In order to design a model that allows accurate prediction of chamber temperature profi les during pressurization, a number of assumptions need to be made. The assump- tions made for a particular vessel system should provide the closest prediction of the process as infl uenced by factors such as the chamber system, insulation conditions, compression medium composition, etc. (see Table 5.3).
5.4.1.1 Assumptions for the Chamber System
Of the two main compression systems existing for high-pressure processing, the indirect system using an external intensifi er design is most commonly selected for sterilization purposes. Therefore, an indirect pressure chamber, rather than a plunger press design, should be the modeling system of choice.
As mentioned in Section 5.2.2.2, modern high-pressure sterilization systems include a series of design features and controls to ensure initial temperature homoge- neity inside the sample carrier before pressure is applied. Thus, initial temperatures in the vessel furnace (if any), the fl uid surrounding the polymeric carrier, the poly- meric carrier inner fl uid, and food packages forming the system ought to be assumed homogenous and constant (at thermal equilibrium). In particular, the temperatures of the fl uid and food packages inside the polymeric carrier should be the same (Ts).
Farkas and Hoover (2000) mentioned that the initial temperature Ts must not be less
than 0.5°C below the specifi ed value in all food locations.
In addition, pressure applied to the food sample and compression fl uid must be assumed equal at all points. Most pressure pump systems increase the pressure inside the vessel at a constant rate, therefore the pressurization rate as well as pres- sure release rate can be assumed constant (Otero et al., 2000; Carroll et al., 2003).
The compression heating rate of most polymers chosen to build a liner is still unknown in the public domain. Some of these polymers may have a much higher
compression heating rate than steel (rate is ~0), even matching the compression heat- ing of water (3°C–5°C/100 MPa). Furthermore, it is reasonable to assume that the thermal conductivity of these polymers will remain much lower than stainless steel under pressure and therefore retain compression heat. Thermal conductivity and dif- fusivity of these materials at high-pressure conditions are also unknown, especially as function of temperature and pressure. Therefore, based on the current knowledge, an additional safety factor would be to assume the material has zero compression heating, but still maintains insulating properties.
It is also assumed that the steel vessel has a predefi ned constant volume, thus neglecting the expansion of the pressure vessel due to associated piping during com- pression. Vessel expansion may add several percentage points in fl uid to the vessel’s volume (Otero and Sanz, 2003). A fi lled 100 L vessel will require an additional vol- ume of water (15–20 L) for it to reach a pressure of 680 MPa, and some of this energy exchange might not only translate into a pressure or viscosity increase, but also into a vessel volume change.
The vessel walls should be considered, as discussed before, to have variable temperature over the wall surface during pressure application (Hartmann et al., 2004), rather than an “infi nite reservoir where heat is rapidly distributed and tem- perature gradients in the steel vanish immediately” (Hartmann and Delgado, 2002b). Furthermore, it should be assumed the chamber is completely fi lled with water at the beginning. The thermostat adapted to the heating system (including a water jacket or heat resistors) might also show variations during holding time, thereby giving a fl uctuating boundary condition. These fl uctuations should also be ignored when developing a model. Radiation heating from the vessel walls can also be assumed as negligible.
As mentioned in Section 5.3.2.3, different approaches to boundary conditions for temperature and velocity prediction on the liquid–solid interfaces can be applied. Furthermore, in vertical systems, it may be assumed that the entrance of compression fl uid is at the geometrical center, allowing consideration of a 2D axis-symmetric sys- tem. This assumption is not possible for horizontal vessels since convective motion due to gravity is not axis symmetric; therefore, a full 3D model is required.
5.4.1.2 Assumptions for Compression Fluid
Based on previous discussion in Section 5.2.1.2, it can be assumed the compression liquid is pure water, since the compression fl uid used in industrial-type vessels for pasteurization and sterilization purposes is actually drinking water with no addi- tives. Therefore, a model could include thermophysical properties for water only (plus properties of food and carrier material).
In theory, the heat generated by compression is dissipated by a combination of conduction and convection within the pressurizing fl uid in the chamber, and by transfer across the chamber wall into the surroundings (Hartmann and Delgado, 2002a,b; Carroll et al., 2003). Assuming an external intensifi er is used, a certain volume of fl uid is forced into the chamber to reach the target pressure, thereby creat- ing convective currents. Carroll et al. (2003) and Kowalczyk et al. (2004) assumed the convection effect within the pressurizing fl uid is negligible based on the fact that during the pressure holding time, the pressurizing fl uid and chamber volume are
typically undisturbed. However, the model developed by Knoerzer et al. (2007) has shown that buoyancy forces due to temperature and thus density gradients lead to a fairly strong convection.
Furthermore, Carroll et al. (2003) calculated the resultant error for a labora- tory plunger press system (17 mm in diameter) and attributed a 20% error caused by neglecting the contribution of convection. Hartmann and Delgado (2003b) have shown that even though the incoming pressurizing fl uid is tempered before enter- ing the high-pressure vessel, it is not heated further due to the effect of pressure (in reaching temperature of existing fl uid in chamber), and it may thus “cool down” the bottom section of the vessel as shown in a 6.3 L vessel initially at 40°C. Knoerzer et al. (2007) also established that convective currents inside the vessel, especially in the absence of a carrier, play a major role in the temperature value achieved as well as uniformity.
In a comparative study between an indirect system without packages and a direct system with packages fi lled with water, Hartmann and Delgado (2003b) assumed that all liquids are Newtonian, compressible and chemically inert. The fl uid was assumed to be initially at rest and in thermal equilibrium. Hartmann (2002) esti- mated a Reynolds number during pressurization of approximately 10. Based on this, the fl ow of the liquid was assumed as laminar. In addition, once target pressure is reached, it should be assumed the infl ow of compression fl uid stops.
During “instant” pressure transfer during come-up time, increase of mass in the pressure medium leads to a volume reduction in the samples. This phenomenon can be neglected by assuming the volume as constant and density as a function of pressure.
5.4.1.3 Assumptions for Food Packages
For food packages, the fi rst possible assumption is that the thickness of the packag- ing material allows for suffi cient heat penetration and does not affect the temperature distribution at the end of preheating period. Furthermore, Hartmann and Delgado (2003b) pointed out that it should be assumed that deformation of packages obeys a pre- scribed kinematics, to maintain its integrity and to not provide signifi cant resistance to compression. In addition, the compression heating effect of the packaging material layer surrounding the food should be assumed as similar to water.
The pressure of compression fl uid should be assumed as almost identical to that of contained food in the package. This assumption has the following implications:
No air headspace should be assumed to remain inside the package. •
Gas released from food structure due to temperature rise at preheating step •
or due to mechanical hydrostatic shrinking of food should be negligible. Shrinkage due to compression of contained air should be negligible. •
A further assumption is that the food does not change its composition, structure, and phase state between initial and termination points of the process (Farkas and Hoover, 2000). However, the HPHT used might produce compositional and struc- tural changes (e.g., changes in porosity or density) in selected food composites. The most common occurrence in high-protein foods is the pressure-induced protein
denaturation (Otero and Sanz, 2003). Thus, chemical/physicochemical reactions and changes in food volume or compressibility that might affect mass and heat transfer pathways can be neglected.
The shape, amount, and position of pouches in the vessel can also affect the way heat is transferred during preheating and pressurization (Table 5.3). An initial approach should consider several options: (a) no pouch inside, (b) one pouch fi xed at the geometric center of the vessel, and (c) several pouches geometrically distributed and fi xed within the vessel (undisturbed by fl ow of incoming pressure transmit- ting fl uid). The location, size, and shape of the sample should be fi xed to establish boundary conditions. An initial consideration due to the cylindrical shape of the vessel could be to have a cylindrical type of package for an axis-symmetric model (Hartmann and Delgado, 2003b).
Thermal gradients due to differences in compression heating properties between sample and sample holder can also be neglected. Due to lack of knowledge on the thermophysical properties of different food components, these can be assumed simi- lar to water. Depending on whether a solid, liquid, or solid:liquid mixture, or porous material is contained in a fl exible container, mass transfer considerations can be considered negligible as an initial approach.
Gravity infl uence, however, cannot be assumed as negligible. Especially during holding stage, natural convection is mainly infl uenced by gravitational forces (Knoerzer et al., 2007). Carroll et al. (2003) assumed the food and fl uid properties to be isotropic but still dependent on temperature and pressure. Nevertheless, temperature differences throughout the vessel lead to nonisotropic material properties, which need to be accounted for.
5.4.1.4 Assumptions for Processing Conditions
In this case, a single pressurization step may be considered and the processing times (including for preheating and pressurization) may be assumed constant based on a constant fl uid inlet velocity. Depending on inlet geometry and velocity, the governing differential equations for either laminar or turbulent conditions have to be selected. Input variables for the model may be the initial temperature inside the product and vessel (Ts), target pressure P1, pressure rate, holding time [tp1 − tp2], and decompres-
sion rate (Figure 5.1). CFD software packages allow starting from an initial tempera- ture distribution from a previous model (e.g., by considering vessel interactions with all components or by accounting for the product and carrier preheating step) or by using different initial temperatures in different components. For example, Juliano et al. (2008) studied the effect of having a colder top vessel lid at the start of the pressurization process (discussed in Chapter 6).