The computed and measured transport properties are summarized in Table 1. In general, the agreement between experimental and computed transfer coefficients is reasonable, but for both bricks, further improvements could be expected by changing the resolution at which the X-ray microtomographic images were acquired.
For the clinker brick, the volume imaged in the 256 x 256 x 256 array is greater than needed to be representative of the microstructure. For this material, the problem is that the individual slit-like pores are very small and are typically only one to three pixels in width. Thus, the connectivity of the 3-D image is less than that of the original microstructure, and this system would benefit from an increase in resolution in the µCT data set. This can be clearly seen in the results where the vapor diffusivities computed using the finite element (more connected) computation are much greater and much closer to the experimental values than those determined using finite differences. In fact, the overall average of the finite difference and finite element values, 0.0016, is within 20 % of the measured value, a reasonable agreement. One can also note a high degree of anisotropy in the sample microstructure as evidenced by the ratio of 2 to 3 between minimum and maximum values for the transfer coefficients computed in each of the three principal directions.
In terms of permeability, the computed values are on the average a factor of 3 too high in comparison to the single experimental value. Some of this variation could be due to the anisotropy present in this material. In hindsight, it would have been very useful to experimentally measure the transfer coefficients of this material in each of the three principal directions. The computed permeability values are also likely too high due partially to the resolution problem. Because the smallest resolvable pores are 6.65 µm (1 pixel) in size and permeability scales as pore diameter squared , if 4 µm pores were instead the true characteristic feature of the microstructure, the computed permeabilities would be a factor of (6.65/4)2=2.76 too high, very close to the observed average ratio of computed to experimental values. Once again, an increase in the µCT data set resolution, such that the pores were on average at least 3 pixels wide, would be beneficial.
For the lime silica brick, conversely, the pores are quite large and well delineated in the 3-D image. In this case, the problem is one of obtaining a large enough image to provide a representative elementary volume for the heterogeneous microstructure, as the microstructure in Fig. 2 is dominated by the presence of a single large grain in the image's upper central region. Fortunately, the vapor diffusivity results are fairly insensitive to system size, and all computed values agree fairly well with the single measured value of diffusivity (the overall average computed value being within 2 % of the experimental one). Because the pore space is very well connected in the 3-D image for the lime silica brick, there is a much smaller difference between the values provided by the finite difference and finite element techniques than for the clinker brick.
For permeability, in an attempt to obtain a representative elementary volume, computations were performed on both the central 100 x 100 x 100 and 200 x 200 x 200 portions of the 3-D microstructure. As can be seen in Table I, little change was observed in going to the larger systems, suggesting that in this case, the X-ray microtomographic data really needs to be acquired at a lower resolution (larger sample volume) to provide a more representative 3-D image for computing permeability for this brick. On average, the computed values are a factor of about 3 too high in comparison to the single experimental value, which was obtained on a much larger sample area (100 cm2 vs. 0.029 cm2 for the 256 pixel x 256 pixel tomographic images).
|Property||Clinker brick||Lime silica brick|
|Total porosity (%)||20||30|
|Measured Vapor Diffusivity (m 2/h)||0.002||0.004|
|Computed Vapor Diffusivity (m2/h)1||0.0003,0.0005,0.0007||0.0032,0.0022,0.0027|
|Computed Vapor Diffusivity (m2/h)2||0.0020,0.0027,0.0036||0.0053,0.0044,0.0058|
|Measured Air Permeability (µm 2)||0.006||0.039|
|Computed Air Permeability (µm 2) 3||0.024,0.008,0.013||0.062,0.17,0.027|
|Computed Air Permeability (µm 2) 4||0.032,0.011,0.019||0.11,0.23,0.088|