# Numerical Investigation of the Influence of Aerodynamic Loads on the Resonant Frequency of a Compressor Blade Made of EI-961 Alloy

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## Abstract

**:**

## 1. Introduction

## 2. Resonance Frequency Calculation

#### 2.1. Object of the Study

#### 2.2. Literature Data

#### 2.3. Analytical Calculations

- $l=53$ mm—length of the beam (blade);
- $E=210$ GPa—Young’s modulus;
- $\rho =7850$ kg/m${}^{3}$—material density;
- $A=39.0567$ mm${}^{2}$—cross-sectional area (at the foot of the blade);
- $J=22.7$ mm${}^{4}$—section moment of inertia.

## 3. Numerical Analysis

#### 3.1. Fluid Flow Analysis

- At the inlet—static pressure 101.325 hPa;
- On the inlet—speed 98 m/s (corresponding to the flight speed of the aircraft);
- At the outlet—the outlet was realized with a mass flow of 201 g/s (in case of 22,490 RPM—for other analysis was calculated linearly);
- Domain—rotational with the assumed rotor speed (variable value in the analysis);
- Working medium—compressible gas—air with parameters corresponding to the reference atmosphere [30].

#### 3.2. Structural Analysis

#### 3.3. Modal Analysis

## 4. Results Comparison

## 5. Conclusions

- The first form of resonant vibrations, for the tested compressor blade, occurs at about 770 Hz.
- The result of analytical calculations gives a satisfactory value only for the first form of resonance vibrations.
- The first of resonant vibrations one is purely of bending mode/form. The second and third form are bending-torsional ones.
- Numerical calculations show circa 3% agreement with the experimental data.
- In the case of the third mode of natural vibrations, the resonance frequency changes by about 40 Hz, taking into account the aerodynamic loads.
- The influence of aerodynamic loads on the resonance frequencies of the compressor blade decreases with increasing of the rotational speed.
- Aerodynamic loads increase the deflection of the blade and increase the value of reduced stresses, which does not have a significant effect on the resonance of the blade.
- The change in the resonant frequency was related to the change in the geometry of the blade due to the action of aerodynamic loads (greater deflection and rotation of the blade causes a minimal change in the resonance frequency).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Structure of the SP (with no aerodynamic loads consideration) and SAL analysis Fluid Structure Interaction).

**Figure 4.**Relative static pressure distribution in the cross-section connecting the fluid domain for the rotational speed of 31,486 RPM (cross-section in 50% of the height of the blade −76 mm from the axis of rotation).

**Figure 5.**The distribution of the relative velocity (taking into account the rotational speed) in the cross section that covers the fluid domain for the rotational speed of 31,486 RPM (cross-section in 50% of the height of the blade −76 mm from the axis of rotation).

**Figure 7.**Free vibration modes of the blade: (

**a**) I-st, (

**b**) II-nd and (

**c**) III-rd mode (SAL analysis) (results scaled to 1 mm deformation, where blue means 0 mm and red means 1 mm).

**Table 1.**List of the resonant frequencies of the compressor blade of the PZL-10W engine, experimentally estimated [25].

Resonance Frequency ${\mathit{f}}_{\mathit{res}},\mathit{Hz}$ | ||
---|---|---|

I-st Mode | II-nd Mode | III-rd Mode |

770.31 | 2445.31 | 3600 |

**Table 2.**Summary of the results of the calculated frequencies of resonant vibrations of the beam with the geometry convergent with the compressor blade.

Resonance Frequency ${\mathit{f}}_{\mathit{res}},\mathit{Hz}$ | ||
---|---|---|

I-st Mode | II-nd Mode | III-rd Mode |

784.85 | 4918.83 | 13,756.74 |

Rotational Velocity, RPM | Eq. Stress ${\mathit{\sigma}}_{\mathit{eqv}}$, MPa | Max. Deformation, mm | I-st Mode, Hz | II-nd Mode, Hz | III-rd Mode, Hz |
---|---|---|---|---|---|

0 | 0 | 0 | 789.39 | 2518 | 3598.238 |

11,000 | 114.7966 | 0.301005 | 841.2594 | 2556.473 | 3678.684 |

22,490 | 479.8689 | 1.258249 | 985.3016 | 2665.851 | 3807.039 |

31,486 | 940.543 | 2.466169 | 1136.907 | 2784.595 | 3968.938 |

Rotational Velocity, RPM | Eq. Stress ${\mathit{\sigma}}_{\mathit{eqv}}$, MPa | Max. Deformation, mm | I-st Mode, Hz | II-nd Mode, Hz | III-rd Mode, Hz |
---|---|---|---|---|---|

0 | 44.18 | 0.00379 | 789.62 | 2521.6 | 3640.3 |

11,000 | 158.9653 | 0.452119 | 841.4552 | 2559.462 | 3680.356 |

22,490 | 524.0332 | 1.409334 | 985.4381 | 2668.793 | 3808.517 |

31,486 | 984.7064 | 2.617247 | 1137 | 2787.488 | 3970.206 |

**Table 5.**Summary of differences between SP and SAL analyzes for different rotational speeds of the compressor vane.

I-st Mode, Hz | II-nd Mode, Hz | III-rd Mode, Hz | |
---|---|---|---|

0 | −0.23 | −3.6 | −42.0621 |

11,000 | −0.19583 | −2.98917 | −1.6714 |

22,490 | −0.13644 | −2.94283 | −1.47802 |

31,486 | −0.09243 | −2.89317 | −1.26754 |

**Table 6.**List of resonant frequencies of an axial compressor blade of a turbine engine, estimated numerically and experimentally.

I-st Mode | II-nd Mode | III-rd Mode | |
---|---|---|---|

Experiment | 770.31 Hz | 2445.31 Hz | 3600 Hz |

SP analysis (with no aerodynamic loads consideration) | 789.39 Hz | 2518 Hz | 3598.24 Hz |

Error to exp. | −19.08 Hz | −72.69 Hz | 1.76 Hz |

Percentage difference to exp. | −2.48% | −2.970% | 0.049% |

SAL analysis (with aerodynamic loads considered) | 789.62 Hz | 2521.6 Hz | 3640.3 Hz |

Error to exp. | −19.31 Hz | −76.29 Hz | −40.3 Hz |

Percentage difference to exp. | −2.51% | −3.12% | −1.12% |

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**MDPI and ACS Style**

Bednarz, A.; Puchała, K.; Sałaciński, M.; Hutsaylyuk, V. Numerical Investigation of the Influence of Aerodynamic Loads on the Resonant Frequency of a Compressor Blade Made of EI-961 Alloy. *Materials* **2022**, *15*, 8391.
https://doi.org/10.3390/ma15238391

**AMA Style**

Bednarz A, Puchała K, Sałaciński M, Hutsaylyuk V. Numerical Investigation of the Influence of Aerodynamic Loads on the Resonant Frequency of a Compressor Blade Made of EI-961 Alloy. *Materials*. 2022; 15(23):8391.
https://doi.org/10.3390/ma15238391

**Chicago/Turabian Style**

Bednarz, Arkadiusz, Krzysztof Puchała, Michał Sałaciński, and Volodymyr Hutsaylyuk. 2022. "Numerical Investigation of the Influence of Aerodynamic Loads on the Resonant Frequency of a Compressor Blade Made of EI-961 Alloy" *Materials* 15, no. 23: 8391.
https://doi.org/10.3390/ma15238391