The two dynamic mathematical models were developed into computer simulation software entitled 'Packaging Simulation for Design' (or PackSim). Both simulation tools were dynamic in nature so required the use of an Ordinary Differential Equation (O.D.E.) solver to calculate the solutions to these simultaneous equations. The following sections will cover the solution method implemented in this software, the software language used and fmally the structure that was implemented in the coding.
5.4. 1 . Solution Method
The Runge-Kutta-Fehlberg method was utilised for solution of the ODEs used in both the dynamic pre-cooling and bulk storage models implemented in the PackSim code. Merts ( 1 996) outlined the benefits of using this ODE integrator.
5.4.2. Computer Implementation
5.4.2.1. Dynamic 'Packaging Simulationfor Design '
An internationally recognised standard programming language, C++, was utilised for programming, and in particular, the fifth generation, Rapid Application Development (RAD) software, C++ Builder® (Version 1 .0, developed by Borland International Inc., Scotts Valley, California). This software has the ability to run on any 32-bit operating
system (primarily Windows 95, Microsoft Corporation, Redmond, WA).
This dynamic simulation model incorporated the equations for the pre-cooling model discussed in Section 5 . 1 and the bulk storage model discussed in Section 5.2. The structure of the code was object-oriented, which is particularly beneficial as it allows the 'plugging-in' of component mathematical models, and provides allowance for retrofit of new, improved component models. An outline of the component linkages within the dynamic simulation software is presented in Figure 5 . 1 0.
The input datafiles, developed for 'PackSim', contain the data required to implement a successful solution of the ODEs. This datafile includes information regarding the product, fluid and packaging materials, a description of the system under investigation and a description of the flows across the external as well as the descretised internal system boundaries.
Pre-cooling Model (Heat Transfer}
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Bulk Storage Model (Mass Transfer)
Figure 5.10. Structure of the dynamic simulation system and the individual component linkages.
The datafile generator used for assembly of the data for implementation into the 'PackSim' model was developed using Microsoft Excel (Microsoft Corporation, Redmond, WA), a spreadsheet package, which allows rapid, yet efficient calculation of the necessary data. The datafile generator required system specific data for the product, fluid, package and packaging materials for each configuration (the required information varied depending upon which model, pre-cooling or bulk-storage, was being used). These information are summarised in Table 5.2.
Table 5.2.
Specific data required by the datafile generator to create the 'PackSim' input datafile for both the pre-cooling simulation model and the bulk-storage simulation model.
Pre-coolin Simulation Model
Package Properties Dimensions of package
Velocity of fluid into, and around package Area of ventilation
Flow velocity profile
Number of internal zones in each direction Number of external zones
Number of different packaging materials
Product Properties
Specific heat capacity Thermal conductivity Radius of each item
Respiratory coefficients (if required) Number of product items
Mass of individual product Volume of individual product Surface area of individual product Fluid Properties
Specific heat capacity Density
Thermal conductivity Viscosity
Packaging Material Properties Specific heat capacity Density
Thermal conductivity Material thickness
External Zone Properties
Initial fluid temperature Final fluid temperature
Internal Zone Properties
Initial fluid temperature Initial product temperature
For each Zone Boundary: Dimensions of the zone boundary
Area of boundary occupied by each mode of heat transfer
Bulk Stora e Simulation Model
Package Properties
Dimensions of package
Velocity of fluid into, and around package Area of ventilation
Flow velocity profile
Number of internal zones in each direction Number of external zones
Number of different packaging materials Product Properties
Temperature
Water activity
Mass transfer coefficient Respiration rate
Number of product items Mass of individual product Volume of individual product Surface area of individual product Fluid Properties
Temperature
Atmospheric pressure
Density
Packaging Material Properties
Material adsorption coefficients Material mass transfer coefficient Material thickness
External Zone Properties Fluid temperature
Fluid relative humidity Internal Zone Properties Initial fluid relative humidity
For each Zone Boundary:
Dimensions of the zone boundary
Area of boundary occupied by each mode of mass transfer
The datafile generator was used to manipulate these input data into a smaller number of specific data, which summarised the physical system for modelling. The resulting data, which are then transferred to the simulation model for implementation, are described in Table 5.3.
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Table 5.3.
Specific data created by the datafile generator as an input datafile for both the pre-cooling simulation model and the bulk-storage simulation model. Pre-coolin Simulation Model
Package Properties
Number of internal zones in each direction Number of external zones
Number of boundaries in each direction Number of different packaging materials Product Properties
Specific heat capacity Thennal conductivity Radius of each item
Respiratory coefficients (if required) Fluid Properties
Specific heat capacity Density
Thennal conductivity
Packaging Material Properties Specific heat capacity Material thickness Natural Convection Data Correction factor
Distance between product items External Zone Properties Initial fluid temperature Final fluid temperature Internal Zone Properties Initial fluid temperature Fluid mass in zone Initial product temperature Product mass in zone Product - Fluid UA value.
Codes for boundaries contacting zone For Zone Boundaries in each direction: Status of zones on each side of boundary Number of such zones
Packaging material present (if required) Packaging material mass
Velocity of fluid across boundary
U A value across the boundary for
each mode of heat transfer
Bulk Stora e Simulation Model Package Properties
Number of internal zones in each direction Number of external zones
Nwnber of boundaries in each direction Number of different packaging materials Product Properties
Temperature Water activity
Mass transfer coefficient Respiration rate
Fluid Properties Temperature
Atmospheric pressure Density
Packaging Material Properties Material adsorption coefficients Material mass transfer coefficient Material thickness
External Zone Properties Fluid temperature
Initial fluid relative humidity Final fluid relative humidity Internal Zone Properties Fluid volume
Initial fluid relative humidity Product mass in zone Product Fluid KA value
Codes for boundaries contacting zone Packaging Material Data/or each Zone Packaging material present (if required) Packaging material mass
Mass flow per unit pressure for each mode of mass transfer involving packaging materials
For Zone Boundaries in each direction: Status of zones on each side of boundary Number of such zones
Velocity of fluid across boundary
KA value across the boundary for each mode of mass transfer
The results output from the simulation programme was designed to be brief, yet provide the user with some information as to the accuracy of the modelling solution (the information presented in this results file is described in Table 5.4). A system energy (pre cooling model) or mass (bulk storage model) balance was completed for each model run and its result presented at the base of the datafile.
Table 5.4.
Information delivered in the 'PackSim' results file for both the pre-cooling simulation model and the bulk-storage simulation model.
Pre-coolin Simulation Model
Description of packaging system Time of output
Fluid temperature for each zone Product temperature for each zone Successful / Failed solver iterations Initial and fmal system energies System energy balance
Bulk Stora e Simulation Model Description of packaging system Time of output
Relative humidity for each zone Product mass for each zone
Packaging material mass for each zone Successful / Failed solver iterations Initial and fmal system masses S stem mass balance
The guidelines for the successful use of 'Packaging Simulation for Design' are included as Appendix 3, whilst the executable code is included as Appendix 5 (on diskette). The author and Massey University hold the full source code.
5.4.2.2. Steady-state 'Weight Loss Simulator '
This simulator incorporated the equations presented for the steady-state bulk storage scenario presented in Section 5.3. In development of this steady-state simulation tool, ease and accuracy of use as well as the ability for use on most computer systems was paramount.
Once again, e++ Builder was utilised for programming. The software was developed so that the user (to reduce the incidence of inaccurate system specification) performed the calculations within the code, with manipulation of a small number of factors. The input data required to implement the simulation model are described in Table 5.5. These data include information regarding the product, fluid and packaging materials, as well as a description of the system under investigation. The results file briefly summarises the results for the packaging system.
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Table 5.5.
Specific data required for the 'Weight Loss Simulator' . In ut data for 'Wei bt Loss Simulator'
Product Properties Product, type and number Mass transfer coefficient Respimtion rate
Mass of a single product item Surface area of a single product item Water activity
Storage Conditions Fluid type
Atmospheric Pressure Storage facility tempemture Stomge facility relative humidity In-package fluid tempemture In-package product temperature
Packaging Configuration Properties Package dimensions
Package porosity factor
Number of product items in package Number of boundary packaging materials Number of internal packaging materials Packaging Material Properties
Total vent area
Total vent area with f1uid f10w Fluid f10w rate
Material mass Material area Material thickness
Material effective diffusivity Material adso tion coefficients
The results output is presented to the user on the screen, but is also stored in a results file (SimResults.txt) in the root directory for the program (the information delivered in this file is described in Table 5.6). This results file is designed to allow easy manipulation of data within a spreadsheet for graphing of results.
Table 5.6.
Information delivered in the 'Weight Loss Simulator' results file. 'Wei bt Loss Simulator' Results
Packaging system description including: - product, variety and size
- package construction Initial f1uid mass Final fluid mass Fluid water
Initial packaging material mass Final packaging material mass
Packaging material water vapour uptake Steady-state internal f1uid relative humidity Steady-state rate of product water loss
rate of loss
The structure of this simulator is shown diagrammatically in Figure 5 . 1 1 , whilst the essential workings and guidelines for use are presented in Appendix 4. A copy of the executable code for this simulation software is included as Appendix 5 (on diskette).
Fluid Properties Steady-State Simulator Results Output Product Properties
includes : Packaging system description Fluid moisture uptake
Moisture uptake by packaging materials Steady-state internal fluid relative humidity Steady-state rate of product water loss Steady-state rate of product respiratory loss
Figure 5.1 1. Structure of the steady-state simulator and the individual component
linkages.