Thermo-elastic Characteristics of Thermal Barrier Coating in a Gas Turbine Combustion Chamber with an Intermediate FGM Layer

This study is focused on the analysis of thermos-elastic characteristics of a gas turbine combustion chamber, where the inner surface experiences a higher temperature while the outer region of the wall should be thermally conductive to dissipate the heat of combustion. Using a single material is not suitable to ensure the above two requirements simultaneously. Instead of using a single material, a layered combustion chamber with high-temperature material at the inner region and thermally conductive material at the outer region can be a solution. This produces the problem of a sharp interface where disbonding occurs due to high thermal stresses. The problem of sharp interface can be eliminated by using a functionally graded material (FGM) layer in between the inner and outer layers of the combustion chamber. The present study considers a gas turbine combustion chamber consisting of three layers: the inner layer is used as a thermal barrier coating, the intermediate layer is a smooth transition from the inner layer to the outer layer, and the outer layer is a thermally conductive material. ANSYS simulation is used for the analysis of thermos-elastic characteristics of the combustion chamber with homogeneous and FGM intermediate layers. The effect of linear and nonlinear material distributions in the FGM layer on the thermos-elastic characteristics is studied. A comparison of results reveals that thermal stress smoothly changes from the inner layer to the outer layer in the case of the FGM intermediate layer compared to the homogeneous intermediate layer. This suggests that a combustion chamber with an FGM intermediate layer is more reliable than a homogeneous intermediate layer.


Introduction
To enhance the long-run endurance of composite material, Functionally Graded Material (FGM) is one of the sensible configurations.The gradual variation in composition and microstructure across the dimensions that results in the enhancement of the properties is the main characteristic of a Functionally Graded Material (FGM) [1].A two-component composite with an integrative gradient from one component to the opposite is referred to as Functionally Graded Material (FGM).In 1305 (2024) 012031 IOP Publishing doi:10.1088/1757-899X/1305/1/012031 2 distinction, composites are traditionally homogeneous mixtures, thus the desirable properties of the component elements are compromised.As the vital proportions of associate Functionally Graded Material contain the unaltered form of every element that eliminates the compromise of desirable properties [2].For composites and polymeric materials, the concept of compositional and structural gradients in material microstructure was first put forth in 1972.In 1972, Bever researched various gradient composites, looked into the general material characteristics, and reported the potential uses for graded composites.Shen stated in 1972 that variations in the chemical nature of the monomers, the molecular composition of the polymers, and the supramolecular structure or morphology of the polymers may all contribute to the gradation of polymeric material.The design, fabrication, and evaluation of a gradient structure for a reusable rocket engine were not studied until 1985 when continuous texture management was used to enhance adhesion strength and minimize thermal stress [3].During a house plane project in 1984 in Japan, a proposed thermal barrier material that could withstand a surface temperature of 2,000 K and a gradient of 1,000 K across a cross-section of about 10 mm served as the inspiration for the FGM.After that, extensive research on FGM thin films has been conducted, and they are almost commercially available [1].This idea has gained popularity in Europe recently, especially in Germany.Takezono et al. developed numerical and analytical formulations of the thermal stress and deformation states for axisymmetric shells of FGM subjected to thermal loading caused by fluid and demonstrated that the composition and material distribution profile affect temperature distribution, stress distribution, and deformation in an FGM [4].A new technique was used to numerically analyze temperature and stress distributions in a circular hollow cylinder composed of FGM [5].By using the direct solution of the Navier equation in an FGM hollow cylinder under radially symmetric loads, Jabbaria et al. evaluated the mechanical and thermal stresses [6].The infinitesimal theory of elasticity is used to obtain power series solutions for displacements and stresses in functionally graded cylindrical vessels subjected to internal pressure alone [7].By varying the material properties arbitrarily, Xian-Fang and Xu-Long perform an elastic analysis on a pressurized functionally graded material (FGM) annulus or tube [8].An analysis of the thermal and plastic stresses in cylindrical functionally graded material (FGM) vessels using the Tresca yield criterion and small deformation theory is outlined [9].Several current works are carried out to emphasize material selection, processing methods, analytical modeling, and FGM applications.The difficulties in creating these materials for diverse scientific and technological disciplines are overviewed [12].Tanvir et al. studied thermos-elastic characteristics of a thick-walled FGM cylinder with pressure applied internally [10].Their investigation is founded on an approximation technique created by Afsar and Sekin to assess the stress intensity factors of edge cracks in FGM cylinders [11].In the method done by Afsar and Seikin, the fracture characteristics were analyzed for the FGM cylinder.By their developed method elastic fields, such as stress, strain, and displacement were not analyzed.From the above studies, it is observed that various aspects of different structural elements consisting of FGM have been analyzed to know their characteristics.However, the thermos-elastic characteristics of a three-layered thick-walled cylinder with an intermediate FGM layer with 204 NS, NIMONIC 263 material have not been so far analyzed in ANSYS.A three-layered cylinder with an intermediate FGM layer may have potential application in the combustion chamber of a gas turbine or gas turbine to achieve better performance.Therefore, the study of such a cylinder is an utmost importance to know its characteristics under temperature gradient field and internal pressure.So the objectives of this study will be based on the above statement.

Ttemperature Distribution
For a cylinder the heat conduction equation is IOP Publishing doi:10.1088/1757-899X/1305/1/012031 Where T represents temperature, r is the radius of the cylinder, k is thermal conductivity city, ̇ is heat transfer rate.For steady state and axisymmetric conditions with no heat generation, the above equation, where hen temperature is independent of z, reduces to The solution to the above equation is If the cylinder is subjected to temperature Ti and T0 at the inner and outer surfaces, respectively, the constant C1 and C2 can be determined from equation (3) as The heat flux through the cylinder wall is given by Now, we consider a thick-walled circular cylinder.The cylinder is assumed to consist of three layers as shown in Fig. 1.The radius of the layers is designatedd by r1, r2, r3 and r4.The temperature at these surfaces are T1, T2, T3 and T4, respectively.In this case, the temperature distribution can be given by While the inner and outer surface temperatures are known, the temperatures of the intermediate layer (T2 and T3) can be determined by solving equation (8).

Stress Distribution
The radial stress for a thick-walled cylinder is Where ri is the inner radius, or is the outer radius, pi is the inner absolute pressure and po is the outer absolute pressure.

Cylinder with intermediate FGM layer
The FGM cylinder is divided into n layers of infinitesimal thickness using a technique that has been modified to determine the stress in the cylinder as shown in Fig. 1.Each layer is presumptively different from the others but with constant volume fractions and material properties.The ith layer's inner and outer radii are represented by ri-1 and ri, respectively, where ro=Ri and rn=Ro.The pressures at the ith layer's inner and outer surfaces are, respectively represented by Pi-1 and Pi, For this system, the stress field in the ith layer for plane strain and axisymmetric conditions can be readily derived as Where, The first term on the right-hand side of the second equation (10) arises from the applied pressure p and sec the and second term arises from the applied temperature.The displacement component in the ITH layer derived as Where   is Poisson's ratio and Ei is Young's modulus of ian th layer othe f FGM cylinder.The unknown pressures pi and    are determined by solving the following system of simultaneous linear equations, which are obtained from the condition that (   −  +1  ) vanishes at r=ri ; Where And

Cylinder with a homogeneous intermediate layer
Now for a homogeneous cylinder following the same procedure as the FGM cylinder the elastic field is caused because of the applied pressure p and the incompatible eigenstrain ϵ * .In this case the stress field in the ith layer is derived as Where The displacement components are obtained as Where   is Poisson's ratio and Eo is Young's modulus of homogeneous material.The unknown pressures   ℎ and   ,ℎ are determined by solving the following system of linear algebraic equations, which are obtained from the condition that (  ℎ −  +1 ℎ ) = 0 and r=ri ; Where And Where  ,  is the stress component in the ith layer of the homogeneous cylinder due to the equivalent eigenstrain.Here j=r, θ and z.The materials used in the 3-layered cylinder are 204NS, AMDRY 962, and NIMONIC 263.They are used as a dense layered coat layer and substrate layer respectively.

Mesh Generation and Grid Independence Test:
For the two-dimensional one-fo the ur portion of the FGM cylinder cross-section one-fe, face meshing and edge meshing are done which creates quadrilateral mesh throughout the model.As several meshes can influence the result grid independence test is done to confirm the result.The minimum radial stress is used for mesh validation where the analysis is done for a range of elements at inner pressure 10MPa and non-linear variation of properties.

Linear and Non-linear Properties Variation of Intermediate Layer:
In the 3-layered cylinder the thickness of the first layer is 0.6mm, the intermediate layer is 0.3mm, the and last layer is 5mm.

Temperature Distriution Profile
The graphical representation of the temperature distribution of three-layered cylinders with intermediate homogeneous and intermediate FGM layers is shown in Fig. 6 when 10MPa internal pressure is applied.From the graph it is seen that at intermediate layer temperature slightly differs.For FGM temperature slightly lowers at the intermediate layer.A very slight difference is seen because the temperature is independent of the material used in the cylinder.Similarly for linear and non-linear properties variation temperature distribution is shown in Fig. 8 While internal pressure is zero.There is no variation in temperature distribution when properties are varied because the material is independent.

Thermo-elastic characteristics:
When the cylinder of a gas turbine combustion chamber is subjected to internal pressure, three principal stresses are built up in the cylinder materials, they are circumferential or hoop stress, radial stress and longitudinal stress.The longitudinal stress is very negligible in the long thick thick-walled cylinder.The cylinder is also subjected to strain and deformations.These are thermo-elastic characteristics of a cylinder.Simulated thermo-elastic characteristics analysis of the cylinder with intermediate homogeneous and intermediate FGM layer are developed by ANSYS based on the analytical approach.

Radial stress analysis:
Comparison between radial stress distribution of intermediate homogeneous layered cylinder and intermediate FGM layered cylinder is shown in Fig. 10.From the graphical comparison it is observed that at the intermediate layer for homogeneous material, stress drastically changes and causes a sharp interface at the intermediate layer.Misfit strain can be caused by these effects and thus finally crack forms.But for FGM material the sharp interface is reduced and the drastic change of radial stress is also reduced which is shown in Fig. 10.Their equivalent distributions are compared graphically in Fig. 16 where internal pressure is kept 10MPa.It is observed that less equivalent stress distribution is obtained from nonlinear varying conditions.

Equivalent elastic strain analysis:
When the pressure is 10MPa with outer and inner layer temperatures 1100⁰c and 100⁰c applied then for the FGM layer there develops a smooth change of equivalent elastic strain and profile compared with the intermediate homogeneous layer which are observed in Fig. 1.

Figure 17. Equivalent elastic strain distribution of Intermediate homogeneous layer and FGM layer
For the nonlinear properties variation when the inner pressure is 10MPa, there develops a lower equivalent elastic strain profile at the intermediate layer which is shown in Fig. 18.

Conclusions
For evaluating thermal stress and temperature distribution in a thick-walled 3-layered FGM cylinder for a gas turbine combustion chamber has been rigorously studied where 204NS and Nimonic 263 are used as the first and last layer for their higher temperature and pressure resistance ability and middle layer material property is varied from first to last layer for FGM property.
• It is observed that FGM in the intermediate layer results in better performance similar to that of single-phase materials by unifying the best properties • The finite element analysis results for cylindrical (204NS/FGM/Nimonic 263) FGM indicate that, radial, hoop and equivalent stresses are reduced in the middle layer and thus finally a better profile of these stresses • So sharp interphase between the first and last layer is reduced • Better directional, total deformation and equivalent elastic strain are achieved for the FGM intermediate layer • All these results prove that this model can resist high thermal stress and can be used in gas turbines, combustion chambers, boilers etc. where high temperatures and pressures are produced • If the FGM layer properties are varied non linearly the sharp interphase between the two layers is reduced as the above-mentioned stresses are reduced and changes uniformly all over the body • Increasing the layers between the 204NS and Nimonic 263 gives better and more uniform results than before

Figure 1 .
Figure 1.One-fourth cross section of three layered cylinder

Figure 2 .
Figure 2.a.Cross section (one-fourth portion) of a 3-layered cylinder A three-layered cylinder for a gas turbine combustion chamber is shown in Fig. 2.a.where 204 NS, AMDRY 962 and, NIMONIC 263 materials are used.204NS is used as an inner layer, Amdry 962 as an internal remediate layer, and Nimonic 263 as an outer layer for this cylinder with an intermediate homogeneous layer.The mechanical and thermal properties of each layer are shown in Table 1.These properties are given as input in ANSYS workbench 16.0 to build up the model of 3 3-layerecylinderser with an intermediate homogeneous layer.The temperature distribution profiles and thermos-elastic stresses of the cylinder model are analyzed by the finite element package ANSYS (Work-Bench 16.0) and Wolfram Mathematica 10.0 which are based on the theories and mechanical and thermal properties shown in Table1.For the homogeneous and FGM intermediate layered cylinder of the gas turbine combustion chamber, the temperature of the inner layer is 1100⁰C (inner boundary) and the outer layer temperature is 100⁰C (outer boundary) in the analysis.

Figure 2 .
Figure 2.b.Cross section (one-fourth portion) of a 3-layered cylinder with FGM intermediate layer

Figure 3 .
Figure 3.a.Cross section (one fourmeshesth portion) of a 3-layered cylinder after mesh generation.
Figure 3.b.shows that the Minimum Radial stress value becomes steady after the element number 3000.

12 Figure 6 .
Figure 6.Temperature distribution of Intermediate homogeneous layer and FGM layer

Figure 9 .
Figure 9. Temperature distribution of intermediate FGM layered cylinder in ANSYS and MATHEMATICA model

Figure 10 .
Figure 10.Radial Stress distribution of Intermediate homogeneous layer and FGM layer

Figure 11 .Figure 12 .
Figure 11.Radial Stress for FGM (Intermediate layer) 2D cylinder when properties are varied linearly and nonlinearly and internal pressure is 10 Mpa

Figure 13 .
Figure 13.Hoop stress distribution of Intermediate homogeneous layer and FGM laye

Figure 14 .
Figure 14.Hoop Stress for FGM (Intermediate layer) 2D cylinder when properties are varied linearly and nonlinearly and internal pressure is 10 MPa 3.5.Equivalent stress analysis: According to the data obtained from the ANSYS of a cylinder with an intermediate homogeneous layer and FGM layer Fig. 15 graph is plotted.The graph shows that for intermediate homogeneous layer equivalent stress changes downward drastically but for FGM material it increases smoothly at the intermediate layer and finally a lower stress profile is obtained to the outer layer.

Figure 15 .Figure 16 .
Figure 15.Equivalent stress distribution of Intermediate homogeneous layer and FGM layer

Figure 18 .
Figure 18.Equivalent elastic strain distribution for FGM (Intermediate layer) 2D cylinder when properties are varied linearly and nonlinearly and internal pressure is 10 MPa 3.7.Deformation analysis For the total and directional deformation when the pressure is 10MPa with outer and inner layer temperatures 1100⁰c and 100⁰c applied the FGM intermediate layer exhibits a smooth and better profile compared with the homogenous intermediate layer which are shown in the Fig. 19 and 20.

Figure 19 .
Figure 19.Total Deformation for intermediate FGM and homogeneous 2D cylinder

Figure 20 .
Figure 20.Deformation for intermediate FGM and homogeneous 2D cylinder

Figure 21 .Figure 22 .
Figure 21.Total deformation profile of cylinder with intermediate FGM layer

)
Now for equivalence of the stress field in the FGM and homogeneous cylinder we can write

Table 1 .
Mechanical and Thermal Properties of Each Layer