Carrier optimisation in a pilot-scale high pressure sterilisation plant – An iterative CFD approach employing an integrated temperature distributor (ITD)

Journal of Food Engineering 97 (2010) 199–207

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Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng

Carrier optimisation in a pilot-scale high pressure sterilisation plant – An iterative CFD approach employing an integrated temperature distributor (ITD) Kai Knoerzer a,*, Roman Buckow a, Belinda Chapman b, Pablo Juliano a, Cornelis Versteeg a a b

CSIRO Food and Nutritional Sciences, Innovative Foods Centre, Private Bag 16, Werribee, VIC 3030, Australia CSIRO Food and Nutritional Sciences, P.O. Box 52, North Ryde, NSW, Australia

a r t i c l e

i n f o

Article history: Received 26 May 2009 Received in revised form 9 September 2009 Accepted 7 October 2009 Available online 13 October 2009 Keywords: CFD High pressure High pressure thermal Modelling Optimisation Insulating carrier Thermal sterilisation

a b s t r a c t High pressure thermal (HPT) processing is a candidate for commercial scale food sterilisation. During HPT processing, heat is generated volumetrically within the vessel as a result of rapid pressurisation, typically to pressures of 600 MPa or more. As for traditional retort processes, the temperature profile in the vessel should ideally be uniform at all stages of the process in order to minimise the occurrence of under- and over-processing of individual food containers. Insulating polymeric carriers are employed in (pilot-scale) HPT processing with the aim of maximising heat retention and improving temperature uniformity. However, polymeric carriers can occupy a large portion of the vessel volume, thus compromising load capacity. Load capacity issues are a limiting concern for scale-up of HPT processing to commercial scale. As tool for optimising polymeric carrier design, we have developed an iterative software routine that progressively alters the carrier wall thickness in a previously developed computational fluid dynamics (CFD) model, and coupled this with an integrated temperature distributor (ITD) routine, which allows us to describe, in a single parameter, overall process performance in terms of heat retention and uniformity. The use of the combined carrier wall thickness/ITD routines was demonstrated for optimising the design of a polymeric carrier in a 35 L pilot-scale high pressure sterilisation plant, the ITD concept to have applications in HPT processing beyond carrier design, including as a parameter to describe process safety. Crown Copyright  2009 Published by Elsevier Ltd. All rights reserved.

1. Introduction High pressure thermal (HPT) processing is a candidate technology for high-temperature short-time commercial sterilisation of chill- and ambient stable low-acid food products. Commencing with moderate initial product and pressure chamber temperatures of 60–90 C, HPT processing currently employs pressures of up to 700 MPa to increase the temperature of the preheated food to inactivate bacterial spores (Matser et al., 2004; Margosch et al., 2004; Bull et al., 2009). Temperature increase during pressurisation is induced by compressive work against intermolecular forces and assuming that there are no thermal losses, the temperature reached during pressurisation can be readily derived (Knoerzer et al., 2007, 2010; Juliano et al., 2009):

dT ap ðP; TÞ ¼ T dP qðP; TÞ  C p ðP; TÞ

* Corresponding author. Tel.: +61 3 9731 3353; fax: +61 3 9731 3201. E-mail address: [email protected] (K. Knoerzer).

ð1Þ

where T denotes the absolute temperature in K, P the pressure in Pa, aP the thermal expansion coefficient in K1, q the density in kg/m3 and CP the specific heat capacity in J/kg K. Product and compression fluid temperature may rise up to 40 C during high-pressure treatment, depending on the initial temperature, target pressure, and compression heating properties of the compressed material. Due to the low compressibility of metal, the pressure vessel will not undergo significant compression heating (Ting et al., 2002). Thus, the compression heating of the pressurised food and fluid inside the vessel is much higher than the heating of the steel vessel, leading to the development of thermal gradients (Denys et al., 2000; Otero and Sanz, 2003; Knoerzer et al., 2007; Juliano et al., 2009), causing heat loss towards the chamber walls. Also, cooler, albeit preheated, compression fluid entering the vessel during pressurisation provides an additional heat sink; in vertical high pressure systems, the fluid inlet region can thus be the coldest spot in the process (Knoerzer et al., 2007; Juliano et al., 2009; Hartmann and Delgado, 2003b; Hartmann et al., 2004). As for traditional thermal processing, maximising the uniformity of vessel temperature is also a highly desirable element in HPT processing. Uniform temperature distribution reduces the

0260-8774/$ - see front matter Crown Copyright  2009 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2009.10.010

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Nomenclature specific heat capacity, J/(kgK) CP specific heat capacity of PTFE, J/(kgK) CP,PTFE constant, m4/kg4 Cl d diameter of compression fluid inlet tube, mm D decimal reduction time, min decimal reduction time at Tref, min Dref carrier wall thickness, mm dwall F thermal death time, min g gravity constant 9.81, m/s2 h height, mm hbottom height of bottom closure of carrier, mm height of HP chamber, m hc hcarrier_int internal height of carrier, mm height of top closure of carrier, mm htop k turbulent kinetic energy, kg2/K2 k1,k2 thermal conductivity, W/(m K) compression heating coefficient, Pa1 kC kPTFE thermal conductivity of PTFE, W/(m K) turbulent thermal conductivity, W/(m K) kT n boundary normal direction N number of survivors, CFU/g number of survivors at time t = 0, CFU/g Nref P pressure Pa, MPa pressure rate, MPa/s prate target pressure, MPa Ptarget Q volumetric compression heating rate, W/m3 r horizontal position (radial direction), m internal radius of HP chamber, m rc external radius of carrier, m rcarrier rmin,rmax radial limits for ROI, m rtop/bottom radius of top and bottom closure of carrier, mm radius of HP inlet tube, mm rtube external radius of HP vessel, m rvessel S entropy, J/K T temperature, C or K t time, s end of process, s tf come-up time, s th hold time = tr  th, s thold initial temperature, C or K Tinit Tmax,adiabatic temperature after adiabatic compression, C or K temperature gradient, K TD process time of interest, s tprocess time of pressure release, s tr reference temperature, C or K Tref wall temperature (bottom of HP chamber), C Twall

occurrence of under- and over-processing, which in turn contributes to the delivery of quality products, that are microbiologically safe. Many authors (Otero and Sanz, 2003; Hartmann, 2002; Hartmann and Delgado, 2002, 2003a; Hartmann et al., 2003; Otero et al., 2007; Ghani and Farid, 2007; Knoerzer et al., 2007; Juliano et al., 2009) have considered thermal gradients produced during HPT processing. Various inserts have been proposed to improve temperature uniformity for HPT processing (Juliano et al., 2009; Knoerzer et al., 2007). Amongst these, the most suitable appear to be product carriers made from polymeric insulating materials, for example polytetrafluoroethylene (PTFE) or polypropylene (PP), which typically have low thermal conductivities. However, these insulating carriers can occupy a significant portion of the vessel volume. Therefore, it is desirable to design carriers with a minimal but sufficient wall thickness, to maximise load capacity of the vessel while simultaneously maximising heat retention

V Vusable Vwater !

v vin vz

z zmin,zmax zT

specific volume, m3/kg usable volume/load capacity, m3 water volume in HP chamber, m3 velocity vector, m/s inlet velocity, m/s velocity in z-direction, m/s vertical position (axial direction), m axial limits for ROI, m thermal sensitivity, C or K

Greek symbols aP thermal expansion coefficient, K1 b water compressibility e dissipation rate of turbulence energy, m2/K3 gT turbulent viscosity, kg/(m K) g dynamic viscosity, Pas p circular constant, 3.14159. . . q density, kg/m3 qPTFE density of PTFE, kg/m3 Abbreviations 2D two-dimensional 3D three-dimensional ASME American Society of Mechanical Engineers CFD computational fluid dynamics CFU colony forming units FEM finite element method HP high pressure HPT high pressure thermal HPP high pressure processing ITD integrated temperature distribution (value) NIST National Institute for Standards and Technology OS operation system PP polypropylene PTFE polytetrafluorethylene PLC programmable logic controller RAM random access memory ROI region of interest Operator d differential @ partial differential f function r nabla operator (vector differential operator)

and uniformity. Computational fluid dynamic (CFD) modelling can be employed as an efficient tool in the design of such optimised carriers. The objective of the work presented here was to design a carrier for HPT processing, improved with respect to its wall thickness and thus load capacity, taking into account minimisation of temperature distribution, and maximisation of usable vessel volume. The CFD model used in the procedure was based on the validated model of Knoerzer et al. (2007) to predict temperature and flow distribution in a 35 L HPHT pilot-scale unit, and more specifically inside an insulating PTFE carrier (Knoerzer et al., 2007; Juliano et al., 2009). To realise our objective, we first developed a procedure, based on a MATLAB (The Mathworks Inc., Natick, MA, USA) software routine interfacing to a COMSOL Multiphysics (COMSOL AB, Stockholm, Sweden) CFD model, capable of progressively modifying the carrier geometry as determined by the carrier wall TM

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thickness. By extracting the models’ solutions, evaluating process performance and load capacity, we were then able to determine the optimum design for maximum heat retention, temperature uniformity and usable volume. These elements were implemented as features in the software routine in the form of a single dimensionless parameter, the integrated temperature distributor (ITD).

2. Materials and methods 2.1. Iterative CFD model 2.1.1. High pressure high temperature system The HPT model was based on a Flow Pressure Systems QUIN TUS Food Press Type 35L-600 sterilisation plant (Avure Technologies, Kent, WA, USA). The system consists of a thick wire-wound cylindrical stainless steel vessel (capacity 35 L) with two restrained end closures, an external low pressure pump, a pressure intensifier and necessary system controls and instrumentation. Compression fluid is injected from the bottom of the vessel through 3.2 mm diameter high pressure tubing. Compression is realised by the external intensifier which uses preheated water from the low pressure pump. The stainless steel vessel is heated by resistors surrounding the structure (maximum temperature 90 C). Water can also be circulated through the vessel to ensure thermal equilibrium before pressurisation.

2.1.2. Model of high pressure high temperature system The geometry of the model high pressure chamber is depicted in Fig. 1. The actual system incorporates some non-axis-symmetric features, notably the pressurising fluid inlet; however, to make the problem more tractable, an axis-symmetric system has been simulated, with the fluid inlet moved to the centreline. The original model of Knoerzer et al. (2007) included the chamber space, a water inlet at the bottom centre, the carrier, and a water domain. The model was validated by comparison with actual temperature measurements taken at nine points evenly distributed in an axis-symmetric cross-section of a metal carrier. In this work, the CFD model was modified according to Juliano et al. (2009) to include the vessel lid and side walls, and an air boundary layer surrounding the walls. The model of the polymeric carrier was refined to represent the actual carrier’s geometry as accurately as possible. 2.1.3. Model for carrier optimisation For optimisation of the carrier, the carrier wall thickness was defined as a variable ranging between 0 mm 6 dwall 6 70 mm. The top and bottom closure dimensions of the carrier were fixed (rtop/ bottom = 90 mm, hbottom = 65 mm, htop = 30 mm). The distance between the outer carrier wall and inner vessel wall was kept constant at 5.5 mm (Fig. 2). Product pouches inside the carrier, as used in real-life processes, will have a significant impact on the temperature and flow evolution during the process. As forced and natural convection will be reduced by the presence of such pouches, it is likely that heat losses are also reduced. The purpose of this study was to evaluate the performance of thermal insulation of the product carrier at varying wall thicknesses and the carrier was assumed to not contain any product, which represents the worst case with respect to anticipated overall heat losses. In all modelling scenarios, two COMSOL Multiphysics application modes were selected and coupled: (i) the k  e Turbulence Model, applied to the water domain only (inactive at the solid regions occupied by the carrier), and (ii) the convection and conduction model, applied in both liquid and solid regions. TM

2.1.4. Governing equations The thermo- and fluid-dynamic behaviour of the pressure medium is described by conservation equations of mass (Eq. (2)), momentum and energy (Chen, 2006).

@q ! þ r  ðq v Þ ¼ 0 @t

ð2Þ

where q is the density as function of pressure and temperature and ! v is the velocity vector. As shown by Knoerzer et al. (2007), the inflowing pressurisation water enters through the high pressure system inlet at a high velocity, creating turbulent flow in the bottom region. Turbulence was solved by applying the k  e model that included an additional ‘‘turbulence viscosity” and ‘‘turbulent thermal conductivity” in the equations for conservation of momentum and energy, respectively, to take the contributions of turbulent eddies into account (Nicolaï et al., 2007; COMSOL Multiphysics, 2006). The turbulent viscosity gT is given by:

gT ¼ qC l

Fig. 1. Configuration of model geometry and mesh in a vertical cross section of the high pressure vessel steel structure containing the PTFE carrier (example of carrier wall thickness dwall = 10 mm). The outer cylinder shows the high pressure chamber, the inner cylinder the carrier, and all shaded areas the axis-symmetrical computational domains. (For coloured illustrations please refer to the online version of this article).

k

2

e

ð3Þ

where Cl = 0.09 (Launder and Spalding, 1974), k is the turbulent kinetic energy and e the dissipation rate of turbulence. Here the momentum equation (extended according to COMSOL Multiphysics (2006)) gives the following expression:



q

 @~ v ! ! ! þ ð v  rÞ v ¼ rP þ r  ððg þ gT Þ  r v Þ þ qg @t

ð4Þ

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qC p

  @T ! þ v  rT ¼ Q þ r  ððk1 þ kT ÞrTÞ @t

ð5Þ

where k1 is the thermal conductivity, and Cp is the specific heat capacity. PrT is the turbulent Prandtl number. The source term Q arises from compression, by rewriting Eq. (1):

Q ¼ T aP

dP dt

ð6Þ

2.1.5. Process conditions The pressure–time profile was defined in the program as an input linearly increasing from ambient pressure to 600 MPa within 130 s. Based on a water compression, b, of 17%, the inlet velocity vin was calculated using:

v in ¼

b  V water 4  2 th pd

ð7Þ

where Vwater is the volume of water in the vessel (excluding carrier volume), th the pressure come-up time, and d the diameter of the inlet tube (3.2 mm). Based on carrier wall thicknesses ranging from 0 mm (no carrier walls, only top and bottom closure present) to 70 mm, the inlet velocity was determined as ranging from 5.3 m/s (at dwall = 0 mm) to 1.2 m/s (at dwall = 70 mm), due to the change in water volume requiring compression during the fixed compression time (130 s). The carrier was assumed to be incompressible, and thus incapable of undergoing compression heating. The Reynolds number at the inlet was between 13,000 and 57,400, calculated for a inlet velocity of 1.2 m/s and 5.3 m/s assuming a high pressure tubing diameter of 3.2 mm, water density of 1100 kg/m3 and a dynamic viscosity of 0.325 mPa s, averaged for pressures between 0.1 and 600 MPa and temperatures from 90 to 121 C. Thus, the plume of fluid entering the vessel was clearly turbulent. Once the maximum pressure of 600 MPa is reached the inlet tube is closed, i.e. velocity is set to zero, and the pressure is maintained for a set time (here 300 s). After the pressure holding period the inlet tube opens and water flows out with a pressure decrease from 600 MPa to atmospheric pressure within 15 s. The pressure come-up and decompression times were based on the specifications of the modelled high pressure pilot plant (Flow  Pressure System QUINTUS Food Press Type 35L-600 sterilisation plant (Avure Technologies, Kent, WA, USA)). The pressure hold time of 5 min was selected based on the assumption that this would be around the preferred (by industry) maximum hold time for a commercial high pressure thermal process, and is illustrative only.

Fig. 2. CFD model (based on the finite element method (FEM)) of the HP system with carrier dimensions indicated (red: load capacity, pink: carrier wall, dark grey: carrier top and bottom closure). (For coloured illustrations please refer to the online version of this article).

! where v denotes the average velocity, P is the pressure, g represents the dynamic viscosity of the compressed fluid, and g represents the gravity constant. In addition to the continuity equation, the k  e closure includes two extra transport equations solved for both k and e using empirical model constants (COMSOL Multiphysics, 2006). The k  e closure equations were coupled with the energy conservation equation for heat transfer through convection and conduction, assuming non-isothermal flow. This equation was modified from Kowalczyk et al. (2004) and extended according to COMSOL Multiphysics (2006) by including the turbulent thermal conductivity kT (with kT = CPgT/PrT):

2.1.6. Initial condition The pressure chamber and carrier are completely filled with water at the start of the process. The pressure medium is initially at rest and the carrier, vessel wall, and pressure medium are at thermal equilibrium at 90 C.

Therefore; for t ¼ 0;

T ¼ T init ¼ 90  C 8r; 8z < hc ;

where hc is the height of the chamber from the bottom to the vessel lid. As the lid was not actively heated and not closed during the preheating of the vessel, it was initially at 30 C. 2.1.7. Boundary conditions Fluid–solid boundaries had to be defined for the k  e turbulence mode on the liquid domain, whereas thermal boundaries were defined for convection and conduction mode for all domains. Symmetry boundary conditions on the axis (r = 0) were assumed and can be simplified to the following expressions:

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n  ðkrTÞjr¼0 ¼ 0 and n 

! v jr¼0 ¼ 0

8z 2 specific domain; 8t > 0

ð8Þ

where n is the direction perpendicular to the boundary. An inflow velocity boundary condition was defined for the inlet tube for come-up and holding times:

v z jr ¼ v in ; 8r 2 ½0; rtube ; 8t 2 ½0; th ;

ð9Þ

where rtube = 1.6 mm, th = 130 s

and

temperature as variables, sufficiently fitted the data in the relevant pressure and temperature range. Equation parameters are provided in Knoerzer et al. (2007). These equations were then implemented in the model. Properties for PTFE were taken as constants, independent of temperature and pressure variations as Cp,PTFE = 1050 J/kg K, kPTFE = 0.24 W/mK, and qPTFE = 2200 kg/m3). The expansion coefficients of the solids (steel and PTFE) were assumed to be zero. The viscosity only had to be set in the water domains, active in the k  e Turbulence Model.

v in ¼ 0; 8t 2 ½th ; tr 

A pressure condition was also imposed in this boundary:

P ¼ prate  t;

z ¼ 0;

8r 2 ½0; r c ;

8t 2 ½0; t h ;

ð10Þ

With rc = 0.095 m. For come-up time: prate = Ptarget/th = 4.62 MPa/s, "t 2 [0, th]. For holding time: prate = 0 and P = Ptarget = 600 MPa, "t 2 [th, tr]. With tr  th = 300 s, i.e. tr = 430 s. For decompression a normal flow pressure condition was imposed. In this case, the change in pressure was assigned to vary as follows (where tf = 445 s):

prate ¼

Ptarget ¼ 40 MPa=s; 8z 2 ½0; hc ; tf  tr

TM

ð11Þ

A logarithmic wall function condition as described by Knoerzer et al. (2007) is assumed at the interior vessel and carrier walls. More background information can be found in Launder and Spalding (1974). The inlet boundary was set to a constant temperature until the end of pressure holding and was estimated to be at 85 C:

T in ¼ 85  C;

8t 2 ½0; tr ;

z ¼ 0;

8r 2 ½0; r tube 

ð12Þ

This temperature was selected based on measurements in the described system, which is capable of pre-heating the compression fluid to only 85 C. The vessel bottom internal wall temperature was assumed to decrease linearly from 90 C to 85 C during come-up time, and to maintain constant temperature during the pressure holding and release steps. Thus:

  t T wall ¼ 90  5  C; 8t 2 ½0; th ; th and T wall ¼ 85  C;

z¼0

ð13Þ

8t > t h ; 8r 2 ½1:6 mm;r v essel 

where rvessel = 0.265 m Continuity of heat flux is assumed at all fluid–solid and solid– solid boundaries:

n  ðk1 rTÞ ¼ n  ðk2 rTÞ;

8r; 8z 2 specific domain;

8t > 0 ð14Þ

where k1 and k2 are the thermal conductivities of the two respective subdomains, and n is the normal boundary direction. During the decompression step pressure fluid was released from the chamber. A convective heat flux condition was used on the inlet/outlet boundary:

! n  ðk  rTÞ ¼ n  qC P T v ;

8t > tr;

TM

TM

8r 2 ½0; r c ;

8t 2 ½t r ; tf 

2.1.9. Computational methods The partial differential equations describing the model were solved with the finite element method (FEM). A commercial software package, COMSOL Multiphysics (COMSOL AB, Stockholm, Sweden) was used, incorporating toolboxes for simultaneously solving multiphysics problems. Computations were carried out on a workstation running the 64bit OS Windows 2003 server. Two dual-core processors (each 2.33 GHz) and 20 GB RAM allowed for solving each model for the different carrier wall thicknesses within approximately 45 min of computation time. An interface to the COMSOL Multiphysics model was programmed in MATLAB 7.6 (Mathworks, Natick, MA, USA). Based on this interface a software routine progressively modified the model with respect to carrier wall thickness (ranging from 0 mm to 70 mm wall thickness) and compression fluid inlet velocity. The initial step changes in wall thickness were set to 5 mm. After solving the model, the software routine extracted the transient temperature distributions, automatically determined the area within the carrier as the region of interest (ROI), calculated the ITD value and the usable volume inside the carrier (see next sections for further explanations and formulas) and stored the results in three vectors for wall thickness, ITD value and usable volume, respectively. Values for the ITD and usable volume were normalised to their respective maximum values, and plotted versus the carrier wall thickness. The optimised carrier wall thickness was determined from the intersection of both profiles. Following a preliminary evaluation of the optimum wall thickness with respect to ITD value and usable volume, the software routine repeated the iterative approach of progressively modifying carrier wall thickness in 1 mm steps around a range of ±5 mm with respect to the preliminary optimum. The values from this second step were included in the respective vectors. Finally, the software routine normalised the ITD values and load capacities for the different carrier wall thicknesses to their respective maximum values to allow for final evaluation. The percentage of maximum ITD and usable volume at specific wall thicknesses were determined from the graph’s ordinate (y-axis). Overall, the computation time for solving all models and analysing the data was about 24 h for the system used.

8r 2 ½0; 1:6 mm; z ¼ 0 ð15Þ

2.1.8. Material properties Physical properties, including expansion coefficient, density, specific heat capacity, thermal conductivity and viscosity of the water and their variation with pressure and temperature were obtained from the NIST/ASME database (Harvey et al., 1996). It was found that a first order polynomial equation, with pressure and

2.2. Integrated temperature distributor (ITD) In order to conveniently evaluate a process with respect to temperature performance, a parameter is required that accounts not only for temperature profiles in discrete locations in the vessel or carrier, but also for the temperature variations across the volume. Preferably this parameter is dimensionless and universally applicable to any equipment size and process time, making it a convenient tool for comparisons between different types and scales of equipment and processes. Sterilisation processes in the food industry are typically described in terms of their ability to inactivate specific target microorganisms, such as Clostridium botulinum or Geobacillus

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stearothermophilus. The decimal reduction time D (min) of any microorganism at a given temperature is expressed as

D¼

t log N ref  log N

ð16Þ

where N is the number of survivors (typically colony forming units (CFU) per gram or mL) at time t, and Nref is the initial number of microorganisms (Ball, 1943). Traditionally, the temperature dependence of the D value is expressed in terms of the thermal resistance constant, zT (C), using the following model:

zT ¼ 

ðT  T ref Þ ðlog Dref  log DÞ

ð17Þ

where the reference decimal reduction time Dref (in min) is at a reference temperature Tref (in C), within the range of temperatures T (in C) used to generate experimental data. In thermal processing of commercial food products F-values (thermal death times) are often used to relate the temperature history of a process to a reference temperature:

F¼

Z

t

TðtÞT ref

10

zT

dt

ð18Þ

0

where F is the accumulated lethality expressed as equivalent time at a specific reference temperature Tref, for a specific zT (Bakalis et al., 2001). However, the F-value model has been questioned due to the assumption of the linearity of the inactivation kinetics of target bacterial spores as well as the linearization of the temperature dependence of the D-value to obtain the zT value. Therefore, we propose an equation to evaluate the thermal process performance in an HPHT process throughout the vessel without requiring inputs from microbial kinetic parameters and only accounting for temperature and time data:

R1 R rmax R zmax ITD ¼

r min

zmin

10

TðtÞdt 0 T target t process TD

drdz

ðr max  r min Þ  ðzmax  zmin Þ

ð19Þ

where rmin, rmax, zmin, zmax cover the ROI (in this case, the carrier volume), tprocess is the process time of interest (in this case, the holding

time where most of the heat loss is expected), T D is a temperature gradient of 10 K and Ttarget is the targeted hold temperature of the process. The target hold temperature in this study, Ttarget = 120.6 C, was the calculated adiabatic heating of the compression fluid upon pressurisation to 600 MPa, assuming an initial temperature of 90 C. The contributions of compression and decompression time were not included in calculations, due to the relatively short times and rapid temperature changes associated with those process phases. The ITD is made dimensionless by relating the integrated temperature profiles in each location to the process (holding) time and T D , and the surface (volume) integral to the area (volume) of the ROI. The flowchart for the determination of the ITD value is shown in Fig. 3. Depending on whether the calculation is applied to an axissymmetric or full 3D temperature distribution, the ITD value represents either the pseudo-volumetric 2D or volumetric 3D thermal process performance. The following conclusions can be drawn from the calculated ITD value (in combination with the integrated temperature distribution plot):  ITD = 1: perfect target temperature uniformity with respect to process time and distribution.  ITD < 1: under processing in some or all parts of the carrier volume.  ITD > 1: over-processing in some or all parts of the carrier volume. Since in this study the target temperature was set assuming adiabatic temperature increase, and since the vessel and carrier wall temperature increase during compression is expected to be lower, ITD values cannot be greater than 1. Hence, only perfect time/temperature uniformity (in an adiabatic carrier system without temperature gradients) or under processing can be expected.

2.3. Usable volume Beside process thermal performance (ITD), the usable volume (or load capacity) is perhaps the most important parameter to con-

Fig. 3. (a) Example of a temperature distribution in a HP process (at discrete time); depiction of region of interest (ROI, purple) inside carrier. (b) Flowchart of ITD determination. (c) Example output of integrated temperature distribution (carrier wall thickness dwall = 15 mm). (For coloured illustrations please refer to the online version of this article).

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205

Fig. 4. Examples of simulated temperature distributions in the HP system for three different wall thicknesses (a) dwall = 0 mm, (b) dwall = 5 mm, (c) dwall = 70 mm at the end of hold time (t = 430 s). (For coloured illustrations please refer to the online version of this article).

sider when optimising HPT processes, due to commercial requirements for high product volume and throughput. In our model, increasing values for dwall led to a decrease in load capacity according to the following equation:

V Usable ¼ p  ðr carrier  dwall Þ2  hcarrier

int

ð20Þ

Where rcarrier is the carrier’s external radius (=90 mm), dwall is the carrier wall thickness (=variable) and hcarrier_int is the carrier’s internal height (=1035 mm). Considering the range of 0 mm 6 dwall 6 70 mm, the load capacity can be as low as Vusable = 1.3 L and as high as 26.3 L. The load capacity of the current carrier as provided by the manufacturer is Vusable = 12 L. 3. Results and discussion Fig. 4 shows examples of resultant temperature distributions at the end of the pressure hold time (430 s of the total processing time) for three different wall thicknesses, dwall = 0 mm, 5 mm and 70 mm, respectively. At a wall thickness of 0 mm (no carrier wall), the lack of insulation is clearly demonstrated, with temperatures not exceeding 105 C at the end of pressure holding (Fig. 4a). Furthermore, at the end of the pressure come up time, the temperature did not reach the adiabatic heating temperature of 120.6 C at any point in the carrier (data not shown). In Fig. 4b, a uniform temperature distribution at the end of the hold time is observed, with average temperatures close to 118 C inside the carrier, indicating good thermal insulation. Fig. 4c shows the temperature distribution for the maximum simulated wall thickness of 70 mm. In this case, the thick carrier walls decrease the usable volume to just 1.3 L. Together with the small usable volume, the large thermal mass of the PTFE, which is assumed not to undergo compression heating, results in poorer process performance than for the 5 mm carrier. Thus, although the carrier walls insulate the carrier contents from the cooler vessel walls, they themselves also act as heat sinks, resulting in the formation of temperature gradients and heat loss.

Fig. 5. Normalised ITD values and load capacity versus variable carrier wall thickness. Also shown is the carrier wall thickness of the current system (dwall = 28 mm) and the optimum of carrier wall thickness with respect to process performance and load capacity. (For coloured illustrations please refer to the online version of this article).

Fig. 5 shows the dependence of the ITD and load capacity values, normalised to their respective maximum values, on carrier wall thickness. The ITD value is close to zero for the scenario without carrier walls, and then increases with increasing values for dwall until a maximum value (0.54 before normalisation, corresponding to an average heat loss over time across the carrier volume of 2.6 C) is reached at a wall thickness of 7 mm. Achieving the maximum ITD value requires sacrifice of around 15% of the maximum usable volume of the vessel (see Fig. 5). The decline with further

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increasing dwall can be explained by the increase of the heat sink effect of the PTFE carrier, assuming no compression heating of the plastic. The intersection of the curves may be used to determine the optimised carrier wall thickness with respect to both temperature performance and usable volume, in this case dwall = 4 mm (Fig. 5). At this optimised carrier wall thickness, just 9% of both the maximum ITD value and load capacity are sacrificed, suggesting an increase from a 12 L carrier capacity to a 24 L capacity at normalised ITD values close 0.9. 4. Conclusion and outlook For the economical implementation of a process in the food industry, high throughputs with minimised cost-of-manufacture are essential. Needlessly reducing ‘‘expensive” HPT process volume by overdesigning insulating polymeric carriers can potentially jeopardise the uptake of this emerging batch processing technology. CFD modelling has proven to be a versatile tool in computer-aided process engineering, allowing for testing of equipment prior to actual manufacture, thus reducing expensive and labour-intensive trial-and-error constructions. Here we have demonstrated the implementation of CFD models in a software routine to optimise HPT process carrier design with respect to wall thickness. The software routine progressively and automatically changed the carrier wall thickness, solved the model, extracted the model solution and evaluated the solution with respect to thermal performance and load capacity. In this manner, the carrier wall thickness could be optimised to maximise temperature performance alone (7 mm), or both usable volume and temperature performance (4 mm). In either case, considering the actual wall thickness (dwall = 28 mm) of our current PTFE carrier, together with the resultant temperature performance (normalised ITD < 0.90) and usable volume (<50%) in our actual HPT plant, the value of this iterative CFD modelling approach in design of future carriers is clearly demonstrated. Future modelling routines can include more accurate information on carrier material properties as these become available, including compression heating values and thermal conductivities, thus also facilitating the selection of carrier material. The developed ITD concept conveniently permits the description of process performance in a single parameter that encompasses target temperature and temperature distribution concepts. The ITD is therefore a useful tool in its own right, with potential application to all elements of HPT process equipment design with potential to affect heat development and transfer. As for traditional retort sterilisation processes, temperature uniformity and the attainment of critical processing temperatures are likely to be crucial to the development of microbiologically safe HPT processes for low-acid foods. Several pressure–temperature-time combinations have been proposed for effective bacterial endospore inactivation (Ardia et al., 2003; Margosch et al., 2006; Ananta et al., 2001; Rajan et al., 2006; Patazca et al., 2006), but recent work (Bull et al., 2009) suggests that, at least with respect to the target pathogen C. botulinum, HPT processing should be regarded first and foremost as a thermal process. As such, both processors and regulators may appreciate the simplicity of the ITD concept, which could be easily extended to an integrated inactivation distributor (IID) determined via coupling with models describing microbial inactivation, for sense-checking HPT process safety. Acknowledgments The authors wish to thank Dr Michelle Bull and Prof Peter J. Fryer for helpful discussions. Furthermore, Avure Technologies is thanked for providing critical technical data. Gratefully acknowl-

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