Thermal Sterilization of Food Using CFD

Transcription

1 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan 13 Thermal Sterilization of Food Using CFD A.G. Abdul Ghani and Mohammed M. Farid CONTENTS 13.1 Introduction CFD and the Food Industry Simulations of Thermal Sterilization in a Vertical Can Computational Grid Physical Properties Assumptions Used in the Numerical Simulation Governing Equations and Boundary Conditions Results of Simulation Simulations of Thermal Sterilization in a Top Insulated Can Results of Simulation Simulation of Bacteria Deactivation and Vitamins Destruction during Sterilization Convection and Temporal Discretization Governing Equations for Heat, Mass, and Momentum Transfer Kinetics of Bacteria Deactivation and Vitamin Destruction Results of Simulation Simulation of a Horizontal Can during Sterilization Conclusions Nomenclature References INTRODUCTION Conventional canning processes extend the shelf life of food products and make the food safe for human consumption by destroying the pathogenic microorganisms. Despite the significant advances made in the techniques used for food preservation, canning is still the most effective method. Sterilization of canned food is usually done by steam heating to a temperature sufficient to kill the microorganisms. The time required for the sterilization process depends on the product specifications, container type and size, and its orientation, as well as the heating medium characteristics. Excessive heating will affect food quality and its nutritive properties. Most mathematical models available for the analysis of thermal sterilization of food in cans are based on conduction heating, which has simplified analytical and numerical 331

2 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan 332 Computational Fluid Dynamics in Food Processing solutions. However, detailed analysis of convection heating in the liquid that is heated in a can is important. During the natural convection heating, the velocity in the momentum equations is coupled with temperature in the energy equation, because the movement of fluid is solely due to buoyancy force. Because of this coupling, the energy equation needs to be solved simultaneously with the momentum equations. Estimation of the heat transfer rate to the food in the can is essential to optimize processing conditions and improve product quality. Also a better understanding of the mechanism of the heating process will lead to an improved performance in the process and may be to some energy savings. Basic principles for determining the performance of different, but related processes have been presented [1,2]. The numerical predictions of the transient temperature and velocity profiles during natural convection heating of canned liquid foods in a still retort have been carried out [3]. Water was used to simulate liquid food, which was heated in a cylindrical can using steam. The water in the can was found stratified with an increasing temperature toward the top of the can. They predicted significant internal circulation of the fluid at the bottom of the can and showed that the slowest heating zone (SHZ) is doughnut shaped and is lying close to the bottom of the can at about one-tenth of the can height. Sterilization of a viscous liquid food in a metal can positioned upright and heated from all sides (T w ¼ 1218C) in a still retort was simulated [4]. The equations of continuity, momentum, and energy conservation for an axisymmetric case were solved to provide plots of temperature, velocity, and streamlines for natural convection heating and the results were compared with pure conduction contour plots. They also presented a simulation for the same can when its bottom and top surfaces were insulated [4]. The model liquid food was assumed to have viscosity varying with temperature but having constant specific heat and thermal conductivity. The results indicated that natural convection tends to push the slowest heating region to the bottom of the can. Sterilization of a can filled with a viscous liquid sodium carboxymethyl cellulose (CMC), heated by condensing steam on all sides and also with a top insulated (i.e., the presence of an air gap), was recently simulated [5]. The temperature difference from top to bottom of the can at the end of 2574 s of heating was 128C for the can with top insulated whereas it was 108C for the case of can heated from all sides. The results also show that the locations of the SHZ for both cases are similar. This is due to the strong effect of the natural convection current, even when the liquid was highly viscous. In some of the simulations, the wall was not assumed to be at a constant temperature and instead a convective boundary was implemented [5]. The results of such simulations showed very little difference from those predicted for constant wall temperatures, which is attributed to the large heat transfer coefficient of the condensing steam. In the work presented in this chapter, sterilization of canned liquid food in a still retort was numerically studied and analyzed using computational fluid dynamics (CFD). Natural convection heating within a can of liquid food during sterilization is simulated by solving the governing equations for continuity, momentum, and energy conservation for an axisymmetric case using a commercial CFD package (PHOENICS). The results were presented in the form of transient temperature, concentration profiles, velocity profiles, and flow patterns. Different liquid foods were used in the simulations; sodium carboxymethyl cellulose, carrot orange soup, and concentrated cherry juice were used as the model liquids. Density variations are governed by the Boussinesq approximation (a commonly used assumption for buoyancy problems, whereby the density variations are not explicitly modeled but their effect is represented by a buoyancy force that is proportional to temperature gradient). Specific heat, thermal conductivity, and volume expansion coefficient were all assumed constants, while viscosity was assumed function of temperature.

3 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan Thermal Sterilization of Food Using CFD CFD AND THE FOOD INDUSTRY Computational fluid dynamics offers process engineers a powerful design and investigative tool. Its application would assist in a better understanding of the complex physical mechanisms that govern the thermal, physical, and rheological properties of food materials. CFD has recently been applied to food processing applications. It has seen applications in many different processing industries, including airflow in clean rooms, ovens, and chillers; flow of foods in continuous-flow systems; and convection patterns during thermal processing [6]. When considering the flow of food products, it is often necessary to take the rheological nature of a food into account because this will dictate its flow behavior. Most foods exhibit some form of non-newtonian behavior and many different flow models have been used to describe such behavior. As for turbulence problems, the inclusion of a non-newtonian flow model requires the solution of an extra equation. However, it should be noted that the current state of CFD does not permit the prediction of turbulent flow for non-newtonian fluids; this is at the forefront of numerical non-newtonian rheology research [7]. The PHOENICS code used in our simulations is based on the finite volume method, as developed by Patankar and Spalding [8]. The key characteristic of this method is the immediate discretization of the integral equation of flow into the physical 3D space, i.e., the computational domain covers the entire can, which is divided into a number of divisions in the three dimensions. The details of this code can be found in the PHOENICS manuals, especially the PHOENICS input language (PIL) manual [9]. The observation of the movement of the SHZ is a difficult task and requires knowing detailed transient flow patterns and temperature profiles, due to the complex nature of heat transfer in natural convection heating. For this purpose, the partial differential equations, governing such a system, need to be solved in their entirety using numerical techniques. The results were compared with those obtained by Kumar and Bhattacharya [10] for the viscous liquid, and with Datta and Teixeira [3] for water as a liquid food. The following four case studies are discussed in this chapter SIMULATIONS OF THERMAL STERILIZATION IN A VERTICAL CAN Sterilization of liquid food contained in a metal can positioned upright and heated at 1218C from all sides was simulated and the results were presented. Sodium carboxymethyl cellulose was used as a model liquid. The computations were performed for a can with a radius of m and height of m (Figure 13.1). The governing equations for continuity, momentum, and energy conservation were solved using a commercial CFD package (PHOENICS), which is based on finite volume method. Transient flow patterns and temperature profiles within the model liquid (sodium carboxymethyl cellulose) were simulated. The model liquid food was assumed to have constant properties except for the viscosity (temperature dependent) and density (Boussinesq approximation). The action of natural convection forces the SHZ to migrate toward the bottom of the can as expected. The magnitude of the axial velocity was found to be in the range of 10 5 to 10 4 ms 1 and this magnitude varied with time and position in the can COMPUTATIONAL GRID The boundary layer occurring at the heated walls and its thickness are very important parameters to the numerical convergence of the solution. Temperature and velocities have their largest variations in this region. To adequately resolve this boundary layer flow, i.e., to keep the discretization error small, the mesh should be optimized and a large

4 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan 334 Computational Fluid Dynamics in Food Processing T = T w = 1218C, v r = 0, v z = m g T =T w = 1218C v r = 0 v z = m T = T w = 1218C, v r = 0, Initial conditions T =T 0, v r = 0, v z = 0 v z = 0 FIGURE 13.1 Grid mesh used in the simulations with 3519 cells: 69 in the axial direction and 51 in the radial direction (the mesh is for a full can). concentration of grid points is needed in this region. If the boundary layer is not resolved adequately, the underlying physics of the flow is lost and the simulation will be erroneous. On the other hand, in the rest of the domain where the variations in the temperature and velocity are small, the use of a fine mesh will lead to increases in computation time without any significant increase in computation accuracy. Thus a nonuniform grid system is needed to resolve the physics of the flow properly. The nonuniform grid system was used in the simulations with 3519 nodal points (Figure 13.1): 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 CMC 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 IBM RS6000 workstations at the University of Auckland, New Zealand PHYSICAL PROPERTIES In the simulation of water and CMC, the viscosity was assumed to be a function of temperature. A second order polynomial used to define the viscosity as required by PHOE- NICS was of the form m ¼ a þ bt þ ct 2 (13:1) Food materials are in general highly non-newtonian and hence the viscosity is a function of both shear rate and temperature with a flow behavior index typically less than 1. Due to the

5 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan Thermal Sterilization of Food Using CFD 335 extremely high viscosity of the CMC used in the simulation, which causes liquid velocities to be very low, the shear rate calculated from previous simulation [5] was found to be of the order of 0:01 s 1. Because of the low shear rate the viscosity may be assumed independent of shear rate and hence the fluid will behave as Newtonian fluid. This Newtonian approximation is valid for most liquid 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 [11]. The parameters a, b, and c used to calculate the values of viscosity of CMC at different temperatures were 4:135, 6: ,and2: , respectively. The variation of the density with temperature is usually expressed [12] as r ¼ r 0 [1 b(t T 0 )] (13:2) where b is the thermal expansion coefficient of the liquid, and T 0 and r 0 are the temperature and density at the reference condition [12]. The density was assumed constant in the governing equations except in the buoyancy term (Boussinesq approximation), where Equation 13.2 was used to describe its variation with temperature. For viscous liquids, the viscous forces are high and thus the Grashof number is low. This can be shown clearly for CMC at which Grashof number is in the range (using maximum temperature difference and maximum viscosity). The magnitude of the Grashof number gives a good indication whether the natural convection flow is laminar, transitional, or turbulent ASSUMPTIONS USED IN THE NUMERICAL SIMULATION To simplify the problem, the following assumptions were made:. axisymmetry, which reduces the problem from 3D to 2D;. heat generation due to viscous dissipation is negligible; this is due to the use of a high viscous liquid [13];. Boussinesq approximation is valid;. specific heat (C P ), thermal conductivity (k), and volume expansion coefficient (b) are constants (Table 13.1); TABLE 13.1 Properties of the Liquid Food (CMC) Measured at Room Temperature Used in the Simulation Property Density ( r) a Specific heat (C P ) Thermal conductivity (k) Volumetric expansion coefficient ( b) Consistency index (m 0 ) Activation energy (E) Value 950 kg m J kg 1 K 1 0:7 Wm 1 K 1 0:0002 K 1 0: Pa s n 30: kj kg mol 1 Source: From Kumar, A. and Bhattacharya, M., Int. J. Heat Mass Tran., 34, 1083, a r ¼ constant and varies only in the gravitational force term in the momentum Equation 13.5 according to Equation 13.2.

6 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan 336 Computational Fluid Dynamics in Food Processing. assumption of no-slip condition at the inside wall of the can is valid;. condensing steam maintains a constant temperature condition at the outer surface of the can; and. thermal boundary conditions are applied to liquid boundaries rather than the outer boundaries of the can, because of the low thermal resistance of the can wall GOVERNING EQUATIONS AND BOUNDARY CONDITIONS The partial differential equations governing natural convection motion in a cylindrical space are the Navier Stokes equations in cylindrical coordinates [14]. The boundary conditions used were as follows: At the can boundary, r ¼ R, At the bottom of the can, z ¼ 0, At symmetry, r ¼ 0, T ¼ T w, v z ¼ 0 v r ¼ 0 for 0 z H (13:3) T ¼ T w, v z ¼ 0 v r ¼ 0 for 0 r ¼ ¼ 0 v r ¼ 0 for 0 z H (13:5) At the top of the can, z ¼ 0, v z ¼ 0 v r ¼ 0 for 0 r R (13:6) Initially the fluid is at rest and is at a uniform temperature T ¼ T w, v z ¼ 0, v r ¼ 0 at 0 r R, 0 z H (13:7) The same set of governing equations describes a wide variety of flow situations in liquids and gases. The boundary and initial conditions (Equation 13.3 through Equation 13.7) are the most important parameters that specify the desired solution among many solutions possible for the set of equations. To obtain a good convergence of the numerical solution to these governing partial differential equations, it was necessary to apply a proper under-relaxation or an overrelaxation. The improper over-relaxation or under-relaxation parameter can easily make the computations impracticably long. Many of these optimum parameters are not known at the initial stage and can only be found through numerical experimentation RESULTS OF SIMULATION Figure 13.2 shows the temperature profile, velocity vector, and flow pattern of the CMC in a can heated by steam condensing along its outside surface. Figure 13.2a shows the influence of natural convection current on the movement of the SHZ in the can (i.e., the location of the lowest temperature at a given time). It shows that the location of the SHZ is not at the geometric center of the can as it is in the case of conduction heating. As heating progresses,

7 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan Thermal Sterilization of Food Using CFD E E E E E E E E E E E E E E E 4 (a) (b) (c) FIGURE 13.2 (See color insert following page xxx.) (a) Temperature profile, (b) velocity vector, and (c) flow pattern of CMC in a vertical can heated by condensing steam after 1157 s. The right-hand side of each figure is centerline. (From Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P.J., J. Food Eng., 41, 55, 1999.) AQ1 the SHZ is pushed more toward the bottom of the can. The SHZ keeps moving during heating and eventually stays in a region that is about 10% 12% of the can height from the bottom. Both Figure 13.2b and Figure 13.2c show the recirculating flow created by the buoyancy force, created by temperature variation (from the wall to the core). The secondary flow formation was evident in the case studied as shown clearly in Figure 13.2b and Figure 13.2c SIMULATIONS OF THERMAL STERILIZATION IN A TOP INSULATED CAN In this section, the effect of the presence of an air gap (i.e., head space) at the top of the can on the heat transfer rate is presented. This is important since it represents a real practical situation. The governing equations, physical properties, size of can, and assumptions used to simplify the problem are the same as those used in the previous case. The boundary conditions used were the same as those used earlier in the previous case except for the top of the can, which was assumed insulated as shown in Equation At the top of the can, z ¼ 0, v r ¼ 0, v z ¼ 0 at z ¼ H (can top), 0 r R (13:8) The assumption of top insulation was used to represent the case of a can with a head space, which is the common situation for canned foods RESULTS OF SIMULATION Figure 13.3 shows the velocity vector in a can filled with CMC and heated at 1218C from the bottom and sides only (i.e., top insulated) after 1157 s of heating. The velocity vector

8 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan 338 Computational Fluid Dynamics in Food Processing 0.0E+0 2.5E 5 5.0E 5 7.6E 5 1.0E 4 1.3E 4 1.5E 4 1.8E 4 2.0E 4 2.3E 4 2.5E 4 2.8E 4 3.0E 4 3.3E 4 3.5E 4 FIGURE 13.3 Velocity vector profile (m s 1 ) in a top insulated can filled with CMC and heated by condensing steam after 1157 s. The right-hand side of the figure is centerline. field shown in Figure 13.2b (for can heated from all sides) is similar to that shown in Figure 13.3 (top insulated) with a slightly higher velocity due to more efficient heating in the former. The major difference between the heating in both cases is discussed in the next paragraph. Figure 13.4 shows the temperature profiles in the top insulated can filled with CMC and heated by condensing steam for different periods of time during thermal sterilization. This figure shows that the SHZ extends from the center of the can to the wall and tends to migrate to the bottom of the can as heating progresses. The results do not show any major difference from that shown for the can heated from all sides. Figure 13.2a and Figure 13.4c show that (a) (b) (c) (d) FIGURE 13.4 (See color insert following page xxx.) Temperature profiles in a can filled with CMC and heated by condensing steam (top insulated) after periods of (a) 54 s, (b) 180 s, (c) 1157 s, and (d) 2574 s. The right-hand side of each figure is centerline.

9 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan Thermal Sterilization of Food Using CFD 339 the temperature difference from top to bottom of the can at the end of 1157 s is almost the same. These two figures show that the location of the SHZ 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 is not sufficient to make a major change in the heating process. The convection currents are strong enough to minimize this difference even for such a viscous fluid as the one used in the current simulation SIMULATION OF BACTERIA DEACTIVATION AND VITAMINS DESTRUCTION DURING STERILIZATION The objective of this part of the work is to provide an improved quantitative understanding of the effect of natural convection upon bacteria inactivation and vitamins destruction during thermal sterilization of canned liquid foods. A computational procedure was developed for predicting the changes in live bacteria concentration and in vitamins such as vitamins C (ascorbic acid), B1 (thiamin), and B2 (riboflavin) during sterilization processing of canned food. The numerical approximations and model parameters were the same as those used in the previous simulations CONVECTION AND TEMPORAL DISCRETIZATION An important consideration in CFD is the discretization of the convection terms in the finite volume equations. The accuracy, numerical stability, and the boundedness of the solution depend on the numerical scheme used for these terms. The central issue is the specification of an appropriate relationship between the convected variables, stored at the cell center, and its value at each of the cell faces [16]. The convection discretization scheme used for all variables in our simulations is the hybrid-differencing scheme (HDS). The HDS of Spalding [17] used in PHOENICS switches the discretization of the convective terms between central differencing scheme (CDS) and upwind differencing scheme (UDS) according to the local cell Peclet number. The cell Peclet number Pe (ratio of convection to diffusion) for bacteria and vitamins within the flow domain in the z-direction is Pe ¼ v zdz a (13:9) where v and Dz are respectively the typical velocity and typical distance of the cell in the z-direction. The mass diffusivity a of the bacteria and vitamins in the fluid may be described by Stokes Einstein equation: AQ2 a ¼ KT 6pma (13:10) where K is the Boltzman constant, T is the temperature, m is the apparent viscosity, and a is the radius of the particle. The calculated cell Peclet numbers within the flow domain in this study are of the order of 10 4 for bacteria and vitamins, and hence it is reasonable to ignore the diffusion of bacteria and vitamins, thereby reducing computation time. Within PHOENICS, the temporal discretization is fully explicit.

10 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan 340 Computational Fluid Dynamics in Food Processing GOVERNING EQUATIONS FOR HEAT, MASS, AND MOMENTUM TRANSFER The governing equations of continuity, momentum, and energy are the same as those used in the previous section. In addition to these equations, the following equations for concentrations of bacteria and vitamins are introduced: Mass balance on Mass balance on rv rb þ v þ rb ¼ D rv þ v þ rv ¼ D v 1 r C 2 C 2 k b C rb (13:11) k v C rv (13:12) The relative concentrations of bacteria and vitamins (C rb and C rv ) in Equation and Equation are taken as a dimensionless species concentrations, which are defined as the ratio of real time concentrations (C b and C v ) to the initial concentrations (C bo and C vo ) multiplied by 100. The boundary conditions used for bacteria deactivation and vitamins destruction are: At the can boundary, r ¼ ¼ 0 ¼ 0 (13:13) At the bottom of the can, z ¼ ¼ 0 ¼ 0 (13:14) At symmetry, r ¼ ¼ 0 ¼ 0 (13:15) At the top of the can, z ¼ ¼ 0 ¼ 0 (13:16) Other boundary conditions for temperature and velocities are the same as those used in Section (Equation 13.3 through Equation 13.6). The initial conditions used are: T ¼ T 0, AQ3 C rb ¼ 100, C rv ¼ 100, v r ¼ 0, and v z ¼ 0. The model liquid is assumed to have constant properties except for viscosity (temperature dependent) and density (Boussinesq approximation). The simplifications used in the simulation are the same as those used in Section Further, AQ4 the effect of molecular diffusion of bacteria and vitamin C is neglected due to the relatively strong influence of the convection motion. This assumption has been verified by Ghani et al. [18], which allows omitting the diffusion terms in Equation and Equation KINETICS OF BACTERIA DEACTIVATION AND VITAMIN DESTRUCTION The rate of bacteria deactivation and vitamin destruction is usually assumed to follow first order kinetics [19]. It is known that the reaction rate constants are functions of temperature and are usually described by Arrhenius equation: For bacteria: k b ¼ A b exp E b R g T (13:17)

11 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan Thermal Sterilization of Food Using CFD 341 TABLE 13.2 Kinetic Data for Some Reaction Processes in the Concentrated Cherry Juice Used in Our Simulations Property D 121 (min) Reported D 121 (min) Used E a (kj mol 1 ) Reported E a (kj mol 1 ) Used For bacteria deactivation Clostridium botilinum For vitamins destruction Ascorbic acid (C) Thiamin (B1) Riboflavin (B2) Source: From Fryer, J.P., Pyle, D.L., and Rielly, C.D., in Chemical Engineering for the Food Industry, Blackie Academic and Professional, London, For vitamins: k v ¼ A v exp E v R g T (13:18) where A b and A v are the reaction frequency factors, E b and E v are the activation energies for the two processes, respectively, R g is the universal gas constant, and T is the temperature. Accurate kinetic parameters such as reaction rate constants and activation energy are essential to predict quality changes during food processing [20]. In food process engineering, the decimal reduction time (D) is used more often. The relationship between the reaction rate constant and the decimal reduction time is [21] k T ¼ 2:303 D T (13:19) The decimal reduction times and activation energies of bacteria inactivation and destruction of vitamins C, B 1,andB 2 are represented in Table The reaction rate constants k b and k v at 1218C for bacteria and different types of vitamins are calculated using Equation and the reported values of D. Equation and Equation are then used to calculate the constants of Arrhenius equation A b and A v. They were s 1 for bacteria, , , and s 1 for vitamins C, B 1, and B 2, respectively. The magnitude of Grashof number for the viscous liquid used in our simulation is in the range of (using maximum temperature difference and maximum viscosity), which gives a good indication that natural convection flow is laminar. The Arrhenius equation, used to describe the kinetics of the biochemical changes, is introduced to the existing software package using a FORTRAN code RESULTS OF SIMULATION As discussed earlier, the effects of the temperature distribution in the can on bacteria inactivation and the destruction of different types of vitamins are studied by introducing their kinetics in the heat transfer analysis. Figure 13.5 represents the results of the simulation

12 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan 342 Computational Fluid Dynamics in Food Processing (a) (b) (c) 0.0E+0 8.8E 5 1.8E 4 2.6E 4 3.5E 4 4.4E 4 5.3E 4 6.2E 4 7.0E 4 7.9E 4 8.8E 4 9.7E 4 1.1E 3 1.1E 3 1.2E 3 FIGURE 13.5 (See color insert following page xxx.) Deactivation of bacteria in a can filled with CMC and heated by condensing steam after (a) 180 s, (b) 1157 s, and (c) 2574 s, respectively. The right-hand side of each figure is centerline. (From Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P.J., J. Food Eng., 42, 207, 1999.) AQ5 for a metal can filled with CMC, steam heated from all sides (at 1218C). Figure 13.5a shows that during the early stage of heating, the bacteria are killed only at locations close to the wall of the can, and live bacteria concentration is not influenced by the flow pattern shown in Figure 13.2c. Figure 13.5b and Figure 13.5c show the results of the simulation after much longer time periods of 1157 and 2574 s, respectively. The bacteria concentration profiles are very different from those observed at the beginning of the heating. The liquid and thus the bacteria carried with it at the SHZ locations are exposed to much less thermal treatment than the rest of the product [22]. Figure 13.5b and Figure 13.5c show that bacteria inactivation is influenced significantly by both the temperature and the flow pattern observed in Figure Profiles of temperature distribution, bacteria concentration, and concentrations of vitamins C (ascorbic acid), B1 (thiamin), and B2 (riboflavin) in a can filled with cherry juice during thermal sterilization were obtained through numerical simulations. These profiles are presented in Figure The properties of concentrated cherry juice used in the current simulations are: r ¼ 1052 kg m 3, C P ¼ 3500 Jkg 1 K 1, k ¼ 0:554 Wm 1 K 1, and b ¼ 0:0002 K 1 as reported by Hayes [23]. The simulation highlights the dependency of the concentration of vitamins on both temperature distribution and flow pattern as sterilization proceeds (Figure 13.6). The relative bacteria concentration in the SHZ shown in Figure 13.5 is a good measure of food sterility. However, in the case of vitamin destruction, it is necessary to calculate the vitamin average concentration in the whole can, which is calculated as the weighted average of the local concentrations as follows [24]: C ave ¼ 2 X L X R R 2 rcdzdr (13:20) L Z¼0 r¼0 The average percentage destruction of the relative concentration of vitamin C is found to be about 25%. The corresponding concentrations for vitamins B1 and B2 are 70% and 3%, respectively, which show the strong influence of sterilization temperature on vitamin B1. Fellows [25] has reported a percentage loss of 50% 75% of vitamin B1 (Thiamin) in canned and bottled foods, which is in agreement with the results obtained from our simulation.

13 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan Thermal Sterilization of Food Using CFD 343 Residual vitamin C (%) Residual vitamin B1 (%) Residual vitamin B2 (%) FIGURE 13.6 (See color insert following page xxx.) Vitamins C, B1, and B2 destruction in a can filled with concentrated cherry juice and heated by condensing steam after 1640 s. The right-hand side of each figure is centerline. (From Fellows, P.J., Food Processing Technology, Principles and Practice. Woodhead Publishing Series in Food Science and Technology, Cambridge, 1996.) 13.5 SIMULATION OF A HORIZONTAL CAN DURING STERILIZATION In this part of the work, sterilization of a canned liquid food in a metal 3D can lying horizontally and heated at 1218C from all sides was predicted and analyzed. Carrot orange soup was used as a model liquid food. The properties of carrot orange soup used in the current simulation were: r ¼ 1026 kg m 3, C P ¼ 3880 Jkg 1 K 1, k ¼ 0:596 Wm 1 K 1, and b ¼ 0:0002 K 1. The properties were calculated from the values reported [23,26] for all the food materials used in the soup, using their known mass fractions. A nonuniform grid system was used in the simulation with 105,000 cells: 50 in the radial direction, 70 in the vertical direction, and 30 in the angular direction, graded with a finer grid near the wall in radial and vertical directions. The natural convection heating of carrot orange soup was simulated for 3000 s. It took 10 steps to achieve the first 200 s of heating, another 10 steps for the next 800 s, and the last 10 steps for the remaining 2000 s. This required 17 h of CPU time on the UNIX IBM RS6000 workstations at the University of Auckland. For the horizontal cylinder, the analysis must be based on 3D [27]. The buoyancy force caused by density variation with temperature was governed by the Boussinesq approximation shown in Equation 13.2, which was used in the body force term of the momentum equation in the radial direction. Figure 13.7 shows the radial angular temperature profile of carrot orange soup in a 3D cylindrical can lying horizontally and heated by condensing steam after 600 s at two different planes in the direction of (a) radial angular plane; (b) radial vertical plane. The can shown in this figure is in the horizontal position. The inclination shown is only to provide more clearly a 3D image. This figure shows the actual shape of the SHZ, which is settled toward the bottom surface of the can. The effect of natural convection in the horizontal can was found smaller than that in the vertical can due to the can having height greater than its diameter. AQ6

14 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan 344 Computational Fluid Dynamics in Food Processing (a) (b) FIGURE 13.7 (See color insert following page xxx.) Radial angular plane temperature profile of carrot orange soup in a 3D cylindrical can lying horizontally and heated by condensing steam after 600 s at two different planes in the direction of (a) radial angular plane and (b) radial vertical plane. (From Ghani, A.G., Farid, M.M., and Chen, X.D., J. Food Eng., 51, 77, 2002.) AQ CONCLUSIONS CFD is a powerful tool for simulating a large number of food process operations such as thermal sterilization in cans. The CFD analysis presented in this chapter shows that the coldest region in a can during sterilization is influenced significantly by the free convection of the liquid food, which is induced by the heating at the can s wall. This causes the coldest region of minimum bacteria inactivation to be pushed toward the bottom of the can, unlike conduction heating of solids where it usually lies at the geometric center of the can. A similar conclusion was reached for food sterilization in a horizontal can but with lower influence of the free convection. The simulations also show that the location of minimum damage to vitamins does not necessary coincides with the location of the slowest heating region due to the continuous free convection motion of the liquid. NOMENCLATURE A b reaction frequency factor for bacteria (s 1 ) A v reaction frequency factor for vitamins (s 1 ) a radius of the particle (m) C ave weighted average local concentration of vitamins (kg m 3 ) C b concentration of bacteria in food liquid (number of bacteria m 3 ) C v concentration of the vitamins in food liquid (kg m 3 ) C bo initial concentration of bacteria (number of bacteria m 3 ) C vo initial concentration of vitamins (kg m 3 ) C rb relative bacteria concentration (C b =C bo ) C rv relative vitamin concentration (C v =C vo ) C P specific heat of liquid food (J kg 1 K 1 ) D T decimal reduction time (min) D b diffusion coefficient of bacteria (m 2 s 1 ) D v diffusion coefficient of vitamins (m 2 s 1 ) E b activation energy of bacteria deactivation (kj (kg mol) 1 ) E v activation energy of vitamins destruction (kj (kg mol) 1 ) G r Grashof number, G r ¼ gbdtl3 r 2 m 2

15 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan Thermal Sterilization of Food Using CFD 345 g acceleration due to gravity (m s 2 ) H height of the can (m) K Boltzman constant k thermal conductivity of liquid being heated (W m 1 K 1 ) k b reaction rate constant of bacteria at temperature T (s 1 ) k v reaction rate constant of vitamin at temperature T (s 1 ) L height of the can (m) Pe Peclet number, Pe ¼ udz a p pressure (Pa) r radial position from center line (m) R radius of the can (m) R g gas constant (kj (kg mol) 1 K 1 ) t heating time (s) T temperature (8C) wall temperature (8C) T w T 0 initial temperature (8C) v z velocity in vertical direction (m s 1 ) v r velocity in radial direction (m s 1 ) v u velocity in angular direction (m s 1 ) z distance in vertical direction from the bottom (m) GREEK SYMBOLS a thermal diffusivity (m 2 s 1 ) b thermal expansion coefficient (K 1 ) m apparent viscosity (Pa s) r density (kg m 3 ) r 0 initial density (kg m 3 ) REFERENCES 1. N. May. Guidelines No. 13, 16, and 17, the Campden and Chorleywood Food Research Association, A. Wilbur. Unit operation for the food industries, Food Processing and Technology, Ohio State University, , A.K. Datta and A.A. Teixeira. Numerically predicted transient temperature and velocity profiles during natural convection heating of canned liquid foods. Journal of Food Science 53(1): , A. Kumar, M. Bhattacharya, and J. Blaylock. Numerical simulation of natural convection heating of canned thick viscous liquid food products. Journal of Food Science 55(5): , A.G. Ghani, M.F. Mohammed, and X.D. Chen. A CFD simulation of the coldest point during sterilization of canned food. The 26th Australian Chemical Engineering Conference, Port Douglas, Queensland, September 1998, No G. Scott and P. Richardson. The application of computational fluid dynamics in the food industry. Trends in Food Science and Technology 8: , S.D. Holdsworth. Rheological model used in the prediction of the flow properties of food products, a literature review. Transaction of Institute of Chemical Engineers 71(C4): , S.V. Patankar and D.B. Spalding. A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows. International Journal of Heat and Mass Transfer 15(10): , PHOENICS Reference Manual, Part A: PIL, Concentration Heat and Momentum Limited, TR 200 A, Bakery House, London SW 19 5AU, UK.

16 Da-Wen Sun/Computational Fluid Dynamics in Food Processing 9286_C013 Page Proof page :58pm Compositor Name: JGanesan 346 Computational Fluid Dynamics in Food Processing 10. A. Kumar and M. Bhattacharya. Transient temperature and velocity profiles in a canned non-newtonian liquid food during sterilization in a still-cook retort. International Journal of Heat and Mass Transfer 34(4=5): , J.F. Steffe, I.O. Mohamed, and E.W. Ford. Rheological properties of fluid foods: data compilation. In M.R. Okos (ed.), Physical and Chemical Properties of Foods. St. Joseph, MI: Transaction of American Society of Agricultural Engineers, B. Adrian. Heat Transfer. New York: John Wiley and Sons, 1993, pp A.F. Mills. Basic Heat and Mass Transfer. New York: Irwin, R.B. Bird, W.E. Stewart, and E.N. Lightfoot. Transport Phenomena. New York: John Wiley and Sons, A.G. Ghani, M.M. Farid, X.D. Chen, and P.J. Richards. Numerical simulation of natural convection heating of canned food by computational fluid dynamics. Journal of Food Engineering 41(1): 55 64, M.R. Malin and N.P. Waterson. Schemes for convection discretization on PHOENICS. The PHOENICS Journal 12(2): , D.B. Spalding. A novel finite-difference formulation for differential expressions involving both first and second derivatives. International Journal of Numerical Methodology Engineering 4: 551, A.G. Ghani, M.M. Farid, X.D. Chen, and P. Richards. A computational fluid dynamics study on the effect of sterilization temperatures on bacteria deactivation and vitamin destruction. Journal of Process Mechanical Engineering 215(Part E): 1 9, H. Reuter. Aseptic Processing of Foods. Lancaster, PA: Technomic Publishing Company Inc., S. Ilo and E. Berghofer. Kinetics of color changes during extrusion cooking of maize gritz. Journal of Food Engineering 39: 73 80, D.R. Heldman and R.W. Hartel. Principles of Food Processing. New York: Chapman and Hall, A.G. Ghani, M.M. Farid, X.D. Chen, and P.J. Richards. An investigation of deactivation of bacteria in canned liquid food during sterilization using computational fluid dynamics (CFD). Journal of Food Engineering 42: , G.D. Hayes. Food Engineering Data Handbook. New York: John Wiley and Sons, AQ8 24. A.G. Ghani, M.M. Farid, X.D. Chen, and P.J. Richards. Numerical simulation of biochemical changes of canned food during sterilization of viscous liquid using computational fluid dynamics. 10th World Congress of Science and Technology, Sydney, Australia, 3 8 October P.J. Fellows. Food Processing Technology, Principles and Practice. Cambridge: Woodhead Publishing Series in Food Science and Technology, M.S. Rahman. Handbook of Food Preservation. Food Science and Technology. A series of monographs, textbooks, and reference books. New York: Marcel Dekker Inc., A.G. Ghani, M.M. Farid, and X.D. Chen. Numerical simulation of transient temperature and velocity profiles in a horizontal can during sterilization using computational fluid dynamics. Journal of Food Engineering 51: 77 83, J.P. Fryer, D.L. Pyle, and C.D. Rielly. Chemical Engineering for the Food Industry. Blackie Academic and Professional, London, Author Queries AQ1: Please check if the insertion of (a), (b) and (c) in the figure caption of Fig 13.2 is correct. AQ2: Kindly note that u is changed to v. please check if it is fine. AQ3: Please check if cross reference to section is correct. AQ4: Please check if cross reference to section is correct. AQ5: Please check if the insertion of (a), (b), and (c) in figure 13.5 is correct. AQ6: Please check for the completeness of this sentence. Is it a 3D analysis for a horizontal cylinder? AQ7: Please check if the insertion of (a) and (b) in figure 13.7 is correct. AQ8: Are the intials for the author Hayes in reference 23 correct?