Foam-Mat Freeze Drying of Egg White—Mathematical Modeling Part II: Freeze Drying and Modeling

Foam-mat freeze drying is one of the promising methods of drying, which utilizes advantages of both freeze drying and foam-mat drying. Egg white with its excellent foaming properties makes a suitable candidate for foam-mat freeze drying. Experiments were conducted to study foam-mat freeze drying of egg white, in an effort to determine the suitability of this method. Xanthan gum (XG) at 0.125% concentration was used as stabilizer for foaming. The results showed that the addition of xanthan gum during foaming has a positive impact in reducing the total drying time and also produces excellent quality egg white powder. The addition of stabilizer also plays an important role in improving drying. Simple models were applied for determining drying time and diffusion coefficients during freeze drying.     

聚丙烯流化床降温干燥数学模拟

分析了聚丙烯流化床干燥器(D502)的特点,根据其特点建立了降温干燥数学模型,确定了模型成立的条件,采用工业数据进行了计算分析,该模型具有实用价值。     

A Thermo-Hydro-Mechanics Bidirectional Coupling Mathematical Model for Drying of Biological Porous Medium

Based on Fickian diffusion theory, Fourier's law of heat conduction and thermoelasticity mechanics, a thermo-hydro-mechanics bidirectional coupling mathematical model has been developed to simulate the hot air convective drying of biological porous media. The transient model, composed of a system of partial differential equations, was solved by finite difference methods. The numerical results were compared with available experimental data obtained during the drying of potatoes. The numerical results obtained using the mathematical model were in good agreement with the experimental data. Numerical simulations of the drying curve variations and the spatio-temporal distributions of moisture, temperature, and drying stresses and strains were evaluated.     

微波真空组合干燥果蔬的研究

本文论述了微波真空组合干燥的基本原理及干燥特点,剖析了国内外微波真空组合干燥果蔬的研究进展情况,探讨了影响微波真空干燥果蔬品质的主要因素及应用前景。     

Microwave-Vacuum Drying of Wood: Model Formulation and Verification

Based on the mechanism of moisture and heat transfer in wood during microwave-vacuum drying (MVD), a one-dimensional mathematical model to describe the process of wood MVD was established and verified by experiments in this research. The results showed that the process of MVD of wood experienced three distinct periods: (1) accelerating rate with rapid warming-up drying period, (2) a constant temperature and constant rate drying period, and (3) a heating-up with falling rate drying period. Compared with conventional hot air drying, the total drying process is almost governed by a constant rate period in vacuum-microwave drying of wood. The predicted temperature and moisture content in wood match well with the experimental data, the square of the relevant coefficient of the values of simulation and test is above 0.9, and the simulation precision of the change rule of the moisture is higher than that of the temperature.     

Mathematical Modeling and Simulation of Drying Using Two Industrial Concurrent and Countercurrent Rotary Dryers for Ammonium Nitrate

Drying of ammonium nitrate (AN) is accomplished in the Shiraz Petrochemical Complex (SPC) using a concurrent rotary dryer following a countercurrent rotary dryer. A mathematical model for these rotary dryers including heat and mass transfer was developed. The model was checked against industrial-scale data, which showed a good agreement. The average absolute deviation of the simulation results compared to the industrial data for the concurrent dryer was 4.0% for solids moisture, 1.3% for solids temperature, and 1.8% for air temperature and for the countercurrent dryer it was 9.0% for the solids moisture, 2.0% for solids temperature, and 4.6% for air temperature. These simulation results reveal that for outlet solid moisture, inlet AN moisture, and air temperature as well as the outlet temperature of product, the inlet solid and air temperature have major effects for both concurrent and countercurrent flow.     

Inactivation Kinetics of Yeast Cells during Infrared Drying

In this study, aqueous yeast suspensions were used to investigate the effects of drying (in an infrared heating environment) on the survival of yeast. The processes were modeled mathematically using a range of kinetics rate equations. The model parameters for each kinetic rate expression were obtained using a Matlab optimization procedure and the more suitable models describing the inactivation processes were identified. In order to provide the data for model validation, experiments were conducted using freshly prepared yeast suspensions. Additional experiments were also performed that further demonstrate the protective effects of sucrose and skim milk solids on yeast survival during drying. The simple Arrhenius equation was found to be a good model for predicting yeast survival during the control experiments, when heat was applied without dehydration occurring. Models incorporating both temperature and moisture content were more effective in describing yeast inactivation during drying. The model that gave the best predictions included the drying rate and the rate of temperature change as variables; the predicted activation energy for yeast deactivation was closest to that obtained from heating-only experiments in comparison with the other models examined. The results from this work are discussed and future prospects are suggested.     

Drying of Fruits and Vegetables: Retention of Nutritional/Functional Quality

In the past, research and development in drying has focused on the process and technology and food drying was performed mainly to extended the shelf life without much importance on retaining quality attributes. Recently, however, efforts have been made to develop high-quality dried foods. This is achieved by utilizing novel drying technologies, by improving and optimizing existing drying methods, and by maximizing quality attributes such as structure, color, flavor, nutrition, etc. In an effort to highlight quality aspect of dried foods and biomaterials, a special issue of Drying Technology [2005, 23(4)] was published. The objective of this article is to present an overview of quality attributes normally considered in the drying of food and biomaterials and highlight the recent advances in drying methods for the retention of nutritional and functional properties of fruits and vegetables.     

Modeling Power Transformer Field Drying Processes

Power transformer field drying is becoming a habitual practice because water is damaging for transformer insulation, and its presence increases the probability of unexpected failures. Different drying methods are currently being used by electrical companies but sometimes without a profound knowledge of the drying processes involved, and consequently drying is not as effective as would be desirable.

Physical models have been developed by the authors in order to study power transformer drying processes. The use of the models will help to plan more effective drying processes, tailoring the drying times and drying conditions for each particular case. The models have been tested in a test transformer fitted with sensors. In order to monitor the process, insulation samples were extracted from the transformer before and after the process.

In this article, several transformer drying procedures are described. Theoretical models and their experimental validation processes are reported. Finally, some general recommendations about transformer drying in the field are provided.     

Drying of Fruits and Vegetables: Retention of Nutritional/Functional Quality

In the past, research and development in drying has focused on the process and technology and food drying was performed mainly to extended the shelf life without much importance on retaining quality attributes. Recently, however, efforts have been made to develop high-quality dried foods. This is achieved by utilizing novel drying technologies, by improving and optimizing existing drying methods, and by maximizing quality attributes such as structure, color, flavor, nutrition, etc. In an effort to highlight quality aspect of dried foods and biomaterials, a special issue of Drying Technology [2005, 23(4)] was published. The objective of this article is to present an overview of quality attributes normally considered in the drying of food and biomaterials and highlight the recent advances in drying methods for the retention of nutritional and functional properties of fruits and vegetables.     

Mathematical Modeling of the Coupled Transport Phenomena and Color Development: Finish Drying of Trellis-Dried Sultanas

A mathematical model for simulation of simultaneous heat and mass transport was developed to describe the drying kinetics during finish drying of trellis-dried sultanas. In this model, the governing partial differential equations for heat and mass transfer for a solid spherical body were numerically solved using a finite difference technique. In addition, a kinetic model was coupled to the heat and mass transfer calculations to simultaneously predict the evolution of product color during the drying process. This allows predictions of moisture content, temperature, and color profiles of the product in a space–time domain during the drying process as a function of various operating conditions.

Predictions compared well with the experimental values, implying that the proposed numerical model can be used with confidence for the simulation of the important transport phenomena in optimizing the design and operation of a drying system for sultanas that maximizes the retention of the desired product color. The work has demonstrated the importance of establishing optimal and closely controlled drying conditions because significant effects of the key operational parameters on drying kinetics and the associated changes of product color were found. The modeling approach proposed here can be extended to other products and for incorporation of other product quality indices.     

Mathematical Modeling of the Fluidized Bed Drying of Cubic Materials

The unsteady‐state simultaneous heat and mass transfer between gas and potato cubes during the drying process in a batch fluidized bed was described by a mathematical model. Mass transfer was considered to occur in three dimensions whereas heat transfer between the gas and dried material was assumed to be lumped. It was found that the model could describe the drying process with acceptable accuracy. The moisture profile inside the material at any cross‐section and at any time can be predicted by the model.     

Optimization of Vapor Compression for Cost Savings in Drying Processes

Energy saving from vapor compression entails additional costs for the vapor compressors and larger heating surfaces of the drier. Thus, they are offset to a certain degree. An analytically solvable mathematical model is presented for determining the maximum cost savings with the optimum pressure ratio of the compression. According to this, the maximum cost savings depends only on five parameters, namely, the specific cost ratios of drier to fuel and compressors to fuel, the price ratio of power and fuel, the difference between the moisture contents of the inlet and outlet of the drier and the pressure level inside the drier. Above dy = 1 kg_H2O/kg_DS (DS – dry substance) the specific cost ratio of drier to fuel proves to be dominant and thus decisively determines the optimum pressure ratio. Hence, one can explain why, e.g., in the case of brown coal drying higher pressure ratios are required than in the case of sludge drying and here again higher ones than in the case of evaporization processes for liquids.     

喷雾干燥法烟气脱硫过程的数学模拟

影响喷雾干燥法烟气脱硫过程的因素很多，如液滴初始粒径、液滴初始速度、烟气入口温度、烟气入口速度和SO2入口浓度等。在分析喷雾干燥塔内气液两相流动及单个粒子与气相之间传热传质过程的基础上，建立了喷雾干燥法烟气脱硫过程的数学模型，模拟分析并讨论了上述各因素对脱硫效率的影响，并通过实验对模型进行了验证。     

Waste Heat Integration of Coating Paper Machine Drying Process

The paper sheet drying process consumes about 70% of the total energy required in coated papermaking, and almost all the thermal energy used in the process can be found in the exhaust air; thus, it has significant potential to recover the heat. With the aim of saving energy, the recovered energy is usually used to heat different process streams instead of steam.

This article examines the drying process of an operating coating paper machine to demonstrate an optimization method. To study the possibility of improving energy efficiency, thermodynamic analysis was conducted. The reasons why there is so much heat lost during drying were investigated. Based on the results of the energy and exergy analysis, a new waste heat integration scheme is presented. Furthermore, the performance of the proposed scheme has been evaluated. The results of the case study show an energy efficiency improvement of 7.3% and a specific energy consumption reduction of 4.6% with profitable investments.     

Mathematical Modeling the Drying of Poplar Wood Particles in a Closed-Loop Triple Pass Rotary Dryer

Closed-loop drying systems are an attractive alternative to conventional drying systems because they provide a wide range of potential advantages. Consequently, type of drying process is attracting increased interest. Rotary drying of wood particles can be assumed as an incorporated process involving fluid–solid interactions and simultaneous heat and mass transfer within and between the particles. Understanding these mechanisms during rotary drying processes may result in determination of the optimum drying parameters and improved dryer design. In this study, due to the complexity and nonlinearity of the momentum, heat, and mass transfer equations, a computerized mathematical model of a closed-loop triple-pass concurrent rotary dryer was developed to simulate the drying behavior of poplar wood particles within the dryer drums. Wood particle moisture content and temperature, drying air temperature, and drying air humidity ratio along the drums lengths can be simulated using this model. The model presented in this work has been shown to successfully predict the steady-state behavior of a concurrent rotary dryer and can be used to analyze the effects of various drying process parameters on the performance of the closed-loop triple-pass rotary dryer to determine the optimum drying parameters. The model was also used to simulate the performance of industrial closed-loop rotary dryers under various operating conditions.     

An Experimental and Modeling Investigation on Drying of Ragi (Eleusine corocana) in Fluidized Bed

Experimental investigation on drying of ragi (Eleusine corocana) in a fluidized bed has been attempted covering the operating parameters such as temperature, flow rate of the drying medium, and solids holdup. The drying rate was found to increase significantly with increase in temperature and marginally with flow rate of the heating medium and to decrease with increase in solids holdup. The duration of constant rate period was found to be insignificant, considering the total duration of drying and the entire drying period was considered to follow falling rate period. The drying rate was compared with various simple exponential time decay models and the model parameters were evaluated. The Page model was found to match the experimental data very closely with the maximum root mean square of error (RMSE) less than 2.5%. The experimental data were also modeled using Fick's diffusion equation and the effective diffusivity coefficients were estimated. The effective diffusion coefficient was found to be within 5.7 to 14 × 10^?11 m²/s for the range of experimental data covered in the present study with RMSE less than 5%.     

An Experimental and Modeling Investigation on Drying of Ragi (Eleusine corocana) in Fluidized Bed

Experimental investigation on drying of ragi (Eleusine corocana) in a fluidized bed has been attempted covering the operating parameters such as temperature, flow rate of the drying medium, and solids holdup. The drying rate was found to increase significantly with increase in temperature and marginally with flow rate of the heating medium and to decrease with increase in solids holdup. The duration of constant rate period was found to be insignificant, considering the total duration of drying and the entire drying period was considered to follow falling rate period. The drying rate was compared with various simple exponential time decay models and the model parameters were evaluated. The Page model was found to match the experimental data very closely with the maximum root mean square of error (RMSE) less than 2.5%. The experimental data were also modeled using Fick's diffusion equation and the effective diffusivity coefficients were estimated. The effective diffusion coefficient was found to be within 5.7 to 14 × 10^-11 m²/s for the range of experimental data covered in the present study with RMSE less than 5%.     

Drying of agar gels using supercritical carbon dioxide

The use of supercritical carbon dioxide (scCO₂) for the removal of water from agar gels has been investigated and compared to air and freeze drying. Experiments were conducted to evaluate how gel formulation (with and without sucrose) and drying conditions (with and without ethanol as a co-solvent, flow rate and depressurisation rate) affected the microstructure of the gels dried using scCO₂. X-ray micro-computed tomography (X-ray micro-CT) was used to determine the voidage (% open pore space) of the dried structures, which can be used to indicate the extent of drying-induced structural collapse (in general, the lower the voidage, the greater the collapse). For formulations containing sucrose, which displayed the best structural retention, voidage was found to increase in the order: air drying (4% voidage) < supercritical drying with pure CO₂ (48%) < supercritical drying with ethanol-modified CO₂ (68%) < freeze drying (76%). The relatively high voidage of samples dried in the presence of ethanol, was due in part to foaming of the gels, hypothesised to result from an interaction between the agar and ethanol, rather than an effect of the supercritical fluid. CO₂ flow rate (1 vs. 3 l/min) during supercritical drying and depressurisation rate (0.4 vs. 1.6 MPa/min) had no effect on the dried microstructure.     

Experimental and Theoretical Investigation of Drying of Carrots in a Fluidized Bed with Energy Carrier

A pilot scale fluidized bed dryer with an inert energy carrier (steel, glass beads ranging from 2.7 to 6.5 mm) was used to investigate the drying of carrots. The effects of sample diameter, inert material type, inert material diameter, amount of inert material, air velocity, and temperature on the rate of drying were studied. A mathematical model was proposed for predicting the drying rate and temperature of drying material. It was found that presence of inert particles enhance the rate of drying. The results of this study also revealed that, although the rate of drying increases with decreasing sample diameter, increasing the inert material thermal conductivity, and increasing air temperature, but the inert material diameter and air velocity have no significant effects on the rate of drying. The independence of rate of drying on air velocity especially in well-fluidized systems indicates that external diffusion is not a controlling step in this process. Also the presence of inert materials causes the drying material to reach more rapidly to its final internal temperature.