Thermal Food Processing

Radio Frequency Dielectric Heating 479
15.4.2 MODELING APPROACH
Mathematical electromagnetic models for layered composite dielectrics can be
adapted to model the composite food, packaging, and air–water barrier layered
arrangement. These models can then be combined with a two- or three-dimensional
electric field FEM model or FDM model program, such as described by
Roussy and Pearce 39 and Ishii, 38 to account for any material heterogeneities and
field penetration variations. Examples of electromagnetic field FEM programs
for complex composite geometrical structures include the High Frequency
Structure Simulator (HFSS) and the Maxwell Extractor electromagnetic field
solver programs developed by Ansoft, Inc., of Pittsburgh, PA. These programs
can solve for electromagnetic field quantities in a FEM mesh or grid (twodimensional),
or in tetrahedral or other shape finite-element blocks (threedimensional)
based on imported arrays of electrical permittivity (both storage
and loss terms), electrical conductivity, and magnetic permeability tensors for
all the constituent components. They can also be based on mechanical drawings
(e.g., AutoCAD.DXF format) of the complex geometrical structures, such as
packaged foods.
A separate simulation run will need to be conducted for every value of
frequency as well as for every value of temperature, since the dielectric terms
are functions of both. The electric field solutions are exported to a program that
calculates the power delivered and heat generated for a given time increment in
each finite-element block. These arrays of heat generation values can then be
used as heat source terms in a FEM or FDM heat transfer conservation of energy
program. The energy program also accounts for thermal fluxes between adjacent
finite-element blocks based on modeled values for thermal conductivity between
blocks, for the thermal heat capacity of the blocks, and for various boundary
conditions between the blocks. Then the true temperature rise vs. time can be
solved for each FEM block with a two-dimensional model.
The overall computer simulation will iterate cyclically back and forth between
the electromagnetic field program and the heat transfer program. Each cycle will
correspond to some time increment, and the solution for temperature rise in each
FEM block will be used to influence the imported dielectric and conductivity
properties for each FEM block in the next run of the electromagnetic field. This
overall simulation can then be used to predict the temperature rise vs. time of all
the various constituents of the composite packaged samples. By containing the
temperature dependence of the dielectric properties of the food and packaging
constituents, this model will aid in predicting thermal runaway or hot spots when
different heterogeneities are assumed and small thermal mass pockets of lossy
dielectric materials exist (e.g., water or food trapped in package seams). The level
of complexity of the model will depend on assumptions relating to material
homogeneity, composite constituent geometry, and field penetration depth nonuniformity.
Yang et al. 45 investigated the application of a three-dimensional finite-element
computer program package, TLM-Food-Heating (FAUSTUS Scientific Corp.,