# A Multi-Level Approach for Simulation of Storage and Respiration of Produce
## CFD Simulation of the REV
### Results and Discussion  
A parametric study has been conducted to test the applicability of the present technique. The Reynolds number has been used to enforce a mass flow rate in the periodic direction of interest and all three principal directions have been tested. It is important that all directions be considered since proper specification of permeability/inertial coefficients and heat/gas exchange coefficients for a porous-continuum model of the same domain requires knowledge of anisotropy of all processes. The Reynolds number has been calculated based on the average fruit diameter and the extrinsic velocity [1; 2], and ranges from 0.1 to 200 covering most of the laminar flow regime. The Reynolds numbers correspond to a range of extrinsic velocities of 10\({}^{-5}\) to 0.05. This range was guided by the work of [PERSON] et al. [3; 4]. Figure 9 shows the flow obstruction in terms of pressure drop per unit length across the range of Reynolds numbers considered. For the lateral flow cases in the x or z directions, the pressure drop is low because the airflow is not forced to flow through the produce. In these cases, the airflow takes the path of least resistance and most of it passes through the region between the produce stack and the box top. The vertical flow direction (y) has the highest drag because the airflow is forced directly through the produce stack. A higher pressure drop is predicted for airflow through packed tomatoes owing to the fact that avocadoes are more \"streamlined\". It is also of interest to look into the heat transfer characteristics. Figure 10 displays the variation of Nusselt number with Reynolds number on the assumption of established flow in the direction of interest. The cases for tomatoes were based on a fixed surface temperature of 12 \({}^{\circ}\)C and an upstream temperature of 7 \({}^{\circ}\)C, while for avocadoes, the surface temperature was 5 \({}^{\circ}\)C with a 2 \({}^{\circ}\)C upstream value. These surface temperatures were specified based on the ASHRAE best storage recommendations [41] for different produce. In this manner, the simulations represent the near steady-state storage condition under which the produce can remain for a long period of time. In addition, the fixed-temperature condition enables use a log-mean-temperature-difference (LMTD) approach, similar to that used in [1; 2], for calculating the convective heat transfer coefficient, which can then be applied in porous continuum simulations. It is noticed here that heat transfer is highest for vertical-direction (\(y\)) flow, owing once again to the fact that flow in this direction is forced to pass throughout the stacked produce, while in the x or z directions, much of the air can pass over the stack. In this case, the key difference is between the vertical direction heat transfer and the lateral direction heat transfer (i.e., \(x\) or \(z\) directions or general lateral flow). Vertical flow happens if the airflow is forced in that direction. In some cases when a uniform flow through the stacks is important, sealing (e.g., plastic wrap) may be placed around vertical stacking of produce and hence the only flow that can occur is vertical. In spite of this heat transfer dependence on flow direction, an averaged Nusselt number over \(x,y\) and \(z\) is reported in Figure 10, as a means for characterizing a collective effect of heat exchange between produce and surrounding air. This averaged characterization may be used in porous continuum modelling, as shown shortly, for general application purposes, when there is no unique orthogonal direction of flow throughout the domain, or when there is presence of both regions of vertical and lateral flow. Figures 11 and 12 show contours of mass fractions of CO\({}_{2}\), O\({}_{2}\) and temperature for tomatoes; and CO\({}_{2}\), ethylene and temperature for avocadoes, respectively, for Reynolds numbers of 0.1, 1 and 50.