Mathematical modeling of the heat transfer and flow field of liquid refrigerants in a hydrofluidization system with a stationary sphere

Hydrofluidization is a method of chilling and freezing of foods that uses a circulating system that pumps the refrigerating liquid upwards through orifices and/or nozzles into a refrigerating vessel, thereby creating submerged agitating jets and increasing heat transfer to foods during freezing. The objective of this work was to develop a model to estimate the fluid flow and heat and mass transfer in a hydrofluidization system. A study case of modeling and validating the heat transfer to a single stationary copper sphere of 20-mm diameter impinged by a single round jet of liquid was carried out using computational fluid dynamics. The simulations were performed using parameters such as: velocity of the liquid at the orifice exit (2.36–7.07 m s⁻¹), temperature of the liquid refrigerant (−5 to −15 °C) and distance between the orifice and the stagnation point of the sphere (1 and 5 cm). In general, the errors of the model were in the order of magnitude of the uncertainty of the experimental data of Nusselt number averaged over the sphere surface. Also, the simulated heat transfer and flow field parameters were comparable with those obtained in literature for similar systems.     

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。     

计算流体力学在食品传热传质过程中的应用

对计算流体力学(CFD)技术进行了简单介绍，并对采用CFD技术模拟食品加工过程中的传热传质过程的研究现状进行了综述，探讨了采用CFD对这些传热传质过程进行数值模拟的优势。CFD模拟的结果详细、直观，模拟得到的流体流动和各种热力学参数的分布信息，可以为装置的设计、传热过程的优化提供参考。     

A new arrangement of blades in scraped surface heat exchangers for food pastes

The present study analyses the performance of a scraped surface heat exchanger (SSHE) equipped with a new arrangement of blades to achieve higher thermal efficiencies than the conventional SSHE. This new design of exchanger, named here as scraped surface heat exchanger with alternate blades, A-SSHE, may be particularly suited to treat high viscous fluids, like food pastes. Experimental and numerical tests were carried out on an industrial scale A-SSHE used to heat hazelnut paste, an intermediate product widely used in Italian confectionery industry. Experimental tests include physical, chemical and rheological characterization of the hazelnut paste and the evaluation of the overall heat transfer coefficient as a function of rotational speeds and mass flow rates. Three-dimensional axial-symmetric CFD simulations of the A-SSHE were performed by using the software Fluent 6.2. For comparison, the same numerical tests were carried out for an equivalent SSHE with a conventional blades design (C-SSHE). Our studies show that the A-SSHE gives heat transfer coefficient values almost twice that of an equivalent C-SSHE, and that the numerical results are consistent with the experimental observations. The analysis of the fluid dynamics and of the thermal profiles suggests that the higher heat transfer efficiency of A-SSHE may be attributed to the occurrence of backmixing phenomena.     

Heat transfer coefficient for nitrogen droplets film-boiling on a food surface

A method of measuring heat transfer rates from a solid food surface to liquid nitrogen droplets on it has been developed using 0.5 sec repeat-shot photography. Droplet diameters were varied from 0.1 to 2.5 mm and food surface temperatures from +30 to -100°C. All measurements were carried out at atmospheric pressure. The mean heat transfer coefficients were determined using an energy balance for the droplets. An empirical dimensionless correlation equation was established, and the significance of the results for food freezing by liquid nitrogen sprays is critically discussed.     

Heat transfer modelling in a ventilated cavity loaded with food product: Application to a refrigerated vehicle

A simplified heat transfer model of a refrigerated vehicle was developed in which two loads (front and rear) are considered. The front load located near the supply air duct is subjected to higher air velocity and lower air temperatures compared with the rear load, leading to product temperature heterogeneity. The model takes into account heat transfer by convection between the internal air and the load, between the external air and the walls of vehicle and by conduction in these walls. Air infiltration during door openings is also considered. Model validation was carried out by comparing the calculated product temperatures with those obtained from transport of fruits and frozen foods in a semi-trailer. Good agreement between the experimental and calculated results was obtained.     

Mathematical modeling of the heat and mass transfer in a stationary potato sphere impinged by a single round liquid jet in a hydrofluidization system

The hydrofluidization (HF) is a method of chilling and freezing of foods which consists in a circulating system that pumps a refrigerating liquid upwards through orifices or nozzles, creating agitating jets. The objectives of this work were to develop a mathematical model to represent the combined heat and mass transfer between a food and a refrigerant liquid medium in a HF system and to validate the model using a single stationary sphere of food impinged by a single round jet of liquid. The food domain consisted of a rigid solid matrix, a liquid phase and the ice phase. Transport equations were applied to each phase and solved by a control-volume approach. The transport phenomena in the fluid domain were studied by computational fluid dynamics. The surface heat transfer coefficients obtained from fluid flow simulations were used to model the heat and mass transfer inside the food. Experimental central temperature and average solute uptake profiles were obtained when potato spheres were placed in a HF system using a NaCl-water as refrigerant and considering different temperatures (−10 and −15 °C), flow rates (1 and 3 L min⁻¹), and orifice-sphere distances (1 and 5 cm). The predicted values agreed well with the experimental ones, the maximum root mean square errors being 3.3 g NaCl kg⁻¹ potato and 2.9 K for the average solute concentration and temperature profiles studied, respectively. The simulations improved the understanding of the HF process and it may help to study and control different operation scenarios.     

用于食品冷冻温度控制的模糊控制系统设计

目的:提高食品进入冷冻隧道的速度控制回路和温度控制回路的设定值调整能力。方法:对传送带速度和温度控制回路进行了单独处理,设计用于食品冷冻温度控制的模糊控制系统。该控制系统包括用于食品传送带滚子转速的比例—积分—微分控制器、用于冷冻隧道温度调节的比例—积分控制器,并采用Takagi-Sugeno模糊控制器来设定温度调节比例—积分控制器的温度设定点。结果:待冷冻食品的质量流量从650 kg/h增加到700 kg/h、驱动辊的转速从1.62 r/min增加到1.75 r/min时,最终食品温度可快速恢复到约-18℃;食品入口发生+5℃的温度干扰时,模糊控制器动作,从而将食品的出口温度保持在预期值-18℃附近。结论:所设计的控制系统通过选择允许快速响应和相对较低超调的系统参数,可实现输出变量的值不会在设定值附近出现大幅波动。     

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.     

Computational fluid dynamics (CFD) analysis of pipeline in the food pellets cooling system

Pellet cooling-drying machine with a pneumatic conveying system is used to transfer heat and moisture of hot and moist pellets in the food and animal feed plants. During heat transfer along the pipeline, very fine pellets and flour is sucked in to the pipe and settling phenomenon is accrued. The sediment of fine particles and pellets leads to the erosion and wear in the pipeline especially at the warm and humid condition. In the present research, the reported problem in Faradane Feed Processing Company, consisting of the erosion of facilities and settling in the pipeline of pellet cooling-drying system was analyzed. A computational fluid dynamics modeling (CFD) based on the Euler-Euler method was developed to investigate the particle distribution and settling inside the vertical and horizontal pipeline as a function of pipeline diameter, particle size, flow velocity, and inlet volume fraction of particles. The results indicated that, the particle sediment along the vertical pipeline was lower than the horizontal pipeline and particle size had the greatest influence on the distribution and position of settling. Increasing of particle size from 62 μm to 250 μm was leaded to the rise in the particle sediment up to 54%.     

Control of ice crystal nucleation and growth during the food freezing process

Freezing can maintain a low-temperature environment inside food, reducing water activity and preventing microorganism growth. However, when ice crystals are large, present in high amounts, and/or irregularly distributed, irreversible damage to food can occur. Therefore, ice growth is a vital parameter that needs to be controlled during frozen food processing and storage. In this review, ice growth theory and control are described. Macroscopic heat and mass transfer processes, the relationship between the growth of ice crystals and macroscopic heat transfer factors, and nucleation theory are reviewed based on the reported theoretical and experimental approaches. The issues addressed include how heat transfer occurs inside samples, variations in thermal properties with temperature, boundary conditions, and the functional relationship between ice crystal growth and freezing parameters. Quick freezing (e.g., cryogenic freezing) and unavoidable temperature fluctuations (e.g., multiple freeze–thaw cycles) are both taken into consideration. The approaches for controlling ice crystal growth based on the ice morphology and content are discussed. The characteristics and initial mechanisms of ice growth inhibitors (e.g., antifreeze proteins (AFPs), polysaccharides, and phenols) and ice nucleation agents (INAs) are complex, especially when considering their molecular structures, the ice-binding interface, and the dose. Although the market share for nonthermal processing technology is low, there will be more work on freezing technologies and their theoretical basis. Superchilling technology (partial freezing) is also mentioned here.     

CFD modelling of flow and scalar exchange of spherical food products: Turbulence and boundary-layer modelling

The performance of several steady Reynolds-averaged Navier–Stokes turbulence models and boundary-layer modelling approaches is evaluated for a single sphere, by comparison with empirical data for a Reynolds number range of 10–3.2 × 10⁴. A sphere serves here as a representative model for many spherical food products. The shear stress transport (SST) k–ω turbulence model performs exceptionally well when combined with low-Reynolds number modelling (LRNM) of the boundary layer, which confirms that the turbulence model characteristics are particularly suitable to deal with this specific flow problem. Especially the k–ε turbulence models are less accurate at higher Reynolds numbers (>10²). Boundary-layer modelling with wall functions (WFs) leads to inaccurate flow-field and scalar transfer predictions, compared to LRNM. However, LRNM grids and their inherently higher computational cost are often not practically feasible, leaving WFs as the only option. It is shown that using cell sizes on the sphere surface of a few millimetres, typical for CFD studies on food products, can compromise accuracy, and grids with smaller cell sizes are actually required.     

牛肉冻结过程中模拟及热值传递理论分析

以冰箱冻结牛肉为研究对象,考虑牛肉冻结过程中变物性特点,采用等效热容法处理相变潜热,再用计算流体力学(CFD)数值模拟技术对该冻结过程进行模拟,并建立描述三维食品冻结过程的微分方程,通过数值模拟得出冻结时间的模拟值,各测点(T1、T2、T3、T4、T5)模拟计算的冻结时间与试验冻结时间的误差分别为5.45%,3.90%,5.80%,4.24%,9.60%,各点实时温度的模拟平均误差是1.79℃。结果表明,数值模拟能较好地预测牛肉的冻结时间。     

食品物料冻结点测定方法研究

通过对多种食品物料冻结过程中电导率的测定,研究了电导率、温度和时间三者的关系,发现当物料温度降至0℃以下某温度时,其电导率会出现急剧下降的现象。而突变点的温度与用传统的温度测定方法所得冻结点的数值相吻合,证明电导率发生突降时的温度即为物料的初始冻结点,从而可建立一种食品物料冻结点测定的新方法。并通过此方法研究了富士苹果冻结点温度与水分含量、可溶性固形物(SSC)的关系,通过建立数学模型可以根据可溶性固形物含量或水分含量,确定富士苹果的冻结点温度。结果表明:富士苹果冻结点温度与水分含量呈高度正相关,其回归方程为Y=0.5611X-51.761;冻结点温度与可溶性固形物含量呈高度负相关,其回归方程为Y=-0.5565 X+3.1001;可溶性固形物含量与水分含量呈高度负相关,其回归方程为Y=-0.9995X+97.821。     

食品液氮速冻处理的热力与经济分析

主要介绍了液氮速冻处理的几种形式,讨论了食品流态化速冻装置的特点,分析了食品液氮速冻过程的热力特性和技术经济特点,并通过具体算例比较了食品速冻处理的几种方案,说明了液氮速冻与常规机械式流态化装置联合运行的可行性。分析结果还表明,液氮流态化速冻装置产品质量高,但运行成本也高,目前还只适合于生产高质量的、具有高附加值的产品。     

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.     

Emerging techniques for assisting and accelerating food freezing processes: A review of recent research progresses

Freezing plays an important role in food preservation and the emergence of rapid freezing technologies can be highly beneficial to the food industry. This paper reviews some novel food freezing technologies, including high-pressure freezing (HPF), ultrasound-assisted freezing (UAF), electrically disturbed freezing (EF) and magnetically disturbed freezing (MF), microwave-assisted freezing (MWF), and osmo-dehydro-freezing (ODF). HPF and UAF can initiate ice nucleation rapidly, leading to uniform distribution of ice crystals and the control of their size and shape. Specifically, the former is focused on increasing the degree of supercooling, whereas the latter aims to decrease it. Direct current electric freezing (DC-EF) and alternating current electric freezing (AC-EF) exhibit different effects on ice nucleation. DC-EF can promote ice nucleation and AC-EF has the opposite effect. Furthermore, ODF has been successfully used for freezing various vegetables and fruit. MWF cannot control the nucleation temperature, but can decrease supercooling degree, thus decreasing the size of ice crystals. The heat and mass transfer processes during ODF have been investigated experimentally and modeled mathematically. More studies should be carried out to understand the effects of these technologies on food freezing process.     

热泵式流化床干燥装置及其应用优势

热泵式流化床干燥装置干燥食品的突出优点是节能和食品干燥质量好。本文对热泵式流化床干燥食品的特点进行了简要介绍，对热泵式流化床的结构性能进行了较深入的分析。对这种新型装备的推广与普及所需解决的问题及其技术思路进行了探讨，并对热泵式流化床食品干燥成套装备的市场应用前景进行了预测。     

Two-dimensional CFD modeling and simulation of crustless bread baking process

A special type of baking oven was developed where crustless bread was made by gently baking the dough at controlled temperature by spraying water at prefixed intervals on the surface of the dough. In this study, a two-dimensional (2D) CFD model for crustless bread during baking has been developed to facilitate a better understanding of the baking process. Simultaneous heat and mass transfer from the bread during baking was successfully simulated. It was found that core temperature of the bread reached at 95 °C at the end of baking where as moisture of the bread satisfies the normal bread quality. The model can be successively applied to study the unsteady heat and mass transfer from the crustless bread during baking.     

南极磷虾肉冻融循环过程水分的迁移及微观结构变化

为解决新零售预制烤鱼经冷冻复热后口感下降的问题,选取草鱼为研究对象,以水分含量、持水力、水分分布及组成和微观结构等为指标,探究鱼肉油炸、冷冻、复热不同阶段的品质变化规律。结果表明,随冻融循环次数增加,鱼肉肌纤维破坏程度增加,水分含量显著降低（P<0.05）,持水性变差,脂肪氧化和蛋白降解程度显著增加（P<0.05）,风味发生改变。复热后,冻融1次鱼肉仍能保持较好口感,但冻融2次后鱼肉感官评分较低,且肌原纤维小片化指数、TBARS和TCA-可溶性肽含量较冷冻前样品分别增加了24.44%、225.84%和52.85%。综上,当油炸预制鱼产品在贮运流通过程中发生冻融次数超过2次时明显降低产品食用品质和消费者接受度。