## 3 Results and Discussion
### Influence of Self-Compaction on the Airflow Resistance  
Figure 3a shows the experimental data of the pressure drop \(\Delta P\) vs. airflow velocity \(v_{a}\) at bulk depths \(H_{b}\) of 1.0, 2.0, 3.0 and 3.4 m at 1 h storage time \(t\). The overall variation of \(\Delta P\) during the measurement cycle was relatively small, with the standard deviation ranging from 0.51 to 24.86 Pa, which indicated that the data were highly reproducible and tightly clustered around the mean values. The experimental data exhibited a progressive increase in pressure drop \(\Delta P\) with increasing air velocity \(v_{a}\) and bed depth \(H_{b}\), which were comparable to those of [PERSON] and [PERSON] [12] for similar moisture content and velocities smaller than 0.15 m\(\cdot\)s\({}^{-1}\). This can be explained by the application of the same filling procedure that produced a dense bulk configuration as is typically used in practice. A similar trend of pressure drop for wheat was reported by [PERSON] et al. [37] for sprinkle filling. However, the results of \(\Delta P\) vs. \(v_{a}\) were higher than those of [PERSON] [17] and [PERSON] et al. [23], which can be attributed to the differences in wheat varieties and filling methods, resulting in higher resistance to airflow and higher pressure drops. When fitting the Matthies and Petersen [31] to the experimental data and using the default pore volume \(\varepsilon_{0}\) of 0.421 as obtained from laboratory measurements, where the curves were found to increasingly deviate with increasing airflow velocity \(v_{a}\) and bulk depth \(H_{b}\). For \(H_{b}\) = 1.0 m, a decent fit is observed for \(v_{a}\leq\) 0.10 ms\({}^{-1}\), after which the model tends to underestimate the experimental data values by up to 11.78%. Notably, this tendency becomes more prominent with the increase of \(H_{b}\) to 2.0, 3.0 and 3.4 m, where differences increase with a deviation up to 19.62, 24.61 and 28.92%, respectively. Hence, the observed results were found to be irreconcilable with the homogeneous and isotropic consideration of grain bulk reported in literature, for which the pressure drop curves between depths \(H_{b}\) are linearly equidistant at a given velocity \(v_{a}\), as the curves from \begin{table}
\begin{tabular}{c c c} \hline \hline
**Product Factor \(k\), -** & **Mathematical Model** & \(\mathbf{R^{2}}\), -** \\ \hline
2.00 & \(y=-8.027\times 10^{-3}\,x+0.390\) & 0.986 \\
2.10 & \(y=-8.141\times 10^{-3}\,x+0.395\) & 0.986 \\
2.20 & \(y=-8.215\times 10^{-3}\,x+0.400\) & 0.985 \\
2.73 & \(y=-8.693\times 10^{-3}\,x+0.422\) & 0.986 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Linear models for describing the relationship between the pore volume \(\varepsilon\) and bulk depth \(H_{b}\) at different product factor \(k\) and coefficient of determination \(R^{2}\). Figure 2: Pore volume \(\varepsilon\) vs. bulk depth \(H_{b}\) for product factor \(k\) of 2.00, 2.10, 2.20 and 2.73. Horizontal dashed line refers to the default pore volume \(\varepsilon_{0}\) at bulk depth \(H_{b}\) of 0.1 m. Solid lines represent linear model fitting; dashed lines represent extrapolations beyond the dataset utilized for fitting. It can be seen that the model exhibit an inferior performance with the data deviating from \(\Delta P_{pred}\) = \(\Delta P_{obs}\) line and clustering towards the line \(\Delta P_{pred}\) = 0.73\(\Delta P_{obs}\) + 54.70 with \(R^{2}\) = 0.993 and thus revealing an average underestimation of 22.0%. This disparity, however, is likely to increase as velocity \(v_{a}\) exceeds the limit used in this study. To account for the spatial change of the pore volume in the grain bulk caused by self-compaction, the experimental data were refitted for each bulk depth \(H_{b}\) by adjusting the \(\varepsilon\) values.