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Journal of Heat Transfer | Volume 130 | Issue 3 | Research Paper
Research Papers: Porous Media

Tomography-Based Determination of the Effective Thermal Conductivity of Fluid-Saturated Reticulate Porous Ceramics

[+] Author and Article Information
Jörg Petrasch, Birte Schrader

Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland

Peter Wyss

 Laboratory for Electronics/Metrology, EMPA Material Science and Technology, 8600 Dübendorf, Switzerland

Aldo Steinfeld

Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland and Solar Technology Laboratory, Paul Scherrer Institute, 5232 Villigen, Switzerlandaldo.steinfeld@eth.ch

J. Heat Transfer 130(3), 032602 (Mar 06, 2008) (10 pages) doi:10.1115/1.2804932 History: Received August 30, 2006; Revised May 31, 2007; Published March 06, 2008
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The effective thermal conductivity of reticulate porous ceramics (RPCs) is determined based on the 3D digital representation of their pore-level geometry obtained by high-resolution multiscale computer tomography. Separation of scales is identified by tomographic scans at 30μm digital resolution for the macroscopic reticulate structure and at 1μm digital resolution for the microscopic strut structure. Finite volume discretization and successive over-relaxation on increasingly refined grids are applied to solve numerically the pore-scale conduction heat transfer for several subsets of the tomographic data with a ratio of fluid-to-solid thermal conductivity ranging from 10−4 to 1. The effective thermal conductivities of the macroscopic reticulate structure and of the microscopic strut structure are then numerically calculated and compared with effective conductivity model predictions with optimized parameters. For the macroscale reticulate structure, the models by Dul’nev, Miller, Bhattachary and Boomsma and Poulikakos, yield satisfactory agreement. For the microscale strut structure, the classical porosity-based correlations such as Maxwell’s upper bound and Loeb’s models are suitable. Macroscopic and microscopic effective thermal conductivities are superimposed to yield the overall effective thermal conductivity of the composite RPC material. Results are limited to pure conduction and stagnant fluids or to situations where the solid phase dominates conduction heat transfer.
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Figures

Grahic Jump Location
+Photograph of Specimen A: a low-porosity (average porosity of 81%) cylindrical 10pores∕in. Rh-catalyst coated SiC-made RPC sample
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Photograph of Specimen A: a low-porosity (average porosity of 81%) cylindrical 10pores∕in. Rh-catalyst coated SiC-made RPC sample
Figure 1

Photograph of Specimen A: a low-porosity (average porosity of 81%) cylindrical 10pores∕in. Rh-catalyst coated SiC-made RPC sample

Grahic Jump Location
+CT reconstruction of a cross section of the RPC’s Specimen A. Some central channels are indicated by 1.
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CT reconstruction of a cross section of the RPC’s Specimen A. Some central channels are indicated by 1.
Figure 2

CT reconstruction of a cross section of the RPC’s Specimen A. Some central channels are indicated by 1.

Grahic Jump Location
+3D digital reconstruction of a slice of the RPC’s Specimen A, based on the macroscale CT data set and the isosurface at the segmentation gray value
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3D digital reconstruction of a slice of the RPC’s Specimen A, based on the macroscale CT data set and the isosurface at the segmentation gray value
Figure 3

3D digital reconstruction of a slice of the RPC’s Specimen A, based on the macroscale CT data set and the isosurface at the segmentation gray value

Grahic Jump Location
+Photograph of Specimen C: a single strut sample of the Rh-catalyst coated SiC-made RPC sample, showing the triangular cross-sectional geometry of the central channel
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Photograph of Specimen C: a single strut sample of the Rh-catalyst coated SiC-made RPC sample, showing the triangular cross-sectional geometry of the central channel
Figure 4

Photograph of Specimen C: a single strut sample of the Rh-catalyst coated SiC-made RPC sample, showing the triangular cross-sectional geometry of the central channel

Grahic Jump Location
+CT cross-sectional reconstruction of the strut Specimen C
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CT cross-sectional reconstruction of the strut Specimen C
Figure 5

CT cross-sectional reconstruction of the strut Specimen C

Grahic Jump Location
+3D digital reconstruction of the strut Specimen C, based on the microscale CT data set and the isosurface at the segmentation gray value
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3D digital reconstruction of the strut Specimen C, based on the microscale CT data set and the isosurface at the segmentation gray value
Figure 6

3D digital reconstruction of the strut Specimen C, based on the microscale CT data set and the isosurface at the segmentation gray value

Grahic Jump Location
+Schematic of steady-state conduction heat transfer through a two-phase cubic sample of RPC, with temperature boundary conditions T1 and T2 on two of the opposing faces of the cube and adiabatic conditions on the remaining four faces of the cube
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Schematic of steady-state conduction heat transfer through a two-phase cubic sample of RPC, with temperature boundary conditions T1 and T2 on two of the opposing faces of the cube and adiabatic conditions on the remaining four faces of the cube
Figure 7

Schematic of steady-state conduction heat transfer through a two-phase cubic sample of RPC, with temperature boundary conditions T1 and T2 on two of the opposing faces of the cube and adiabatic conditions on the remaining four faces of the cube

Grahic Jump Location
+Isothermal contour lines of the normalized temperature distribution (T−T2)∕(T1−T2) in a cross-sectional plane obtained from pore-level direct numerical simulation of conduction heat transfer on a subset of Specimen A. Boundary conditions: T=T1 at the bottom (z=0mm) and T=T2 at the top (z=9mm). The solid areas are depicted in black.
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Isothermal contour lines of the normalized temperature distribution (T−T2)∕(T1−T2) in a cross-sectional plane obtained from pore-level direct numerical simulation of conduction heat transfer on a subset of Specimen A. Boundary conditions: T=T1 at the bottom (z=0mm) and T=T2 at the top (z=9mm). The solid areas are depicted in black.
Figure 8

Isothermal contour lines of the normalized temperature distribution (T−T2)∕(T1−T2) in a cross-sectional plane obtained from pore-level direct numerical simulation of conduction heat transfer on a subset of Specimen A. Boundary conditions: T=T1 at the bottom (z=0mm) and T=T2 at the top (z=9mm). The solid areas are depicted in black.

Grahic Jump Location
+Ratio of the macroscale and microscale effective thermal conductivities (ke,macro∕ke,micro) as a function of the ratio of the fluid and strut thermal conductivities (kf,macro∕ke,micro), obtained by the macroscale direct numerical simulation of 12 nonoverlapping subsamples of Specimens A and B with varying porosity. Indicated by a dashed line are the regions where the GCI is below and above 10%.
View Large  |  Save Figure  |  Download Slide (.ppt)
Ratio of the macroscale and microscale effective thermal conductivities (ke,macro∕ke,micro) as a function of the ratio of the fluid and strut thermal conductivities (kf,macro∕ke,micro), obtained by the macroscale direct numerical simulation of 12 nonoverlapping subsamples of Specimens A and B with varying porosity. Indicated by a dashed line are the regions where the GCI is below and above 10%.
Figure 9

Ratio of the macroscale and microscale effective thermal conductivities (ke,macro∕ke,micro) as a function of the ratio of the fluid and strut thermal conductivities (kf,macro∕ke,micro), obtained by the macroscale direct numerical simulation of 12 nonoverlapping subsamples of Specimens A and B with varying porosity. Indicated by a dashed line are the regions where the GCI is below and above 10%.

Grahic Jump Location
+Ratio of the macroscale and microscale effective thermal conductivities (ke,macro∕ke,micro) as a function of the ratio of the fluid and strut thermal conductivities (kf,macro∕ke,micro), obtained by the macroscale direct numerical simulation and by the ke models: (a) parallel and serial bounds, Dul’nev’s model, and three-resistor model; (b) Calmidi’s and Mahajan’s model (analytical), model of Bhattacharya , and Boomsma and Poulikakos’s model for reticulate structures; (c) Calmidi and Mahajan’s (empirical) and Miller’s models
View Large  |  Save Figure  |  Download Slide (.ppt)
Ratio of the macroscale and microscale effective thermal conductivities (ke,macro∕ke,micro) as a function of the ratio of the fluid and strut thermal conductivities (kf,macro∕ke,micro), obtained by the macroscale direct numerical simulation and by the ke models: (a) parallel and serial bounds, Dul’nev’s model, and three-resistor model; (b) Calmidi’s and Mahajan’s model (analytical), model of Bhattacharya , and Boomsma and Poulikakos’s model for reticulate structures; (c) Calmidi and Mahajan’s (empirical) and Miller’s models
Figure 10

Ratio of the macroscale and microscale effective thermal conductivities (ke,macro∕ke,micro) as a function of the ratio of the fluid and strut thermal conductivities (kf,macro∕ke,micro), obtained by the macroscale direct numerical simulation and by the ke models: (a) parallel and serial bounds, Dul’nev’s model, and three-resistor model; (b) Calmidi’s and Mahajan’s model (analytical), model of Bhattacharya , and Boomsma and Poulikakos’s model for reticulate structures; (c) Calmidi and Mahajan’s (empirical) and Miller’s models

Grahic Jump Location
+Ratio of the microscale effective thermal conductivity to the pure solid thermal conductivity (ke,micro∕ks) as a function of the ratio of the fluid-to-solid thermal conductivities (kf,micro∕ks), obtained by the microscale direct numerical simulation and by the ke models
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Ratio of the microscale effective thermal conductivity to the pure solid thermal conductivity (ke,micro∕ks) as a function of the ratio of the fluid-to-solid thermal conductivities (kf,micro∕ks), obtained by the microscale direct numerical simulation and by the ke models
Figure 11

Ratio of the microscale effective thermal conductivity to the pure solid thermal conductivity (ke,micro∕ks) as a function of the ratio of the fluid-to-solid thermal conductivities (kf,micro∕ks), obtained by the microscale direct numerical simulation and by the ke models

Grahic Jump Location
+Contour map of the ratio of the overall effective thermal conductivity to the pure solid thermal conductivity (ke,macro∕ks) as a function of microscale fluid-to-solid thermal conductivity ratio (kf,micro∕ks) and macroscale fluid-to-solid thermal conductivity ratio (kf,macro∕ks). εmacro=0.90, εmicro=0.12.
View Large  |  Save Figure  |  Download Slide (.ppt)
Contour map of the ratio of the overall effective thermal conductivity to the pure solid thermal conductivity (ke,macro∕ks) as a function of microscale fluid-to-solid thermal conductivity ratio (kf,micro∕ks) and macroscale fluid-to-solid thermal conductivity ratio (kf,macro∕ks). εmacro=0.90, εmicro=0.12.
Figure 12

Contour map of the ratio of the overall effective thermal conductivity to the pure solid thermal conductivity (ke,macro∕ks) as a function of microscale fluid-to-solid thermal conductivity ratio (kf,micro∕ks) and macroscale fluid-to-solid thermal conductivity ratio (kf,macro∕ks). εmacro=0.90, εmicro=0.12.

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