# New Insights into Flow for a Low-Bypass-Ratio Transonic Fan with Optimized Rotor

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## Abstract

**:**

## 1. Introduction

## 2. Optimization System

## 3. Rotor Blade Optimization

_{ar}keeps rising along the blade’s leading edge from hub to shroud. On the other hand, M

_{ar}’s apparent improvement is only seen from 60% H/h to the blade’s trailing edge. Abovementioned phenomena indicate that rotor optimization mainly works on the transonic region at the upper half of the blade, i.e., the positions where the shock wave occupy. All these results have proved the optimization of the rotor blade to be an effective method to improve the aerodynamic performance of the fan stage.

_{is}gets closer to the downstream after Camber_Opt, indicating that the shock wave on the blade suction surface is delayed. Moreover, the delay of the shock wave in the rotor blade passage could expand the throttling range of the transonic fan, which highlights the advantage of the design technique. After camber line optimization, the maximum value of M

_{is}is also reduced, indicating that the shock wave’s intensity has also been weakened. One of the other notable defections in the baseline configuration is the deviation of incidence angle which presented as the crossing of the M

_{is}line at the blade leading edge. This problem is solved completely by Angle_Opt. In fact, although the position of the shock wave in Angle_Opt is moved slightly upstream compared with Camber_Opt, the location of the shock wave is still in the downstream in comparison with the baseline case, and the flow characteristics at the blade leading edge are improved greatly. In fact, near the rear region of the shock wave, the isentropic Mach number is decreased by Angle_Opt, which indicates that the rotor would have a better pressure rise capability.

_{m}, which is in line with the design concept of the high-load transonic fan.

## 4. Vorticity Dynamics Diagnosis

#### 4.1. Mathematical Explicit Relation between Vorticity Dynamics Parameters vs. Performance Parameters

_{θ}denotes the azimuthal vorticity and is defined as:

_{r}/∂z are ignorable at the inlet or outlet plane of fan/compressor, the Equation (1) could be simplified as:

_{θ}. Moreover, according to Equation (2), in the core flow region of the blade passage, ∂u

_{r}/∂z ≈ ∂u

_{z}/∂r ≈ 0, so ω

_{θ}≈ 0. In the hub region where ∂u

_{r}/∂z << ∂uz/∂r and ∂u

_{z}/∂r > 0, ω

_{θ}≈ −∂u

_{z}/∂r < 0. In the casing region where ∂u

_{r}/∂z << ∂u

_{z}/∂r and ∂u

_{z}/∂r < 0, ω

_{θ}≈ −∂u

_{z}/∂r > 0. Consequently, in order to improve the throughflow capability of the compressor, the reduction of area for the vortex regions near the hub and the casing is required. In other words, the increase of the mass flow rate calls for the decrease of the boundary layer thickness, which is in consistence with the general principle of fluid dynamics.

_{z}is its axial-component. σ

_{pz}is axial-component of BVFσ

_{p}, S

_{b}denotes rotor blade surface and ∂S

_{b}is the boundary of S

_{b}. According to Equation (12), the M

_{z}consists of two parts: the surface integration of the second-moment of σ

_{pz}is the first part, and the curve integration of the second-moment of static pressure p is the second. Hence, we can see that the lower σ

_{pz}is, the higher M

_{z}will be, which would have more beneficial effects on the total pressure ratio for the fan/compressor rotor blade passage. Therefore, the axial component of the BVF σ

_{pz}is an important parameter that reflects the aerodynamic performance of the fan/compressor.

#### 4.2. Flow Diagnosis Based on Vorticity Dynamics

_{m}= 14%, c/C

_{m}= 42%, c/C

_{m}= 70% and c/C

_{m}= 90%, respectively. Compared with the baseline case, significant reduction of the vortex intensity is achieved by the optimization, which is particularly obvious in the tip region of the rotor blade. This phenomenon further demonstrates that the rotor optimization could obtain a more reasonable configuration of the shock wave in the transonic fan, which would therefore enhance the through flow capability according to Equation (3).

_{pz}) on the blade suction surface is shown in Figure 11. According to the demonstrations above, the increment of σ

_{pz}in the boundary layer area is detrimental to the performance of the compressor due to the reduction in the total aerodynamic torque. As can be seen in Figure 11, the positive peak of σ

_{pz}is weakened and shifted towards the upper part of the blade in the optimized case, which indicates that the flow loss caused by the shock wave is reduced significantly, and the fluid will be able to receive larger axial torque when it travels through the rotor blade passage.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

c | Local meridian curve distance |

C_{m} | Total meridian curve distance |

h | Local span distance |

H | Blade height |

m’ | Normal coordinate for the streamline |

$\dot{m}$ | Mass flow rate |

Ma | Mach number |

M | Moment vector, Mach number |

$\overline{n}$ | Corrected Rotating speed |

p | Pressure |

r | Radial coordinates |

S | Entropy |

T | Temperature |

u | Non-dimensional coordinate in basic airfoil plane, absolute velocity |

z | Axial coordinates |

α | Out flow angle |

Δβ | viation on metal angle |

δ | Deviation angle |

η | Efficiency |

θ | Circumferential coordinates |

Δθ | Deviation on tangential lean angle |

μ | Dynamic viscosity |

ν | Kinematic viscosity |

π | Pressure ratio |

ρ | Density |

σ_{p} | Boundary vorticity flux |

τ | Shear stress |

ω | Vorticity |

Subscripts/Superscripts | |

1 | Inlet conditions |

2 | Outlet conditions |

r | Relative conditions |

r, θ, z | Radial, circumferential, axial components |

is | Isentropic |

* | Total condition |

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**Figure 3.**Comparisons of aerodynamic parameters for the rotor blade: (

**a**) Adiabatic efficiency; (

**b**) Total pressure ratio; (

**c**) Relative Mach number.

**Figure 6.**Performance map for the fan stage: (

**a**) The total pressure ratio vs. mass flow rate; (

**b**) The adiabatic efficiency vs. mass flow rate.

**Figure 13.**Vector lines (τ, ω) and entropy on the rotor blade suction side: (

**a**) Vector lines (τ, ω) and specific entropy; (

**b**) Vector lines (τ, ω) and axial gradient of entropy.

**Figure 14.**Vector lines (τ, ω) and static pressure on the rotor blade suction side: (

**a**) Vector lines (τ, ω) and specific static pressure; (

**b**) Vector lines (τ, ω) and axial gradient of static pressure.

Case | Grid Distribution (Streamwise × Pitchwise × Radial) | Total Grid Cell Number | Performance Parameters | |||
---|---|---|---|---|---|---|

Rotor | Stator | Efficiency | Pressure Ratio | Mass Flow Rate | ||

1 | 39 × 11 × 75 | 43 × 11 × 75 | 768,754 | 0.88596 | 1.9735 | 8.8543 |

2 | 59 × 19 × 75 | 63 × 19 × 75 | 1,250,734 | 0.88879 | 1.9743 | 8.8586 |

3 | 71 × 23 × 75 | 75 × 23 × 75 | 1,512,658 | 0.88913 | 1.9739 | 8.8611 |

4 | 111 × 37 × 75 | 119 × 37 × 75 | 2,595,228 | 0.88905 | 1.9740 | 8.8607 |

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

Number of rotor and stator blade | 13, 36 |

Mach number in relative coordinates for rotor blade tip | 1.3848 |

Loading coefficient for rotor blade tip | 0.463 |

Flow coefficient for rotor blade tip | 0.500 |

Hub-to-tip ratio of the rotor passage | 0.460 |

Corrected design angular velocity (rpm) | 28,000.0 |

Corrected rotor tip tangent velocity (m/s) | 410.0 |

Clearance for rotor blade tip (mm) | 0.50 |

Mass flow rate at design angular velocity for fan (kg/s) | ≥9.34 |

Adiabatic efficiency at design-point | ≥0.87 |

Total pressure ratio at design-point | ≥2.05 |

Mass flux $\dot{\mathit{m}}$ (kg/s) | Pressure Ratio π* (−) | Efficiency η* (−) | ||||
---|---|---|---|---|---|---|

Value | (%) | Value | (%) | Value | (%) | |

Baseline | 8.94 | 0 | 2.10 | 0 | 0.853 | 0 |

Camber_Opt | 9.31 | +4.14 | 2.15 | +2.38 | 0.886 | +3.87 |

Angle_Opt | 9.45 | +5.70 | 2.15 | +2.38 | 0.891 | +4.45 |

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## Share and Cite

**MDPI and ACS Style**

Liu, M.; Zhang, Z.; Liang, Z.; Xiao, H.; Chen, H.; Yang, X.; Shao, C.
New Insights into Flow for a Low-Bypass-Ratio Transonic Fan with Optimized Rotor. *Energies* **2023**, *16*, 7230.
https://doi.org/10.3390/en16217230

**AMA Style**

Liu M, Zhang Z, Liang Z, Xiao H, Chen H, Yang X, Shao C.
New Insights into Flow for a Low-Bypass-Ratio Transonic Fan with Optimized Rotor. *Energies*. 2023; 16(21):7230.
https://doi.org/10.3390/en16217230

**Chicago/Turabian Style**

Liu, Mingjun, Zhenjiu Zhang, Zhuoming Liang, Haibing Xiao, Huanlong Chen, Xianqing Yang, and Changxiao Shao.
2023. "New Insights into Flow for a Low-Bypass-Ratio Transonic Fan with Optimized Rotor" *Energies* 16, no. 21: 7230.
https://doi.org/10.3390/en16217230