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    A dynamic modelling methodology for the simulation of industrial refrigeration systems : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Biotechnology and Bioprocess Engineering at Massey University
    (Massey University, 1992) Lovatt, Simon James
    A dynamic modelling methodology has been developed for the computer simulation of industrial refrigeration systems. A computer program, RefSim, has been developed which embodies the new methodology. RefSim contains a total of 33 separate models - 11 derived from existing models, six which are substantially enhanced and 16 which are new. In general, these models were derived from thermal considerations and ignored the effect of hydrodynamic processes in the refrigeration circuit. Models can be dynamically linked together as specified by the input data in order to simulate a complete plant. The program includes a set of simulation utilities which reduce the amount of work required to develop models. The object-oriented features of inheritance, encapsulation and polymorphism are used extensively. Substantial model development was carried out to achieve accurate predictions of the heat release profile during chilling and freezing of food product as product cooling makes the greatest contribution to both mean and peak heat loads in many industrial refrigeration plants. The new ordinary differential equation (ODE) model was tested against finite difference (FD) calculations for a range of product shapes and Biot numbers. The ODE model predicted to within ±10% of the FD calculation during almost all of the cooling process under the test conditions. The ODE model required several orders of magnitude less computation than FD while being capable of extension to shapes that could not be handled by FD. To test the new ODE model against experimental data, a differential air temperature method to measure the cooling food product heat load profile was developed. Both the FD and ODE methods predicted the heat load profile of freezing meat cartons to within the experimental margin for error (±10%). The ODE model also predicted the heat load profile of freezing lamb carcasses to a similar level of accuracy. Three refrigeration plants (a laboratory water chiller, a 18500 lamb per day meat processing plant, and a 6000 lamb/1000 beef per day meat processing plant) were surveyed to obtain data for testing the whole simulation environment. RefSim was found to predict the measured data satisfactorily in most cases. The results were superior to those from a commercial refrigeration simulation environment and comparable to an enhanced version of that environment which included the new ODE product heat load model. Differences between the measured values and those predicted by Refsim were probably more attributable to uncertainties in the simulation input data than to model deficiencies. RefSim was found to be a flexible environment which was general enough to simulate both simple and complex refrigeration systems. Unusual components could be simulated by combining existing models rather than implementing custom models. Nevertheless, the simulation results have indicated a number of areas for further model improvement. The effects of air mixing and the thermal buffering of structural materials were shown to be modelled poorly for some refrigerated rooms. There is some scope for improving the chilling stage of the ODE product heat load model.
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    Prediction of chilling times of foods : a thesis presented in partial fulfilment of the requirement for the degree of Doctor of Philosophy in Process and Environmental Technology at Massey University
    (Massey University, 1994) Lin, Zhang
    Chilling is one of the most important branches of food preservation under low temperature as it retains, more closely than any other means, the "fresh" quality and appearance of the food. No simple method to predict chilling times for a wide range of geometric shapes without major disadvantages was found in the literature. Investigation via a set of test problems showed that for each available method, there were ranges of conditions under which accuracy of prediction reduced significantly. This justified development and testing of a new method. A theoretical and experimental study of methods for predicting the chilling times of both regularly and irregularly shaped foods was carried out. Using the sphere as a reference shape and based on the first term of the series analytical solution, empirical mathematical expressions for extending the existing concept of equivalent heat transfer dimensionality E to take account of the effect of geometry on unsteady state heat conduction processes, which has been successfully applied in freezing time prediction, were derived. These cover a wide range of heat transfer environmental conditions and multi-dimensional regular and irregular geometries. Empirical formulae for the lag factor, L, as a function of object geometric shape were also developed for the thermal centre and mass-average temperatures. Guidelines to define object geometry for irregular shapes were established. The recommended dimensional measurement approach uses actual measurements of the three dimensions of an irregular geometry to define the dimensional ratios for an equivalent ellipsoid. The neglect of sharp protrusions and of hollows in taking measurements is recommended. Experimental chilling data for foods found in the literature, were limited in usefulness for model testing because the experimental conditions were usually not sufficiently accurately measured, described or controlled. Therefore, a comprehensive set of 3879 analytical solution simulations, 351 finite element method procedures and 165 experiments of chilling processes were made over a wide range of conditions. The chilling experiments were carried out using sixteen different two- and three-dimensional irregularly shaped objects made of Tylose, a food analogue, or of Cheddar cheese. Experiments for bricks of Cheddar cheese with uniformly distributed voids were also conducted because of the scarcity of published experimental data for chilling of products with voids. For regular geometries (short cylinder, squat cylinder, infinite rectangular rod, rectangular brick, oblate and prolate spheroids), and across a wide range of conditions and product shape ratios the methodology predicted chilling times to within -7.6 to 5.6% of the theoretical solutions for the thermal centre position and ±9.4% for the mass-average condition. For many commonly encountered conditions the lack of fit was considered acceptably low when likely data uncertainties are taken into account. When the guidelines for defining an equivalent ellipsoid and the simple method were tested, the 95% confidence interval of the percentage difference comparing predictions with the experimentally measured chilling times for thermal centre temperatures of two-dimensional irregular geometries was -3.1 to 14.4%. For three-dimensional irregular geometries, the equivalent interval was -6.4 to 11.6%. No experimental testing of predicted mass-average temperatures was carried out. The simple prediction method failed to match the experimental data in a similar manner to the finite element method. Lack of fit was probably more due to experimental error than errors in the form of geometric approximation and the prediction method itself. In situations where the product contains significant uniformly distributed voids, either the simple empirical prediction method or any relevant analytical solution can be applied if an "equivalent thermal conductivity" is defined. Keey's method, with a distribution factor dependent on voidage fraction, is recommended for calculating the equivalent thermal conductivity on the basis of best fit to experimental data but ranges of applicability require further investigation. It could not be established whether natural convection in the voids was a significant enhancer of the cooling rate. In many industrial applications, data such as heat transfer coefficients and thermal properties are difficult to estimate, and non-uniformity of chilling conditions is difficult to avoid. The overall accuracy of predictions in such applications is unlikely to be significantly increased through further reduction in the inherent inaccuracy of the proposed methodologies. The methodologies are therefore suitable for routine industrial use.
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    Prediction of chilling times of foods subject to both convective and evaporative cooling at the product surface : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Biotechnology and Bioprocess Engineering at Massey University
    (Massey University, 1995) Chuntranuluck, Sawitri
    No published chilling time prediction method which covers a wide range of practical conditions, and which can be applied using only simple algebraic calculations for chilling with evaporation at the product surface has been proven accurate. The objective of the present work was to develop and test a simple chilling time prediction method with wide application for situations where significant evaporation as well as convective cooling occurs from the product surface. A numerical method (finite differences) was used to simulate convection and evaporation at the product surface in cooling of solid products of simple shape (infinite slab, infinite cylinder, and sphere) with constant surface water activity. Semi-log plots relating temperature change to be accomplished to time were linearised by appropriate scale transformations based on die Lewis relationship. The effect of evaporation on cooling rate was measured by considering the slope and intercept of such plots, and comparing these to the slope and intercept that would arise in convection-only cooling. The enhancement of cooling rate due to the evaporative effect depended on six parameters; initial product temperature, cooling medium temperature, Biot number, relative humidity, product shape factor, and surface water activity. Four simple algebraic equations were curved-fitted to the numerically simulated data for predicting temperature-time profiles at centre and mass average positions in the product. The numerically generated results and the simple algebraic equations agreed well with a mean difference close to 0% for all three shapes, and 95% confidence bounds of about ±3% for the infinite cylinder, and ±5% for the infinite slab and the sphere geometries. To test the simple models, chilling experim ents were conducted in a controlled air flow tunnel across a range of conditions likely to occur in industrial practice. Trials were conducted using infinite cylinders of a food analogue as an idealised product (with saturated salt solutions percolating over a wet cloth on the product surface to maintain constant surface water activity), and carrots (both peeled and unpeeled) as examples of real food products. Measured centre temperatures for both the idealised products and peeled carrots were predicted by the proposed method, assuming a constant surface water activity, within a range of differences which was almost totally explainable by experimental uncertainty. For unpeeled carrots, predictions mode using three different surface water activities in the model (one to represent the initial condition, one to represent the active chilling phase, and one to represent the quasi-equilibrium state at the end of chilling) agreed sufficiently well with experimental centre temperature data for the lack of fit to be largely attributable to experimental uncertainty. No experimental verification for prediction of mass-average temperatures was attempted. The proposed method is recommended for predicting chilling times of food products of infinite slab, infinite cylinder or sphere shapes, across a wide range of commonly occurring chilling conditions provided the product has constant surface water activity. The establishment of bounds on a theoretical basis for limiting the ranges in which surface water activity values are selected for making predictions for products with non-constant surface water activity is proposed, and some guidance on application of these bounds established. Further work to refine the use of these bounds for a range of food products, to consider a wider range of shapes, to test the ability of the proposed method to predict mass-average temperatures is recommended.
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    Evaluation of dynamic models for refrigeration system components : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Process and Environmental Technology at Massey University
    (Massey University, 1996) Estrada Flores, Silvia
    There is a paucity of proven models for predicting the energy transients of walls used in low temperature applications and pressure vessels commonly used in refrigeration plants. The aim of this work was to investigate how the accuracy of feasible models for these situations was affected by changing model complexity. Wall models were developed by assuming each wall layer could be represented by one of five possible thermal behaviours: null, resistance only, capacity only, alternating resistance and capacity (lumped) or fully distributed resistance and capacity. A range of feasible models for each of four common low temperature wall types was investigated by comparison of simulated behaviour to predictions by a finite element model (which was itself validated by comparison to experimental data for wall systems). Several model evaluation measures are presented to aid engineering judgement in selecting appropriate wall models for particular applications. Only resistance needs be considered for accurate prediction of mean heat flux entering a room. It is recommended that metal layers be represented by capacity only models, thin insulation layers by resistance only models, thicker insulation layers by lumped or fully distributed models, and concrete layers by lumped or fully distributed models. The recommended number of zones within a lumped or distributed model for a layer rises as the amplitude of the expected repeating temperature cycle for that layer increases. Four models of different complexity were derived to represent a typical industrial intercooler (pressure vessel). These models were tested by comparison of predictions to the measured time-temperature response of two pilot plant calorimeters containing R134a, when subjected to changing heat inputs. The measured response rate was most strongly influenced by sensible heat storage in the calorimeter shells and liquid refrigerant. Little difference in predictions by the four models was obtained in spite of the less complex models neglecting many known physical phenomena. A model considering only the thermal capacity in the shell and liquid refrigerant predicted rates of temperature change within 10% of predictions by all other models, and also close to the experimental data. An industrial case study suggested that the conclusions from the calorimeter study may be valid over much wider ranges. Suggestions are made on ways to improve the simplest model accuracy, and to gain greater benefit from the more complex models.