Figure 4-1 shows a SEM picture of the material sample. The structure typically consists of struts, cell membranes, broken cells, and unbroken cells. A total of 14 samples were produced for analysis in this study, all with partially open cell structures and broken cell ratios (see the definition below) ranging from 90% to 98%.
Table 4-1 summarizes the measurement results of the 14 samples. The samples fall into two distinct groups with different solid volume fraction. The first group has a lower solid volume fraction (referred to as LSFG) and includes L1 to L6 with 0.0413<f <0.0494. The s
second group has a higher solid volume fraction (referred to as HSFG) and includes H1 to H8 with 0.0615<f <0.0706. The variation of solid volume fraction exerts a profound influence s on VIP heat transfer, as explained later. Figures 4-2 and 4-3 show examples of spectral transmittance and spectral extinction coefficient, respectively. Note that this spectrum does not reveal CO2 absorption, which could occur at 2.7 , 4.3m , 9.4m , 10.4m , and m 15 , or Hm 2O absorption, which could occur at 2.7 and 6.3m . This indicates that the m amount of CO2 and H2O trapped in the unbroken cells is insignificant in terms of influencing radiation heat transfer. This is reasonable since most of the cells in the samples are broken and
4-1-1 The Relationship Description of Physical Properties
Figure 4-4 plots the broken cell ratio versus the cell size of the 14 samples. The data visibly falls into two groups based on the solid volume fraction. The HSFG cell sizes are typically larger than LSFG cell sizes. Both groups show an almost linear dependence of cell size on open cell ratio. The trend in Fig. 4-4 can be explained by the fact that a higher solid volume enables the cells to expand further before they are broken, and therefore they have a larger cell size after foaming. On the other hand, to obtain a higher broken cell ratio, some of the unbroken cells must be expanded further until they are broken. Consequently, this also increases the average cell size.
4-1-2 The Effects of Foam parameters
Figures 4-5 and 4-6 plots the Rosseland mean extinction coefficient data against variations in cell size and broken cell ratio, respectively. All the extinction coefficient data falls into a single straight line when plotted against the broken cell ratio, as Fig. 4-06 shows.
This indicates that the broken cell ratio is the dominant factor in determining the extinction coefficient. The VIP extinction coefficient consists of two parts, the absorption part, , and the scattering part, , that is, s e s. The former represents the absorption effect of solid material and depends largely on the solid volume fraction. The latter is affected by the geometry of the porous foam structure, which is characterized by the average cell size and the
broken cell ratio. For the 14 samples investigated in this study, the solid volume fraction plays a minor role in determining the extinction coefficient, as Fig. 4-6 indicates. The group with a higher solid volume fraction exhibits only a slight increase in extinction coefficient compared with the lower solid volume fraction group, although the average solid volume fractions of the two groups differ by more than 44% (0.045 to 0.065). This can be explained by the fact that the solid volume fraction of the samples is so small that the extinction is dominated by scattering and the contribution of absorption is insignificant. The apparent dependence of extinction coefficient on cell size, as Fig. 4-5 shows, could be interpreted as the dependence on broken cell ratio, since cell size and broken cell ratio are well correlated under a specific volume fraction, as Fig. 4-4 indicates.
4-1-3 The Influences of Lower Solid Fraction
Figure 4-7 shows the equivalent thermal conductivities of the lower solid volume group, including the total thermal conductivity, k , the thermal conductivity by solid conduction, t k , s and the equivalent thermal conductivity by radiation, k . Figure 4-7 shows that as the cell r size decreases, which creates more conduction transport routes in the solid material, solid conduction increases. On the other hand, radiation decreases as the cell size decreases. Note that the decrease in radiation (increase in extinction coefficient) is attributable to the change in broken cell ratio, as explained earlier. Consequently, there is a best cell size (best broken
In Fig. 4-7, the lowest total thermal conductivity is around 6.5 (mWm1K1), which occurs at a broken cell ratio of approximately 0.95 and corresponds to a cell size of about 120 .m
4-1-4 The Influences of Higher Solid Fraction
Figure 4-8 shows the thermal conductivities of the higher solid volume fraction group, with a trend similar to that in Fig. 4-7. The best broken cell ratio falls at around 0.97, corresponding to a cell size of 300 , and results in the lowest total thermal conductivity of m
7.6 (mWm1K1). Similar dependence of total thermal conductivity on cell size is found in the simulation work by Placido et al. [33], who assumed constant gas contribution in fully-closed cell structures and concluded a best cell size of around 100 . However, they also m concluded that the minimum total conductivity corresponds to the minimum radiative conductivity in fully-closed cell structures [33], in contrast to the results of partially-open cell structures in Fig. 4-7 and Fig. 4-8.
The total thermal conductivity of the lower solid volume fraction group (Fig. 4-7) is generally lower than that of the higher solid volume fraction group (Fig. 4-8). This difference is caused by a change in solid conduction, which accounts for more than 80% of the heat transfer in the samples (see Fig. 4-7 and Fig. 4-8). The equivalent thermal conductivity of radiation, which is generally responsible for less than 20% of the total heat transfer, shows a relatively weak dependence on the solid volume fraction, which is consistent with earlier
proportion of radiative contribution to total heat transfer, namely, 20% of the total heat transfer in vacuum are attributed to radiative transfer.