An Extended-Layerwise/Solid-Element method is proposed for solving thermo-chemo-mechanical coupling problem of typical aero-engine turbine blade with thermal barrier coatings. And the method has been demonstrated to be affective through numerical examples given in this paper. The overall structure of this paper is well organized and the methodology is clearly described. For authors, the following points need to be noted:

1. The detailed information of the fluid-structure interaction analysis model should be presented in Section 7.4, e.g., the meshing can be given out in Figure 18;

2. More numerical results of fluid-structure interaction analysis can be presented, and Figure 18 is divided into two Figures;

3. What is the meaning of color in Figure 8?

4. Where is the Figure 7 come from? The reference should be cited.

5. Grammatical errors, e.g., “are denote as”, and missing words, e.g. title of Fig 13, need to be checked throughout the whole article. Some descriptions are unclear, e.g., title of Fig 14.

Author Response

Firstly, we sincerely appreciate the reviewers for their constructive comments concerning our article entitled “Dynamic coupling analysis on thermo-chemo-mechanical field and fluid-structure interaction for aero-engine turbine blade with functional gradient thermal barrier coatings (TBCs)” (No. coatings-1917793). According to the comments, the manuscript has been carefully revised to meet the requirements of your journal. Any changes in the revised version are highlighted with a red-color background. Point-by-point responses to the reviewers are listed below.

What is the meaning of color in Figure 8?

Response:

Thank you for pointing out this problem. The meanings of those colored workflows have been added in Figure 8. In details, the brown area represents the workflow for constructing the TBCs model by using extended layerwise (XLW) method; the green area represents the workflow for constructing the substrate model by using solid element (SE) method. In those two workflows, the boundary conditions are defined, and then the sparse matrices and governing equations of the two methods are determined, respectively. The blue area represents the workflow of flow-thermal coupling analysis by using COMSOL finite element software. The obtained non-uniform thermal load of the model wall is then input into XLW/SE method to calculate the mechanical response of the blade structure. The grey area represents the workflow for assembling the governing equation of the overall structure, which is based on internal and external degrees of freedoms (DOFs) and coordination conditions. Finally, the vectors and Q_{t +}_∆_t are obtained by iterative calculation through time integration.

Where is the Figure 7 come from? The reference should be cited.

Response:

Thank you for pointing out this problem. The citation of Figure 7 has been added in the revised manuscript. The reference is: Hass, D.: Thermal barrier coatings via directed vapor deposition. University of Virginia. 62(1), 470 (2001).

More numerical results of fluid-structure interaction analysis can be presented, and Figure 18 is divided into two Figures;

Response:

Thank you for your suggestion. Figure 18 has been separated into two figures. In the revised manuscript, the geometrical model and 3D mesh model are shown in Figure 18. The uneven temperature field of turbine blade with multi-film cooling holes is also analyzed and shown in Figure 19. Since the blade adopts porous gas film for structure cooling, the wall temperature of cooling holes in the flow jet direction can be reduced, showing effective thermal protection. Nevertheless, there is a continuous high-temperature region in the leading, upper and lower edges of the model wall facing an incoming flow. The reason is that there are no cooling holes in this region, so that it is difficult to realize an effective cooling.

The detailed information of the fluid-structure interaction analysis model should be presented in Section 7.4, e.g., the meshing can be given out in Figure 18;

Response:

Thank you for your suggestion. In the revised manuscript, the detailed information of the fluid-solid coupling analysis model is now given in Section 7.4. The geometrical model and 3D mesh model of the turbine blade with multi-film cooling holes are given in Figure 18.

Grammatical errors, e.g., “are denote as”, and missing words, e.g. title of Fig 13, need to be checked throughout the whole article. Some descriptions are unclear, e.g., title of Fig 14.

Response:

Thank you for pointing out this problem. The language throughout the article has been carefully re-checked. The grammatical errors, for example, “are denote as” has been corrected to “denote”. The title of Figure 13 has been corrected to “Nephograms of TCM responses of non-destructive TBCs structure by using XLW/SE method and COMSOL finite element software”. The title of Figure 14 has been corrected to “TBCs structure with debonding and delamination”.

Author Response File: Author Response.pdf

Reviewer 2 Report

Although the authors have presented numerous computations and simulations , it is quite unclear as to what specific problem they seek to address through this work.

It would be useful if the authors could clearly elucidate the insights that their work has provided and how it could be utilized to improve turbine blade / coating application design.

Several studies on the modelling and simulation of TBCs exist in the literature , however they add value only when presented in the context of the real world application and their associated challenges. For instance in Figure 2 (FGM structure) - it has been well known since the early days of TBCs that such approaches offer solutions for through thickness stress management. However as modern day engines run under much harsher conditions such approaches face severe limitations and without the introduction of new materials compositions any further advancement is stifled.

Author Response

Response Letter

Although the authors have presented numerous computations and simulations, it is quite unclear as to what specific problem they seek to address through this work.

Response:

Thank you for pointing out this problem. The multi-physics coupling analysis of areo-engine turbine blade with TBCs is a complex engineering problem. For a TBCs structure in service, its damage forms and failure modes are diversified due to the complex environmental conditions. However, at present, the relevant research on the damage mechanism and thermal-fluid-solid coupling analysis of TBCs structure are still scarce. Most research is based on the simple plate model, semicircular model, etc., rather than the complex curved structure close to the actual blade structure. In addition, the geometric dimensions of the coatings and blade differ greatly, which is a cross-scale problem. Hence, using traditional solid element to construct the grids will increase the grid number and computation, which also increases the complexity of finite element analysis. To address the above problem, the XLW/SE method are proposed in this article. Compared with traditional methods, the XLW/SE method has the following advantages:

The XLW method can construct the coating model similar to a thin-walled structure with less calculation, which is convenient for the analysis of damaged structures. Referring to the cited references [22]-[29] in the article, the finite element governing equation considers the DOFs of physical quantities of the upper and lower surfaces. It makes the XLW method can be easily coupled with other methods through the coordination conditions and internal force balance conditions. The SE method is easy to model complex structures. Combining the advantages of the two methods, the XLW/SE method is established.
The XLW/SE method can be used to construct the damage analysis model and perform multi-physics coupling analysis without any geometric assumptions. The accuracy of analysis is acceptable. In this study, such method can facilitate the thermo-chemo-mechanical and thermo-fluid-structure coupling analysis of complex curved structures with several typical damage forms, which is difficult to achieve by other methods.

In the revised manuscript, the above knowledge gaps and the problems to be addressed are mentioned in Section 1.

It would be useful if the authors could clearly elucidate the insights that their work has provided and how it could be utilized to improve turbine blade/coating application design.

Response:

Thank you for your suggestion. The dynamic coupling analysis method proposed in this study will be of significant meaning both in theory and practice, and has the prospect of further expansion. The highlights of this research work are as follows:

From the theoretical point, this study proposes the XLW/SE method to construct the thermo-chemo-mechanical and thermo-fluid-solid coupling analysis model of the areo-engine turbine blade with functionally graded TBCs. The effectiveness of this method is verified through numerical examples, considering two typical damages including interlayer delamination and interface debonding.
From the practical point, the XLW/SE method enables to solve the coupling effects of the complex curved surface structure with TBCs, and analyze the impacts of damage and non-uniform temperature field on the deformation displacement, concentration diffusion and temperature conduction. In addition, this study has adopted the proposed method to a real-world engine turbine blade, so as to obtain the dynamic coupling solution of the temperature field, concentration field, flow field and deformation field. Furthermore, it can also predict the damage location and size according to the variations of temperature and concentration, which has certain practical application value.
The research work of this paper mainly focuses on temperature conduction, ion diffusion and deformation displacement. On the basis of the existing research, the interface oxidation problem and calcium magnesium aluminum silicate (CMAS) corrosion problem of thermal barrier coatings with complex curved surface structure can be studied, which provides a guarantee for further revealing the failure mechanism of TBCs. Furthermore, the analysis results can provide guidance for improving the structural design of turbine blade.

In the revised manuscript, the above highlights are mentioned in Section 8.

Several studies on the modelling and simulation of TBCs exist in the literature, however they add value only when presented in the context of the real world application and their associated challenges. For instance in Figure 2 (FGM structure) - it has been well known since the early days of TBCs that such approaches offer solutions for through thickness stress management. However as modern day engines run under much harsher conditions such approaches face severe limitations and without the introduction of new materials compositions any further advancement is stifled.

Response:

Thank you for your suggestion. We fully agree with your viewpoint on introducing new material compositions into TBCs. The research work in this article is a foundational work, which needs further improvements to ensure the normal operation of turbine engine under harsher environmental conditions. Currently, our research team has made some progress in this regard, for example, the introduction of Eu³⁺ into yttria-stabilized-zirconia (YSZ) TBCs to improve the thermal insulation performance and interfacial fracture toughness of the coatings. In future work, the mechanical properties of this new material will be analyzed by numerical calculation method (i.e., XLW/SE method), and verified through experiments. In the revised manuscript, the above is mentioned in Section 8.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Thanks to the authors for responding to the comments

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Dynamic Coupling Analysis on Thermo–Chemo–Mechanical Field and Fluid–Structure Interaction for Aero-Engine Turbine Blade with Functional Gradient Thermal Barrier Coatings

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