# Thermomechanical stress analysis for gas turbine blade with cooling structures

Multidiscipline Modeling in Materials and Structures

ISSN: 1573-6105

Publication date: 3 December 2018

## Abstract

### Purpose

Blade tip clearance has always been a concern for the gas turbine design and control. The numerical analysis of tip clearance is based on the turbine components displacement. The purpose of this paper is to investigate the thermal and mechanical effects on a real cooling blade rather than the simplified model.

### Design/methodology/approach

The coupled fluid-solid method is used. The thermal analysis involves solid and fluid domains. The distributions of blade temperature, stress and displacement have been calculated numerically under real turbine operating conditions.

### Findings

Temperature contour can provide a reference for stress analysis. The results show that temperature gradient is the main source of solid stress and radial displacement. Compared with thermal or mechanical effect, there is a great change of stress magnitude for the thermomechanical effect. Large stress gradients are found between the leading and trailing edge of turbine cooling blade. Also, the blade radial displacement is mainly attributed to the thermal load rather than the centrifugal force. The analysis of the practical three-dimensional model has achieved the more precise results.

### Originality/value

It is significant for clearance design and life prediction.

## Keywords

#### Citation

Tong, F., Gou, W., Li, L., Gao, W. and Feng Yue, Z. (2018), "Thermomechanical stress analysis for gas turbine blade with cooling structures", *Multidiscipline Modeling in Materials and Structures*, Vol. 14 No. 4, pp. 722-734. https://doi.org/10.1108/MMMS-08-2017-0081

### Publisher

:Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

## 1. Introduction

Blade tip clearance is changeable during the engine working process. In different conditions, the turbine components deformations under all kinds of loads are distinct. The existence of tip clearance leads to numerous sources of loss, especially the tip leakage loss. The influence of tip clearance is always a focus for engineers and scientists. It has been considered that the variations of blade tip clearance value have a great influence on the tip leakage flow and turbine efficiency (Papa *et al.*, 2002; Sang *et al.*, 2009; Schabowski *et al.*, 2014; Lavagnoli *et al.*, 2016; Cho *et al.*, 2017; Vikram *et al.*, 2017; Lee and Joo, 2017; Tong *et al.*, 2015). Ma *et al.* (2011) have studied that the tip clearance value with 0.2 mm increase leads to the increase in fuel consumption by 0.3 percent. For the higher engine efficiency, the smaller value should be devised. Meanwhile, the clearance value cannot be too small for preventing the touch between the rotor blade and stator case. Thus, the reliable measurement and precise prediction for tip clearance are essential.

On the one hand, there are lots of mature applications for turbine tip clearance measurement. The sensor type is a common means to estimate the tip clearance, especially capacitance sensor (Sarma and Barranger, 1992; Sheard and Kiileen, 1994; Sheard, 2011). Drumm and Haase (2000) and Fabian *et al.* (2002) have studied that the complex engine environment is a trouble for the capacitance sensor system. Then the researchers have devised the fiber optic sensor, which is used for measuring the blade movement. It has been found that the fiber optic sensor needs clean cases and it is not feasible for the engine system (Cao *et al.*, 2006; Jia and Zhang, 2011; Gil-Garcia *et al.*, 2015). For a more practical application, eddy current sensor has been proposed. It can avoid the above problems and achieve accurate blade tip timing data (Mandache *et al.*, 2012; Cardwell *et al.*, 2008). However, the blade tip clearance measurement is complex and hard to be installed. The repair work will incur a lot of cost.

On the other hand, the numerical analysis has been used for predicting the turbine components variations. In the beginning, the reduced order clearance model has been established, which is based on the deformation of turbine interacting parts. And the tip clearance change has been observed by these simplified models (Kypuros and Melcher, 2003; Melcher and Kypuros, 2003; Nielsen and Moll, 2004; Fei *et al.*, 2013; Teng *et al.*, 2016). Agarwal *et al.* (2008) have developed a reduced order model to predict the tip clearance change. The average growths of turbine components have been obtained by a lumped model approximation. They have concluded that the numerical calculation can be used for tip clearance preliminary design and operational displacement analysis.

At present, two-dimensional finite element models are widely applied to calculate turbine section growth. The numerical methods are the empirical formulas based on a lot of experiments and the engine mission (Peng *et al.*, 2013; Bozzi *et al.*, 2012). Then the simplified models predict the change of blade tip clearance by deflection data (Roth *et al.*, 2005). To characterize each component movement accurately, the researchers put forward three-dimensional finite element models. Fang *et al.* (2012) have investigated the radial displacement under the thermal and centrifugal loads. The simulation has been carried out by a simplified three-dimensional blade model. The inner cooling structures have been predigested. The results have shown that the thermal load is the main cause of the blade radial movement. However, there are some differences between the simplified models and the actual turbine parts. The results of the simplified models can influence the tip clearance control.

Accordingly, accurate evaluations of high-pressure turbine components (hub, blade, and shroud) radial displacements play a significant role in the tip clearance design. The thermal load is an important factor for the running clearance. Therefore, the main work in this paper is to model and validate the high-pressure turbine blade radial displacement due to thermal load. The investigation of high-pressure turbine blade variation is divided into two parts: the thermal analysis by computational fluid dynamics software of ANSYS CFX and the displacement calculation by computational solid dynamics software of ABAQUS.

The outstanding advantage of this work is the adoption of practical three-dimensional blade model. The numerical results are more accurate for the running clearance design than those of the simplified models. Moreover, the data of high-pressure turbine blade temperature, stress and movement can provide a fundament for blade structure layout and life prediction.

## 2. Numerical method

### 2.1 Geometry model

A schematic of computational domains is given in Figure 1. As shown, there are solid domain and fluid domain. The internal cooling structures of rotor blade include serpentine passages and pin-fin cooling, which provide the good cooling effect. Also, the tip shroud construction can improve its stiffness. This three-dimensional blade is modeled by UG software. Compared with the two-dimensional finite element and reduced models (Fang *et al.*, 2012), the analysis of an actual three-dimensional model in this paper will achieve more accurate results. Moreover, the blade thermal analysis is not the heat transfer coefficient formulas but the solid-fluid solution which is a finite volume research of solid and fluid domains. The fluid domain consists of two parts, the inner cooling air flow and the outer hot gas flow. The cooling air circulates through the blade inner cooling channels, and the hot gas mainstream flows around the turbine blade.

### 2.2 Computational approach

In order to discuss the change of blade tip clearance under the real engine mission, the thermal-structural coupling analysis is performed. The simulation is divided into two main processes: the first step is a finite volume solution which is the computational fluid dynamics analysis, and the second step is a finite element solution which is the computational solid dynamics analysis. The results of computational fluid dynamics analysis are loaded on the finite element solution as a boundary condition.

#### 2.2.1 Thermal analysis

The computational fluid dynamics analysis has been performed by ANSYS CFX v.14 in this study. The solutions for finite volume are solved by the compressible Renolds-averaged Navier-Stokes equations. There are many kinds of turbulence models with corresponding equations. According to real turbine operating conditions and Menter’s original papers (Menter, 1992, 1994, 2009), the Shear Stress Transport model is selected. It can render a better simulation for the solid-fluid coupling solution. And for the mesh of the computational models, the unstructured mesh has been set. The type of elements is mainly the tetrahedral grid. The max element of the global seed size is 5.0. The max mesh size of the minor structures, e.g., film holes and pin fins, is 0.3. Also, the prism grids have been meshed for the fluid domain. The first mesh height is 0.01 and the layers number is 15, which ensure that the wall grid yplus is less than 1.0 for the Shear Stress Transport model. The medium turbulence intensity of 5 percent is used for the inlet boundary. The solution is considered to be converged when the maximum residual is on the order of 10^{−5}, which typically requires between 500 and 1,000 iterations.

There are three different turbine operating conditions to investigate the blade radial variation of thermal and centrifugal effects. For the mainstream, the inlet total temperatures and pressures are set, and the total pressures are provided. The boundary condition of coolant inlet is set by mass flow. For the rotor blade, a rotational speed is simulated as the centrifugal load in the different operating stage. Three cases, 100 percent (Case 1), 95 percent (Case 2) and 91 percent (Case 3) of the maximum rotational speed, are calculated. The thermal analysis can acquire blade heat transfer characteristics, which is loaded as a thermal effect on the finite element of the second structural analysis.

#### 2.2.2 Structural analysis

The commercial program ABAQUS has been used for the computational solid dynamics analysis. Because of the blade temperature gradient, finite element simulation should consider both the thermal and elastic effects. The blade material is K444. The material parameters in different temperature status are given, for example, elastic modulus, conductivity, expansion and so on. The type of grid elements is C3D10. The element shape is Tetrahedron, and the technique is free. The approximate global size is 0.001. The structural boundary is divided into several parts, including the displacement restriction and load steps. At the bottom of blade rabbet, there are several nodes fixed by *x*, *y*, *z* directions displacement. The blade platform and tip shroud are restricted by periodic symmetry. The angular velocity around the rotational axis is loaded as a centrifugal effect on all blade nodes. In order to discuss the thermal effect, it needs to create the predefined temperature field on the whole blade. The heat transfer results of the thermal analysis are interpolated on the finite element nodes by Fortran codes.

The purpose of stress simulation is to validate the thermal and centrifugal effects on the rotor blade. The computational solid dynamics analysis can achieve the radial movement and the stress contour. The critical region will be concluded. Therefore, these results are the bases of tip clearance control and blade cooling design.

#### 2.2.3 Temperature validation

Blade temperature contours represent the measurement of heat transfer process. In order to get a better review of numerical research, three different blade cross sections along the blade span are located, Figure 2. Planes *a*, *b* and *c* represent the tip, mid height and base region of the blade, respectively.

Temperature contours in three planes for different cases are shown in Figures 3-5. The blade temperature is the highest for Case 1, and it is the lowest for Case 3, which are corresponding to the real turbine conditions. Obviously, there is a vigorous temperature change across the blade pressure side and suction side. Blade inner channel temperature is lower than that of the other parts, and high temperature region is located at the blade trailing edge. All measurements are consistent with the cooling manner and flow pattern. The inner cooling structures make a better coolant effect on the inner channel, and the mixing flow between cooling air and hot gas reduces the coolant effect on the trailing edge.

## 3. Results and discussion

According to the research works of Fang *et al.* (2012) and Liu and Fang (2011), blade stress and radial displacement distributions are analyzed in this study. And the above blade temperature contours can provide a basis for the structural analysis. In order to get a better review of the numerical results, three different blade cross sections along the blade span are located, Figure 2. Planes *a*, *b* and *c* represent the tip, mid height and base region of the blade, respectively. Hence, the results of blade radial displacement between a simplified model (Fang *et al.*, 2012; Liu and Fang, 2011) and three-dimensional cooling blade are contrasted under thermal or/and mechanical effect.

### 3.1 Thermal analysis

The blade temperature generates strain in the material, which is the source of thermal stress. The stress distributions under heat transfer process are shown, Figures 6-8, corresponding to the temperature distributions of Figures 3-5. The thermal stress changes along the blade span are similar for Case 1-3. The maximum stresses appear in the plane *a*, near the tip of blade. And the blade middle section distributes the low-stress magnitude.

As shown, the thermal stress is changing along the blade radial direction. The main cause is the temperature gradient in blade material. Because of the coolant effects on the tip shroud and blade basis, the thermal gradients near planes *a* and *c* are bigger than those around the middle section of blade span. Moreover, the structure pattern also has an impact on the stress variation. The construction form near plane *a* is simple, which declines the constraint. The discontinuous material around the trailing edge is a better illustration. The temperature gradient and structure style effects cause the maximum stress magnitudes in plane *a*.

Blade temperature generates strain in all directions, and thermal stress is changing along the blade span. According to Hook’s law, material parameters have a great influence on solid strain or deformation rate which is a linear relationship with thermal stress. The results of blade radial displacement under thermal effect are listed in Table I. By comparing the blade radial displacement results between simplified model and actual cooling model, it is observed that the thermal blade radial displacement of the cooling model is smaller than that of a simplified model. The difference is attributed to the temperature gradient. The research of simplified model is loading the thermal boundary on the blade area components, which are established by Hypermesh software. However, every node temperature and stress is distinct and the numerical method of area component is not precise for the thermal analysis that leads to larger blade radial displacement.

### 3.2 Mechanical analysis

The numerical stresses at different rotational speeds have been investigated in this study. The results of blade cross section are given, Figures 9-11. Under the action of rotation, the solid material stress is mainly caused by mechanical force. The solid mass, rotational radius and speed have a direct impact on the centrifugal load. For three different operating conditions, the value of mechanical stress gradually decreases from the blade basis to the tip region.

As noticed, the minimum stresses are located at the tip section of plane *a*, and the basis location at plane *c* distributes the maximum stresses. The difference for this stress change is attributed to the centrifugal force. It is obviously found that the solid mass is a main factor on the mechanical stress, which is in correspondence with plane *c*. By comparing the results of the thermal and mechanical stress, the stress magnitude produced by thermal effect is much larger. That is, centrifugal force plays a small role in the blade stress distribution.

In the only rotation condition, solid material displacement is due to mechanical stress. And centrifugal force is the main source of stress. The blade radial displacements under mechanical effect for two numerical models are listed in Table II. In contrast with the thermal case, the blade radial displacement of the cooling model is larger than that of the simplified model. Obviously, there is a larger solid mass of actual cooling blade which produces greater mechanical stress.

### 3.3 Thermomechanical analysis

During the turbine operating process, rotor blade is loading both the thermal and centrifugal effect. Hence, the solid temperature and rotation influence the material stress. The results of thermomechanical stress are illustrated in Figures 12-14. The stress distributions for different conditions are similar. There is the smallest thermomechanical stress at the middle height of the blade span. And the maximum stress magnitude is located in blade tip region around trailing edge.

By comparing three kinds of stress distributions, thermomechanical stress magnitude is slightly larger than that produced thermally and thermal stress is on an average three times larger than the mechanical one. It is founded that the blade stress is mainly redounded to temperature gradient rather than centrifugal force. However, the larger stress changes between leading edge and trailing edge of the blade are caused by thermomechanical source, which may lead to the blade crack, especially in the cooling channels near plane *c*. It is concluded that the blade basis is the critical region and it is a focus of the blade life design. In addition, blade tip region distributes maximum thermomechanical stresses, corresponding to the thermal condition. The reason for this stress change is tip leakage flow from the pressure side to suction side, which makes a complex flow around trailing edge. And it intensified convective heat transfer process.

By considering the thermal-structure coupled analysis, the results of blade radial displacement are shown, Table III. The difference in the thermomechanical effect between the simplified model and the cooling model is similar to the thermal one, and it demonstrates that temperature gradient is the main source of blade stress. Furthermore, by comparing Tables I-III, mechanical blade radial displacement is almost one order smaller than the other two conditions. And the blade radial displacement values under thermomechanical effect are larger than the sum of thermal and mechanical blade radial displacement. It is concluded that the combined temperature and rotation effect causes the larger solid stress.

## 4. Conclusion

The actual blade with the cooling passages and structures has been calculated numerically. The blade temperature, stress and radial displacement under three different turbine operating conditions are analyzed by the fluid-solid coupling method. For the results of material stress and displacement, the thermal or/and mechanical effects are considered respectively. And the conclusions are as follows:

The consideration of blade cooling structures obtains a more practical blade heat transfer characteristic. And the computational fluid dynamics method is more beneficial for the heat transfer analysis than the third kind thermal boundary.

The thermomechanical analysis shows that the thermal-structural coupling effect is more severe than the sum of thermal and mechanical loads, and the temperature gradient has a direct impact on the blade critical section.

The heat transfer and thermomechanical analysis provide the foundation for the blade design, which can extend the engine service life effectively.

## Figures

Blade radial displacement under thermal effect

Case 1 | Case 2 | Case 3 | |
---|---|---|---|

Blade radial displacement of simplified model/mm (Liu and Fang, 2011) | 1.42 | 1.31 | 1.27 |

Blade radial displacement of cooling model/mm | 1.40 | 1.30 | 1.24 |

Difference/% | −1.41 | −0.76 | −2.36 |

Blade radial displacement under mechanical effect

Case 1 | Case 2 | Case 3 | |
---|---|---|---|

Blade radial displacement of simplified model/mm (Liu and Fang, 2011) | 0.165 | 0.150 | 0.139 |

Blade radial displacement of cooling model/mm | 0.172 | 0.156 | 0.144 |

Difference/% | +4.07 | +3.85 | +3.47 |

Blade radial displacement under thermomechanical effect

Case 1 | Case 2 | Case 3 | |
---|---|---|---|

Blade radial displacement of simplified model/mm (Liu and Fang, 2011) | 1.62 | 1.52 | 1.42 |

Blade radial displacement of cooling model/mm | 1.59 | 1.50 | 1.41 |

Difference/% | −1.85 | −1.32 | −0.70 |

## References

Agarwal, H., Akkaram, S., Shetye, S. and McCallum, A. (2008), “Reduced order clearance models for gas turbine applications”, 49th AIAA/ASME/ASCE/AHS/ASC/Structures, Structural Dynamics, and Materials Conference, pp. 1-7.

Bozzi, L., Perrone, A. and Giacobone, L. (2012), “Procedure for calculation of component thermal loads for running clearances of heavy-duty gas turbines”, Proceedings of ASME Turbo Expo, Vol. 4 No. 68184, pp. 1863-1875.

Cao, S.Z., Duan, F.J. and Zhang, Y.G. (2006), “Measurement of rotating blade tip clearance with fibre-optic probe”, Journal of Physics: Conference Series, Vol. 48 No. 1, pp. 873-877.

Cardwell, D.N., Chana, K.S. and Russhard, P. (2008), “The use of eddy current sensors for the measurement of rotor blade tip timing: sensor development and engine testing”, Proceedings of ASME Turbo Expo 2008: Power of Land, Sea and Air, Vol. 2 No. 50792, pp. 179-189.

Cho, S.Y., Cho, C.H. and Choi, S.K. (2017), “An experimental study of partial admission losses with various blade tip clearances using a linear cascade”, Energy, Vol. 122, pp. 627-637.

Drumm, M. and Haase, W.C. (2000), “High performance rotor monitoring”, 19th Digital Avionics Systems Conference, Proceedings, IEEE, Vol. 2, pp. 6E4/1-6E4/8.

Fabian, T., Kang, S., Prinz, F. and Brasseur, G. (2002), “Capacitive blade tip clearance measurements for a micro gas turbine”, IEEE Instrumentation and Measurement Technology Conference, Vol. 2, pp. 1011-1015.

Fang, Y.L., Liu, Y.B., Yu, Y.H. and He, X. (2012), “The radial displacement of the HPT blade under the effects of the temperature field and the centrifugal”, Energy Procedia, Vol. 16, pp. 1627-1634.

Fei, C.W., Bai, G.C. and Fan, J.C. (2013), “Calculation and analysis for transient blade-tip radial running clearance of HPT”, Journal of China Aeronautical Manufacturing Technology, Vol. 439 No. 19, pp. 70-74.

Gil-Garcia, J.M., Garcia, I., Zubia, J. and Aranguren, G. (2015), “Blade tip clearance and time of arrival immediate measurement method using an optic probe”, Metrology for Aerospace, pp. 118-122.

Jia, B.H. and Zhang, X.D. (2011), “An optical fiber blade tip clearance sensor for active clearance control applications”, Procedia Engineering, Vol. 15, pp. 984-988.

Kypuros, J.A. and Melcher, K.J. (2003), “A reduced model for prediction of thermal and rotational effects on turbine tip clearance”, NASA/TM.

Lavagnoli, S., Maesschalck, C.D. and Paniagua, G. (2016), “Analysis of the heat transfer driving parameters in tight rotor blade tip clearances”, ASME Journal of Heat Transfer, Vol. 138 No. 1, pp. 011705-011710.

Lee, S.W. and Joo, J.S. (2017), “Heat/mass transfer over the cavity squealer tip equipped with a full coverage winglet in a turbine cascade: Part 2 – data on the cavity floor”, International Journal of Heat and Mass Transfer, Vol. 108, pp. 1264-1272.

Liu, Y.B. and Fang, Y.L. (2011), “The finite element analysis for HPT blade tip clearance variation of gas turbine”, Chinese Journal of Ship Research, Vol. 6 No. 6, pp. 78-82.

Ma, Y.Z., Li, G.P., Zhang, Y.K. and Liu, H.G. (2011), “Tip clearance optical measurement for rotating blades”, International Conference on Management Science and Industrial Engineering, pp. 1206-1208.

Mandache, C., Mcelhinney, T. and Mrad, N. (2012), “Aircraft engine blade tip monitoring using pulsed eddy current technology”, 4th International Symposium on NDT in Aerospace, pp. 1-9.

Melcher, K.J. and Kypuros, J.A. (2003), “Toward a fast-response active turbine tip clearance control”, ISABE, 1102, pp. 1-9.

Menter, F.R. (1992), “Improved two-equation k”, Turbulence Models for Aerodynamic Flows, NASA TM 103975.

Menter, F.R. (1994), “Two-equation eddy-viscosity turbulence models for engineering applications”, AIAA Journal, Vol. 32 No. 8, pp. 1598-1605.

Menter, F.R. (2009), “Review of the shear-stress transport turbulence model experience from an industrial perspective”, International Journal of Computational Fluid Dynamics, Vol. 23 No. 4, pp. 305-316.

Nielsen, A.E. and Moll, C.W. (2004), “Modeling and validation of the thermal effects on gas turbine transients”, Proceedings of ASME Turbo Expo 2004: Power of Land, Sea and Air, Vol. 53344, pp. 1-12.

Papa, M., Goldstein, R.J. and Gori, F. (2002), “Effects of tip geometry and tip clearance on the mass/heat transfer from a large-scale gas turbine blade”, Proceeding of ASME Turbo Expo, Vol. 30192, pp. 1-9.

Peng, K., Fan, D., Yang, F., Fu, Q. and Li, Y. (2013), “Active generalized predictive control of turbine tip clearance for aero-engines”, Chinese Journal of Aeronautics, Vol. 26 No. 5, pp. 1147-1155.

Roth, A.B., Doel, D.L. and Cissel, J.J. (2005), “Probabilistic matching of turbofan engine performance models to test data”, Proceedings of ASME Turbo Expo 2005: Power of Land, Sea and Air, Vol. 1 No. 68201, pp. 541-548.

Sang, W.L., Hyun, S.M. and Seong, E.L. (2009), “Tip gap height effects on flow structure and heat/mass transfer over plane tip of a high-turning turbine rotor blade”, International Journal of Heat and Fluid Flow, Vol. 30 No. 2, pp. 198-210.

Sarma, G.R. and Barranger, J.P. (1992), “Capacitance-type blade-tip clearance measurement system using a dual amplifier with ramp/DC inputs and integration”, IEEE Transactions on Instrumentation and Measurement, Vol. 41, No. 5 pp. 674-678.

Schabowski, Z., Hodson, H., Giacche, D., Power, B. and Stokes, M.R. (2014), “Aeromechanical optimization of a winglet-squealer tip for an axial turbine”, ASME Journal of Turbomachinery, Vol. 136 No. 7, pp. 071004-071012.

Sheard, A.G. (2011), “Blade by blade tip clearance measurement”, International Journal of Rotating Machinery, Vol. 2011, pp. 1-13.

Sheard, A.G. and Kiileen, B. (1994), “A blade by blade tip clearance measurement system for gas turbine applications”, International Gas Turbine and Aeroengine Congress and Exposition, V005T15A007.

Teng, F., Zhang, X.D. and Xie, S.Y. (2016), “Research on variation mechanism of three-dimensional blade tip clearance of aero-engine”, 13th International Conference on Ubiquitous Robots and Ambient Intelligence, pp. 1-6.

Tong, F.J., Gou, W.X. and Li, L. (2015), “Investigation on heat transfer of a rotor blade tip with various film cooling holes arrangements and groove depths”, Advances in Mechanical Engineering, Vol. 7 No. 2, pp. 1-9.

Vikram, V., Gowda, B.H.L. and Prasad, B.B.S.S.S. (2017), “Influence of endwall clearance on HSV and passage flow between two turbine cascade blades”, Fluid Mechanics and Fluid Power, pp. 833-842.

## Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 51575444), Aerospace Science and Technology Foundation (Grant No. 2017-HT-XGD) and Aviation Power Foundation (Grant No. 6141B090319).