# A Multi-Level Approach for Simulation of Storage and Respiration of Produce
## 1 Introduction  
Research continues to be directed towards food processing, refrigeration and storage. Phenomena of moisture loss and food respiration, and metabolic processes like ripening and transpiration are generally the focus with interest in maximizing the efficiency of transportation and increasing the shelf life of produce, meat, and other products. Computational fluid dynamics (CFD) is a design tool that is used to simulate airflow and heat/mass transfers and can be used to provide information related to the study and optimization of such processes. The present work describes a CFD approach for studying respiration and ventilation in the bulk storage of produce. The approach includes parameterization of produce shape, introduction of a model to generate packing arrangements, development of a respiration model for produce-level simulations on single commodities, simulation of full crates at the produce-level (the representative elemental volume REV), and an extension to porous continuum modelling, which facilitates the modelling of large quantities of packed produce. The approach is used to simulate arrangements of tomatoes and avocadoes, given the availability of experimental data for validation. As alluded to above, CFD modelling can be used to study details of individual pieces of produce, a packing arrangement of produce pieces, or an entire region of packed produce by consideration of it as a so-called porous continuum. While the porous continuum approach enables simulation of large regions for design and processing purposes, it requires that the regions containing the packed goods or produce be relegated to simple volumes with interstitial properties that characterize the influence of the packed structure on flow. Studies at the shape-level (or produce-level) are classified as \"microscopic\", whereas studies conducted at the porous-continuum level are classified as \"macroscopic\". For microscopic simulations of one or more pieces, the point equations for mass, momentum and energy conservation coupled with turbulence must be solved on a computational mesh that is fine enough to resolve all details of the flow and mass/energy exchanges between the produce and the surrounding air. For macroscopic calculations, the transport equations are volume-averaged and the influence of the detailed shape and packing arrangement are characterized by drag and exchange models, which require closure coefficients. The closure process can be either physically based, which depends on selection of a representative elementary volume (REV) of the porous media [1; 2], or empirical in that it depends on experimental verification and sensitivity analysis of closure parameters [3; 4]. An REV is defined as a small volume that is representative of the internal structure of a larger domain. REVs can be comprised of hundreds (e.g., produce crates), thousands or millions (e.g., pores inside metal foams) of like shapes packed in some arrangement that may or may not have a repeating pattern. The choice of an REV is not always an easy task since it needs to be representative of the geometry in question. In the present study, we consider a packed crate (or box) of irregularly shaped produce as the REV, since this is a \"repeating\" pattern in a storage facility. For simulated results of such a REV to be accurate, the shapes of the produce in the REV must be representative of the produce considered. While a spherical shape may be adopted to characterize produce like apples [3; 4], the deviation from sphericity is significant in cases of strawberries [5], avocadoes [6] and for certain types of tomatoes and many other fruits and vegetables. Within the general area of porous media characterization and modelling, there has been significant effort directed over the past decades towards development of idealized shape models.