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Research Papers: Conduction

Thermal Modeling and Analysis of a Thermal Barrier Coating Structure Using Non-Fourier Heat Conduction

[+] Author and Article Information
Stephen Akwaboa

Mechanical Engineering, Pinchback Building, Baton Rouge, LA 70813;  Southern University and A&M College, Baton Rouge, LA 70813stephen_akwaboa@subr.edu

Patrick Mensah, Ebubekir Beyazouglu, Ravinder Diwan

Mechanical Engineering, Pinchback Building, Baton Rouge, LA 70813;  Southern University and A&M College, Baton Rouge, LA 70813

J. Heat Transfer 134(11), 111301 (Sep 28, 2012) (12 pages) doi:10.1115/1.4006976 History: Received July 18, 2011; Accepted May 24, 2012; Published September 26, 2012; Online September 28, 2012

This paper presents a numerical solution of the hyperbolic heat conduction equation in a thermal barrier coating (TBC) structure under an imposed heat flux on the exterior of the TBC. The non-Fourier heat conduction equation is used to model the heat conduction in the TBC system that predicts the heat flux and the temperature distribution. This study presents a more realistic approach to evaluate in-service performance of thin layers of TBCs typically found in hot sections of land based and aircraft gas turbine engines. In such ultrafast heat conduction systems, the orders of magnitude of the time and space dimensions are extremely short which renders the traditional Fourier conduction law, with its implicit assumption of infinite speed of thermal propagation, inaccurate. There is, therefore, the need for an advanced modeling approach for the thermal transport phenomenon taking place in microscale systems. A hyperbolic heat conduction model can be used to predict accurately the transient temperature distribution of thermal barrier structures of turbine blades. The hyperbolic heat conduction equations are solved numerically using a new numerical scheme codenamed the mean value finite volume method (MVFVM). The numerical method yields minimal numerical dissipation and dispersion errors and captures the discontinuities such as the thermal wave front in the solution with reliable accuracy. Compared with some traditional numerical methods, the MVFVM method provides the ability to model the behavior of the single phase lag thermal wave following its reflection from domain boundary surfaces. In addition, parametric studies of properties of the substrate on the temperature and the heat flux distributions in the TBC revealed that relaxation time of the substrate material, unlike the thermal diffusivity and thermal conductivity has very little effect on the transient thermal response in the TBC. The study further showed that for thin film structures subject to short time durations of heat flux, the hyperbolic model yields more realistic results than the parabolic model.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of thermal barrier coating structure on gas turbine blade airfoil with five cooling channels

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Figure 2

A cross section of TBC system showing the thicknesses (mm) of the substrate, bond coat, TGO, and top coat (not drawn to scale)

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Figure 3

Model of TBC-substrate system

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Figure 4

Grid independent studies

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Figure 5

Validation of the numerical results with the work of Lor and Chu subject to the same conditions td  = 1, t = 0.2, k = 10, α = 1, and τ = 1

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Figure 6

Solution for (a) hyperbolic and (b) parabolic conditions for a large simulation time (800,000 iterations), (c) steady state solution of the hyperbolic and parabolic solution subject to the boundary conditions specified in Sec. 3

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Figure 7

Heat flux and temperature solutions for α = 10, k = 1, and τ = 1

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Figure 8

Heat flux and temperature solutions for α = 1, k = 10, and τ = 1

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Figure 9

Heat flux and temperature solutions for α = 1, k = 1, and τ = 10

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Figure 10

Plots showing substrate thermal conductivity effects on temperature distribution in TBC and partial domain of substrate

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Figure 11

Plots showing substrate thermal diffusivity effects on temperature distribution in TBC and partial domain of the substrate aat various times

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Figure 12

Plots showing substrate relaxation time effects on temperature distribution in TBC and partial domain of the substrate at various times

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Figure 13

Plots showing substrate relaxation time effects on temperature distribution in TBC and partial domain of the substrate at various times

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Figure 14

Steady state TBC surface temperature as a function of TBC thickness

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Figure 15

One-dimensional mesh of the two domains

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Figure 16

Computational molecule for MVFVM

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Figure 17

Interface computational molecule

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