 2.1.2. Boundary Conditions

#### 2.2. PAT Experimental Tests

^{3}is used to stabilize the upstream pressure. This air-vessel allows to regulate the flow and pressure in order to reach the steady flow conditions; a recirculating pump is also necessary since this is a loop pipe system; at downstream of the operating system an open free surface tank with the capacity of 0.5 m

^{3}keeps the recirculating flow constant in the pipe system. The pressure inside of the air-vessel varies between 20 and 35 m w.c.; ball valves located at downstream to induce flow variations are used; an electromagnetic flowmeter is located at upstream; two pressure transducers are used to register the pressure variations in a picoscope acquisition data system to be visualized in the laptop and later processed.

## 3. Results and Discussion

#### 3.1. PAT Characteristics

_{0}, H

_{0}, and η

_{0}), the machine was tested in the hydraulic lab previously described. The experiments were carried out for different rotational speeds and different flows in steady state conditions for different rotational speeds: 810, 930, 1050, 1170, 1275 and 1500 rpm. For each rotational speed, different operation points were recorded with flow values between 2.9 and 5.5 L/s. The below flow limit was established by the runaway curve, where the flow decreases when the speed increases for this type of impeller [22]. In Figure 7, the minimum flows to put the PAT working that was 2.9 L/s for the rotational speed of 810 rpm, while was 4.1 L/s when the machine rotated with 1500 rpm. Figure 7 also shows the increase of the recovered head when the rotational speed grows, keeping the flow constant, a characteristic of radial impellers.

#### 3.2. CFD and Experiments

#### 3.3. Head Drop Estimation

^{3}/s; N is the rotational speed of the machine in rps; and D is the impeller diameter in m.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

BEP | Best Efficiency Point |

CFD | Computational Fluids Dynamics |

FVM | Finite Volume Methods |

PATs | Pumps working as Turbines |

SAR | Solution Adaptive Refinement |

SIMPLE | Semi Implicit Method for Pressure-Linked Equations |

VOS | Variable Operation Strategy |

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**Figure 5.**Components of the experimental facility: (

**1**) HDPE pipe; (

**2**) recirculating pump; (

**3**) air-vessel tank; (

**4**) flowmeter; (

**5**) PAT; (

**6**) picoscope and acquisition data; (

**7**) downstream regulating tank; (

**8**) pressure transducers and (

**9**) general view.

**Figure 8.**Absolute static pressure contours for Q = 4.50 L/s: (

**a**) N = 810 rpm; (

**b**) N = 930 rpm; (

**c**) N = 1050 rpm; (

**d**) N = 1170; (

**e**) N = 1275 rpm; (

**f**) N = 1500 rpm.

**Figure 9.**Experimental and numerical values for different rotational speeds: (

**a**) N = 810 rpm; (

**b**) N = 930 rpm; (

**c**) N = 1050 rpm; (

**d**) N = 1170; (

**e**) N = 1275 rpm; (

**f**) N = 1500 rpm.

**Figure 12.**Discretization of the average percentage of the head drop for different rotational speeds.

Rotational Speed (rpm) | Refinement Level | Fluid Cells | Number of Iterations | Tolerance | Simulation Time (s) |
---|---|---|---|---|---|

810 | 2 | 100631 | 430 | 0.001 | 4402 |

930 | 2 | 100651 | 449 | 4416 | |

1050 | 2 | 100691 | 459 | 4423 | |

1170 | 4 | 101936 | 677 | 5472 | |

1275 | 5 | 102274 | 961 | 8225 | |

1500 | 4 | 101936 | 477 | 4973 |

N/N_{0} | Mean Square Error | |
---|---|---|

Head | Efficiency | |

0.77 | 0.0197 | 0.0262 |

0.89 | 0.0266 | 0.0241 |

1.00 | 0.0264 | 0.0233 |

1.12 | 0.0236 | 0.0305 |

1.21 | 0.0268 | 0.0944 |

1.43 | 0.0869 | 0.0966 |

**Table 3.**Simulation pressure results in different cross section (from A to F) in Figure 10 for different rotational speeds.

N (rpm) | 810 | N/N_{0} | 0.77 | N (rpm) | 930 | N/N_{0} | 0.89 | ||||||

Q (L/s) | Head values (m w.c.) | Q (L/s) | H (m w.c.) | ||||||||||

A | B | C | D | E | F | A | B | C | D | E | F | ||

2.90 | 4.67 | 3.59 | 3.12 | 1.30 | 1.28 | 1.09 | 2.98 | 4.39 | 3.50 | 2.97 | 1.26 | 1.23 | 0.94 |

3.34 | 5.01 | 3.93 | 3.29 | 1.33 | 1.25 | 1.07 | 3.29 | 5.10 | 3.81 | 3.27 | 1.54 | 1.53 | 1.12 |

3.79 | 5.78 | 4.37 | 3.48 | 0.69 | 0.68 | 0.34 | 4.05 | 6.78 | 5.40 | 4.78 | 1.59 | 1.56 | 1.15 |

4.26 | 6.18 | 4.64 | 4.04 | 1.36 | 1.33 | 0.92 | 4.21 | 7.11 | 5.61 | 5.13 | 1.41 | 1.38 | 0.90 |

4.55 | 7.18 | 5.55 | 4.95 | 1.67 | 1.51 | 1.16 | 4.56 | 8.89 | 6.99 | 6.50 | 1.80 | 1.78 | 1.18 |

4.89 | 8.96 | 7.01 | 6.28 | 1.82 | 1.77 | 1.19 | 4.94 | 8.99 | 6.79 | 6.26 | 1.59 | 1.52 | 0.99 |

5.06 | 8.19 | 6.08 | 5.41 | 1.33 | 1.30 | 0.79 | |||||||

N (rpm) | 1050 | N/N_{0} | 1.00 | N (rpm) | 1175 | N/N_{0} | 1.12 | ||||||

Q (L/s) | H (m w.c.) | Q (L/s) | H (m w.c.) | ||||||||||

A | B | C | D | E | F | A | B | C | D | E | F | ||

2.91 | 5.49 | 4.31 | 3.82 | 1.54 | 1.51 | 1.30 | 2.91 | 6.66 | 5.34 | 4.80 | 1.10 | 1.08 | 0.81 |

3.25 | 5.61 | 4.39 | 4.01 | 1.51 | 1.49 | 1.16 | 3.25 | 7.49 | 6.07 | 5.56 | 1.76 | 1.74 | 1.44 |

3.80 | 4.94 | 3.72 | 3.16 | 0.62 | 0.61 | 0.24 | 4.28 | 8.33 | 6.86 | 6.24 | 1.40 | 1.36 | 0.98 |

4.28 | 7.04 | 5.56 | 4.91 | 1.59 | 1.54 | 1.15 | 4.49 | 9.61 | 8.00 | 7.24 | 1.60 | 1.56 | 1.16 |

4.49 | 7.92 | 6.25 | 5.64 | 1.58 | 1.55 | 1.08 | 4.62 | 9.14 | 7.27 | 6.56 | 1.60 | 1.56 | 1.09 |

4.62 | 8.50 | 6.76 | 6.29 | 1.94 | 1.88 | 1.41 | 4.94 | 9.94 | 7.95 | 7.23 | 1.75 | 1.74 | 1.15 |

5.10 | 10.73 | 8.48 | 7.71 | 1.58 | 1.55 | 0.89 | |||||||

N (rpm) | 1275 | N/N_{0} | 1.21 | N (rpm) | 1500 | N/N_{0} | 1.43 | ||||||

Q (L/s) | H (m w.c.) | Q (L/s) | H (m w.c.) | ||||||||||

A | B | C | D | E | F | A | B | C | D | E | F | ||

3.55 | 7.10 | 5.72 | 5.19 | 1.24 | 1.23 | 0.87 | 4.06 | 10.47 | 8.91 | 8.38 | 1.53 | 1.51 | 1.09 |

4.17 | 7.48 | 5.96 | 5.42 | 1.67 | 1.65 | 1.23 | 4.22 | 11.85 | 10.09 | 9.55 | 2.22 | 2.20 | 1.75 |

4.51 | 9.94 | 8.33 | 7.71 | 1.91 | 1.89 | 1.44 | 4.43 | 11.42 | 9.84 | 9.22 | 1.89 | 1.87 | 1.45 |

4.64 | 10.46 | 8.74 | 8.26 | 2.00 | 1.97 | 1.46 | 4.55 | 11.39 | 9.79 | 9.26 | 1.53 | 1.45 | 0.96 |

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**MDPI and ACS Style**

Pérez-Sánchez, M.; Simão, M.; López-Jiménez, P.A.; Ramos, H.M. CFD Analyses and Experiments in a PAT Modeling: Pressure Variation and System Efficiency. *Fluids* **2017**, *2*, 51.
https://doi.org/10.3390/fluids2040051

**AMA Style**

Pérez-Sánchez M, Simão M, López-Jiménez PA, Ramos HM. CFD Analyses and Experiments in a PAT Modeling: Pressure Variation and System Efficiency. *Fluids*. 2017; 2(4):51.
https://doi.org/10.3390/fluids2040051

**Chicago/Turabian Style**

Pérez-Sánchez, Modesto, Mariana Simão, P. Amparo López-Jiménez, and Helena M. Ramos. 2017. "CFD Analyses and Experiments in a PAT Modeling: Pressure Variation and System Efficiency" *Fluids* 2, no. 4: 51.
https://doi.org/10.3390/fluids2040051