Modeling Flow and Heat Transfer During Freezing of Foods in Forced Airstreams

ABSTRACT: Mathematical modeling of food freezing has been limited to the modeling of the internal heat transfer where the external convective heat-transfer coefficients are assumed or empirically estimated. Previous procedures followed to solve the external boundary layer in tandem with the internal heat transfer were constrained by numerical complexities due to the transient nature of the heat transfer, requiring unsteady formulation for the flow. In this article, attempts have been made to decouple the flow and heat transfer equations for the external boundary layer flow over a food product being frozen. The flow equations have been solved as a steady-state problem using Falker-Skan transformations of the boundary layer equation. The heat-transfer equation for fluid flow is solved as an unsteady-state problem in conjunction with the internal heat transfer and phase change inside the product undergoing freezing. The model is validated for a case of air-impingement freezing.     

Freezing Time Prediction for Slab Shape Foodstuffs by an Improved Analytical Method

An improved analytical method for predicting the freezing time with one dimensional heat transfer for slabs was developed. Tylose- MH-1000 was used as a model test material. The new model is similar to Plank's equation, but has a more theoretical basis. Total enthalpy difference instead of latent heat and weighted average temperature difference instead of the temperature difference between initial freezing point and freezer temperature were used in the improved prediction method. Linear regression was used to estimate shape parameters. Four different foods were used to test the model. Predicted times for foods were within 6% of the measured times.     

数值模拟在食品冻结过程中的应用

文章主要通过综述冻结过程的数值模型、求解微分方程、预测冻结时间及分析送风速度、温度和送风方式等,讨论数值模拟技术在食品冻结过程中的应用现状;总结了国内外研究者针对不同冻结对象所采用的数值模拟方法,为今后数值模拟方法在食品传热过程中进一步发挥作用提供理论参考。     

Numerical simulations of chilling and freezing processes applied to bakery products in irregularly 3D geometries

Finite element algorithms implemented in numerical codes were developed by the authors for irregular 3D food systems, to simulate: (i) the chilling process considering domains of different thermo-physical properties, and (ii) the freezing operation using a combined enthalpy and Kirchhoff transformation. The specific heat of the food materials were measured using Differential Scanning Calorimetry and the heat transfer coefficients of the low temperature equipments were determined; this information was further used as inputs in the model.     

Prediction of Freezing and Thawing Times of Foods Using a Numerical Method Based on Enthalpy Formulation

An explicit numerical method, involving enthalpy formulation, to predict temperature distribution in foods during freezing and thawing was developed. The accuracy of the proposed method was validated using published experimental data obtained for freezing and thawing of Tylose. The enthalpy formulation avoids the problems of strong discontinuity experienced when the apparent specific heat formulation is used in predicting temperatures for situations involving phase change. The proposed method predicts temperatures in good agreement with experimental data. The computer code can be easily programmed on a desk-top computer for use in teaching and research on predicting freezing and thawing rates in foods.     

Recent developments in novel freezing and thawing technologies applied to foods

This article reviews the recent developments in novel freezing and thawing technologies applied to foods. These novel technologies improve the quality of frozen and thawed foods and are energy efficient. The novel technologies applied to freezing include pulsed electric field pre-treatment, ultra-low temperature, ultra-rapid freezing, ultra-high pressure and ultrasound. The novel technologies applied to thawing include ultra-high pressure, ultrasound, high voltage electrostatic field (HVEF), and radio frequency. Ultra-low temperature and ultra-rapid freezing promote the formation and uniform distribution of small ice crystals throughout frozen foods. Ultra-high pressure and ultrasound assisted freezing are non-thermal methods and shorten the freezing time and improve product quality. Ultra-high pressure and HVEF thawing generate high heat transfer rates and accelerate the thawing process. Ultrasound and radio frequency thawing can facilitate thawing process by volumetrically generating heat within frozen foods. It is anticipated that these novel technologies will be increasingly used in food industries in the future.     

食品超高压处理过程中传热模型和相转变的研究进展

食品超高压处理技术是食品领域的一项新技术,在食品工业中的应用越来越广泛.但目前超高压处理过程中食品的温度分布和传热模型仍未研究清楚,采用数学方法对食品超高压处理过程中的传热现象进行模拟可以有效地均匀化和优化超高压处理条件,这对于实际生产具有指导意义.本文综述了食品在超高压处理过程中的传热模型和相转变的研究进展,对超高压低温条件下的冻结和解冻过程也进行了讨论.     

Parametric Analysis for Thawing Frozen Spheroidal (Prolate and Oblate) or Finitely Cylindrical Food

A screening analysis was performed to determine the influence of independent parameters (18) on thawing times of frozen spherical (prolate and oblate) and finitely cylindrical foods using a computerized simulation procedure assuming food volume shrinkage from density changes and temperature dependent physical properties. Of 18 independent parameters, 6 were significant for both foods: thawing medium temperature, initial freezing point, Biot number, radiative heat exchange, a parameter for effective specific heat and shape factor (nonsignificant influence of volumetric changes). Predictive regression equations were developed for estimating thawing time as function of significant parameters. Predictive equations were validated experimentally. A sensitivity analysis showed errors in thawing time were influenced most strongly by food dimensions, followed by operational temperatures, thermophysical properties and convective surface heat-transfer coefficient.     

Numerical Simulation and Experimental Investigation of Conjugate Heat Transfer between a Turbulent Hot Air Jet Impinging on a Cookie-shaped Object

ABSTRACT: Numerical simulation of the flow field and conjugate heat transfer for a turbulent jet impinging on the surface of a model cookie were carried out at different nozzle-to-plate spacings. Numerical predictions were compared with the experimental results on average and the local heat-transfer coefficient. Results indicated good agreement between the numerical and experimental results over the range of jet velocities, that is, 10 to 40 m/s, which corresponds to Reynold's number range of 7500 to 32000 based on the jet orifice diameter. Numerical simulation also confirmed that the surface heat-transfer coefficient was independent of the thermo-physical properties of the cookie. The local heat-transfer coefficient on the top surface of the cookie was highest at the center of the impinging jet.     

A Novel Method for Simultaneous and Continuous Determination of Thermal Properties during Phase Transition Applied to Calanus finmarchicus

Abstract: The thermal properties of a product are the most important parameters for practical engineering purposes and models in food science. Calanus finmarchicus is currently being examined as a marine resource for uncommon aquatic lipids and proteins. Thermal conductivity, specific heat, enthalpy and density were measured over the temperature range from −40 to +20 °C. The initial freezing point was determined to be −2.3 °C. The thermal properties were recorded continuously on 4 samples using a new method, and the results were compared with predictive models. The accuracy of the new method is demonstrated by different calibration runs. Significant differences in the thermal conductivity of the frozen material were found between the parallel-series model and the data, whereas the model of Pham and Willix (1989) or the Maxwell–Euken adaption showed better agreement. The measured data for specific heat, enthalpy, and density agreed well with the model. Practical Application: The thermal data obtained can be used directly in food engineering and technology applications, for example, in a thin layer model for freezing food for which precise thermal data for each layer are now available, enabling the more accurate prediction of freezing times and temperature profiles. Dimensionless numbers (such as the Biot number) can also be based on measured data with minor deviations compared to more general modeled thermal properties. Future activities will include the generation of a comprehensive database for different products.     

Two Dimensional Heat Conduction in Food Undergoing Freezing: Development of Computerized Model

A model was developed to simulate two dimensional heat conduction in anisotropic food which was undergoing a freezing process. This model utilized a well verified transient state heat conduction equation. We assumed convective and radiative heat exchanges as well as moisture loss on the boundary surface of food to develop our model. Empirical formulae, whose applicability was verified, were used to estimate the temperature dependent thermophysical property values of food in the model. Since the model is nonlinear, a computer program package was prepared to solve it numerically by applying a finite element method. Sample application of computerized procedure was presented for simulating rectangular or finitely cylindrical food.     

Determination of Local Heat-Transfer Coefficients Around a Circular Cylinder Under an Impinging Air Jet

Heat transfer coefficients around a model food shaped as a circular cylinder placed on a flat surface and impinged by a slot air jet has been determined using an inverse heat transfer method. The determination was based on time-temperature data measured with a thermocouple in the cylinder and in the air jet. The cylinder was rotated around its horizontal axis to determine the heat-transfer coefficients at different locations around the cylinder. A sensitivity analysis using Monte Carlo simulations was also performed. The local heat-transfer coefficients determined, were compared to computational fluid dynamics (CFD) simulations using the k-ω SST and RSM models. The heat-transfer coefficients determined from temperature measurements was larger than predicted by the CFD simulations. The heat-transfer rates were in better agreement on the upper part of the cylinder, including the decrease along the cylinder due to flow separation, than on the lower part close to the wake recirculation area. The SST model predicted in general a slightly higher heat-transfer rate on the upper part of the cylinder and slightly lower on the lower part of the cylinder, as compared to the RSM model.     

Freezing Time Prediction: An Enthalpy-Based Approach

Equations were developed for prediction of freezing times of foods of slab geometry, for three different boundary conditions, using a method of solving for enthalpy per unit volume instead of temperature. Experimental verification was performed for the operation with a convective heat transfer boundary condition, using ice cream and green peas in a granular packed bed as test materials. Results indicate good prediction of freezing times over a range of conditions. Results of thawing tests are less satisfactory if the ambient temperature lies in the zone of rapidly changing food properties. A comparison with literature predictions is presented.     

Microwave assisted freezing part 1: Experimental investigation and numerical modeling

The aim of this study was to develop an innovative process dedicated to enhancing the quality of frozen food using microwaves. A microwave assisted freezing device was designed at the laboratory scale to perform experiments in controlled conditions. Small samples of methylcellulose gels were frozen using nitrogen gas in a TE₁₀ waveguide, where microwaves at 2.45 GHz were emitted intermittently or continuously. A numerical model was also developed to obtain results difficult to measure such as the local electric field and the corresponding energy density. The phase change part of the model was based on an enthalpy formulation and on the growth of spherical ice crystals. An original “hybrid 2D-3D” solving methodology was used to reduce the duration of the simulations. Favourable comparisons between the predicted temperatures and the experimental data highlighted the relevance of the models used for the thermophysical and dielectric properties. The analysis of the interactions between microwaves and matter, performed with numerical simulations, revealed the role of the freezing front as a boundary. The strong influence of sample size and of dielectric properties on the power density distribution were also illustrated when comparing our results with those published previously. The scientific knowledge obtained through this study and the original structure of the numerical model will be used to optimize microwave assisted freezing and link the process parameters to the reduction of ice crystal size highlighted in the companion paper.Industrial relevanceMicrowave assistance during freezing can improve frozen product quality by reducing ice crystal size. This innovative and promising process has not yet been given much attention. Developing an accurate model which describes microwave – matter interactions during phase change permits numerical simulations that can facilitate the design of industrial equipment, and determine optimal product dimensions.     

火腿鼓风冷却过程的三维数值模拟

食品的冻结速率是影响冷冻食品质量的主要因素之一。近年来数值模拟在食品冷却过程中得到了广泛的应用。本文应用有限容积法对火腿鼓风冷却过程进行数值模拟,研究了火腿冷却到指定温度3℃时的时间,并将计算结果与实验结果进行比较分析。结果表明:在外界空气温度为1℃时,大约需要12h左右,火腿的中心温度可以达到指定的冷却温度,且数值模拟的结果与实验结果符合得很好。这说明数值模拟能有效地预测食品冷却过程。     

Thermodynamic Analysis of the Freezing and Thawing of Foods: Ice Content and Mollier Diagram

On the basis of the freezing point depression equation, an ice content equation was derived. The required parameters are similar to equations for enthalpy and apparent specific heat previously developed. Validity and accuracy of the equation are demonstrated with experimental data for meat, fish and fruit juices. Cohesive data for enthalpy, apparent specific heat and ice content are calculated for a wide range of temperatures between 20 and -40°C. The calculated results are consistent with values obtainable through enthalpy-moisture content-temperature (Mollier) diagrams developed by Riedel.     

Numerical modelling of conjugate heat and mass transfer during hydrofluidisation food freezing in different water solutions

A novel method of hydrofluidisation food freezing is numerically investigated in this paper. This technique is based on freezing small food products in a liquid medium under highly turbulent flow conditions when the heat transfer coefficient is higher than 1 000 W⋅m⁻²⋅K⁻¹, which depends on the operating and flow conditions. A numerical model was developed to characterise the freezing process in terms of the heat transfer and diffusion of liquid solution components into the food product. The study investigates the freezing process of spherical samples in binary solutions of ethanol (30%) and glycerol (40%) and ternary solution of ethanol and glucose (15%/25%). The developed model was employed to determine the concentration of the liquid solution in food samples and to quantify the effect of sample size, heat transfer coefficient, solution temperature and concentration on the process. The food sample size varied from 5 to 30 mm, and the heat transfer coefficients varied from 1 000 to 4 000 W⋅ m⁻²⋅ K⁻¹. The results confirm that a freezing time of 15 min for 30 mm diameter samples or less than 1 min for 5 mm diameter samples can be achieved with the hydrofluidisation method. The solution uptake was influenced by the solution type, sample size and process parameters and varied from 8.9 to 35 g of solute per kg of product for ethanol-glucose and glycerol solutions, respectively. This paper quantifies the advantages and possible limitations of hydrofluidisation, which has not yet been entirely studied, especially in terms of the mass absorption of different solutes.     

A model for heat transfer in cryogenic food freezing

An experimental study of the heat transfer between liquid nitrogen sprays and a model food (a gelatine slab) was carried out under conditions similar to those in a cryogenic freezer. Measurements of heat flux and local mass flow rates of the spray were made at various liquid N₂ pressures and various temperature differences between the spray and the food surface.
At higher spray pressures, the heat transfer coefficient increases with the mass flux density of the liquid available at the food surface. The quantity of liquid nitrogen sprayed onto the solid surface, the mean droplet size, spray velocity, surface coverage and the mean temperature difference between the boiling nitrogen and the food surface are major factors influencing the rate of heat transfer during the freezing process. Although the heat transfer coefficients at the food surface are much less than those obtained for individual droplets, the model provides useful data.
The results are critically discussed in relation to cryogenic freezing of foods.     

Parametric Analysis for the Freezing of Spheroidal or Finitely Cylindrical Objects with Volumetric Changes

Parametric analyses were performed to examine heat transfer in freezing of spheroidal (including prolates and oblates) and finitely cylindrical foods through computerized simulation which considered volumetric changes. The boundary conditions included convective surface heat and moisture transfer and radiative surface heat transfer. Regression equations for freezing time estimation were developed through screening and central composite analyses and verified experimentally using a food simulator with physical properties similar to lean beef. Sensitivity analysis showed the convective surface heat transfer coefficient was the most significant factor affecting accuracy of calculated freezing time followed by operational temperatures, ther-mophysical properties and food dimensions. Effect of volumetric expansion on freezing time estimation was not significant.     

青豆速冻过程冻结时间的数值计算

青豆近似为球状，采用完全隐式差分法，建立描述近似青豆的球状食品冻结过程传热特性的偏微分方程：通过数值计算获得青豆冻结时间的数值解，并与实验值比较。结果表明：数值法计算结果与实测值吻合较好，具有较高的精度。