A zTurbulent Conjugate Heat-transfer Model for Freezing of Food Products

ABSTRACT: A 3-dimensional conjugate heat-transfer model for the analysis of freezing food products has been developed. The food-freezing process is a multi-medium, multi-phase, and transient heat-exchange phenomenon in connection with the cooling flow around the food items. The developed numerical model couples the energy equation with the Navier-Stokes equations outside the food items to simulate the velocity distribution around the food items and the heat flux across the food surfaces. The conjugate heat-transfer methodology and enthalpy method was used to solve the energy equation across the fluid-solid interface into the food item. The heat convection in the fluid and conduction in the foods are implicitly coupled to predict the heat-transfer rate and the enthalpy change during its freezing process. The conjugate heat-transfer model presented here is applicable to perform various heat-transfer calculations involved in the design of storage and refrigeration equipment and to estimate the process time required for freezing of foods. The article presents the mathematical model used, the outline of the numerical scheme, and the results of computations. The model-predicted results are compared with the experimental data available in the literature. Overall good agreement was obtained.     

Mathematical Models for Nonsymmetric Freezing of Beef

A microscopic balance with simultaneous change of phase together with equations for predicting the thermal properties as a function of the ice content and a cryoscopic descent model are used to simulate the nonsymmetric freezing of a beef slab. The equations are solved numerically to obtain temperature profiles as well as freezing times. Comparison with experimental results shows good agreement. A variation of the thermal center position throughout the freezing process is detected and assumptions to predict its position in the different periods of freezing are supplied. On the basis of these assumptions a simplified model for calculating processing times in plate freezers is proposed, showing good agreement with experimental freezing times and with predictions obtained from the numerical model.     

A Converging-Front Model for the Asymmetric Freezing of Slab-Shaped Food

In food freezing situations where heat flows at different rates from the two surfaces of a slab, a Plank-type converging-front model enabled the position of the thermal center and hence the freezing time, to be calculated. The thermal center was defined as the point where the freezing fronts meet, i.e. the last point to cross the “mean freezing temperature”. Finite-difference calculations showed that this model successfully accounted for the effect of asymmetry in heat transfer coefficient or coolant temperature and enabled previously developed simplified prediction methods to be applied to asymmetric situations.     

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.     

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.     

A Simplified Model for Freezing Time Calculations in Foods

A model is proposed for freezing time calculations which combines Plank's equation with the unsteady heat transfer solutions for the cooling of a slab of constant properties through the addition of pre-cooling, change of phase and tempering periods. The change of thermal properties with the ice content is taken into account by proposing average values for the different periods. No adjustable parameters are used in developing the model. Results are compared for the case of beef freezing with those obtained numerically by using a heat transfer model with simultaneous change of phase and with experimental measurements showing good agreement.     

平板状食品冻结时间的数值预测

采用有限差分法获得平板状食品冻结时间的数值解。对凝固区（两相区）的参数进行处理,使食品在整个冻结过程可以选用统一的差分格式;通过凝固区释放热量的累积效果,判断凝固区界面的移动;对常见的平板状食品的冻结过程进行计算机模拟来预测冻结时间,并通过实验来验证可靠度。结果表明,这种计算方法可以应用在实际生产中。     

Boiling on the surface of a rotating disc

An experimental unit to study heat-transfer characteristics while boiling at subatmospheric pressure of a horizontal smooth spinning disc was designed and built. Evaporation experiments were carried out with the speed of rotation varying from 0 to 1000 rpm and the feed flow rate from 1 to 5 litre/min. The boiling temperature varied between 40 and 50 °C. Water and corn syrup were used as test liquids. Results are presented from the experimental measurement of the heat flux on the disc as a function of the wall superheat. The heat-transfer coefficient for water, in the low range of heat flux (10–30 kW/m²), increased from about 2 to 9 kW/m²K when the speed of rotation increased from 0 rpm to 1000 rpm. In the upper range of heat flux (60–100 kW/m²), it increased from about 5 to 16 kW/m²K for the same increase in the speed of rotation. The feed flow rate between 1 and 5 litre/min had no significant influence on the heat-transfer coefficient in the range of 200–600 rpm. With the 60 °Brix corn syrup, the heat-transfer coefficient at 10 °C temperature difference increased from about 0.8 to about 2.3 kW/m²K when the speed of rotation increased from 0 to 1000 rpm. A simple theoretical relation was derived which predicts the heat-transfer coefficient for water at inlet Reynolds numbers 500–1000 relatively well, but underpredicts the results for corn syrup at inlet Reynolds numbers 10–100.     

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.     

MEASUREMENT OF THE HEAT TRANSFER COEFFICIENT IN A THAWING TUNNEL

In a convective (air) thawing tunnel designed in the department of Food Engineering at Lund, and previously applied for the thawing of meat, we have measured the heat transfer coefficient using an ice model with a geometry which could be approximated to an infinite slab. The heat transfer coefficient was deduced from the agreement between experimental and simulated (using a commercial numerical program) data. The results could be summarized by the following equation: Nu = 1.27Re^0.553. Thus, the dependency of the heat transfer coefficient on the Reynolds number agrees well with correlations found in the literature for similar kinds (freezing, thawing) of application. In particular the found Nusselt relationship was in a very good agreement with the Heldman correlation for freezing of foodstuffs in the turbulent regime.     

Freezing rate simulation as an aid to reducing crystallization damage in foods

In food freezing processes the presence of large ice crystals is a serious drawback when a good final quality of the product is desired. To study the size and distribution of those crystals, a large piece of pork muscle has been frozen by liquid nitrogen evaporation. A mathematical model to simulate different cooling rates at the surface of the product was solved using a finite element method; this model satisfactorily fitted experimental data and predicted local freezing rates at different locations in the meat tissue. The model was applied to find the freezing rates that led to a good quality product, related to an optimum distribution of small ice crystals located inside and outside the tissue fibres.     

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.     

The Leidenfrost Phenomenon: Experimental Investigation of the Vaporization of Nitrogen Droplets on a Food Surface

The vaporization of liquid nitrogen droplets at rest on a gelatin slab of food material was investigated in relation to heat transfer in food freezing. Measurements were made of changes in droplet sizes during evaporation using a photographic technique while varying the slab surface temperature from + 10°C to - 120°C at atmospheric pressure. The measured values of the vaporization time were about 12% higher than those theoretically predicted, and about 15% lower for droplets contaminated with moisture.     

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.     

COLLECTION of ACCURATE EXPERIMENTAL DATA FOR TESTING the PERFORMANCE of SIMPLE METHODS FOR FOOD FREEZING TIME PREDICTION

Objective testing of the accuracy of food freezing time prediction formulae requires experimental data to be of high quality. It is shown that there are shortcomings in commonly used experimental methods, particularly relating to minimizing heat transfer in all but the required dimensions in experiments with the slab and infinite cylinder shapes, in maintaining uniformity of surface heat transfer coefficients across a sample, and in measurement of surface heat transfer coefficients. Broad guidelines to ensure that the errors introduced by experimental techniques are negligibly small are proposed. Major published experimental data sets are compared to these guidelines and comments made on their likely accuracy.     

A NUMERICAL METHOD OF SIMULATING THE AXISYMMETRICAL FREEZING OF FOOD SYSTEMS

A numerical method is developed to simulate the temperature progression of freezing a food system. It is assumed to have a constant density and to be macroscopically homogeneous during the freezing operation. The simulated results are compared with the measured temperature progression in the center of a beef slab immersed in a-39°F bath.     

Freezing of tilapia fillets in an air blast freezer

This paper explores the numerical simulation of freezing tilapia fillets of five different geometries, which are the slab, elliptical, disc, spherical and cylindrical shapes, in an air blast freezer. The air velocities and temperatures inside the freezer are varied in the simulation to determine the freezing times and energy consumptions for freezing the tilapia fillets of different shapes. The results show that the cylindrical-shaped fillet has the longest freezing time and also required the most energy for freezing. The slab-shaped fillet has the shortest freezing time, but the spherical-shaped fillet requires the least energy to freeze. The simulation is also applied to a case study to compare the processing rate, energy consumption and the cost of freezing the fillets of different shapes. The freezing cost for a tray of spherical-shaped fillet is the lowest among all.     

Definition of the optimal freezing rate-2. Investigation of the physico-chemical properties of beef M. longissimus dorsi frozen at different freezing rates

The influence of freezing rate on weight loss during the freezing, thawing and cooking, on water-binding capacity, on sensory and other physico-chemical properties of beef M. longissimus dorsi was investigated. The changes in myofibrillar proteins in muscle samples frozen at different freezing rates were also investigated.

The greatest weight losses during the freezing, thawing and cooking were registered at slow freezing procedures (freezing rate of 0·22 cm/h and 0·29 cm/h), when the meat was tougher and less soft. The solubility of myofibrillar proteins was least from those muscles frozen at such freezing rates.

The freezing of samples at freezing rates of 3·33 cm/h and 3·95 cm/h had less influence on their physico-chemical characteristics. The solubility of the myofibrillar proteins from such samples was greatest, and the cooked samples were the most tender.

From analysis of the results it was concluded that optimal conditions for meat freezing seem to be those when the average freezing rate is 2–5 cm/h.     

Fluid Flow and Heat Transfer in Air Jet Impingement in Food Processing

ABSTRACT: Air impingement technology is gaining popularity in food-processing operations such as baking, freezing, drying, and toasting. In this article, physical characteristics of impinging jets, such as turbulent mixing in the free jet region, stagnation, boundary-layer formation, recirculation, and their interactions with food products in terms of heat and mass transfer have been reviewed. The discussion includes experimental methods used for measurement of heat and mass transfer for single and multiple slot and circular jets. Procedures used for measurement of heat-transfer coefficient such as lumped sensor method, micro-calorimetric approach, and use of flux sensors are presented. Typical qualitative and quantitative flow-field studies using planar visualization and laser Doppler anemometry have been reviewed. Numerical modeling of air impingement systems is discussed with special consideration of problems arising in food-processing systems.     

Determination of Heat Transfer Coefficients for Continuous Belt Freezers

Air-product heat-transfer coefficients for belt freezers were determined experimentally. Measurements were performed for foods (beef hamburgers) and a model substance (copper disk) using a prototype tunnel. Air flow parallel, as well as perpendicular, to the belt, was employed; in the latter case moving upwards or downwards through the belt. From the measured temperatures, heat-transfer coefficients were calculated using appropriate mathematical methods. Values obtained for both types of materials were compared, and the usefulness of the test substance was discussed. From these data, simple and precise regressions were obtained, useful to predict the coefficient for the above mentioned types of air flow and valid over a wide range of operating conditions in belt freezers.