a cfd simulation of the coldest point during sterilisation

A CFD SIMULATION OF THE COLDEST POINT DURING STERILISATION OF CANNED FOOD

Abdul Ghani A. Ghani, Mohammed Mehdi Farid*, and Xiao Dong Chen Food Science & Process Engineering Group, Department of Chemical & Material Engineering, The University of Auckland, Private Bag 92019, Auckland, New Zealand. *Corresponding author: fax: 649-3737463, email: [email protected]

SUMMARY Canning is one of the most effective means of preserving food. Food after being canned has to undergo thermal treatment to deactivate most organisms, ie sterilisation. This process is usually done using steam to heat the food in the can to a temperature and hold it for a period sufficient to kill the microorganisms. Excessive heating will affect food quality and its nutritive properties. Heat is transferred through the liquid food in the can by both conduction and natural convection. If heat transfer is controlled by conduction only, then the coldest point during the heating process will be at the geometric centre of the can. However, such condition does not prevail except when the canned food is solid. Natural convection causes the coldest point to move towards the bottom of the can. In this paper, a computational fluid dynamics software package (CFD) was used to predict temperature distribution in a can filled with liquid food. The partial differential equations, describing the conservation of mass, momentum, and energy, were solved numerically. Saturated steam at 121 oC was used as a heating media. The simulation shows that over time, the coldest point migrates towards the bottom of the can due to natural convection currents. With low viscosity fluids (close to that of water) the coldest point approaches the bottom of the can. The simulation on viscous liquid food shows similar phenomena. The effect of presence of air gap at the top of the can had negligible effect on the temperature distribution in the liquid. Hydrodynamic interpretation of the phenomena, including fluid swirling, is presented in this paper.

INTRODUCTION Canning of food is a key method of food preservation. The objective of canning is to increase food shelf life and ensure its safety. Despite the significant advancement made in food preservation techniques, sterilisation is still common. For this reason estimates of the heat transfer rates are

required in order to obtain optimum processing conditions and to improve product quality. A better understanding of the heating mechanisms involved will assist in improved control of the processes and an increased energy saving. Basic principles for determining the thermal processing methods have been presented in several books (1,2). A number of numerical heat transfer studies have been done to model sterilisation processes showing the temperature distributions within the liquid food material. Foods like canned tuna, thick syrups, and purees are assumed to be heated by conduction. For these foods, the required processing time may be determined by analytical or numerical solution of the heat conduction equation. Akterian ( 3 ) developed a numerical model for the determination of the unsteady-state temperature field in heated canned solid foods of various shapes under convective boundary conditions. The heat conduction equation is solved by means of finite difference approach. Dincer et al. ( 4 ) studied transient heat transfer during sterilisation of canned solid foods in order to determine the adequate heat transfer rate. Their model was also based on solving the conduction equation using constant wall temperature as a boundary condition. Lanoiselle et al. ( 5 ) developed a linear recursive model to represent the heat transfer inside a can during sterilisation in a retort and to predict the internal temperature of canned foods during thermal processing. In many previous studies, conduction was assumed as the only mode of heat transfer which is true only for solids. Natural convection occurs due to density differences within the liquid caused by temperature gradient. Datta and Teixeira ( 6 ) predicted numerically the transient flow patterns and temperature distribution during natural convection heat transfer of a liquid in a uniformly heated cylindrical can and a recirculating flow pattern. Water was used to simulate liquid food and found to be stratified inside the container with increasing temperatures towards the top. The slowest heating location in the fluid was a doughnut-shaped region close to the bottom of the can at about one-tenth of the can height. They predicted significant internal circulation at the bottom of the can.

The use of CFD in the prediction of temperature distribution in food during sterilisation CFD has seen applications in many different processing industries, but it is only in recent years that the technique has been applied to food processing, including air flow in clean rooms, ovens, chillers, and industrial driers When considering the liquid food flow, it is often necessary to take the rheological nature of the food into account because this will dictate its flow behaviour. Most foods exhibit some form of nonNewtonian behaviour and many different flow models have been used to describe such behaviour. Sterilisation of viscous liquid food in a metal can sitting in an upright position and heated from all sides ( T = 121oC ) in a still retort was simulated by Kumar et al. (7). They also presented a simulation for the same can when its bottom and top surfaces were insulated (8). The latter condition may represent an important industrial configuration due to the presence of an air gap at the top of the can. Equations of mass, momentum and energy conservation for a cylindrical coordinate system were solved and plots of temperature, velocity and streamlines were presented for natural convection heating. The liquid was assumed to have a temperature dependent viscosity but a constant specific heat and thermal conductivity were assumed. The results indicate that natural convection causes the slowest heating point ( coldest point ) to move towards the bottom of the can. In this work, a commercial fluid dynamics software package, known as PHOENICS (Concentration, Heat and Mass Limited (CHAM), London), was used to solve the governing partial differential equations. This is a general purpose code that uses the finite volume method. The details of this code can be found in the PHOENICS manuals (9). The objective in this work is to study the effect of natural convection current on the movement of the coldest point in a canned liquid food and compare the results with those obtained by Kumar et al. (7,8). The effect of the presence of air gap at the top of the can on the heat transfer rate is also studied.

THE GOVERNING EQUATIONS AND BOUNDARY CONDITIONS The transient temperature and velocity profiles during natural convection heating of a liquid in a cylindrical can are predicted. In natural convection heat transfer, the driving force for the liquid motion is the buoyancy motion caused by density variations due to temperature gradient. The partial differential equations governing such motion in a cylindrical space are: Continuity equation:

1 ∂ ∂ (rρv ) + (ρu) = o r ∂r ∂z

(1)

Energy conservation:

∂T ∂T ∂T k =v +u = ∂t ∂r ∂Z ρ C p

 1 ∂  ∂T  ∂ 2 T  r  + 2    r ∂r  ∂r  ∂z 

(2)

Momentum equation in the vertical direction:

 1 ∂  ∂u  ∂ 2 u  ∂u ∂u  ∂p  ∂u ρ + v + u  = − + η  r  + 2  + ρg  ∂t ∂r ∂z  ∂z  r ∂r  ∂r  ∂z 

(3)

Momentum equation in the radial direction: 2  ∂ 1 ∂ ∂v ∂v  ∂p  ∂v  ∂ v rv ρ + v + u  = − + η  + ( )  ∂t ∂r ∂z  ∂r ∂z 2   ∂r  r ∂r

(4)

The boundary conditions are:

T = Tw ,

u = 0,

v=0

at

r = R,

T = Tw ,

u = 0,

v=0

at

z = 0 (can bottom ),

∂T = 0, ∂r

∂u = 0, ∂r

v=0

T = Tw

u = 0,

v=0

at

at

r = 0,

z = H,

0≤ z ≤ H

(5)

0≤r≤R

0≤ z ≤ H

0≤r≤R

(6)

(7)

(8)

and for insulated top ( ie. with an air gap):

∂T =0 ∂z

u = 0,

v=0

at

z = H (can top),

0≤r≤R

(9)

Initially the fluid is at rest at a uniform temperature

T = Ti ,

u = 0,

v=0

at

0 ≤ r ≤ R,

0≤ z≤ H

(10)

The initial temperature used was Ti = 40oC. To simplify the problem it is assumed that the retort reaches the desired temperature instantaneously. A common temperature used in sterilisation of canned foods is 121oC (1,7). Since cans are made of metal which has a low thermal resistance and

steam is condensing on the outer surface of the can wall, it can be assumed that the boundary conditions apply to the inside surface of the can. Most of the previous studies, with the exception of the work presented by Kumar et al. (7,8), have been applied to Newtonian foods ( water or water - like liquid foods ) with constant properties. In reality, foods are generally non - Newtonian and have temperature dependent properties. The objective of this study was to obtain improved quantitative understanding of the natural convection heating of a viscous liquid food during sterilisation and to compare the results with the assumption of pure conductive heating. Computation was performed for a can with radius of 4.048x10-2 m and height of 1.111x10-1 m, similar to that used in the study of Kumar et al. (7) for the purpose of comparison. The can outer surface temperature ( bottom and side ) was assumed to rise instantaneously and be maintained at 121o C. The assumption of top insulation was also simulated representing the case when each can has a head space, which is the common situation for canned foods. Temperature and velocity are expected to have largest variations near the wall because of the active boundary layer effect due to a large temperature radiant. A non-uniform mesh was used in the simulation with 3519 nodal points: 69 in the axial direction and 51 in the radial direction, graded in both directions with a finer grid near the wall. The natural convection heating of the model liquid was simulated for 2574 s. It took 100 steps to achieve the first 180 s of heating, another 100 steps to reach 1000 s and 300 steps for the total of 2574 s of heating. This required 63 h of CPU time on the UNIX computer machine at the University of Auckland. Under-relaxation was needed to keep the computation stable. To simplify the problem, the following assumptions were made: • Axisymmetry which reduces the problem from 3-D to 2-D; • Heat generation due to viscous dissipation is negligible; • Boussinesq approximation is valid; ie. the density difference which causes the flow is due to temperature change only. • Specific heat ( Cp ), thermal conductivity ( k ), and volume expansion coefficient ( β ) are constants ( Table 1 ); • The assumption of no-slip condition at the inside wall of the can is valid; • The condensing steam maintains a constant temperature condition at the can outer surface; • The thermal boundary conditions are applied to liquid boundaries rather than the outer boundaries of the can, because of the low thermal resistance of the cans used in the sterilisation and steam is condensing on the outer can wall.

Non-Newtonian behaviour Food materials are in general non - Newtonian and hence the viscosity is a function of the shear rate. The viscosity is also a strong function of temperature and has a flow behaviour index typically less than one. The viscosity can be described by the following equation: n ∆E η = η0 γn-1 exp (  ) Rg T

(10)

Sodium carboxy-methyl cellulose ( CMC ) suspended in water was used as the model fluid for the simulation and the constants used in the above equation are given in Table 1.

Table 1. Properties of the ‘liquid food’ used in the simulation (7)

Property Value --------------------------------------------------------------------------------------------------------------------Density (ρ) 950 kg m-3 Specific heat ( CP ) 4100 Jkg-1 K-1 Thermal conductivity ( k ) 0.7 Wm-1K-1 Volumetric expansion coefficient ( β ) 0.0002 K-1 Flow behaviour index ( n ) 0.57 0.002232 Pa.sn Consistency index ( ηo ) Activation energy ( ∆ E ) 30.74x103 kJ kgmol-1

Since in natural convection heating the velocities are low, it may be assumed that the shear rate are not high during liquid flow inside the can. At low shear rates of 0.01 s1 (7), the viscosity may be assumed independent of shear rate and hence it will be dependent on temperature only. This Newtonian approximation was found to describe variety of food materials such as tomato puree, carrot puree, green bean puree, apple sauce, apricot puree, and banana puree which are regularly canned and usually preserved by heating (10). Although the CMC was assumed Newtonian fluid at low shear rate, equation (10) was used in this simulation carried out in this work. This is to provide the same values of viscosity used by Kumar and Bhattachaya (7) for the purpose of fair comparison with our simulation results. Density variation were governed by the Boussinesq approximation. The density difference which causes the flow is only due to temperature change, and pressure effect on density can be neglected ( ie. incompressibility assumed ).

RESULTS AND DISCUSSION Flow Pattern As shown in Figures 1 and 3, the liquid adjacent to the wall, top and bottom surfaces will receive heat from the condensing steam in the absence of an air gap at the top. As the liquid is heated, it expands and thus gets lighter. Liquid away from the side wall stays at a much lower initial temperature. The buoyancy force created by the change in liquid density due to temperature variation ( from the wall to the core ) produces an upward flow near the side wall. The hot liquid going up is deflected by the top wall and then travels radially towards the core liquid, which being heavier, moves downwards and towards the wall. Thus a recirculating flow is created with a boundary layer at the side wall, core flow around the center line, and a mixing region at the top. Figures 1 and 3 illustrate the velocity vector fields, which also show that liquid next to the wall is at rest because of the no-slip boundary conditions. The magnitude of the maximum axial velocity at the mid-height near the wall were 0.31

and 0.25 mm s-1 at t= 1157 s, which is in a good agreement with the results of Kumar et al. (7) who used the same viscous liquid ( CMC ) and the same heating conditions. Datta et al. (6) reported much higher velocities for water contained in a can and heated under similar conditions. The magnitudes of the velocity were 35, 16 and 12 mm s-1 after 30, 240 and 450 s of heating. This is also in reasonable agreement with the results of our simulation, which is not shown in this paper (11). Because of these high velocities, the coldest point in the can reached 84 oC after only 120 s of heating, compared to 1200 s for the CMC. As heating progressed, a more uniform liquid velocity was obtained, reducing liquid velocity significantly. The difference in the magnitude of the velocities for water and the more viscous liquid used in our analysis is expected due to the large difference in the viscosity of the two liquids. Hiddink (12) reported that for viscous fluids, the thickness of the ascending liquid region near the wall was greater than that for water which was attributed to the big difference in the values of viscosity of the two fluids. The reported thickness was about 12-14 mm for the viscous liquid as compared to 6-7 mm for water. Kumar et al. (7) illustrated that the thickness of ascending liquid for a more viscous liquid was in the range of 15-16 mm, which is in agreement with the results of this work. Figure 3 shows that the thickness of the ascending liquid is in the range of 16-20 mm. Datta et al. (6) have reported the formation of secondary flow (or eddies formation) at the bottom of the can near the center line. The simulation which has been done by Kumar et al. (7) for thick liquid ( CMC ) did not show any eddies, however in our simulation, the secondary flow was evident in all the cases studied due to the very fine mesh used. Figures 1 and 2 shows clear secondary flow formation at the bottom of the can. Figure 5, for the particle path lines shows that even more clearly. The velocity vector field shown in Figure 1 (for can heated from all sides) is similar to that shown in Figure 3 (top insulated) with a little higher magnitude due to the more efficient heating in the former. The major differences between the heating in both cases is discussed in the next paragraph.

Temperature Distribution and the Coldest Point in the Liquid Food The temperature distribution during heating are presented in the form of isotherms in Figures 2 and 4, for different periods of heating. The isotherms at t=54 s are almost identical to pure conduction heating but over time, the isotherms are seen to be strongly influenced by convection. The coldest point in the can ( i e. the location of the lowest temperature at a given time) is not a stationary point in the liquid undergoing convection heating. Its location is not at the geometric center of the can as it is in the case of conduction heating. Initially the contents of the can was at uniform temperature. As heating began, the mode of heat transfer changed from conduction to convection, and the coldest point moved from the geometric centre to the heel of the can and towards the wall as shown in Figures 2 and 4. It appears that the coldest point kept moving during heating and eventually stayed in a region that is about 10-12% of the can height from the bottom. Traditionally, the movement of the coldest point is a critical parameter in identifying the slowest heating zone ( SHZ ) for products in thermal process designs. The liquid and thus the bacterial spores carried with it at these locations are exposed to much less thermal treatment than the rest of the product. Zechman and Pflug (13) reported a location of the SHZ at about 10% height from the bottom whereas Datta et al. (6) found it to migrate to the bottom 15% of the can. These observations are in agreement with those found in this work and also with those reported by Kumar et al.(7). Figures 2 and 4 also show that the coldest point is more of a region defined by the lowest temperature. The region develops peculiar shape after only short period of heating. The SHZ extends from the centre of the can to the can’s wall and tends to migrate to the bottom of the can as heating progress. The simulation shows, for the first time, the effect of secondary flow on the shape of the SHZ. The effect is to push the SHZ towards the wall of the can as may be clearly seen in both Figures 2 and 4. According to this finding, careful consideration must be made in representing the coldest point by the measured temperature at the axis of the can, particularly at extreme locations close to the top and

bottom, as may be seen in both Figures 2 and 4. The temperature of the coldest region reached about 100 oC in 1800 s, in comparison to 150 s for water. The simulations of sterilisation of a can filled with a thick liquid (CMC), heated by a condensing steam at all sides, and the case where the top is insulated ( ie. there is an air gap present) shows a little difference. Figures 2 and 4 show that the temperature difference from top to bottom of the can at the end of 2574 s was 12 oC for the can with top insulated and 10 oC for the case of can heated from all sides. These two figures show that the location of the slowest heating region and its shape for both cases are similar. The observed difference in the temperature contour at the top of the can between the two cases was not sufficient to make major change in the heating process. The convection currents are strong enough to minimise this difference even for such viscous fluid as the one used in the current simulation.

CONCLUSIONS Transient temperature and velocity distribution evolving during natural convection heating of thick liquid (CMC) in a cylindrical metal can have been simulated by solving the governing equations for continuity, momentum and energy conservation for cylindrical coordinate system using a finite volume. A computational fluid dynamics software package was used to carry out the computations. The results of the simulation shows a recirculating flow inside the can consisting of liquid rising near the wall, radial flow and mixing at the top and bottom, and uniform core flow downwards near the axis. A secondary flow occurs at the bottom of the can due to reverse flow. The liquid inside the container shows an increase in temperature towards the top. The coldest point ( ie. the location of the slowest heating zone ) covers the whole cross sectional area of the can at the early stages of heating while it migrates towards the bottom of the can. The secondary flow at the bottom of the can pushes the coldest point (or region) closer to the wall. The simulations carried out for a can heated with and without an air gap at its top cover show very little differences with regards the temperature distribution, velocity profile, and location of the coldest region, due to the strong effect of natural convection current, even when the liquid was highly viscous.

ACKNOWLEDGMENTS The authors thank Dr. Peter Richards and Mr. Raid Al-Moussawi from the Mechanical Engineering Department for their valuable guidance in using the PHOENICS.

NOMENCLATURE CP ∆E g H k n p r R Rg t T Tw Ti u

specific heat of liquid food [ J kg -1 K-1 ] activation energy [ kJ kg mol-1 ] acceleration due to gravity [ ms -2 ] height of the can [ m ] thermal conductivity of liquid being heated [ W m-1 K-1 ] flow behaviour index pressure [ Pa ] radial position from center line [ m ] radius of the can [ m ] gas constant [ kJ (kg mol )-1 K-1 ] heating time [ s ] temperature [ K ] constant wall temperature [ K ] initial temperature [ K ] velocity in vertical direction [ ms -1 ]

v z α β γ η ηo ρ

velocity in radial direction [ ms -1 ] distance in vertical direction from the bottom [ m ] thermal diffusivity [ m2 s-1 ] thermal expansion coefficient [ K-1 ] shear rate [ s -1 ] apparent viscosity [ Pa.s ] consistency index [ Pa.s ] density [ kg m-3 ]

REFERENCES 1. May N., Guidelines No.13, 16, and 17, The Campden & Chorleywood Food Research Association (1997). 2. Wilbur, A., Unit operation for the food industries, Food Processing and Technology, Ohio State University (1996), 125-136. 3. Akterian, S.G. (1994) Numerical simulation of unsteady heat conduction in arbitrary shaped canned foods during sterilisation processes. J. Food Engineering, 21,.343-354. 4. Dincer, I., Varlik, C., and Gun, H. (1993) Heat transfer rate variation in a canned food during sterilisation. International Comm. Heat Mass Transfer, 20, 301-309. 5. Lanoiselle, J.L., Candau, Y., and Debray, E. (1986) Predicting internal temperature of canned food during thermal processing using a linear recursive model. J. Food Science, 60(3), 715-719. 6. Datta, A.K., and Teixeira, A.A. (1988) Numerically predicted transient temperature and velocity profiles during natural convection heating of canned liquid foods. J. Food Science, 53(1), 191-195.

7. Kumar, A., and Bhattacharya, M. (1991) Transient temperature and velocity profiles in a canned non-Newtonian liquid food during sterilisation in a still - cook retort. International J. Heat & Mass Transfer, 34(4/5), 1083-1096. 8. Kumar, A., Bhattacharya, M., and Blaylock, J. (1990) Numerical Simulation of natural convection heating of canned thick viscous liquid food products. J. Food Science, 55(5), 1403-1411. 9. PHOENICS Reference Manual , Part A : PIL , Concentration Heat and Momentum Limited ,TR 200 A, Bakery House, London SW 19 5AU, U.K. 10. Steffe, J.F, Mohamed, I.O., and Ford, E.W. (1986) Rheological properties of fluid foods: data compilation. In Physical and Chemical Properties of Foods. M.R. Okos (Ed). Am. Soc. Agric Eng. St. Joseph, M.I. 11. Ghani, A.G., Internal Report: The use of CFD in the prediction of temperature distribution in canned food during sterilisation, Chemical and Material Engineering Department , The University of Auckland, 1998. 11. Hiddink, J. Natural convection heating of liquids, with reference to sterilisation of canned food,

Agricultural Research Report No. 839, Center for Agricultural Publishing and Documentation, Wageningen, The Netherlands, 1975. 12. Zechman, L.G., and Pflug, I.J (1989) Location of the slowest heating zone for natural convection heating fluids in metal containers. J. Food Science, 54, 209-226.

Fig. 1 Velocity vector in a can filled with CMC and heated by condensing steam after 1157 s. Right-hand side of the figure is center line.

(a)

(d)

(b)

(e)

(c)

(f)

Fig. 2 Temperature contours in a can filled with CMC and heated by condensing steam after periods of ( a ) 54 s ; ( b ) 180 s ; ( c ) 324 s ; ( d ) 1157 s ; ( e ) 1785 s ; ( f ) 2574 s. Right-hand side of each figure is center line

CL

Fig. 3 Velocity vector in a can filled with CMC and heated by condensing steam ( top insulated, i.e. with an air gap ), after 1157 s. Right-hand side of the figure is center line.

(a)

(d)

(b)

(c)

(e)

(f)

Fig. 4 Temperature contour in a can filled with CMC and heated by condensing steam ( top insulated, i.e. with an air gap ) after periods of ( a ) 54 s ; ( b ) 180 s ; ( c ) 324 s ; ( d ) 1157 s ; ( e ) 1785 s ; ( f ) 2574 s. Right-hand side of each figure is center line.

Fig. 5 Particle path plots of a can filled with CMC and heated by condensing steam. Right-hand side of the figure is center line.