# Investigation into Influence of Wall Roughness on the Hydraulic Characteristics of an Axial Flow Pump as Turbine

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Model and Methods

#### 2.1. Governing Equations

_{ij}: the Reynolds stress; whereas x

_{i}and x

_{j}represent the Cartesian coordinate components in the i and j directions, respectively, u

_{i}and u

_{j}represent the corresponding components of the time-averaged velocity.

#### 2.2. Equivalent Sand-Grain Roughness

_{s}[μm], also known as equivalent sand height [27]. The friction effect only occurs in the upper part of balls, and the equivalent sand-grain roughness only affects the flow in its vicinity. Therefore, the actual flow surface may be rounded as shown in Figure 1b, where the x-axis represents the physical wall surface.

_{a}) that is used to quantify the surface roughness is couched in Equation (3).

_{i}is the distance from the average height of a profile (the mean line) for measurement i, and n is the number of measurements [28]. As the number of measurements approaches infinity, Equation (3) tends to look like Equation (4).

_{s}) can be expressed as to Equation (8).

#### 2.3. The Geometric Model Description

#### 2.4. The Grid Generation Methodology

#### 2.5. Boundary Conditions

^{−5}.

## 3. Results and Discussion

#### 3.1. Experimental Validation of the Numerical Scheme

^{3}/s; the maximum relative errors of pump head and efficiency between experiment and numerical results are 1.60% and 2.89%, respectively. Hence, both the selected mesh arrangement and numerical methods can be considered reliable enough to guarantee the accuracy and reliability of numerical outcomes.

#### 3.2. Effect of Wall Roughness on PAT Performance

_{a}= 0 μm, 6 μm, 60 μm, 120 μm, 240 μm, 480 μm, 960 μm) are selected for the numerical calculation. For each wall roughness, Figure 6a,b show the corresponding performance characteristics (head and efficiency) variation with respect to the activated flow rate. The general remark for both figures is that the order of roughness influence on the head and efficiency for each flow rate is directly connected to the level of roughness; i.e., the deeper the roughness, the higher the performance reduction.

^{3}/s. When the flow rate is in the range of 0.7 Q–1.2 Q, the head at the same working point decreases gradually with the increase in wall roughness. When wall roughness increases from 0–960 μm, the head in each flow rate condition decreases by 21.0%, 14.6%, 9.9%, 7.9%, 9%, 6.9%, and 5% respectively. This demonstrates wall roughness has the maximum effect on pump head at the small flow rate condition, and the effect gradually decreases with increasing flow rate.

#### 3.3. Effect of Wall Roughness on Shaft Power

_{t}) under different flow conditions. As noticed previously (Figure 6), the increase in flow rate corresponds to the same increase in the power of the water flow doing work on the impeller, which actuates the shaft power continuously. Once more, the extent of the wall roughness tends to have the same influence on the shaft power. This is evidenced while considering each flow rate alone; the shaft power displays a gradually decreasing pattern with the increasing wall roughness depth.

^{3}/s), whereas it gradually weakens with further flow rate increase. Reflecting back to Figure 6, the roughness influence on the head is relatively small at the small flow rate, and wall roughness leads to greater shaft power decline. This corresponds to the main reason for the efficiency reduction at small flow rates.

#### 3.4. Effect of Wall Roughness on Internal Flow

#### 3.4.1. Wall Roughness Effect on Relative Flow Velocity over the Blade Pressure Surface

_{t}) histograms of monitoring points (H3, M4, and S4) aligned radially from hub to shroud on the blade pressure surface. The outstanding observation is that as the relative velocity gets high towards outermost spans, the wall roughness keeps reducing the relative velocity according to its size. As tabulated in Table 3, the relative velocity of roughness R

_{a}= 0 μm at H3 is 8.134 m/s, which is 0.87%, 2.75%, 7.15%, 10.14%, 11.23%, 12.3% higher than that of wall roughness R

_{a}= 0 μm, 60 μm, 120 μm, 240 μm, 480 μm, and 960 μm, respectively. The relative velocity of M4 roughness R

_{a}= 0 μm is 14.04 m/s, which is 2.23%, 4.98%, 8.13%, 11.21%, 13.41%, 15.31% higher than that of R

_{a}= 0 μm, 60 μm, 120 μm, 240 μm, 480 μm, and 960 μm, respectively. The relative velocity of S4 roughness R

_{a}= 0 μm is 22.62 m/s, which is 0.89%, 3.58%, 6.45%, 10.01%, 12.34%, 14.12% higher than that of R

_{a}= 0 μm, 60 μm, 120 μm, 240 μm, 480 μm, 960 μm, respectively. It can be seen that the relative velocity of the impeller blade pressure surface increases continuously along the radial direction. As the wall roughness of the impeller shroud, the friction resistance in the boundary layer increases. This results in energy loss increase and a decrease in the relative velocity of the impeller blade.

#### 3.4.2. Effect of Wall Roughness on Impeller Outlet Flow

_{a}is the arithmetic average value of the axial velocity of outlet section (m/s); V

_{ai}is the axial velocity (m/s) of each computing unit (representing each element) at the outlet section; θ is velocity-weighted average swirl angle (deg) of flow at outlet section; V

_{ti}is the transverse velocity (m/s) of each calculation unit in the outlet section; n is the number of computing units on the exit section [30].

^{3}/s, wall roughness has the most significant effect on uniformity of axial velocity distribution, while the effect of wall roughness on uniformity of axial velocity distribution becomes minimal under the large flow rates. In light of previous findings, the low axial velocity uniformity may be one among several reasons that lead to the low operation efficiency of reverse power generation under the small flow conditions.

#### 3.4.3. Effect of Wall Roughness on Streamline of Outlet Conduit

_{a}= 0 μm, 240 μm, and 960 μm) have been selected for comparative analysis. It can be found that with the increase in wall roughness, the streamlines of the outlet conduit grow disordered.

_{a}= 0 μm and 240 μm. Conversely, backflow phenomena relatively occur in the outlet conduit at higher flow rate (1.2 Q), and they become clearer at a deeper wall roughness (R

_{a}= 960 μm). Under the optimal condition, the flow state in the outlet conduit has minor variation with increasing wall roughness. Thus, the wall roughness has the least influence on the streamline state of the slanted axial flow PAT within such best efficiency operations. Under large flow rates (R

_{a}= 240 μm and 960 μm), the flow state in the outlet conduit becomes worse than that with the smooth wall. With the increase in wall roughness, the flow state in the outlet conduit becomes obviously worse; obvious vortex and backflow phenomena grow quite apparent. In conclusion, swirl flow of the outlet conduit becomes significant when the velocity-weighted average swirl angle at the large flow rate is high with rough surface.

#### 3.4.4. Effect of Wall Roughness on Pressure Distribution over the Blade Pressure Surface

_{a}= 960 μm, the pressure of H1, H2, H3, and H4 is 7752 Pa, 23,318 Pa, 37,201 Pa, and 45,172 Pa, respectively. From Table 4, compared with the smooth wall; the pressure decreases by 11%, 8%, 14%, and 13%, respectively. In the middle of the blade, at R

_{a}= 960 μm, the pressures of M1, M2, M3, M4, and M5 are 119,776 Pa, 54,349 Pa, 37,484 Pa, 34,061 Pa, and 11,626 Pa, respectively, compared with smooth wall, the pressures decrease by 11.4%, 5.2%, 3.6%, 3.2%, and 1.1%, respectively. The pressure of the monitoring point M1 under the smooth wall surface is 135,212 Pa. At R

_{a}= 6 μm, 60 μm, 120 μm, 240 μm, 480 μm, and 960 μm, the pressure of M1 decreases by 1.3%, 2.5%, 4.5%, 7.2%, 8.9%, and 11.4% compared with the smooth wall surface. It indicates that when the roughness is greater than 240 μm, the roughness has a great influence on the pressure near the trailing edge. The pressure of M2, M3, and M4 monitoring points has a similar trend with roughness to that of M1. The minimum pressure value at M5 point under the smooth wall is 13,547 Pa. With the increasing wall roughness, the pressure decreases by 0.36%, 0.12%, 3.5%, 7%, 8.5%, 13.5%, and 18.3%, respectively. It can be seen that when the roughness is less than 60 μm, the roughness has little influence on the pressure near the leading edge. From Figure 12c, at R

_{a}= 960 μm, the pressures of S1, S2, S3, S4, and S5 are 151,730 Pa, 59,123 Pa, 51,258 Pa, 45, 943 Pa, and 12,476 Pa, respectively, compared with smooth wall, the pressures decrease by 11%, 14%, 13.2%, 10.8%, and 15%, respectively. It demonstrates that the wall roughness has a great influence on pressure of the blade near the impeller shroud. The results indicate that the boundary layer flow is obviously affected by wall roughness and pressure losses increase significantly due to wall roughness.

#### 3.4.5. Effect of Wall Roughness on Turbulent Kinetic Energy

## 4. Conclusions

- (1)
- Under constant individual flow rates, the gradual deterioration of PAT performance (measured through parameters such as the hydraulic efficiency, head, and shaft power) is conspicuously associated with the increase in wall roughness depth. The later displays a minimum impact on PAT performance only under optimal flow conditions, while for off-design flow conditions, the larger the deviation from the best efficient point, the greater the impact on PAT performance characteristics.
- (2)
- Under turbine operating mode, the increase of wall roughness simultaneously brings about a messy non-uniform distribution of axial velocity and an increase of the velocity-weighted average swirl angle. Furthermore, streamlines within the discharge conduit reflect a disorderly flow pattern, eventually giving rise to backflow structures.
- (3)
- Ultimately, the wall roughness accumulation remarkably triggers the increase of energy losses. This is evidenced by the drop of static pressure on the blade pressure surface and the increase of TKE on the blade. The latter is particularly evident near the impeller shroud. Under the same roughness conditions, the TKE on the blade suction surface proves to be greater than that on the blade pressure surface.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Unstructured mesh of the slanted axial flow pump components. (

**a**)inlet conduit, guide vane (

**b**) impeller, outlet conduit.

**Figure 6.**The slanted axial flow PAT performance varies with flow rate at different wall roughness. (

**a**) Head variation with the flow rate (

**b**) efficiency variation with the flow rate.

**Figure 12.**Streamline of the outlet conduit under different flow rates. (

**a**) 0.7 Q; (

**b**) Q; (

**c**) 1.2 Q.

**Figure 14.**Variation of pressure at the monitoring point with wall roughness. (

**a**) span0.1 (

**b**) span0.5 (

**c**) span0.9.

**Figure 17.**TKE of blade surface under different conditions. (

**a**) TKE on blade pressure surface (

**b**) TKE on blade suction surface.

Parameter | Value |
---|---|

Impeller nominal diameter D [m] | 3.25 |

Design head H [m] | 2.6 |

Design flow rate Q [m^{3}/s] | 45.5 |

Design power P [kW] | 1319 |

Design efficiency η [%] | 88 |

Rotational speed n [r/min] | 122 |

Hydraulic Circuit Components | Grid Size [10^{4}] |
---|---|

Inlet conduit | 79 |

Guide vane | 241 |

Impeller | 334 |

Outlet conduit | 94 |

An all-embracing grid size | 748 |

R_{a} (μm) | H3 | M4 | S5 | |||
---|---|---|---|---|---|---|

Vr (m/s) | Relative Deviation (%) | Vr (m/s) | Relative Deviation (%) | Vr (m/s) | Relative Deviation (%) | |

0 | 8.13 | 14.04 | 22.62 | |||

6 | 8.06 | 0.87% | 13.73 | 2.23% | 22.42 | 0.89% |

60 | 7.91 | 2.75% | 13.34 | 4.98% | 21.81 | 3.58% |

120 | 7.55 | 7.15% | 12.90 | 8.13% | 21.16 | 6.45% |

240 | 7.31 | 10.14% | 12.47 | 11.21% | 20.36 | 10.01% |

480 | 7.22 | 11.23% | 12.16 | 13.41% | 19.83 | 12.34% |

960 | 7.13 | 12.30% | 11.89 | 15.31% | 19.42 | 14.12% |

Span0.1 | Span0.5 | Span0.9 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Point | H1 | H2 | H3 | H4 | M1 | M2 | M3 | M4 | M5 | S1 | S2 | S3 | S4 | S5 |

Deviation (%) | 11 | 8 | 14 | 13 | 11 | 5.2 | 3.6 | 3.2 | 1.1 | 11 | 14 | 13 | 11 | 15 |

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**MDPI and ACS Style**

Kan, K.; Zhang, Q.; Zheng, Y.; Xu, H.; Xu, Z.; Zhai, J.; Muhirwa, A.
Investigation into Influence of Wall Roughness on the Hydraulic Characteristics of an Axial Flow Pump as Turbine. *Sustainability* **2022**, *14*, 8459.
https://doi.org/10.3390/su14148459

**AMA Style**

Kan K, Zhang Q, Zheng Y, Xu H, Xu Z, Zhai J, Muhirwa A.
Investigation into Influence of Wall Roughness on the Hydraulic Characteristics of an Axial Flow Pump as Turbine. *Sustainability*. 2022; 14(14):8459.
https://doi.org/10.3390/su14148459

**Chicago/Turabian Style**

Kan, Kan, Qingying Zhang, Yuan Zheng, Hui Xu, Zhe Xu, Jianwei Zhai, and Alexis Muhirwa.
2022. "Investigation into Influence of Wall Roughness on the Hydraulic Characteristics of an Axial Flow Pump as Turbine" *Sustainability* 14, no. 14: 8459.
https://doi.org/10.3390/su14148459