具有预制孔隙多孔介质冷冻干燥的多相传递模型

基于局部质量非平衡假设,建立了多相多孔介质热、质耦合传递数学模型,理论验证具有预制孔隙的初始非饱和多孔物料对冷冻干燥过程的强化作用。模型考虑了多孔介质的吸湿效应,构建了3种吸附-解吸平衡关系。模型使用基于有限元法的COMSOL Multiphysics软件平台数值求解,并与实验数据进行了比较。结果表明,初始非饱和冷冻物料能够有效地强化冷冻干燥过程。采用不同函数形式的吸附-解吸平衡关系模拟的干燥曲线均与实验数据非常吻合。通过分析物料内部的饱和度、温度和质量源分布,探讨了初始非饱和物料冷冻干燥过程的传热传质机理。初始非饱和物料的干燥速率控制因素主要是传热。模拟考察环境辐射温度对冷冻干燥过程影响的结果表明,所建模型具有良好的预测能力。     

流化床氛围下多孔物料干燥传热传质的数值模拟

用有限差分法数值求解一个热、质传递耦合模型,理论研究多孔物料流化床干燥过程。方程离散采用全隐格式的控制容积方法,三对角矩阵法（TDMA）用来求解线性方程组。选用球形的苹果丁作为多孔物料。在典型操作条件下,通过分析温度、饱和度和压力的分布侧形,讨论了物料内部的热、质传递机理。在对比条件下,考察了气体入口温度、气速和床面积因子对干燥过程的影响。结果表明：干燥过程受气、固相间的耦合传热传质的影响十分明显,干燥时间随气体入口温度和气速的提高而减少;随床面积因子的增大而增加。     

Numerical Investigation on Dielectric Material Assisted Microwave Freeze-Drying of Aqueous Mannitol Solution

The dielectric material assisted microwave freeze-drying was investigated theoretically in this study. A coupled heat and mass transfer model was developed considering distributions of the temperature, ice saturation and vapor mass concentration inside the material being dried, as well as the vapor sublimation-desublimation in the frozen region. The effects of temperature and saturation on the effective conductivities were analyzed based on heat and mass flux equations. The model was solved numerically by the variable time-step finite-deference technique with two movable boundaries in an initially unsaturated porous sphere frozen from an aqueous solution of mannitol. The sintered silicon carbide (SiC) was selected as the dielectric material. The results show that dielectric material can significantly enhance microwave freeze-drying process. For case of the dielectric field strength, E = 4000 V/m under typical operating conditions, the drying time is 2081 s, 30.1% shorter and 47.2% longer, respectively, than those for E = 2000V/m and E = 6000 V/m. The heat and mass transfer mechanisms during the drying process were discussed.     

SIMULATION OF SUPERHEATED STEAM DRYING CONSIDERING INITIAL STEAM CONDENSATION

A heat and mass transfer model was proposed for the superheated steam drying, focusing on phenomena which occur during the initial stage of drying, i.e., condensation of superheated steam on material surfaces and subsequent shift from condensation to evaporation leading to the beginning of the actual drying (Reverse Process Model). Next, drying equations considering the reverse process were formulated for a shrinking/swelling infinite flat plate to calculate moisture content and temperature distributions in a material, changes in mass of a material with time, and a characteristic drying curve. Then, the influence of the initial thickness of a material and the heat transfer coefficient were investigated. In addition, calculation results were compared with experimental ones with regard to the change in mass of material with time and the characteristic drying curve, and good conformance was obtained for the initial stage of drying.     

SIMULATION OF SUPERHEATED STEAM DRYING CONSIDERING INITIAL STEAM CONDENSATION

A heat and mass transfer model was proposed for the superheated steam drying, focusing on phenomena which occur during the initial stage of drying, i.e., condensation of superheated steam on material surfaces and subsequent shift from condensation to evaporation leading to the beginning of the actual drying (Reverse Process Model). Next, drying equations considering the reverse process were formulated for a shrinking/swelling infinite flat plate to calculate moisture content and temperature distributions in a material, changes in mass of a material with time, and a characteristic drying curve. Then, the influence of the initial thickness of a material and the heat transfer coefficient were investigated. In addition, calculation results were compared with experimental ones with regard to the change in mass of material with time and the characteristic drying curve, and good conformance was obtained for the initial stage of drying.     

Numerical Investigation on Dielectric Material Assisted Microwave Freeze-Drying of Aqueous Mannitol Solution

Abstract

The dielectric material assisted microwave freeze-drying was investigated theoretically in this study. A coupled heat and mass transfer model was developed considering distributions of the temperature, ice saturation and vapor mass concentration inside the material being dried, as well as the vapor sublimation-desublimation in the frozen region. The effects of temperature and saturation on the effective conductivities were analyzed based on heat and mass flux equations. The model was solved numerically by the variable time-step finite-deference technique with two movable boundaries in an initially unsaturated porous sphere frozen from an aqueous solution of mannitol. The sintered silicon carbide (SiC) was selected as the dielectric material. The results show that dielectric material can significantly enhance microwave freeze-drying process. For case of the dielectric field strength, E = 4000 V/m under typical operating conditions, the drying time is 2081 s, 30.1% shorter and 47.2% longer, respectively, than those for E = 2000V/m and E = 6000 V/m. The heat and mass transfer mechanisms during the drying process were discussed.     

具有初始孔隙的多孔物料冷冻干燥

实验研究了具有一定孔隙的非饱和多孔物料对液体物料冷冻干燥过程的影响。以甘露醇为主要溶质的待干料液采用“液氮制冰激凌法”制备非饱和物料进行冷冻干燥,并与常规饱和的冷冻物料相比较。结果表明,非饱和冷冻物料确实能够显著地强化液体物料的冷冻干燥过程。干燥产品SEM形貌分析显示,初始非饱和冷冻物料具有连续均匀的固体骨架和孔隙,固体基质更加纤细,孔隙空间更大,可以大大减小传质阻力。考察物料内部各点的温度变化发现,初始非饱和物料内部冰晶确实发生整体升华,但仍然存在主要升华区域;非饱和多孔物料的冷冻干燥过程主要是传热控制,而常规饱和物料冷冻干燥主要是传质控制。操作压力对过程的影响可以忽略。采用辐射/导热组合加热方式可改善初始非饱和多孔物料冷冻干燥过程的传热,进一步缩短干燥时间。     

泡沫金属复合PCM微结构传热储热过程模拟

以石蜡作为相变材料（PCM）,采用六面通圆孔三维结构模型,对泡沫金属复合PCM内相变熔化过程进行了数值模拟。研究了不同材料（Cu、Al、Ni、Fe）泡沫金属孔密度和孔隙率对复合PCM传热和储热性能的影响。结果表明,泡沫金属复合PCM传热过程受热传导和自然对流作用综合影响;随孔密度增加,复合PCM完全熔化时间缩短幅度逐渐减小,且泡沫金属热导率越高,孔密度对传热速率影响越大;泡沫金属复合PCM内存在非热平衡现象,孔密度和孔隙率增加均可减小最大平均温差,但对最终平衡时间的影响却截然不同;此外,泡沫金属复合PCM单位质量储热密度随孔隙率增大而增大,相比泡沫Cu、Ni、Fe复合PCM,泡沫Al复合PCM的单位质量储热密度较大,增加速率也较大。     

紧凑通道内CO2/润滑油混合物沸腾换热特性研究

为了测试润滑油对二氧化碳流动沸腾换热特性的影响,对外径6 mm、内径4 mm紧凑通道内的CO₂/润滑油混合物的换热进行实验研究。实验工况为质量流量2.74～5.61 kg·h^-1,饱和温度-4～8℃,热通量3.2～5 kW·m^-2,油浓度0～6%。结果表明：润滑油浓度越大,CO₂的局部传热系数越小;含1.5%油浓度相对于无油工况下平均传热系数下降了约42.4%; 传热系数随热通量、饱和温度的升高而增加,干涸后随着质量流量的增加传热系数增加;干涸随油浓度的增加、热通量的减小、饱和温度的升高、质量流量的增加而延迟;干涸特性对传热系数有显著影响,干涸阶段占整个换热过程的35.4%。     

ANALYSIS OF HEAT AND MASS TRANSFER DURING DRYING OF PAPER/BOARD

A mathematical model has been successfully developed to study the heat and mass transfer process during paper drying. This model takes into account the consective transfer of vapor and liquid apart from the known transport mechanisms of capillary flow of liquid, diffusion, vaporization-condensation, and heat conduction. The partial differential equations describing temperature, saturation and pressure change within the web during drying with associated boimdary conditions and initial conditions were solved using finite difference method. The model predictions show that during the drying process the web can be conveniently divided into three different zones, namely dry zone, wet zone and an intermediate zone. The movement of liquid and vapor in opposite directions in the intermediate zone is similar to the action of a heat pipe. Also, as drying proceeds the location of the intermediate zone and hence the heat pipe advances progressively through the thickness of the web.     

ANALYSIS OF HEAT AND MASS TRANSFER DURING DRYING OF PAPER/BOARD

ABSTRACT

A mathematical model has been successfully developed to study the heat and mass transfer process during paper drying. This model takes into account the consective transfer of vapor and liquid apart from the known transport mechanisms of capillary flow of liquid, diffusion, vaporization-condensation, and heat conduction. The partial differential equations describing temperature, saturation and pressure change within the web during drying with associated boimdary conditions and initial conditions were solved using finite difference method. The model predictions show that during the drying process the web can be conveniently divided into three different zones, namely dry zone, wet zone and an intermediate zone. The movement of liquid and vapor in opposite directions in the intermediate zone is similar to the action of a heat pipe. Also, as drying proceeds the location of the intermediate zone and hence the heat pipe advances progressively through the thickness of the web.     

Effect of Dielectric Material on Microwave Freeze Drying of Skim Milk

Abstract:

A simultaneous heat and mass transfer model of the dielectric material–assisted microwave freeze drying was derived in this study considering the vapor sublimation-desublimation in the frozen region. The mathematical model was solved numerically by using the finite-difference technique with two moving boundaries. Silicon carbide (SiC) was selected as the dielectric material, and the skim milk was used as the representative solid material in the aqueous solution to be freeze-dried. The results show that the dielectric material can significantly enhance the microwave freeze drying process. The drying time is greatly reduced compared to cases without the aid of the dielectric material. Profiles of the temperature, ice saturation, vapor concentration, and pressure during freeze drying were presented. Mechanisms of the heat and mass transfer inside the material sphere were analyzed. For an initially unsaturated frozen sample of 16 mm in diameter with a 4-mm-diameter dielectric material core, the drying time is 288.2 min, much shorter than 380.1 min of ordinary microwave freeze drying and 455.0 min of conventional vacuum freeze drying, respectively, under typical operating conditions.     

瓷质砖湿坯对流干燥过程的传热传质研究

引用建立于Whitaker的体积平均方程和Darcy定律基础止的多孔介质内部热质传递的等效耦合扩散模型，寻出一组关于液体饱和度、温度和气相压力的新支配方程，应用该方程组对瓷质砖坯体干燥过程进行了数值分析和实验测定。在平均含湿饱和度的变化方面，数值解与实验结果十分吻合。还改变影响坯体干燥过程的一些因素进行计算机模拟计算，通过改变这些因素的大小来考察计算结果，以期获得某些定性或定量的结论，从而用以指导实际生产过程。     

The Role of Nonuniformity in Convective Heat and Mass Transfer through Porous Media,Part 1

Through-air drying is commonly used in the drying of high-quality tissue and towel products. A representative elementary volume method was used to model the fluid flow and heat and mass transfer during through drying in heterogeneous porous biobased materials such as tissue and towel products. Results of flow both upstream and downstream of a modeled porous sheet allowed visualization of the effects of mixing at the top and bottom of the porous medium. The effect of initial nonuniformity on fluid flow and convective heat and mass transfer in heterogeneous porous media was studied. The effect of material nonhomogeneity and associated transport properties on moisture content of the porous material as a function of drying time was studied. Modeling results indicate that for the first time it is possible to simulate the effect of nonuniformity on fluid flow and convective heat and mass transfer in porous media during through-air drying of paper. Moisture and structural nonuniformity contributing to nonuniformity in air flow might contribute significantly to drying nonuniformity. Depending on the moisture regimes and degree of saturation of the convective medium, heat and mass transfer coefficients may have varying effects on the overall drying.     

A MATHEMATICAL MODEL FOR PARALLEL FLOW DRYER FOR SLABS WITH HIGH THERMAL DIFFUSIVITY

An analytical model for the process is developed. The thermal diffusivity of the drying slabs is assumed infinite and the moisture diffusivity constant during the entire drying process.

With specified initial and boundary conditions, the mathematical model yields a two-part solution for the diffusion equation. The first part is valid for the initial drying during which the surface moisture content exceeds the value of fiber saturation. This part of the solution is used until the surface moisture content drops to the fiber saturation value. The moisture profile at the end of this period is used as the initial condition for the second period of drying which takes place under hygroscopic conditions.

Two simplifying assumptions are adapted for the hygroscopic region: 1. The dependence between the surface temperature and the moisture content is linear. 2. Constant (average) absorption heat is used during this second drying period.

For both parts of the solution, the surface moisture gradient is proportional to the local temperature difference between the drying air and the slab surface. This temperature difference can be expressed by means of a water mass balance equation for the part of the dryer between the slab in-feed and the point considered and by using the thermodynamic properties of the humid air.     

Development of a porosity prediction model based on shrinkage velocity and glass transition temperature

Abstract

Pore formation and evolution is a common physical phenomenon observed in food materials during different dehydration processes. This change affects heat and mass transfer process and many quality attributes of dried product. Many mathematical models ranging from emperical to classical models proposed in the literature for predicting porosity during drying of food materials. Classical model is in its infancy as the required materials properties during drying are not avaiable for the material charecterisation. Empirical and semi-empirical models are reasonably well developed in establishing relationships between pore evolution and moisture content and determining experimental based coefficients. However, there are no simplistic models that considered process conditions and material properties together to predict the porosity. The purpose of this work is to develop a simplistic theoretical model for pore formation taking both process parameters and changing material properties during drying into consideration. A new “shrinkage velocity” approach has been introduced and the model has been developed based on this shrinkage velocity taking into account the main factors that influence the porosity including the glass transition temperature. Experimental results show good agreement with simulated results and thus validated the model. This study is expected to enhance the current understanding of pore formation of deformable materials during drying.     

A MATHEMATICAL MODEL FOR PARALLEL FLOW DRYER FOR SLABS WITH HIGH THERMAL DIFFUSIVITY

An analytical model for the process is developed. The thermal diffusivity of the drying slabs is assumed infinite and the moisture diffusivity constant during the entire drying process.

With specified initial and boundary conditions, the mathematical model yields a two-part solution for the diffusion equation. The first part is valid for the initial drying during which the surface moisture content exceeds the value of fiber saturation. This part of the solution is used until the surface moisture content drops to the fiber saturation value. The moisture profile at the end of this period is used as the initial condition for the second period of drying which takes place under hygroscopic conditions.

Two simplifying assumptions are adapted for the hygroscopic region: 1. The dependence between the surface temperature and the moisture content is linear. 2. Constant (average) absorption heat is used during this second drying period.

For both parts of the solution, the surface moisture gradient is proportional to the local temperature difference between the drying air and the slab surface. This temperature difference can be expressed by means of a water mass balance equation for the part of the dryer between the slab in-feed and the point considered and by using the thermodynamic properties of the humid air.     

Dynamic modeling of fixed-bed adsorption of flue gas using a variable mass transfer model

This study introduces a dynamic mass transfer model for the fixed-bed adsorption of a flue gas. The derivation of the variable mass transfer coefficient is based on pore diffusion theory and it is a function of effective porosity, temperature, and pressure as well as the adsorbate composition. Adsorption experiments were done at four different pressures (1.8, 5, 10 and 20 bars) and three different temperatures (30, 50 and 70 °C) with zeolite 13X as the adsorbent. To explain the equilibrium adsorption capacity, the Langmuir-Freundlich isotherm model was adopted, and the parameters of the isotherm equation were fitted to the experimental data for a wide range of pressures and temperatures. Then, dynamic simulations were performed using the system equations for material and energy balance with the equilibrium adsorption isotherm data. The optimal mass transfer and heat transfer coefficients were determined after iterative calculations. As a result, the dynamic variable mass transfer model can estimate the adsorption rate for a wide range of concentrations and precisely simulate the fixed-bed adsorption process of a flue gas mixture of carbon dioxide and nitrogen.     

Cross-Flow Drying of Wheat. A Simulation Program with a Diffusion-Based Deep-Bed Model and a Kinetic Equation for Viability Loss Estimations.

ABSTRACT

A mathematical model of heat and mass transfer for fixed beds was developed according to the modern theory of process simulation and standard laws of thermodynamics and transport phenomena. The mass transfer grain-air was predicted with simplified diffusional expressions together with an equation for the static equilibrium moisture content. Four differential equations were obtained for a grain layer and they were integrated along the bed depth and time with second and a fourth-order methods, respectively. The model was validated by comparing drying time predictions with experimental values, being the average error of 6%. The model was extended into a program for continuous cross-flow drying-cooling     

大面积瓷质砖坯体干燥过程的二维传热传质研究

引用建立于Whitaker的体积平均方程和Darcy定律基础上的多孔介质内部热质传递的等效耦合扩散模型 ,寻出一组关于液体饱和度、温度和气相压力的新支配方程 ,应用该方程组对瓷质砖坯体二维干燥过程进行了数值分析。并将传统干燥器与新型干燥器的模拟数据进行比较 ,以期获得某些定性或定量的结论 ,从而用以指导实际生产过程。