# A Proper Shape of the Trailing Edge Modification to Solve a Housing Damage Problem in a Gas Turbine Power Plant

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## Abstract

**:**

_{l}and C

_{d}and the pressure ratio, including structural dynamics such as a normalized power spectrum, frequency, total deformation, equivalent stress, and the safety factor, found that 6.5 mm curved cutting could deliver the aerodynamics and structural dynamics similar to the original CB. This result also overcomes the previous work that proposed 5.0 mm straight cutting. This work also indicates that the operation of a CB gives uneven pressure and temperature, which get higher in the TE area. The slightly modified CB can present the difference in the properties of both the aerodynamics and the structural dynamics. Therefore, any modifications of the TE should be investigated for both properties simultaneously. Finally, the results from this work can be very useful information for the modification of the CB in the housing damage problem of the other rotating types of machinery in a gas turbine power plant.

## 1. Introduction

_{l}and C

_{d}) from the modifications. The results led to the conclusion that the most suitable modification was the straight cutting at 5 mm at the specific stage which caused pressure ratio alterations less than 0.2%, and the C

_{l}and C

_{d}changed less than 3.7% and 8.7%, respectively. This modification also maintained the aerodynamics at the same level as the original CB. This method has been applied to gas turbine power plants for actual usage and showed steady efficiency of the power generator, as usual. However, this simple method of cutting can be improved to prolong the lifetime of the CB and also maintain the highest efficiency. In general, the original design of the CB without the modifications should be at the optimum conditions, as the production figured the structural dynamics (SD) and AD at each circumstance into the design. These parameters have been taken into account to obtain high durability and efficiency in the generator. Computer simulation has been used in an important role to study the properties of the SD, such as structural analysis, modal analysis, thermal analysis, fatigue analysis, and AD. In the details of the SD, the structural analysis can predict the profile of stress, strain, and other factors [2,3,4,5,6,7]. For modal analysis, it has been used to figure out the natural frequency, mode shape, and total deformation, among other properties [8,9]. Thermal analysis has been applied to investigate thermal stress, thermal strain, and heat transfer [7,10]. Finally, fatigue analysis has been employed to predict the damage, life, and safety factor of the CB [11,12]. For the AD, CFD can simulate the C

_{l}, C

_{d}, pressure, vector flow, and other variables in the compressor stage [1,13,14,15,16,17]. From previous computer simulations, it has been indicated that inappropriate modifications can lead to inefficiency of the generator and also shorten its lifetime. Furthermore, in [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17], most researchers focused their study on such conditions (e.g., steady rotational speed, pressure, temperature, and flow rate). Hence, the AD study has been separated from the SD investigation, because simultaneous investigations of both the AD and the SD can be very complex and troublesome. However, various works mentioned that changes in the AD would certainly affect the SD [12,18]. In conclusion, the most suitable modification of the CB that can deliver full efficiency and sustain its level of operation requires investigations of both the AD and the SD. It is unlikely that the previous work proposed the appropriate simulation of the CB’s modification, which applied these two calculations in their work.

## 2. Theoretical Background

#### 2.1. Aerodynamics

_{tot}is the total enthalpy, which can be related to static enthalpy h(T,p) as follows:

#### 2.2. Structural Dynamics

## 3. Methodology

#### 3.1. CB Modification

#### 3.2. Models

^{+}of 1; the first layer thickness started at 1.41 × 10

^{−3}mm and had a growth rate of 1.10. The inflation created wedge and prism mesh types. After that, the mesh model of the fluid domain was examined via mesh independent analysis to achieve the suitable mesh model. This model was finally adopted to build a structural mesh model later. In the independent analysis process, the maximum size of the mesh in the fluid domain was adapted to be 28–35 mm at a growth rate of 1.15. This setting caused the total elements of the mesh in both domains to be about 7.05–9.95 million elements, with the number of nodes at 2.93–3.20 million. The C

_{l}and C

_{d}were set to be the indicators to determine a suitable mesh model. The numbers of the elements and nodes of each model are illustrated in Table 1. In Figure 4, the mesh model of (a) the fluid’s domain, (b) the interface’s domain, and (c) the solid’s domain of model A are shown. This model was processed with mesh independent analysis; hence, it already was suitable for further simulations. Please note that the mesh around the TE was defined with a higher number of elements than other areas because this TE was the area where the AD property would be investigated. For other models from B–D, they are similar to the model A except only on the numbers of elements and nodes. More details of the mesh independent analysis can be found in Supplementary Materials (Mesh_independent_analysis.pdf). The results of the C

_{l}and C

_{d}at each model exhibited differences at the third decimal places, which will be explained in Section 4.1. With the mesh independent analysis process, these indistinguishable C

_{l}and C

_{d}values expressed a confidential level of the mesh used in this simulation.

#### 3.3. Boundary Conditions and Software Settings

## 4. Results and Discussion

#### 4.1. Aerodynamics

_{l}and C

_{d}, shown in Table 5. The numbers in parentheses represent the percentage changes compared with the results of model A. The C

_{l}and C

_{d}could be altered up to 3.67% and 2.18%, respectively. It might be concluded that the modifications proposed in this work had an insignificant effect on the changes of the C

_{l}and C

_{d}. Model C led to C

_{l}and C

_{d}values more similar to those in model A than the other models, corresponding to the pressure ratio and the NPR reported in Figure 6 and Figure 7.

#### 4.2. Structural Dynamics

_{l}, C

_{d}, and pressure ratio. Moreover, considering the SD properties, such as the TD, ES, NPS, and safety factor, all models exhibited similar results. On the other hand, model B provided more unpleasant results in the AD than models C and D. In conclusion, model C was shown to be the most suitable model, considering the factor of uncomplicated modification and maintenance. Recently, this result has been applied for real use in a gas turbine power plant.

## 5. Conclusions

_{l}, C

_{d}, and normalized power spectrum similar to the original CB. This modification also presented better results than the previous 5 mm straight cutting model and the combination of the 4 mm straight cutting with 6.5 mm curve cutting model. The consistency of all pressure and temperature values from the simulations and the measurements confirmed the confidence of the work. After that, the results of the AD were taken into account for the structural calculations, such as the structural analysis, harmonic response analysis, thermal analysis, and fatigue analysis using ANSYS structural analysis. The simulations revealed the increase of the pressure and temperature from the boundary conditions, especially at the upper edge of the CB. Therefore, in any modifications to the design and development of rotating machinery, the trailing edge area and upper edge should be investigated for both their AD and SD properties simultaneously. Then, the pressure from the aerodynamics calculations were used with a FFT and harmonic response analysis. The calculations found that the modifications had an insignificant influence on the harmonic frequency, total deformation, and equivalent stress. Then, the results from the AD were transferred to the thermal analysis and fatigue analysis. The results showed that the modification did not affect the SD properties, such as the total deformation, equivalent stress, and safety factor. A proper model with 6.5 mm curve cutting was proposed to be the most suitable model to be applied to actual modifications in the factory. This model has been proven to be the solution for the housing damage problem.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

$i,\text{}j$ | 1, 2, and 3 correspond to x, y, and z, respectively |

AD | aerodynamics |

${\omega}_{f}$ | angular frequency (rad/s) |

${F}_{1}$ | blending function |

${\mu}_{t}$ | eddy viscosity (m^{2}/s) |

$\rho $ | density (kg/m^{3}) |

$\left\{F\right\}$ | load vector (N) |

$\overrightarrow{U}$ | mean velocity (m/s) |

$\mu $ | molecular dynamics viscosity (Pa s) |

$\left\{\ddot{u}\right\}$ | nodal displacement vector (m) |

$\left\{u\right\}$ | nodal displacement vector (m) |

$\left\{\dot{u}\right\}$ | nodal velocity vector (m/s) |

$p$ | pressure (Pa) |

${P}_{k}$ | shear production of turbulence |

${\overrightarrow{S}}_{E}$ | source term of energy (N/m^{2} s) |

${\overrightarrow{S}}_{M}$ | source term of momentum (N/m^{3}) |

$\alpha ,\text{}\beta ,\text{}\sigma $ | specific coefficient for SST k-ω |

$\omega $ | specific dissipation rate (1/s) |

$\tau $ | stress tensor (Pa) |

$\left[C\right]$ | structural damping matrix (N s/m) |

SD | structural dynamics |

$\left[M\right]$ | structural mass matrix (kg) |

$\left[K\right]$ | structural stiffness matrix (N/m) |

$T$ | temperature ($\xb0\mathrm{C}$) |

$\left[K\left(T\right)\right]$ | thermal conduction matrix (W/$\xb0\mathrm{C}$) |

$\lambda $ | thermal conductivity (W/m K) |

$\left\{Q(T)\right\}$ | thermal conduction vector (W) |

${h}_{tot}$ | total enthalpy (J) |

$k$ | turbulent kinetic energy (J/kg) |

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**Figure 1.**Housing damage on the compressor blades in a gas turbine power plant [1]. Copyright 2019 MDPI.

**Figure 3.**Solid model of the compressor blade in stage 7 from the gas turbine power plant, showing (

**a**) the original design, (

**b**) 5.0 mm straight cutting, (

**c**) 6.5 mm curve cutting, and (

**d**) 4.0 mm straight cutting with 6.5 mm curve cutting.

**Figure 4.**Mesh model of the (

**a**) fluid’s domain, (

**b**) interface’s domain, and (

**c**) solid’s domain of model A.

**Figure 5.**Boundary conditions. The positions of each blade and the observation’s plan in the calculation show the (gray) stator, (blue) rotor, and (yellow) investigating plane.

**Figure 7.**Plots of the normalized pressure ratio compared to blade spans of (

**a**) 95.5%, (

**b**) 95.8%, (

**c**) 96.0%, and (

**d**) 96.5%.

**Figure 8.**Distribution of the (

**a**) pressure load and (

**b**) temperature load of model A, calculated from the AD and the boundary conditions.

**Figure 9.**Plots of the (

**a**) pressure load in the time domain and (

**b**) NPS after the FFT and normalized by the maximum pressure.

**Figure 10.**Total deformation on the trailing edge of (

**a**) model A, (

**b**) model B, (

**c**) model C, and (

**d**) model D at a 50 Hz frequency using harmonic response analysis calculation.

**Figure 11.**(

**a**) Total deformation (TD) and (

**b**) equivalent (von Mises) stress with and without pressure and temperature loads.

**Figure 12.**Total deformation on the trailing edge of (

**a**) model A, (

**b**) model B, (

**c**) model C, and (

**d**) model D, considering only the trailing edge area.

**Figure 14.**Safety factor on the trailing edge of (

**a**) model A, (

**b**) model B, (

**c**) model C, and (

**d**) model D.

**Table 1.**Numbers of elements and nodes of each model after the mesh independent analysis (MIA) process.

Model | Fluid Domain | Solid Domain | Total | |||
---|---|---|---|---|---|---|

Element | Node | Element | Node | Element | Node | |

A | 7,223,803 | 2,355,794 | 568,389 | 856,710 | 7,792,192 | 3,212,504 |

B | 8,484,301 | 2,919,733 | 598,095 | 901,796 | 9,082,396 | 3,821,529 |

C | 9,068,565 | 3,122,478 | 546,224 | 823,878 | 9,614,789 | 3,946,356 |

D | 7,059,840 | 2,315,809 | 555,843 | 839,031 | 7,615,683 | 3,154,840 |

Numerical Parameters | Setting |
---|---|

Solvers | Pressure-based |

Spatial Discretization | High-resolution scheme for the advection term |

High-resolution scheme for turbulence quantities | |

Convergence Control | Maximum Iteration 1000 |

Convergence Criteria | 1.0 × 10^{−4} |

Time Scale Control | Auto Timescale |

Length Scale Option | Conservative |

Time Scale Factor | Auto Timescale |

Fluid | Air Ideal Gas |

Heat Transfer | Total Energy |

Turbulence | SST k-ω |

Wall Function | High-speed (compressible) wall heat transfer model |

Transient Blade Row Model | Profile Transformation |

Frame Change or Mixing Model | Transient Rotor Stator |

Pitch Change | Automatic |

Property | Value |
---|---|

Density | 7805 kg/m^{3} |

Poisson’s Ratio | 0.195 |

Shear Modulus | 79,300 MPa |

Young’s Modulus | 1.896 × 105 MPa |

Bulk Modulus | 1.037 × 105 MPa |

Tensile Yield Strength | 1000 MPa |

Tensile Ultimate Strength | 1580 MPa |

Thermal Conductivity | |

100 °C | 23.9 W/m·°C |

350 °C | 26.0 W/m·°C |

Coefficient of Thermal Expansion | |

100 °C | 1.120 × 105 °C^{−1} |

350 °C | 1.147 × 105 °C^{−1} |

S-N Curve | 422 Stainless Steel [28] |

Parameter | Measurement | Simulation | Error |
---|---|---|---|

Pressure | 570,000 ± 15% Pa | 619,909 Pa | 8.76% |

Temperature | 197.0 ± 10% °C | 199.3 °C | 1.17% |

Model or Parameter | F_{z} (N) | F_{y} (N) | Area (m^{2}) | C_{l} | C_{d} |
---|---|---|---|---|---|

A | 762.945 | 712.282 | 0.0415014 | 0.245 | 0.229 |

B | 740.563 | 702.746 | 0.0414735 | 0.234 (−3.67%) | 0.227 (−0.87%) |

C | 744.547 | 701.989 | 0.0414946 | 0.240 (−2.04%) | 0.226 (−1.31%) |

D | 766.729 | 717.477 | 0.0414903 | 0.250 (+2.04%) | 0.234 (+2.18%) |

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**MDPI and ACS Style**

Jansaengsuk, T.; Kaewbumrung, M.; Busayaporn, W.; Thongsri, J.
A Proper Shape of the Trailing Edge Modification to Solve a Housing Damage Problem in a Gas Turbine Power Plant. *Processes* **2021**, *9*, 705.
https://doi.org/10.3390/pr9040705

**AMA Style**

Jansaengsuk T, Kaewbumrung M, Busayaporn W, Thongsri J.
A Proper Shape of the Trailing Edge Modification to Solve a Housing Damage Problem in a Gas Turbine Power Plant. *Processes*. 2021; 9(4):705.
https://doi.org/10.3390/pr9040705

**Chicago/Turabian Style**

Jansaengsuk, Thodsaphon, Mongkol Kaewbumrung, Wutthikrai Busayaporn, and Jatuporn Thongsri.
2021. "A Proper Shape of the Trailing Edge Modification to Solve a Housing Damage Problem in a Gas Turbine Power Plant" *Processes* 9, no. 4: 705.
https://doi.org/10.3390/pr9040705