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An illustration of the effect of voxel size for a µCT scan reconstruction with respectively a (a) 37.5 µm and a (b) 8.5 µm voxel size. Foam samples are made in-house. 

An illustration of the effect of voxel size for a µCT scan reconstruction with respectively a (a) 37.5 µm and a (b) 8.5 µm voxel size. Foam samples are made in-house. 

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This paper reviews the available methods to study thermal applications with open-cell metal foam. Both experimental and numerical work are discussed. For experimental research, the focus of this review is on the repeatability of the results. This is a major concern, as most studies only report the dependence of thermal properties on porosity and a...

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... and Razani [55] scanned metal foam samples with four different voxel sizes, ranging from 115 down to 58 µm. They found an asymptotically converging surface-to-volume ratio. Another restriction on the voxel size is imposed by the continuum assumption with no-slip boundary conditions, upon which thermal and hydraulic analysis are commonly based (as is the case for this work). Due to the continuum hypothesis to hold and with air as a working fluid, it is not necessary to have a finer spatial discretization than voxel sizes in the order of 5 µm. As a result, the high resolution scan with a voxel size of 8.5 µm of Figure 5b can be considered highly accurate [25]. µCT scans can be used for a full characterization of the foam sample. However, some authors, like De Jaeger et al. [56], use a hybrid model. For this model, both cell diameters (d 1 and d 2 , as indicated in Figure 3a) and the interfacial strut area (A 0 ) are measured with a µCT scan. This interfacial strut area is the average cross-sectional area in the center of the strut (x/l = 0 in Figure 4). The interfacial strut area shows a difference of merely 4% as the voxel size is reduced from 37.5 µm to 8.5 µm and is therefore not strongly influenced by the roughness. An extensive explanation on how this interfacial strut area can be calculated from µCT data can be found in [34]. With these three parameters, the authors were able to make a model of the complete foam structure. Based on that structure, the porosity and the surface-to-volume ratio can be calculated numerically. This allows the continuum scale roughness, which is resolved by the fine µCT scan to be neglected, for it does not contribute to the heat transfer performance. This is a hybrid model that calculates the porosity and surface-to-volume ratio based on d 1 , d 2 and A 0 , instead of using a correlation to obtain the surface-to-volume ratio σ 0 or performing a full characterization of the foam sample through a µCT scan. The surface-to-volume ratio with this hybrid model for the foam studied in Figure 5 is 859 m −1 . This is very close to the value obtained by µCT with a voxel size of 8.5 µm (860 m −1 ). This once again indicated the necessity of using small voxel ...
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... and Razani [55] scanned metal foam samples with four different voxel sizes, ranging from 115 down to 58 µm. They found an asymptotically converging surface-to-volume ratio. Another restriction on the voxel size is imposed by the continuum assumption with no-slip boundary conditions, upon which thermal and hydraulic analysis are commonly based (as is the case for this work). Due to the continuum hypothesis to hold and with air as a working fluid, it is not necessary to have a finer spatial discretization than voxel sizes in the order of 5 µm. As a result, the high resolution scan with a voxel size of 8.5 µm of Figure 5b can be considered highly accurate [25]. µCT scans can be used for a full characterization of the foam sample. However, some authors, like De Jaeger et al. [56], use a hybrid model. For this model, both cell diameters (d 1 and d 2 , as indicated in Figure 3a) and the interfacial strut area (A 0 ) are measured with a µCT scan. This interfacial strut area is the average cross-sectional area in the center of the strut (x/l = 0 in Figure 4). The interfacial strut area shows a difference of merely 4% as the voxel size is reduced from 37.5 µm to 8.5 µm and is therefore not strongly influenced by the roughness. An extensive explanation on how this interfacial strut area can be calculated from µCT data can be found in [34]. With these three parameters, the authors were able to make a model of the complete foam structure. Based on that structure, the porosity and the surface-to-volume ratio can be calculated numerically. This allows the continuum scale roughness, which is resolved by the fine µCT scan to be neglected, for it does not contribute to the heat transfer performance. This is a hybrid model that calculates the porosity and surface-to-volume ratio based on d 1 , d 2 and A 0 , instead of using a correlation to obtain the surface-to-volume ratio σ 0 or performing a full characterization of the foam sample through a µCT scan. The surface-to-volume ratio with this hybrid model for the foam studied in Figure 5 is 859 m −1 . This is very close to the value obtained by µCT with a voxel size of 8.5 µm (860 m −1 ). This once again indicated the necessity of using small voxel ...
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... X-rays used in the scanning equipment interact significantly different with a solid than with a fluid (or vacuum), allowing for a clear distinction between both phases. However, voxels at the solid-fluid interface contain both phases. Therefore, their grey values can span a large range. For further image processing, they need to be binarized, i.e., allocated to either the solid (one) or fluid (zero) phase. This operation is called grey scale segmentation or thresholding [50]. An overview of different segmentation algorithms is given by Linquist [51] and recently by Ohser et al. [52]. In this work, the algorithm is based on a so-called dual threshold, which defines a threshold interval, combined with a labeling operation [53]. This means that neighboring voxels with grey values within the threshold interval are treated as a subset and are all assigned to a phase. The phase assignment is done by comparing grey values with the averaged threshold level of the interval. Grey values smaller than this averaged value are assigned to the fluid phase, while voxels with larger values are considered as solid material. This algorithm is also used in this work. For a more detailed description of the use of this technique to obtain, e.g., surface-to-volume ratios, the reader is referred to the work of De Jaeger et al. [25]. A drawback of these µCT scans is that they are quite expensive and not straightforward to use in comparison with a microscope or the naked eye. The main difficulty lies in the choice of the averaged threshold level to allocate the voxels to either the solid (one) or fluid (zero) phase. A different threshold can yield significantly different allocations of fluid volumes [34] and, thus, a significantly different foam model. Furthermore, the voxel size itself can also significantly influence the results (as shown in Figure 5). Figure 5a is constructed with a voxel size of 37.5 µm, while Figure 5b, which clearly shows more detail, is made through a scan with a voxel size of 8.5 µm. The surface-to-volume ratio of both reconstructions in Figure 5 is respectively 720 and 860 m −1 : a relative difference of 19%. The scan here is done on at least 16 foam cells. The reported values are average ones. This shows that the voxel size, next to thresholding, is an important parameter [25]. The heat transfer performance of a fixed volume of metal foam is determined by the product of the heat transfer coefficient and the surface-to-volume ratio. The heat transfer coefficient is determined based on the measured performance and the determined surface-to-volume ratio. As long as the thermal performance is reconstructed using the same surface-to-volume ratio that was used to determine the heat transfer coefficient, the correct thermal performance will be ...
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... X-rays used in the scanning equipment interact significantly different with a solid than with a fluid (or vacuum), allowing for a clear distinction between both phases. However, voxels at the solid-fluid interface contain both phases. Therefore, their grey values can span a large range. For further image processing, they need to be binarized, i.e., allocated to either the solid (one) or fluid (zero) phase. This operation is called grey scale segmentation or thresholding [50]. An overview of different segmentation algorithms is given by Linquist [51] and recently by Ohser et al. [52]. In this work, the algorithm is based on a so-called dual threshold, which defines a threshold interval, combined with a labeling operation [53]. This means that neighboring voxels with grey values within the threshold interval are treated as a subset and are all assigned to a phase. The phase assignment is done by comparing grey values with the averaged threshold level of the interval. Grey values smaller than this averaged value are assigned to the fluid phase, while voxels with larger values are considered as solid material. This algorithm is also used in this work. For a more detailed description of the use of this technique to obtain, e.g., surface-to-volume ratios, the reader is referred to the work of De Jaeger et al. [25]. A drawback of these µCT scans is that they are quite expensive and not straightforward to use in comparison with a microscope or the naked eye. The main difficulty lies in the choice of the averaged threshold level to allocate the voxels to either the solid (one) or fluid (zero) phase. A different threshold can yield significantly different allocations of fluid volumes [34] and, thus, a significantly different foam model. Furthermore, the voxel size itself can also significantly influence the results (as shown in Figure 5). Figure 5a is constructed with a voxel size of 37.5 µm, while Figure 5b, which clearly shows more detail, is made through a scan with a voxel size of 8.5 µm. The surface-to-volume ratio of both reconstructions in Figure 5 is respectively 720 and 860 m −1 : a relative difference of 19%. The scan here is done on at least 16 foam cells. The reported values are average ones. This shows that the voxel size, next to thresholding, is an important parameter [25]. The heat transfer performance of a fixed volume of metal foam is determined by the product of the heat transfer coefficient and the surface-to-volume ratio. The heat transfer coefficient is determined based on the measured performance and the determined surface-to-volume ratio. As long as the thermal performance is reconstructed using the same surface-to-volume ratio that was used to determine the heat transfer coefficient, the correct thermal performance will be ...
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... X-rays used in the scanning equipment interact significantly different with a solid than with a fluid (or vacuum), allowing for a clear distinction between both phases. However, voxels at the solid-fluid interface contain both phases. Therefore, their grey values can span a large range. For further image processing, they need to be binarized, i.e., allocated to either the solid (one) or fluid (zero) phase. This operation is called grey scale segmentation or thresholding [50]. An overview of different segmentation algorithms is given by Linquist [51] and recently by Ohser et al. [52]. In this work, the algorithm is based on a so-called dual threshold, which defines a threshold interval, combined with a labeling operation [53]. This means that neighboring voxels with grey values within the threshold interval are treated as a subset and are all assigned to a phase. The phase assignment is done by comparing grey values with the averaged threshold level of the interval. Grey values smaller than this averaged value are assigned to the fluid phase, while voxels with larger values are considered as solid material. This algorithm is also used in this work. For a more detailed description of the use of this technique to obtain, e.g., surface-to-volume ratios, the reader is referred to the work of De Jaeger et al. [25]. A drawback of these µCT scans is that they are quite expensive and not straightforward to use in comparison with a microscope or the naked eye. The main difficulty lies in the choice of the averaged threshold level to allocate the voxels to either the solid (one) or fluid (zero) phase. A different threshold can yield significantly different allocations of fluid volumes [34] and, thus, a significantly different foam model. Furthermore, the voxel size itself can also significantly influence the results (as shown in Figure 5). Figure 5a is constructed with a voxel size of 37.5 µm, while Figure 5b, which clearly shows more detail, is made through a scan with a voxel size of 8.5 µm. The surface-to-volume ratio of both reconstructions in Figure 5 is respectively 720 and 860 m −1 : a relative difference of 19%. The scan here is done on at least 16 foam cells. The reported values are average ones. This shows that the voxel size, next to thresholding, is an important parameter [25]. The heat transfer performance of a fixed volume of metal foam is determined by the product of the heat transfer coefficient and the surface-to-volume ratio. The heat transfer coefficient is determined based on the measured performance and the determined surface-to-volume ratio. As long as the thermal performance is reconstructed using the same surface-to-volume ratio that was used to determine the heat transfer coefficient, the correct thermal performance will be ...
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... X-rays used in the scanning equipment interact significantly different with a solid than with a fluid (or vacuum), allowing for a clear distinction between both phases. However, voxels at the solid-fluid interface contain both phases. Therefore, their grey values can span a large range. For further image processing, they need to be binarized, i.e., allocated to either the solid (one) or fluid (zero) phase. This operation is called grey scale segmentation or thresholding [50]. An overview of different segmentation algorithms is given by Linquist [51] and recently by Ohser et al. [52]. In this work, the algorithm is based on a so-called dual threshold, which defines a threshold interval, combined with a labeling operation [53]. This means that neighboring voxels with grey values within the threshold interval are treated as a subset and are all assigned to a phase. The phase assignment is done by comparing grey values with the averaged threshold level of the interval. Grey values smaller than this averaged value are assigned to the fluid phase, while voxels with larger values are considered as solid material. This algorithm is also used in this work. For a more detailed description of the use of this technique to obtain, e.g., surface-to-volume ratios, the reader is referred to the work of De Jaeger et al. [25]. A drawback of these µCT scans is that they are quite expensive and not straightforward to use in comparison with a microscope or the naked eye. The main difficulty lies in the choice of the averaged threshold level to allocate the voxels to either the solid (one) or fluid (zero) phase. A different threshold can yield significantly different allocations of fluid volumes [34] and, thus, a significantly different foam model. Furthermore, the voxel size itself can also significantly influence the results (as shown in Figure 5). Figure 5a is constructed with a voxel size of 37.5 µm, while Figure 5b, which clearly shows more detail, is made through a scan with a voxel size of 8.5 µm. The surface-to-volume ratio of both reconstructions in Figure 5 is respectively 720 and 860 m −1 : a relative difference of 19%. The scan here is done on at least 16 foam cells. The reported values are average ones. This shows that the voxel size, next to thresholding, is an important parameter [25]. The heat transfer performance of a fixed volume of metal foam is determined by the product of the heat transfer coefficient and the surface-to-volume ratio. The heat transfer coefficient is determined based on the measured performance and the determined surface-to-volume ratio. As long as the thermal performance is reconstructed using the same surface-to-volume ratio that was used to determine the heat transfer coefficient, the correct thermal performance will be ...

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