# Development of Mixed Flow Fans with Bio-Inspired Grooves

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}/s) and ${H}_{pump}$ (m) denotes the head of the pump (the dimension of ${n}_{s}$ is same to ${g}^{3/4}$ (g: gravity acceleration)) [2]. In general, the industrial flow fans require improvement on the fluid dynamic performance and the working stability associated with the vibrations, noise, and unnecessary forces [3]. To this end, recent studies on the industrial pump mainly focus on the effects of its traditional design parameters on the fluid dynamic output or pressure fluctuations [4,5,6,7,8]. For example, the spanwise twist change may increase efficiency by 0.8% but cause larger pressure fluctuation amplitude [5]. The tip clearance (TC) variations even within 0.5 mm can result in significant changes in efficiency and pressure fluctuation [7]. As a result of the previous studies, the performance of the current mixed-flow fans is maximized in the traditional design space. A novel design principle is, therefore, necessary for further improving the performance.

## 2. Materials and Methods

#### 2.1. The Original Impeller and the Computational Fluid Dynamic (CFD) Modelling

#### 2.2. Biomimetic Designs and the Design Method

#### 2.3. Evaluation Method of Aerodynamic and Aeroacoustic Performance

^{4}/s

^{2}, while the value derived from the single blade model is 0.00584 m

^{4}/s

^{2}, which is about 5% lower than the former. Besides, we can also see the obvious TKE reduction near the leading edge from both numerical models, as shown in black circles in Figure 6. Therefore, we believe that it is reasonable to firstly utilize the single blade model in capturing the key flow features of the biomimetic design in terms of the TKE reduction. Furthermore, this model can save our computing time and let us try different biomimetic designs as many times as possible.

#### 2.4. Numerical Grid

## 3. Results

#### 3.1. Groove Form Effects

#### 3.2. Groove Parameter Effects

## 4. Discussion

## 5. Conclusions

- The wavy shape form is better at reducing the TKE associated with the broadband noise than the riblet ones with the same groove cross-section area. However, the riblets on the suction face form outperforms others by excellently solving the tradeoff problem between aerodynamic loss and TKE reduction. Our best design can suppress the turbulence kinetic energy by approximately 38% at the blade leading edge, while its aerodynamic efficiency loss is merely 0.3 percentage points.
- More grooves can result in more TKE reduction at the leading-edge region. Large groove height may harm grooves’ TKE reduction ability. For the riblet design, the riblets’ length does not play a critical role in both aerodynamics and aeroacoustics as long as the length is enough to cover the leading-edge region.
- Bio-inspired grooves can break the leading-edge vortex up into smaller vortices or eddies and result in higher vorticity concentrated at this region. This passive flow control near the leading edge probably suppresses the TKE associated with the broadband noise successfully.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Basic and biomimetic blade designs, groove number N = 9: (

**a**) Whole basic impeller, (

**b**) Basic shape, (

**c**) Wavy shape, (

**d**) Riblet shape_ Suction face, (

**e**) Riblet shape_ Pressure face, and (

**f**) Riblet shape_ Suction face_L1/3. The rectangle region in (

**a**) is exaggerated as in other figures. The lozenge region in (

**b**) is the leading-edge region.

**Figure 3.**Grooves design illustration, groove number N = 5: (

**a**) Wavy shape, (

**b**) Riblet shape_ Suction face, (

**c**) Riblet shape_ Pressure face. The solid red lines are the blade spanwise sections and the dashed red lines the divide blade cross-section into paths (there are 10 paths). The shade areas of the same N are constant regardless of blade forms which denote the groove cross-section area.

**Figure 4.**Locations for turbulence kinetic energy (TKE) quantifying and presenting: (

**a**) Spanwise face, 5 mm from the leading edge chordwise (SF_5mm), (

**b**) Offset face, 1 mm from the suction surface in its normal direction (Off_Suc_1mm).

**Figure 5.**Validation of a 2-blade full-size model by results in our previous study [32]: (

**a**) Experimental facilities, (

**b**) Basic 2-blade full-size model, (

**c**) Local details of the exaggerated region in (

**b**), (

**d**) Results of Total Pressure versus Flow Rate for the “Basic” and the “Serration L15A20” design derived from experiments (EXP) and simulations (SIM), (

**e**) Results of Efficiency versus Flow Rate for the “Basic” and the “Serration L15A20” design derived from experiments (EXP) and simulations (SIM). The operating conditions of the serrations design in (

**d**) and (

**c**) and their nearby ‘basic ones’ are very close to that in Table 1.

**Figure 6.**TKE contours on SF_5 mm of the 2-blade full-size model and the single blade model (the following values in brackets are TKE area integrals, unit: m

^{4}/s

^{2}): (

**a**) Basic 2-blade full-size model (0.112), (

**b**) Serrations’ 2-blade full-size model (0.0997), (

**c**) Basic single blade model (0.00990), (

**d**) Serrations’ single blade model (0.00406). Note that the reduction of TKE for each blade averagely derived from the 2-blade full-size model is 0.00615, while the value derived from the single blade model is 0.00584. The error is 0.00031, which is 5% of 0.00615.

**Figure 7.**Grids of different blade forms: (

**a**) Basic blade surface mesh, (

**b**) Spanwise section mesh of the wavy blade, (

**c**) Spanwise section mesh of the riblets on suction face blade, (

**d**) Spanwise section mesh of the riblets on pressure face blade. The regions in the circle (leading-edge region) in (

**a**) is refined with a grid size of 0.7 mm, which is applied to the other designs meshes as well.

**Figure 8.**A verification of TKE results on Off_Suc_1 mm for different mesh sets: (

**a**) Mesh set 1, (

**b**) Mesh set 2, (

**c**) Mesh set 3.

**Figure 9.**Total Pressure Efficiency versus 1000 $\times $ TKE of different blade designs. (

**a**) Performance of different biomimetic design sets, (

**b**) Exploration of groove parameters for the riblets on suction face designs. Note that the “Rib” set without “Pressure” represents riblets on suction face designs.

**Figure 10.**TKE contours on Off_Suc_1 mm of different blade forms: (

**a**) Basic, (

**b**) Wavy_N9_H3, (

**c**) Rib_N9_H4.2, (

**d**) Rib_N9_H4.2_Pressure.

**Figure 11.**TKE contours on Off_Suc_1 mm of the basic design and various riblets on suction face designs: (

**a**) Basic, (

**b**) Rib_N9_H7.6, (

**c**) Rib_N9_H4.2_L2/3, (

**d**) Rib_N9_H4.2_L1/3.

**Figure 12.**Velocity vectors (in rotational frame) projected on Off_Suc_1 mm: (

**a**) Exaggerated region illustration, (

**b**) Basic, (

**c**) Rib N9 H4.2, (

**d**) Wavy N9 H3. The rectangle region in (

**a**) is exaggerated as in other figures and the circles denote the locations of vortices generated.

**Figure 13.**Axial vorticity on Off_Suc_1 mm and vortex core region (Q = 0.02): (

**a**) and (

**b**) Basic, (

**c**) and (

**d**) Rib N9 H4.2, (

**e**) and (

**f**) Wavy N9 H3. Regions in circles show obvious stronger axial vorticity than the basic.

Parameters | Values |
---|---|

Maximum Diameter of impeller/mm | 426 |

Number of blades | 6 |

Duct length/mm | 412 |

Flow rate/m^{3}/min | 35.7 |

Rotational speed/rpm | 1450 |

Parameters | Values |
---|---|

Groove number N | 5, 7, 9 |

Wavy shape groove height H/mm | 3 |

Riblet height H/mm (for the ones on the suction face) | 3.8 (N = 5) 4.0 (N = 7) 4.2, 5.9, 7.6 (N = 9) |

Riblets length proportion (for N = 9 and H = 4.2mm) | $\frac{1}{3},\frac{2}{3},1$ |

Parameters and Results | Mesh Set 1 | Mesh Set 2 | Mesh Set 3 |
---|---|---|---|

Blade surface grid size/mm | 0.7 | 0.7 (only leading-edge region)/1 | 1.5 |

Rotational domain body size/mm | 3 | 4 | 5 |

Element number ($\times {10}^{6}$) | 6.40 | 2.63 | 1.26 |

y+ on blade (based on Re = 446,000) | 5 | 10 | 25 |

Growth rate of prism layer (blade) | 1.1 | 1.06 | 1.2 |

Prism layer number (blade) | 15 | 11 | 5 |

Outlet total pressure/Pa | 366 | 368 (+0.5%)^{1} | 374 (+2.2%) |

Efficiency ($\times 100\%$) | 81.9 | 81.8 (−0.1 pp) | 81.9 (0 pp) |

1000$\times $ TKE Integrated on SF_5 mm/ m^{4}/s^{2} | 9.77 | 9.74 (−0.3%) | 11.30 (+15.7%) |

^{1}The values in brackets are the errors compared with the Mesh Set 1.

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**MDPI and ACS Style**

Wang, J.; Nakata, T.; Liu, H. Development of Mixed Flow Fans with Bio-Inspired Grooves. *Biomimetics* **2019**, *4*, 72.
https://doi.org/10.3390/biomimetics4040072

**AMA Style**

Wang J, Nakata T, Liu H. Development of Mixed Flow Fans with Bio-Inspired Grooves. *Biomimetics*. 2019; 4(4):72.
https://doi.org/10.3390/biomimetics4040072

**Chicago/Turabian Style**

Wang, Jinxin, Toshiyuki Nakata, and Hao Liu. 2019. "Development of Mixed Flow Fans with Bio-Inspired Grooves" *Biomimetics* 4, no. 4: 72.
https://doi.org/10.3390/biomimetics4040072