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    Mathematical modelling of airflow during forced draft precooling operations : 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
    (Massey University, 2024-11-01) Tapia Zapata, Nicolas Ignacio
    By the year 2020, the kiwifruit industry represents approximately 37 % of the horticultural export industry sector in New Zealand. Thereof, the kiwifruit cold chain aim is to reduce losses due to poor temperature control and energy usage during refrigeration. By forced convection aided by fans in palletised kiwifruit, field heat is removed rapidly prior to storage, thus optimising shelflife of the produce. Previous Computer Fluid Dynamics (CFD) model determined the optimal operating point for palletised kiwifruit during forced-draft cooling. However, CFD requires complex simulation, in detriment to computational efficiency and solving time. Therefore, there is an imperative to provide innovative tools that optimise package design by iterating several designs and that is applicable to the local industry sector for cold chain optimisation. In this spirit, this projects aimed to development of a simplified approach for the prediction of airflow distribution of palletised kiwifruit during forced-draft cooling, that can be coupled with an alternative heat transfer model, thus providing a fast and robust package optimisation routine that can inform cooling performance of several package design and pallet configuration.
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    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
    (Massey University, 2018) Olatunji, Jamal Rimkeit
    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.--Shortened abstract
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    On the acoustical theory of the trumpet : is it sound? : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University, New Zealand
    (Massey University, 1997) Redhead, Grant
    Newton's Second Law of Motion for one-dimensional inviscid flow of an incompressible fluid, in the absence of external forces, is often expressed in a form known as Bernoulli's equation: There are two distinct forms of Bernoulli's equation used in the system of equations which is commonly considered to describe sound production in a trumpet. The flow between the trumpeter's lips is, in the literature, assumed to be quasi-steady. From this assumption, the first term of the above Bernoulli equation is omitted, since it is then small in comparison to the other two terms. The flow within the trumpet itself is considered to consist of small fluctuations about some mean velocity and pressure. A linearized version of Bernoulli's equation (as used in the equations of linear acoustics) is then adequate to describe the flow. In this case it is the second term of the above equation which is neglected, and the first term is retained. Given that the flow between the trumpeter's lips is that same flow which enters the trumpet itself, a newcomer to the field of trumpet modelling might wonder whether the accepted model is really correct when these two distinct versions of the Bernoulli Equation are used side by side. This thesis addresses this question, and raises others that arise from a review of the standard theory of trumpet physics. The investigation comprises analytical and experimental components, as well as computational simulations. No evidence has been found to support the assumption of quasi-steady flow between the lips of a trumpeter. An alternative flow equation is proposed, and conditions given for its applicability. [NB: Mathematical/chemical formulae or equations have been omitted from the abstract due to website limitations. Please read the full text PDF file for a complete abstract.]
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    A CFD modelling system for air flow and heat transfer in ventilated packing systems during forced-air cooling of fresh produce : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Engineering at Massey University
    (Massey University, 2002) Zou, Qian
    Forced-air cooling is the common method for precooling horticultural produce. Ventilated packaging systems are often used to facilitate cooling efficiency. A computational fluid dynamics (CFD) modelling system was developed to simulate airflow and heat transfer processes in the layered and bulk packaging systems during the forced-air cooling of fresh produce. Airflow and heat transfer models were developed using a porous media approach. The areas inside the packaging systems were categorised as solid, plain air, and produce-air regions. The produce-air regions inside the bulk packages or between trays in the layered packages were treated as porous media, in which the volume-average transport equations were employed. This approach avoids dealing with the situation-specific and complex geometries inside the packaging systems, and therefore enables the development of a general modelling system suitable for a wide range of packaging designs and produce. The calculation domains were discretised with a block-structured mesh system that was referenced by global and local grid systems. The global grid system specifies the positions of individual packages in a stack, and the local grid system describes the structural details inside individual package. The solution methods for airflow and heat transfer models were based on SIMPLER (Semi-Implicit Method for Pressure-Linked equations Revised) method schemes, and the systems of linear algebraic equations were solved with GMRES (Generalised Minimum Residual) method. A prototype software package CoolSimu was developed to implement the solution methods. The software package hid the core components (airflow and heat solvers) from user, so that the users without any knowledge of CFD and heat transfer can utilise the software to study cooling operations and package designs. The user interaction components in CoolSimu enable users to specify packaging systems and cooling conditions, control the simulation processes, and visualise the predicted airflow patterns and temperature profiles. When the predicted and measured product centre temperatures were compared during the forced-air cooling of fresh fruit in several layered and bulk packaging systems, good agreements between the model predictions and experimental data were obtained. Overall, the developed CFD modelling system predicted airflow patterns and temperature profiles with satisfactory accuracy.
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    Mathematical modelling of airflow in shipping systems : model development and testing : 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
    (Massey University, 2004) Smale, Nicholas John
    Horticultural exports are of economic significance to New Zealand. Only through providing consistently high quality products to distant markets can New Zealand hope to command a premium price. New Zealand's two major horticultural exports, apples and kiwifruit, are transported to foreign markets by sea; either in refrigerated holds on-board cargo vessels or in refrigerated containers. Long transit times mean that conditions in these systems must be carefully controlled to ensure high quality product arrives at market. Effective distribution of air is a key consideration in transport systems. A mathematical model to describe the flow of air in marine transport systems was developed. The model was based on a resistance network framework, relying on simplification of the complex geometry within the refrigerated space to a discrete number of flow paths and points of convergence and divergence. Correlations quantifying the flow resistance of each channel were required. Some of these correlations were already available, and some were developed specifically for this purpose. A general method for predicting the flow resistance of enclosed conduits based on the Darcy-Weisbach, laminar and Colebrook equations was found to be sufficiently accurate for use. The flow resistance of horizontally vented horticultural packages was quantified and the cause of the flow resistance investigated. Entrance and exit effects were found to be significant, and a relationship between vent size and flow resistance was developed. Air interchange between a vented carton and the general refrigerated space was shown to be a significant mode of heat transfer. The effect of vent design on the rate of air interchange was found to be complex. Quantitative relationships between vent characteristics and rates of air interchange could not be developed; however, some general observations were made. Vent size, aspect ratio and alignment were all found to affect the rate of interchange. An existing method for determining in-package fluid velocities was refined to improve the accuracy of data and reduce the measurement time. A low-cost method for measuring airflows in transport systems was also developed utilising thermistors. These thermistor anemometers were used to monitor velocities in four shipments of fresh produce from New Zealand. Three of the four vessels monitored showed large variation in the circulation rate in the period between evaporator defrosts due to frosting. In some cases, frosting was severe enough to cause loss of delivery air temperature control. Management of defrosts was identified as an area of improvement in refrigerated hold management. Validation of the model developed was performed using four systems: a laboratory scale test-rig, a 40' container and two of the surveyed refrigerated holds. Airflow predictions were used with a heat transfer model to predict in-package temperatures. Comparison of measured and predicted flows and in-package temperatures showed good agreement given uncertainty of geometry and input data. The implications of altering a number of operational and design variables in both containers and refrigerated holds were investigated using the developed models. Increased circulation rates were found to increase cooling rates and reduce temperature variability in both types of systems; however, the magnitude of the benefit decreased with increasing circulation rate. Removal of the floor gratings and the use of pallet bases as an air distribution channel was found to increase temperature variability in both types of systems. The magnitude of the increase was small in a 40' container but substantial in a refrigerated hold. The correlations and models developed in this thesis provide useful tools to analyse and optimise the design and operation of refrigerated marine transport systems.