Heat transfer simulation and retort program adjustment for thermal processing of wheat based Haleem in semi-rigid aluminum containers

Abstract

A mixed computational strategy was used to simulate and optimize the thermal processing of Haleem, an ancient eastern food, in semi-rigid aluminum containers. Average temperature values of the experiments showed no significant difference (α = 0.05) in contrast to the predicted temperatures at the same positions. According to the model, the slowest heating zone was located in geometrical center of the container. The container geometrical center F₀ was estimated to be 23.8 min. A 19 min processing time interval decrease in holding time of the treatment was estimated to optimize the heating operation since the preferred F₀ of some starch or meat based fluid foods is about 4.8–7.5 min.

Introduction

Thermal sterilization is one of the most common ways of food preservation, which is performing in various methods. The first way is to fill and seal the containers before heat treatment, and the other way is to package the heat processed foods in a clean or aseptic environment (Farid and Abdul Ghani 2004; Leaper and Richardson 1999). There have been several studies based on real-time data acquisition systems, along with alternative approaches based on the use of calculated correction factors or mathematical models capable of simulating the heat transfer into canned foods under various processing conditions (Teixeira and Tucker 1997). Computational fluid dynamics (CFD) is an efficient way to study flow behavior and temperature distribution of thermal processing in the food technology (Ghani et al. 1999; Ghani et al. 2003; Scott and Richardson 1997). Several studies have been done based on different shapes of containers and different kinds of foods (Erdogdu and Tutar 2011; Ghani et al. 1999; Varma and Kannan 2006). Semi-rigid aluminum containers are widely used in food industries because of their handling convenience (light weight), high heat transfer proficiency, and attractive shapes. However, studies of heat transfer and flow behavior in thermal sterilization processes in these containers have not yet been performed.

Haleem is a common food as breakfast dish, baby food, and a special dish during Ramadan and Muharram, the holy Islamic months, cooked in a wide geographical zone from Iran to Bangladesh (Sajjad 2011). Haleem is an Arabic name that literally means ‘patient’. This name is chosen because of time consuming procedure of preparation and cooking, while time consideration and food convenience are two important factors that influence food choice in adolescents and parents (Neumark-Sztainer et al. 1999). As a result, it’s logical to provide Haleem in a form of prepackaged food. In this study, the heat transfer of semi-rigid containers of Haleem was studied by CFD techniques. Moreover, the total sterility of the process was estimated and adjusted to design an optimized production system of the mentioned food.

Material and methods

Sample preparation

Wheat based Haleem was cooked according to the recipe, reported by Ardalan Malek (Ardalan Malek 2000).

Thermophysical properties measurement

Density and thermal expansion coefficient

The density was measured by a pycnometer at three temperature steps. The thermal expansion coefficient was calculated based on the Eq. (1) ((Bejan 1993)):

$$\rho ={\rho }_{\mathit{ref}}\left[1-\beta \left(T-T_{\mathit{ref}}\right)\right]$$ 1

Where ρ_ref is the reference density at temperature T_ref and β is the linear thermal expansion coefficient.

Viscosity

The viscosity was measured by a concentric cylinder viscometer (Brookfield DV II+Pro, Brookfield Engineering Lab. Inc., MA, USA) equipped with a cylindrical spindle (LV-1) (cylinder diameter 18.84 mm, length 115 mm, beaker diameter 86.30 mm and 600 ml of sample volume) at 20–60 °C. The viscosity was assumed as a function of temperature. An Arrhenius type equation was used to define viscosity (Pa.s⁻¹) versus temperature (K).

Thermal conductivity

Thermal conductivity was measured using hot wire probe method. The probe contained a hypodermic needle (36 mm long and 0.5 mm diameter), having a 0.05 mm diameter constantan and a thermocouple (type K).

Specific heat

Using a vacuum jacketed calorimeter at 20–60 °C, specific heat was measured according to the method of mixture (Sahin and Sumnu 2006).

Geometry and meshing

A three-dimensional (3D) symmetric geometry was designed according to Alupak type 232 semi-rigid aluminum based containers (manufactured in Switzerland). The length of the bottom of the package was 88 mm and the height was 27.5 mm. There was an angle of 95° between bottom surface and the sidewalls. A ‘uniform’ 1 mm³ mesh size was designed for the internal volume. The number of meshes was 652,306 (Fig. 1).

Fig. 1.

Designed and meshed geometry

Governing equations

Partial differential equations governing natural convection motion of fluids and heat transfer phenomenon in a three dimensional x, y, and z coordinate system are presented as (Ghani et al. 1999):

The continuity equation

$$\frac{{\partial u}_x}{\partial x}+\frac{{\partial u}_y}{\partial y}+\frac{{\partial u}_z}{\partial z}=0$$ 2

The momentum equation

$$\left(\frac{\partial \mathit{\rho V}}{\mathit{\sigma t}}+\nabla .\mathit{\rho V}⨂V\right)=\nabla .(-\mathit{p\delta }+\mu \left(\nabla V+\left(\nabla V){}^t\right)\right)+S_M$$ 3

The energy equation

$$\frac{\partial T}{\partial t}+u_x\frac{\partial T}{\partial x}+u_y\frac{\partial T}{\partial y}+u_z\frac{\partial T}{\partial z}=\propto \left(\frac{{\partial }^{2}T}{\partial x^2}+\frac{{\partial }^{2}T}{\partial y^2}+\frac{{\partial }^{2}T}{\partial z^2}\right)$$ 4

Where u (m/s) is the velocity, p (Pa) is pressure, $\rho$ (kg/m³) is the density, V is the velocity vector, μ is apparent viscosity (Pa s), and $\propto$ (m²/s) is the thermal diffusivity.

Buoyancy force caused by density change due to temperature variations was supposed to be governed by Boussinesq approximation (Eq. 1).

The Rayleigh, a dimensionless number which measures the strength of buoyancy driven flows, was remarked. Rayliegh number was lower than 10⁸ and showed laminar flow behavior during the process (Erdogdu and Tutar 2011).

Boundary conditions and initial values

An unsteady temperature function was imposed to all faces of the geometry in one minute time intervals. This profile which was based on the temperature profile of retort was recorded by measuring ambient temperature near the containers. No-slip boundary condition was supposed for velocity components relative to boundaries (Kannan and Sandaka 2008). At each time step, the retort was assumed to provide constant boundary temperature at the outer surfaces of the packages. The boundary condition used in the simulation was: T = T_w, u = 0, v = 0, w = 0. The initial temperature was assumed as the first temperature which was measured by the thermocouple at the starting time of processing (314.58 K). Come-up and holding time for the processing cycle was 17 and 36 min, respectively. The thermal boundary conditions were applied to the liquid boundaries, since the low thermal resistance of the can walls can be ignored.

Solution methodology

Ansys fluent 12 was used to solve the Navier-Stokes and energy equations simultaneously. The value of residuals root mean square (RMS) was adjusted lower than 10⁻⁴ for continuity and momentum, and 10⁻⁸ for the energy equation in order to achieve an appropriate convergence. The under-relaxation factors were adjusted smaller than 1 to obtain a good convergence of the numerical solution. PISO algorithm was used for pressure-velocity coupling. The simulation was carried out by a Sony VGN-BZ560 Vaio laptop with 2.4 GHz CPU speed and 2 GB RAM. The whole analysis was performed about 800 iterations with respect to the convergence at each time step.

Sterility calculations

In low-acid foods (pH > 4.5), Clostridium botulinum is the most dangerous heat-resistant and spore-forming pathogen and a challenging topic for public health (Barbosa-Canovas et al. 1997). The sterility was assessed by F_value concept. F_value relies on effectiveness of time and temperature on thermal destruction of microorganisms (Sun 2012). The thermal death time F is the total time required to accomplish a stated reduction in a population of vegetative cells or spores. The general form of the formula is presented in Eq. (5):

$$F=\underset{0}{\overset{t}{\int }}{10}^{\raisebox{1ex}{$\left(T-121.1\right)$}\!\left/ \!\raisebox{-1ex}{$z$}\right.}\mathit{dt}$$ 5

Where, 121.1 °C is the reference temperature and T is the predicted or measured temperature in the coldest point of the can and z is the temperature required to change thermal death time by a factor of 10 that is 10 °C for C. Botulinum and F is thermal death time in the cold point.

Process optimization

The graphical method was used to optimize the process according to comparison of the experiment F₀ and F₀ of similar compositional and structural foods. The method could approximately modify the total lethality of the process by adjusting the time-temperature profile of the slowest heating point (SHP) of container on the assumption that the profile of cooling period could be moved horizontally without any change in the slope, to increase or decrease the area below the profile that affects the total F value (Holdsworth 1993).

Validation test

In order to compare the predicted results with experimental operations, three thermocouples (Type K) were installed in three filled (215 g sample) packages and then the packages were sealed at 280 °C using Alcan machine^®. Another thermocouple was devised near the containers, in the water cascading Barriquand steriflow (Roanne^®, France) retort. The thermocouples were attached to Ellab^® data logger (CTF9004) by PT100 cables. The data logger was connected to a personal computer, and E-val 2.1 software was used to export time-temperature profile of each thermocouple at 1 min intervals.

Results and discussion

Thermophysical properties

In order to increase the realizability of predicted model, the thermophysical properties of the sample were measured as functions of temperature: The Density at 20 °C Was 1135 kg m⁻³, and the Volumetric expansion coefficient (β) was estimated to be 2.4 × 10⁻⁴ K⁻¹. The thermal conductivity (k) and specific heat (C_p) of the sample were assumed to be constant values of 0.57 W m⁻¹ K⁻¹ and 3520 J kg⁻¹ K⁻¹, during the process, respectively.

Equation (6) shows the Arrhenius equation describing apparent viscosity (μ) as a function of temperature.

$$ln\mu =\frac{0.0005}{T}+0.0031$$ 6

The activation energy (E_a) was determined to be 4.16 × 10⁻⁶ (kJ/mol).

Validation

The model was validated by comparing average temperature values of the experiments with temperature profile of the probe position point (point P) in the modeled container (x = 5 cm y = 5 cm z = 2 cm), during the process time (Fig. 2). The data are compared in two parts, including temperature increasing period (until the end of heating time) and temperature decreasing period (the cooling period) (Fig. 3).

Fig. 2.

Time-temperature profile of retort, predicted and average of experimented data at the probe position point (x = 5, y = 5, z = 2 cm)

Fig. 3.

Comparison of predicted and average experimented temperature values at the probe position point (x = 5, y = 5, z = 2 cm) a until the end of heating period b cooling period

T student test was used to compare predicted and experimented data. The results showed high similarity between the predicted and experimented values in point P (α = 0.01) for temperature ascending part. However, For descending part of the time-temperature profile, the accordance of the predicted and experimented values in point P was verified at probability level of α = 0.05.

Temperature distribution

The temperature contours at different time steps in the middle horizontal plane and the symmetric vertical plane indicate that the slowest heating zone (SHZ) is located in the geometrical center of the container, as shown in Fig. 4.

Fig. 4.

Temperature distribution: in plane of z = 13.75 a at 17 min b at 75 min, and symmetric plane c at 17 min d at 75 min

The temperature values of all grids were studied at different time steps of the process. The results showed that during first 10 min of the processing, lowest temperature grid was about 0.5 cm far from the geometrical center, in both x and y direction; however it gradually moved toward the center of container geometry. The Slowest heating point remained in the same height (in z direction) during whole process.

Process optimization

The coldest point at the end of heating period (x = 43.99, y = 43.99, z = 13.79 mm) was chosen to be studied for sterilization efficiency.

Results showed 23.8 min as total F₀. The retort temperature program was adjusted to process some Iranian Stews. Since Haleem contains starch and meat (pH = 6.3), the F₀ was compared with starch based and meat based formulations. The amount of F₀, for mashed potato, as a starch based (pH = 6.3) and Chili con carne, as a meat based formula, is 4.8 and 6–7.65 min respectively (Luechapattanaporn et al. 2004; Noronha et al. 1996; Sun 2012).

Thus, the time-temperature was adjusted to reach a lower value of F₀ by using Simpson’s rule for numerical approximation of integration (Holdsworth 1993). Results showed that the product would reach a logical sterility about F₀ = 6.1 min., by decreasing 19 min of heating period (Figs. 5 and 6).

Fig. 5.

Adjusted time-temperature profile in comparison to the time-temperature profile of slowest heating point

Fig. 6.

Adjusted Sum of F₀ in comparison to the processed sum of F₀ in slowest heating point

Conclusion

A mathematical model was developed and experimentally validated to study temperature distribution and sterilization efficiency of semi-rigid containers containing Haleem. The CFD based model showed that the position of SHZ was located in the geometric center of the container. In comparison with heating period, the results of cooling period modelling showed less accordance to validation tests. It might have been affected by setting of starch based formula and swelling of containers during the cooling operation, due to internal pressure. In order to improve the nutritional value and the organoleptic characteristics of this ancient eastern food, the time-temperature profile was adjusted to achieve desired sterilization.