## 4 Conclusions  
In this study, the resistance to airflow of a wheat grain bulk (_Triticum aestivum_ L., cv. 'Pionier') under a set of air velocities, bulk depths and storage times was investigated. The physical characteristics of wheat kernels were experimentally assessed as a prerequisite for modeling the airflow resistance. For the characterization of \(\Delta P\) vs. \(v_{a}\) relationship, the Matthies and Petersen model was employed, for which the product factor \(k\) was tailored for the specific wheat variety and experimental settings used in this study. From the fitting analysis, a goodness of fit with \(R^{2}\) of 0.990, \(RMSE\) of 68.67 Pa and \(MAPE\) of 12.50% was observed for bulk depths ranging between 1.0 and 3.4 m and storage times between 1 and 236 h, which demonstrated a great potential of the employed model to describe the course of the experimental data with decent accuracy. Due to self-compaction, a spatial reduction of pore volume from 0.413 to 0.391 at bulk depths of 1.0 to 3.4 m after 1 h storage time and temporal reduction from 0.391 to 0.370 after 236 h storage time was observed, accordingly. Therefore, a disproportional increase of the pressure drop \(\Delta P\) with bulk depth and storage time was observed, which was in contrast with the assumption of homogeneous and isotropic aerodynamic conditions in grain bulks often made in the literature. Thus, for practical application, higher power is required by the fan to maintain the required airflow velocity in bulk than when estimated from the default pore volume measured by the standard laboratory methods. The variation of pore volume \(\varepsilon\) was modeled and supported the development of a generalized model that could satisfactorily predict the airflow resistance of wheat bulk under self-compaction.  
It could be shown that self-compaction plays a critical role in airflow resistance and therefore should be included in the design and analysis of cooling, aeration and low-temperature drying of in-store grain bulks. Further research should focus on the assessment of airflow resistances under self-compaction for other grains, moisture contents, bulk configurations and airflow velocity range. Moreover, the dynamics of grain compaction  
Figure 7: Standardized regression coefficients from sensitivity analysis including airflow velocity \(v_{a}\), bulk depth \(H_{b}\), pore volume \(\varepsilon\), particle diameter \(d_{e}\), air density \(\rho_{a}\) and dynamic air viscosity \(\mu_{a}\).  
until permanent equilibrium should be further investigated. In addition, advanced numerical methods should be employed for an in-depth analysis of kernel and bulk behavior subjected to a wide range of loads encountered in practice during the storage of grain bulks.  
Conceptualization, I.R., S.S., S.K. and J.M.; methodology, I.R., S.S., S.K. and J.M.; software, I.R.; validation, I.R.; formal analysis, I.R.; investigation, I.R.; resources, I.R. and J.M.; data curation, I.R.; writing--original draft preparation, I.R.; writing--review and editing, I.R., S.S., S.K. and J.M; visualization, I.R.; supervision, J.M.; project administration, I.R., S.S., S.K. and J.M.; funding acquisition, J.M. All authors have read and agreed to the published version of the manuscript.  
This research was financially supported by the German Federal Ministry for Economic Affairs and Energy (BMWi)--Project number KF2607404 LT4.  
Not applicable.  
The authors are grateful to the technical team of the Institute of Agriculture Engineering for their assistance in the construction of components required for the experimental investigation. Special gratitude goes to [PERSON] and [PERSON] for their contributions to sensor development and language editing, respectively. Furthermore, authors are thankful to the editors and reviewers for their constructive comments, which helped to improve the quality and scientific substance of manuscript.  
The authors