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Thermal barrier coatings (TBCs) are deposited on the turbine blade to reduce the temperature of underlying substrate, as well as providing protection against the oxidation and hot corrosion from high temperature gas. Optimal ceramic top-coat thickness distribution on the blade can improve the performance and efficiency of the coatings. Design of the coatings thickness is a multiobjective optimization problem due to the conflicts among objectives of high thermal insulation performance, long operation durability, and low fabrication cost. This work developed a procedure for designing the TBCs thickness distribution for the gas turbine blade. Three-dimensional finite element models were built and analyzed, and weighted-sum approach was employed to solve the multiobjective optimization problem herein. Suitable multiregion top-coat thickness distribution scheme was designed with the considerations of manufacturing accuracy, productivity, and fabrication cost.

Thermal barrier coatings (TBCs) are widely used in advanced gas turbines to provide the thermal and oxidation protection to metallic substrate against high temperature gas [

Generally, the temperature decreases across TBCs at specific operation condition are governed by the material and geometrical properties of the TC layer, especially the thermal conductivity and thickness [

Optimal design of TBCs thickness for gas turbine blade can improve the performance and efficiency of the coatings. It is desirable to have an available, simple, and efficient approach to design the coatings for engineering application. Unfortunately, little work has been reported on this issue. Most investigations about the turbine blade deal with the substrate without TBCs, which fails to take into account the influence induced by the coatings, such as failure analysis of the blade [

Above works provided insight into the influence of TBCs on turbine blade. However, none of them deals with the issue of design of TBCs thickness. Actually, due to the difficulty in meshing a real gas turbine blade having complex external and internal geometry shapes, most numerical works instead utilized two-dimensional or simplified three-dimensional model in their simulations. For example, Yang et al. [

This work aims to develop a procedure for designing TBCs thickness distribution for gas turbine blade. Sophisticated three-dimensional FE model of the turbine blade with TBCs is built and analyzed. The optimization design procedures are presented and applied to obtain the preliminary thickness distributions. Finally, suitable TC thickness distribution scheme is determined according to the quantitative comparison. This work provides a primary coating distribution scheme for turbine blade.

The blade investigated in this work is a first-stage rotor blade in a gas turbine, as shown in Figure

Geometries of a gas turbine rotor blade: (a) blades mounted around a rotor disk, (b) suction side view, (c) pressure side view, (d) top view, (e) dimensions of cross section A-A, and (f) internal cooling passages.

The complexity of geometry makes it challenging to mesh the turbine blade. We built the three-dimensional FE model by using a combination of Altair HyperMesh and ABAQUS packages. Generally, the geometrical model of the substrate built in CAD software was firstly imported into HyperMesh and then meshed with hexahedron and tetrahedron elements. The FE model was subsequently imported into ABAQUS as orphan mesh geometry. The mesh offset technique provided by ABAQUS, which can generate solid mesh layers by offsetting a mesh surface along its normal direction, was then applied to generate mesh layers of TC, TGO, and BC. Small geometrical details of the substrate were defeatured to avoid small elements when generating mesh using HyperMesh. The blade airfoil, platform, and bottom part of the shank were mostly meshed with 8-node solid hexahedron elements except those with bad quality which were replaced by linear tetrahedron elements. The remaining part of the shank was meshed with linear tetrahedron elements, since it is impossible for it to be meshed with hexahedron elements, attributing to its complex external and internal geometries. According to the engineering practice, as shown in Figure

Finite element model of gas turbine blade with TBCs.

The nominal mesh sizes of the airfoil and platform were chosen as 0.8 mm, and the nominal mesh size is 2.5 mm for the shank. The thickness of TC varies in different analysis cases. BC is constantly 150

The total number of elements is approximately 1.0 million, including 0.62 million of hexahedron elements (C3D8R), 0.36 million of tetrahedron elements (C3D4), and 0.02 million of triangular prism elements (C3D6). The mesh sensitive analysis was conducted. The mesh sizes used in the simulations can obtain adequate computational accuracy and ensure acceptable cost.

The TBCs are composed of APS ZrO_{2}-8 wt% Y_{2}O_{3} (8YSZ) TC layer, _{2}O_{3} TGO layer, NiCrAlY BC layer, and nickel superalloy substrate. All layers are considered to be isotropic, homogenous, and temperature-independent. The materials properties are listed in Table

Materials properties used in the finite element model [

Material properties | Top-coat | TGO | Bond-coat | Substrate |
---|---|---|---|---|

Elasticity modulus (GPa) | 48.0 | 400 | 200 | 220 |

Poisson’s ratio | 0.1 | 0.23 | 0.3 | 0.31 |

Thermal expansion coefficient (×10^{−6}/°C^{−1}) |
9.0 | 8.0 | 13.6 | 12.6 |

Thermal conductivity (W/m°C) | 1.2 | 10.0 | 5.8 | 11.5 |

A uniform temperature boundary condition was imposed on the blade without taking into account the thermal radiation and convection. According to the typical thermal conditions in turbine engine [

The evaluations of stress and temperature fields are carried out in ABAQUS by using the sequentially coupled method. This method considers a one-way interaction between stress/deformation and temperature, which is often used for problems where stress field depends on the temperature field, but the reverse is not significant. It is implemented by first conducting an uncoupled steady-state heat transfer analysis and then a stress analysis. Nodal temperature taken from the former analysis is imported into stress analysis as a predefined temperature field.

Generally, the in-service performance, durability, and fabrication cost are three main objectives in determining TBCs thickness for a gas turbine blade. Parameters should be carefully selected to represent above objectives.

For in-service performance aspect, thermal insulation capability is the most important requirement. Application of high thermal insulation TBCs can reduce the temperature of substrate to prolong its lifetime or allows increasing the turbine inlet temperature and thereby improving the engine efficiency. Thus, the temperature difference between TC surface and substrate surface is considered as a performance parameter. Larger temperature decreases across the coatings mean better thermal insulation performance.

The durability of TBCs is mainly related to the intrinsic failure mechanisms of the coatings. Interfacial delamination is one of the major weaknesses of the coatings. Higher thermal stress gives rise to premature delamination and shorter lifetime. Delamination may be avoided when the stresses are low enough. Therefore thermal stress is considered as a parameter controlling the durability of TBCs, which should not exceed a critical value and should be kept as low as possible.

Moreover, the fabrication cost and technical difficulties increase while using thick TBCs, which indicates that thinner TBCs are preferred. The TC thickness is chosen as a parameter to characterize the fabrication cost.

Taking into account the above factors, design of TBCs thickness is a multiobjective optimization problem, which can be formulated as follows.

In this work,

To make the problem easier, an evaluation parameter,

Obviously, smaller value of

The objective function in (

It should be mentioned that this work aims to develop a procedure to design the TBCs thickness instead of focusing on complex optimization algorithm. Thus, the classical weighted-sum approach is employed to solve the multiobjective problem herein. However, other advanced optimization algorithms, such as evolutionary algorithm [

By using the weighted-sum approach, the multiple objectives are scalarized into a single scalar objective as

Generally, the sum of all scalar weights equals one; namely,

In general, the assignment of weights depends on the designer’s decision. In this work, considering that higher performance of TBCs is more attractive, we empirically choose the weight

The objective function in (

The optimization design procedure can be divided into three main processes: preliminary analysis, optimization design, and scheme verification:

In the preliminary analysis process, FE models with uniform TC thickness are analyzed, and

In the optimization design process, the weighted-sum method is applied for each representative position to find an optimal TC thickness. Note that the representative position stands for a region having the same TC thickness. According to the preliminary optimal thickness distributions, the overall coating region is divided into multiple subregions to form the multiregion scheme.

In the scheme verification process, FE model using the multiregion scheme is built and analyzed, and the total objective function

Distribution of the representative positions on the blade.

The detailed optimization procedure is shown in Figure

Optimization design procedure of thermal barrier coating thickness.

Build FE model for the turbine blade using uniform-thickness scheme, where TC is assigned to be uniform throughout the coating region.

Perform thermal and stress analysis using the sequentially coupled method, and the overall temperature and stress fields are obtained.

Select the representative positions on the blade and determine their objective functions

Judge whether all the uniform-thickness schemes have been finished. If not yet, go back to Step

Design a multiregion TC thickness distribution scheme.

Build FE model using the multiregion scheme obtained in Step

Calculate the total objective function

Compare

When using the uniform-thickness scheme, the TC thickness is uniform throughout the coating region. Typical temperature field and that of the substrate are shown in Figure

Temperature fields of the turbine blade (take model of 500

Overall, the FE analysis shows that as the TC thickness increases, the temperature on the airfoil of the substrate is impressively decreased, but the platform is not apparent. To explain the difference between these two parts, typical representative positions A and B are selected and their temperature distributions are given in Figure

Temperature distribution in the coatings with the variation of top-coat thickness on (a) position A (on the airfoil) and (b) position B (on the platform).

The von Mises stress distributions are presented in Figure

Stress distribution within top-coat with the variation of its thickness on (a) position A (on the airfoil) and (b) position B (on the platform).

The Pareto sets for typical representative positions A, C, D, and E (see Figure

Pareto set for representative positions A, C, D, and E on the airfoil (the solid points denote the solutions of

The optimal TC thicknesses for all the representative positions on the airfoil are determined and the preliminary optimal thickness distribution is illustrated in the form of region contour, as shown in Figure

(a) Preliminary top-coat thickness distribution based on uniform-thickness analysis; (b) multiregion top-coat thickness distribution scheme

According to the preliminary results, we proposed three design schemes and then made comparison among them to find a suitable TC thickness distribution. In general, the design of coatings thickness distribution should take the practical spraying process into account. Due to the twisting feature of the airfoil, it is easier to spray the coatings by dividing the subregions along the vertical direction.

The proposed multiregion schemes are illustrated in Figures

The FE model using the above three multiregion schemes was built and analyzed. And then

The sum of objective functions for various top-coat thickness distribution schemes.

In general, the difficulty in spraying the TBCs on the turbine blade is definitely enhanced when the thickness distributions scheme becomes complex. For multiregion schemes,

Actually,

The temperature fields of the blade using design scheme

Temperature fields of the blade using design scheme

The thermal stress distributions in TC and substrate are shown in Figure

Thermal stress fields of the blade using design scheme

This paper proposed a design method to obtain suitable thermal barrier coatings (TBCs) thickness distribution for a real gas turbine blade. Three-dimensional finite element model of the turbine blade with TBCs was built and analyzed, and the weighted-sum approach was used to solve the multiobjective optimization problem. The design method provides quantitative comparison for the selection of TBCs thickness so as to improve the efficiency of the coatings. It is found that the thermal insulation capability and stress level within the coatings on the blade airfoil are enhanced with the increase of top-coat thickness. Nevertheless, the thermal barrier effect of the coatings on the blade platform is not significant. For multiregion schemes, more detailed dividing of subregions can improve the comprehensive superiority of the scheme, but the fabrication difficulty should be considered accordingly. A three-subregion scheme is found to be suitable for engineering application.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work is supported by China 973 Program (2013CB035700) and National Natural Science Foundation of China (11472204 and 11602188).