#
Sensitivity Analysis of BLISK Airfoil Wear^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. BLISK Blade Deterioration

## 3. Design of Experiments

#### Computation Method

## 4. Validation of Meta-Model

## 5. Influence of Wear Parameters

#### 5.1. Pressure Rise Coefficient

#### 5.2. Loss Coefficient

## 6. Conclusions

- (a)
- The pressure coefficient $\Delta p$ was mainly influenced by changes of the trailing edge, stagger angle, and leading edge. All three parameters influenced not only the changed blade, but also the adjacent blade by the same order of magnitude.
- (b)
- A sensitivity analysis of the pressure coefficient showed nearly the same behavior for all three operating points. A thicker trailing edge led to a higher pressure coefficient on the affected blade and a lower pressure coefficient for the adjacent blade. The same behavior could be seen for the stagger angle. The leading edge influence depended on the operating condition.
- (c)
- The loss coefficient $\zeta $ showed strong dependencies on the operating condition. While the thickness-related edge parameter and stagger angle of both blades had a high influence, the max. profile camber only had a strong impact for the cruise condition.
- (d)
- The sensitivity analysis of the loss coefficient showed similar behavior for all operating conditions for the presented wear parameters, apart from the stagger angle. Here the stagger angle showed a contrary behavior for the cruise condition.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

${c}_{p}$ | Non-dimensional pressure coefficient, ($p-{p}_{in})/({p}_{t,in}-{p}_{in}$) |

${c}_{max}$ | Maximum profile camber |

h | Blade height |

l | Blade chord length |

$L{E}_{asy}$ | Leading edge asymmetry |

$L{E}_{stretch}$ | Leading edge stretching |

Ma | Mach number |

p | Pressure |

Re | Reynolds number |

${r}_{LE}$ | Leading edge radius |

${r}_{TE}$ | Trailing edge radius |

${t}_{LE}$ | Leading edge thickness |

${t}_{TE}$ | Trailing edge thickness |

${t}_{max}$ | Maximum profile thickness |

T | Temperature |

$T{E}_{asy}$ | Trailing edge asymmetry |

$T{E}_{stretch}$ | Trailing edge stretching |

${X}_{tmax}$ | Position of max. profile thickness |

${X}_{Cmax}$ | Position of max. profile camber |

$\beta $ | Flow angle |

${\kappa}_{1}$ | Metal angle at leading edge |

${\kappa}_{2}$ | Metal angle at trailing edge |

$\zeta $ | Loss coefficient |

${\eta}_{is}$ | Isentropic efficiency |

$\lambda $ | Stagger angle |

$\sigma $ | Standard deviation |

$\Delta $p | Pressure rise |

in | Beginning of computational domain |

out | End of computational domain |

1 | Beginning of comp. domain |

2 | End of comp. domain |

ax | Axial |

AVDR | Axial velocity density ratio |

A1 | Airfoil 1 |

A2 | Airfoil 2 |

BPR | Bypass ratio |

BLISK | BLade-Integrated-diSK |

CFD | Computational fluid dynamics |

DoE | Design of experiments |

DLR | German Aerospace Center |

HPC | High-pressure compressor |

EGT | Exhaust gas temperature |

LE | Leading edge |

LHS | Latin hypercube sampling |

Q3D | Quasi-3-dimensional |

2D | Two-dimensional |

3D | Three-dimensional |

RANS | Reynolds-averaged Navier–Stokes |

RMSE | Root mean square error |

TSFC | Thrust-specific fuel consumption |

TE | Trailing edge |

Tu | Turbulence intensity |

TLS | Turbulence length scale |

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**Figure 1.**Geometric variances of BLISKs (blade-integrated-disks). (

**a**) Variation of stagger angle for 10 BLISKs; (

**b**) Circumferential rotor blade stagger angle distribution $\lambda $ on BLISK No. 9.

**Figure 2.**Non-dimensional surface pressure distribution ${c}_{p}$ for three operating points at $85\%$ blade height. Q3D: quasi-3D.

**Figure 3.**Mach number distribution for the reference blade section for all three operating conditions. (

**a**) Cruise; (

**b**) Takeoff; (

**c**) Touchdown.

**Figure 4.**Root mean square error (RMSE) of ${\zeta}_{Blade1}$-prediction of the meta model for takeoff condition.

**Figure 5.**Pareto chart of the pressure rise coefficient $\Delta p$ of blade 1 for all three operating points.

Symbol | Parameter |
---|---|

${c}_{max}$ | max. profile camber |

${X}_{{C}_{max}}$ | position of max. profile camber |

l | chord length |

$\lambda $ | stagger angle |

$L{E}_{asy}$ | leading edge asymmetry |

$L{E}_{stretch}$ | leading edge stretching |

$T{E}_{asy}$ | trailing edge asymmetry |

$T{E}_{stretch}$ | trailing edge stretching |

${r}_{LE}$ | leading edge radius |

${r}_{TE}$ | trailing edge radius |

${t}_{LE}$ | leading edge thickness |

${t}_{TE}$ | trailing edge thickness |

${t}_{max}$ | maximum profile thickness |

${X}_{{t}_{max}}$ | position of max. profile thickness |

${\kappa}_{1}$ | metal angle at leading edge |

${\kappa}_{2}$ | metal angle at trailing edge |

Setting | Comment |
---|---|

${p}_{t,entry}$, ${T}_{t,entry}$, ${\alpha}_{entry}$, $T{u}_{entry}$, $TL{S}_{entry}$ | Extracted from 3D-rotor simulation |

Operation point | Cruise, Takeoff, Touchdown |

Walls | No slip walls, hydraulically smooth |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/).

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**MDPI and ACS Style**

Kellersmann, A.; Reitz, G.; Friedrichs, J.
Sensitivity Analysis of BLISK Airfoil Wear. *Int. J. Turbomach. Propuls. Power* **2018**, *3*, 14.
https://doi.org/10.3390/ijtpp3020014

**AMA Style**

Kellersmann A, Reitz G, Friedrichs J.
Sensitivity Analysis of BLISK Airfoil Wear. *International Journal of Turbomachinery, Propulsion and Power*. 2018; 3(2):14.
https://doi.org/10.3390/ijtpp3020014

**Chicago/Turabian Style**

Kellersmann, Andreas, Gerald Reitz, and Jens Friedrichs.
2018. "Sensitivity Analysis of BLISK Airfoil Wear" *International Journal of Turbomachinery, Propulsion and Power* 3, no. 2: 14.
https://doi.org/10.3390/ijtpp3020014