# Research on a Method for Online Damage Evaluation of Turbine Blades in a Gas Turbine Based on Operating Conditions

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Blade Damage Evaluation Model

#### 2.1. Gas Turbine Performance Model

#### 2.2. The Load Calculation Model Based on the Surrogate Model

_{1}. When σ

_{1}> 0, the hazardous zone is subjected to tensile stress, and when σ

_{1}< 0, the hazardous zone is subjected to compressive stress.

#### 2.3. Updated Online Cycle Counting Based on the Four-Point Rainflow Counting Method

#### 2.3.1. Temperature Counting

_{k}, T

_{k+1}, and T

_{k+2}, if (T

_{k+1}− T

_{k})(T

_{k+2}− T

_{k+1}) < 0, then T

_{k+1}is considered as an extreme value point, and it should be stored in the extremum buffer. On the other hand, if (T

_{k+1}− T

_{k})(T

_{k+2}− T

_{k+1}) > 0, then T

_{k+1}is not an extreme value point and should be excluded from further consideration. At the same time, the rainflow counting method based on four points requires at least four extreme values before determining the cycle type. Let us assume that the four consecutive extreme values retrieved from the extremum buffer are T

_{1}, T

_{2}, T

_{3}, and T

_{4}. We can calculate the differences as follows: ΔT

_{1}= |T

_{1}− T

_{2}|, ΔT

_{2}= |T

_{2}− T

_{3}|, and ΔT

_{3}= |T

_{3}− T

_{4}|. If ΔT

_{2}< ΔT

_{1}and ΔT

_{2}< ΔT

_{3}, then it is considered as a full cycle. Otherwise, it is considered as a half cycle and ΔT

_{1}represents the half cycle. This study refers to the references by GopiReddy [31,32] on the rainflow counting method for online evaluation of creep damage, where the relationship between load information and load duration in the case of full cycles is proposed. This study introduces the concepts of cycle start time t

_{T,begin}, cycle end time t

_{T,end}, and cycle duration t

_{T,hold}when considering full cycles. The calculation formulas are as follows:

_{T,begin}= t

_{2}

_{T,hold}= t

_{T,end}− t

_{T,begin}

_{1}, t

_{2}, t

_{3}, and t

_{4}represents the time corresponding to T

_{1}, T

_{2}, T

_{3}, and T

_{4}respectively.

_{T,begin}= t

_{1}

_{T,end}= t

_{2}

_{T,hold}= t

_{T,end}− t

_{T,begin}

#### 2.3.2. Stress Counting

_{a}, and plastic strain value ε

_{pa}corresponding to the latest time point t. The peak identification process is similar to temperature counting in nature. The purpose of removing invalid amplitudes is to eliminate insignificant fluctuations in damage accumulation. The determination of invalid amplitudes requires a threshold value H to be defined. This threshold value H is influenced by multiple variables such as gas turbine structure, operating speed, output power, etc. The value of H varies under different conditions. It should be noted that the determination of the threshold value H does not affect the method proposed in this study.

_{max}= max(σ

_{2}, σ

_{3}), the stress amplitude is calculated as σ

_{a}= (|σ

_{2}− σ

_{3}|)/2, the mean stress is determined as σ

_{m}= (σ

_{2}+ σ

_{3})/2, and the cycle count is incremented by 1. The points σ

_{2}and σ

_{3}are removed, while σ

_{1}and σ

_{4}are retained. The process then continues by reading a new incoming data point and restarting the identification process. The relationship between the loaded information and the loaded time during the reference temperature counting is considered, leading to the introduction of the concepts of cycle start time t

_{σ,begin}, cycle end time t

_{σ,end}, and cycle duration t

_{σ,hold}specifically for full cycles. These concepts are illustrated in Figure 7, and their calculation expressions are as follows:

_{σ,begin}= t

_{2}

_{σ,hold}= t

_{σ,end}− t

_{σ,begin}

_{1}, t

_{2}, t

_{3}, and t

_{4}represents the time corresponding to σ

_{1}, σ

_{2}, σ

_{3}, and σ

_{4}respectively.

_{max}= max(σ

_{1}, σ

_{2}), the stress amplitude is calculated as σ

_{a}= (|σ

_{1}− σ

_{2}|)/2, the mean stress is determined as σ

_{m}= (σ

_{1}+ σ

_{2})/2, and the cycle count is incremented by 0.5. The point σ

_{1}is removed, while σ

_{2}, σ

_{3}, and σ

_{4}are retained. The process then continues by reading a new incoming data point and restarting the identification process. The calculation formula for the time information of the cycle in this case is as follows:

_{σ,begin}= t

_{1}

_{σ,end}= t

_{2}

_{σ,hold}= t

_{σ,end}− t

_{σ,begin}

_{e}represents the characteristic temperature of the identified cycle.

_{pa}= ε

_{pa,end}− ε

_{pa,begin}

_{a}= ε

_{a,end}− ε

_{a,begin}

_{pa,end}represents the plastic strain at the end of the cycle, ε

_{pa,begin}represents the plastic strain at the beginning of the cycle, Δε

_{pa}denotes the range of plastic strain identified in the cycle, ε

_{a,end}represents the total strain at the end of the cycle, ε

_{a,begin}represents the total strain at the beginning of the cycle, and Δε

_{a}denotes the range of total strain identified in the cycle.

#### 2.4. Creep–Fatigue Damage Evaluation Model

#### 2.4.1. Creep Damage Evaluation Model

_{r}is stress rupture time or time to failure, T is the blade material temperature, $\mathsf{\sigma}$ is the stress at the corresponding zone, C is the material constant, and L is the Larson–Miller parameter (LMP).

_{T,hold}to t

_{r}is used to quantify creep damage. The total creep damage is calculated by linearly summing up the creep damage for each cycle based on the Miner linear damage rule [34]. The representation is as follows:

_{c}represents the total creep damage.

#### 2.4.2. Fatigue Damage Evaluation Model

_{a}, σ

_{max}, and temperature fluctuations for damage evaluation. The representation of the SWT model [18] is as follows:

_{pa}, ∆ε

_{a}, and σ

_{max}on cyclic damage. Furthermore, the model introduces a function f(T) to describe the effect of temperature variation on fatigue life. The form of the temperature correction term in the new model and the validation of its accuracy were previously completed in prior work. It is represented as follows:

_{1}~n

_{3}are undetermined constants.

_{f}represents the total fatigue damage, n represents the number of cycles for the i-th cycle, and C(i) is a constant used to determine the type of the i-th cycle, which takes the value of 1 for a full cycle and 0.5 for a half cycle.

#### 2.4.3. Creep–Fatigue Interaction Damage Evaluation Model

## 3. Experiment and Discussion

_{m}for temperature counting is set at 450 °C. The data in Figure 16 are sampled every second. The updated cycle counting method based on the four-point online rainflow counting method is used in this study to perform cycle counting on the inflow load information. By applying the obtained real-time temperature spectrum and stress spectrum to the damage evaluation model, the fatigue damage D

_{f}of the micro turbine stationary blade during the process is calculated as 1.3065 × 10

^{−4}, and the creep damage D

_{c}is calculated as 1.6303 × 10

^{−4}. In this study, a bilinear criterion is temporarily established to evaluate the interaction between the two types of damage, as shown in Figure 17. It should be noted that the provided lifetime criterion in this study is hypothetical. To determine an accurate lifetime criterion, relevant experiments need to be conducted.

_{start}[N

_{start}+ C

_{load change}N

_{load change}+ C

_{trip}N

_{trip}] + C

_{stress}C

_{fuel}Time

_{start}is the start-up weighting factor, N

_{start}is the start-up count, C

_{load change}is the load change weighting factor, N

_{load change}is the load change count, C

_{trip}is the trip weighting factor, N

_{trip}is the trip count, C

_{stress}is the stress weighting factor, C

_{fuel}is the fuel weighting factor, Time is the actual operating hours.

_{OEM}to the micro gas turbine stationary blade is calculated as 4.475 × 10

^{−4}. The OEM’s recommended value is slightly higher than the calculated results of this model, possibly because the OEM considers erosion, abrasion, oxidation corrosion, or other damage mechanisms when calculating the damage to the blade.

## 4. Conclusions

- When obtaining blade load information based on gas turbine operating parameters, the new model utilizes a surrogate model instead of the traditional physics-based model. This improves the accuracy of blade load calculations and ensures real-time performance. However, the variable operating conditions, uncertain start/stop modes, and component degradation in gas turbines can all affect the blade load distribution. Incorporating these factors to build more complex surrogate models will be performed in our subsequent work.
- Regarding the online cycle counting method, the new model enhanced the conventional four-point online rainflow counting method to accommodate the counting of results from elastic–plastic analyses. Moreover, the inclusion of time information during cycle counting allows for the precise recording of load fluctuations, thereby providing accurate input conditions for a subsequent damage assessment. In addition, the online cycle counting method and damage evaluation model complement each other. Designing corresponding characteristic tests for different materials and finding the relationship between load conditions and their damage evolution can also improve the accuracy of the entire model.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

OEM | original equipment manufacturer |

EOH | equivalent operating hours |

LSTM | long short-term memory |

CFD | computational fluid dynamics |

FEA | finite element analysis |

T | temperature |

T_{m} | melting point temperature |

${T}_{\mathrm{mean}}^{\mathrm{e}}$ | equivalent mean temperature |

${\mathrm{S}}_{\mathsf{\sigma}-\mathrm{t}}$ | the area of the polygon in the σ−t diagram |

t_{r} | stress rupture time |

$L\left(\mathsf{\sigma}\right)$ | Larson–Miller parameter |

T_{e} | characteristic temperature |

t | time |

H | threshold for invalid cycle determination |

$E$ | elastic modulus |

${N}_{\mathrm{f}}$ | fatigue cycle count |

${D}_{\mathrm{f}}$ | fatigue damage |

D_{c} | creep damage |

${D}_{\mathrm{O}\mathrm{E}\mathrm{M}}$ | damage recommended by the OEM |

Greek letters | |

${\sigma}_{\mathrm{e}}$ | characteristic stress of the identified cycle |

${\sigma}_{\mathrm{max}}$ | maximum stress |

${\sigma}_{\mathrm{min}}$ | minimum stress |

${\sigma}_{\mathrm{a}}$ | stress amplitude |

${\sigma}_{\mathrm{m}}$ | mean stress |

ε_{pa} | plastic strain |

ε_{a} | total strain |

Δ | range |

Subscripts | |

T | temperature counting |

$\mathsf{\sigma}$ | stress counting |

begin | cycle start time |

end | cycle end time |

hold | cycle duration |

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**Figure 13.**The (

**a**) temperature, (

**b**) equivalent plastic strain, (

**c**) equivalent total strain, and (

**d**) equivalent stress distribution of a certain transient point at steady state.

**Figure 14.**The maximum principal stress distribution of a certain transient point at (

**a**) cold start, (

**b**) steady state, and (

**c**) shutdown.

**Figure 15.**Comparison between simulation results and surrogate model results: (

**a**) temperature, (

**b**) equivalent plastic strain, (

**c**) equivalent total strain, and (

**d**) equivalent stress.

**Figure 16.**The load information of the turbine stationary blade in the hazardous zone throughout the entire “cold start-steady state-shutdown” process: (

**a**) stress and temperature and (

**b**) total strain and plastic strain.

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

Power generation/MW | 2 |

Power generation efficiency/% | 25.7 |

Pressure ratio | 7.5 |

Exhaust flow rate/(Kg/s) | 10.1 |

Turbine inlet temperature/K | 1223 |

Exhaust temperature/K | 803 |

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## Share and Cite

**MDPI and ACS Style**

Zhu, H.; Zhu, Y.; Zhang, X.; Chen, J.; Luo, M.; Huang, W.
Research on a Method for Online Damage Evaluation of Turbine Blades in a Gas Turbine Based on Operating Conditions. *Aerospace* **2023**, *10*, 966.
https://doi.org/10.3390/aerospace10110966

**AMA Style**

Zhu H, Zhu Y, Zhang X, Chen J, Luo M, Huang W.
Research on a Method for Online Damage Evaluation of Turbine Blades in a Gas Turbine Based on Operating Conditions. *Aerospace*. 2023; 10(11):966.
https://doi.org/10.3390/aerospace10110966

**Chicago/Turabian Style**

Zhu, Hongxin, Yimin Zhu, Xiaoyi Zhang, Jian Chen, Mingyu Luo, and Weiguang Huang.
2023. "Research on a Method for Online Damage Evaluation of Turbine Blades in a Gas Turbine Based on Operating Conditions" *Aerospace* 10, no. 11: 966.
https://doi.org/10.3390/aerospace10110966