An integrated modelling approach to inform package design for optimal cooling of horticultural produce : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Technology at Massey University, Palmerston North, New Zealand

Abstract

Forced-air cooling is a widely used pre-cooling process that enables the New Zealand horticultural industry, valued at over NZD $8B in 2016, to maintain the quality of perishable exports. In the typical systems used in New Zealand’s horticultural industry, forced-air cooling involves stacking fruit boxes into pallets, which are stacked together in a refrigerated room, and a fan is used to create a pressure drop through the pallets. This forces cold air through the packaging ventilation and over the fruit, facilitating heat transfer and rapidly cooling the product from the field heat (~20 °C) to the storage temperature (0-2 °C), thus prolonging shelf life and preserving fruit quality.

Package design is linked with cooling performance, as the specifics of the ventilation (i.e. placement and size of vents in the boxes) results in different airflow patterns. Unfortunately, it is not well understood how to predict the performance of a hypothetical design, which is partly why in industry and academia there has been a focus on package design testing – where through experimental or computational means, the performance of a given design is thoroughly tested. Trial-and-error experimental work represents a steep materials cost, and construction and validation of detailed mathematical models can be a highly arduous and specialised task. It would therefore be beneficial to the New Zealand horticulture industry and academia to have a suite of methodologies that can simply and rapidly predict performance of a hypothetical package design. It was proposed that such methods are based upon mathematical modelling, with a focus on flexibility, computational efficiency, and automation. The goal is that such a model can be used to rapidly develop mathematical descriptions of a wide variety of products and cooling scenarios, and if integrated with optimisation routines, will allow swift iteration toward an optimised design.

To meet this goal a new interpretation of the zonal modelling approach was developed and validated at the single box scale for the forced-air cooling of modular bulk packages of polylined kiwifruit – kiwifruit representing the largest horticultural crop in New Zealand (worth NZD $1.7B in 2016). The model focused on developing a simplified heat transfer model, with airflow considerations being a separate research project. The model is fast – with heat transfer solution times on the order of 1-2 seconds; flexible – as the model will solve for any input geometry; and automated – as the model was capable of algorithmically generating the zonal network, requiring no manual input beyond initial configuration settings.

A random stacking model was also developed to complement the heat transfer model. This is capable of automatically generating a realistic bulk fruit geometry inside of any package size or shape in only 150 seconds, relying on only a shape equation for kiwifruit and a weight distribution index as inputs. The stacking model can also simulate the presence of a polyliner wrapping, which is used in many horticultural packaging systems, including for many kiwifruit systems. The model was validated against empirically measured bulk fruit shapes, collected via CT scanning. The random stacking model increased the flexibility of the methodology and opened up the design space considerably for building models of a wide variety of package designs and products, without requiring physical prototypes or requiring “idealised” packaging configurations. The stacking model has an added functionality of predicting the volumetric efficiency of different package types.

Cooling uniformity was identified as a key performance metric for the forced-air cooling process. The airflow pattern imposes a range of rates of cooling for different fruit positions throughout the same pallet. This can have large impacts on the quality and shelf-life of individual fruit, which causes significant logistical problems for pack-house/product managers. A new quantitative heterogeneity index was developed, capable of condensing total process heterogeneity into one dimensionless number, the Overall Heterogeneity Index, or 𝑂𝐻𝐼.

This suite of tools can be used for a variety of tasks. Although the modelling work was only applied to the forced-air cooling of polylined kiwifruit inside of modular bulk packages, building models for other crops, package designs and cooling scenarios is trivial to implement. The speed of the zonal heat transfer model makes it ideal for integration with an iterative optimisation routine, so that many hundreds or thousands of designs can be investigated in a short period of time. The heat transfer model could also be combined with a machine learning algorithm (such as a genetic algorithm) to iteratively approach an optimised design. However, such an implementation requires an equally fast and flexible pallet scale airflow model, which remains a task for further work.