A Model for Drying of an Aqueous Lactose Droplet Using the Reaction Engineering Approach

Spray drying is the primary method for manufacturing of food powders from liquids. Optimal design and optimization of spray drying operations at the fundamental level require both modeling of the drying characteristics of a single droplet and dryer wide simulations using computational fluid dynamics (CFD). An accurate yet simple model for drying of a single droplet, which does not require solution of partial differential equation, is ideal input for CFD simulations. The reaction engineering approach (REA) is shown to be appropriate in this regard. It has been successfully used for prediction of skim and whole milk droplet drying behavior under various drying conditions. In this study, an aqueous lactose solution was dried in droplet form and the appropriate REA model parameters obtained. The change of diameter of the droplet during drying was measured experimentally and compared with the model results.     

A Model for Drying of an Aqueous Lactose Droplet Using the Reaction Engineering Approach

Spray drying is the primary method for manufacturing of food powders from liquids. Optimal design and optimization of spray drying operations at the fundamental level require both modeling of the drying characteristics of a single droplet and dryer wide simulations using computational fluid dynamics (CFD). An accurate yet simple model for drying of a single droplet, which does not require solution of partial differential equation, is ideal input for CFD simulations. The reaction engineering approach (REA) is shown to be appropriate in this regard. It has been successfully used for prediction of skim and whole milk droplet drying behavior under various drying conditions. In this study, an aqueous lactose solution was dried in droplet form and the appropriate REA model parameters obtained. The change of diameter of the droplet during drying was measured experimentally and compared with the model results.     

Sensitivity Analysis of the Reaction Engineering Approach to Modeling Spray Drying of Whey Proteins Concentrate

Whey proteins concentrate (WPC) powder is an important protein source for humans and is commonly produced from whey using a spray-drying technique. Predicting several drying parameters as well as the parameters that govern the quality of the product is essential before manufacturing WPC in industries. Drying kinetics is an essential tool for predicting the drying rate and various parameters that are rate dependent. However, there have been only a few studies published previously on both modeling WPC drying and dryer-wide simulations using different computational tools. In this article we review the application of a reaction engineering approach (REA) to model the droplet drying process. Results based on dryer-wide simulations using the REA are presented. More importantly, a sensitivity analysis of the REA using drying of WPC and skim milk droplets is reported. This analysis will be helpful to select an appropriate drying kinetics model and forms a benchmark for the future WPC drying modeling work.     

Reaction Engineering Approach (REA) to model the drying kinetics of droplets with different initial sizes—experiments and analyses

Droplets with different initial sizes, which are typical in conventional liquid atomization for spray drying applications, will result in varying drying and crust formation histories. It is essential for any droplet drying model to accurately capture such fundamental phenomena. This study used a newly constructed glass-filament single droplet rig to evaluate the applicability of the Reaction Engineering Approach (REA) in describing such effect. For the three initial sizes (1, 2 and 3 μL) tested, the glass filament gravimetric method clearly distinguished the different drying kinetics and the crust formation phenomenon, delineated by the drying behavior. Analysis from the drying kinetics revealed that the main premise of the REA, which utilizes a material-specific master activation energy curve, is applicable to droplets of different initial sizes at all the three air temperatures tested. This allowed the REA to accurately predict the different temperature and moisture histories given by droplets with different initial sizes. The result supports the REA as a good modeling approach for a wide range of initial droplet conditions. A new master curve approach was proposed to predict the diameter change of droplets with different initial concentrations. Validation with the current and past experimental data revealed that this approach has strong potential to account for the different feed concentrations typically found in spray drying applications.     

甘露醇喷雾干燥过程中液滴粒度分布变化的群体粒数衡算模拟和实验研究

利用群体粒数衡算（population balance，PB）计算机模拟和实验研究了甘露醇水溶液的喷雾干燥过程中液滴的粒度分布的变化规律。液滴干燥过程中的颗粒粒度的萎缩速率，在群体粒数衡算模型中描述为液滴的逆（或负）生长项，通过单个液滴反应动力学方法（reaction engineering approach，REA）获得。基于单个液滴干燥的反应工程方法模型REA和群体粒数衡算模型PB集成建立了PBREA模型。PBREA 模型的求解是通过高分辨率数值方法。本文模拟研究了不同工况下，不同粒径液滴的干燥时间、液滴平均含湿量以及液滴粒度分布随时间的变化。结果显示，液滴粒径越大，干燥时间越长，模型预测的颗粒平均粒径为实验值的1.0~1.5倍，粒度分布跨度是实验值的0.61~0.89倍。模拟误差主要来源于液滴及颗粒粒径分布统计精度、单个静止液滴与群体运动液滴干燥的差异、热导率及扩散系数是经验值3个方面。在使用Buchi 290 小型喷雾干燥仪进行的实验中，使用了图像采集和分析方法得到了液滴及颗粒的数密度分布，并和模拟结果做了对比。结果表明该模型可以有效地预测喷雾干燥过程中干燥颗粒的平均粒度及分布跨度。     

Application of the reaction engineering approach (REA) for modeling intermittent drying under time-varying humidity and temperature

A ‘good’ drying model is important for the design of dryer, evaluation of dryer performance and prediction of product quality. Among the available models, the reaction engineering approach (REA) is a lumped model, proven to be simple, robust and accurate to model drying of several materials. In this paper, the REA is implemented to model intermittent drying, which is usually practiced for saving energy consumption and maintaining product quality during drying, under time-varying drying air temperature and humidity, which is a challenging drying case to model. For this purpose, the equilibrium activation energy (ΔE_v,b) is defined according to the drying settings in each time period and combined with the relative activation energy (ΔE_v/ΔE_v,b) generated from the convective drying experimental data obtained under constant drying conditions. The mass and heat balances also implement the corresponding drying settings in each time period during the intermittent drying. The results indicate that the REA can describe both the moisture content and temperature profiles of the intermittent drying under time-varying drying air temperature and humidity well. The accuracy, simplicity and robustness of the REA for the intermittent drying under time-varying drying air temperature and humidity are proven here. This has provided a major and significant extension of the REA on modeling challenging drying cases.     

The Basics of a Reaction Engineering Approach to Modeling Air-Drying of Small Droplets or Thin-Layer Materials

In this article, the development of a reaction engineering approach (REA) to modeling air drying of thin-layer materials or solids droplet/particles, a 10-year-old approach, is critically reviewed. This approach for drying data reduction has been seen to be successful in several applications (droplet drying and layer drying). The historical aspects and its possible relations to the characteristic drying rate curve (CDRC) model, one of the most well-known drying kinetics models, have been articulated. Possible improvements and future prospects are discussed.     

Multiphase modeling of intermittent drying using the spatial reaction engineering approach (S-REA)

Several schemes of energy minimization of drying process including intermittent drying have been attempted. Intermittent drying is conducted by applying different heat inputs in each drying period. An effective and physically meaningful drying model is useful for process design and product technology. The lumped reaction engineering approach (L-REA) has been shown previously to be accurate to model the intermittent drying In L-REA, the REA (reaction engineering approach) is used to describe the global drying rate. In this study, the REA is used to model the local evaporation/condensation rate and combined with the mechanistic drying models to yield the spatial reaction engineering approach (S-REA), a non-equilibrium multiphase drying model. The accuracy of the S-REA to model the intermittent drying under time-varying drying air temperature is evaluated here. In order to incorporate the effect of time-varying drying air temperature, the equilibrium activation energy and boundary condition of heat balance implement the corresponding drying settings in each drying period. The results of modeling using the S-REA match well with the experimental data. The S-REA can yield the spatial profiles of moisture content, concentration of water vapor, temperature and local evaporation/condensation rate so that better understanding of transport phenomena of intermittent drying can be obtained. It is argued here that the REA can describe the local evaporation rate under time-varying external conditions well. The S-REA is an effective non-equilibrium multiphase approach for modeling of intermittent drying process.     

反应工程方法在锂电池真空干燥模拟上的应用

锂离子电池注液之前的真空干燥,对于电芯的循环性能、安全性、稳定性有极其重要的影响。电芯结构设计、材料体系、烘箱尺寸等的不同会导致真空干燥过程存在差异。反应工程方法(REA)在常压、高初始水含量的对流干燥模拟预测上已有广泛应用,本研究将REA干燥理论应用于真空、低初始水含量的干燥过程仿真,发现与实验结果匹配良好。同时考虑了电芯气袋与烘箱环境湿度变化对干燥过程的影响,水含量预测偏差小于10%,利用单因子仿真实验所总结的规律能用于指导锂电池真空干燥工艺的改善。介绍了该模型在生产中的应用情况,也表明REA将在锂电池真空干燥预测上有很好的工业应用前景。     

MTO催化剂离心喷雾干燥制备过程的数值模拟

采用CFD模型对MTO催化剂喷雾干燥过程进行了非稳态数值模拟,得到了10s内热空气的湿含量、温度、速度、速度向量分布,以及催化剂颗粒的运动轨迹、停留时间和粒径分布.通过与试验结果的对比分析表明,模拟结果可信,模拟离心式喷雾干燥过程可行.     

Reduction of a model for single droplet drying and application to CFD of skim milk spray drying

In this work, a novel methodology for the development of a high-accuracy computational fluid dynamics (CFD) model for the spray-drying process is described. Starting point is an own spatially resolving model of droplet/particle drying, which was developed and validated on the basis of a series of single droplet drying (SDD) experiments. This sophisticated model is transformed to a much simpler version: the characteristic drying curve approach, after running the full SDD model in a wide range of operating conditions. Then, the obtained reduced model is implemented into the CFD solver. The CFD spray-drying model takes into account the hydrodynamics of the continuous phase, particle drying kinetics, changes in the particle diameter, and the heat loss from the drying chamber to the environment. Validation of the entire procedure is provided by data obtained from drying experiments performed in a co-current laboratory spray tower. High accuracy of the developed CFD model of skim milk spray drying has been found for both phases, for the mean outlet temperature of the continuous phase (air) and for the change in average particle moisture content along the spray tower (discrete phase).     

反应工程方法在锂电池真空干燥模拟上的应用

锂离子电池注液之前的真空干燥,对于电芯的循环性能、安全性、稳定性有极其重要的影响。电芯结构设计、材料体系、烘箱尺寸等的不同会导致真空干燥过程存在差异。反应工程方法(REA)在常压、高初始水含量的对流干燥模拟预测上已有广泛应用,本研究将REA干燥理论应用于真空、低初始水含量的干燥过程仿真,发现与实验结果匹配良好。同时考虑了电芯气袋与烘箱环境湿度变化对干燥过程的影响,水含量预测偏差小于10%,利用单因子仿真实验所总结的规律能用于指导锂电池真空干燥工艺的改善。介绍了该模型在生产中的应用情况,也表明REA将在锂电池真空干燥预测上有很好的工业应用前景。     

CFD simulation of corn drying in a natural convection solar dryer

A computational fluid dynamics model was developed to simulate the corn drying process in a solar cabinet dryer. Incident solar radiation was modeled using a dual-band spectrum to simulate the absorption of shortwave radiation by corn and account for the greenhouse effect caused by glazing materials. The performance of the dryer was simulated at fair and overcast weather conditions. The model allowed visualization of temperature, humidity, and air velocity profiles in the dryer. The model was validated with experimental results, which showed an overprediction of temperature (8.5%) and humidity (21.4%). The experimental humidity profile suggests that there was stagnation in the airflow of the dryer, which was accurately predicted by the model. The model was used to simulate the dryer’s performance under overcast conditions, and the predicted moisture removal was 32% less than the simulated fair-weather case.     

Multiscale Modeling of Superheated Steam Drying of Particulate Materials

A multiscale model for predicting the superheated steam drying behavior of a packed bed filled with particulate porous material is presented. By using a reaction engineering approach (REA) a semi-empirical model is developed that can describe the heat and mass transfer between a single particle and the surrounding drying agent. By analogy between superheated steam drying and hot air drying, the relative activation energy of the REA model is formulated. Next, the single-particle drying model is fed into a continuum-scale model of a packed bed. The temperature and moisture content of the solid and the vapor temperature are successfully predicted by the bed-scale model. To endow the bed-scale model with predictive capabilities, simulation results are compared with experimental literature data.     

Experimental benchmarking of diffusion and reduced models for convective drying of single rice grains

Abstract

In this work, the drying behavior of single rice grains at moderate and elevated air temperatures (i.e. 60?°C, 120?°C, and 140?°C) is experimentally investigated by using a magnetic suspension balance system. To describe the experimental drying behavior, a diffusion model is developed. The reference moisture diffusivity of the rice grains is determined by using an inverse method, whereas other thermo-physical properties are measured. Next, the diffusion model is reduced to a semi-empirical model within the frame of reaction engineering approach (REA). Both models are successfully benchmarked against the experimental observations. The results indicate that the moisture diffusivity of rice grains can be represented as a linear function of the moisture content and the drying process at high temperatures is controlled by both intra- and extra-particle mass transfer resistances. In addition to these results, this study favors a practical application of the REA in drying calculations to derive a simple, robust, and extrapolative semi-empirical model since the parameter of this model seems to be insensitive to variations of drying conditions.     

Modeling Intermittent Drying of Wood under Rapidly Varying Temperature and Humidity Conditions with the Lumped Reaction Engineering Approach (L-REA)

For improving product quality and minimizing energy consumption during drying, intermittent drying is often recommended. The mathematical models that are used to describe intermittent drying are usually transport phenomena based, complex models. In this study, the lumped reaction engineering approach (L-REA) is implemented to model wood drying under rapid periodically changed drying air temperature and humidity with high number of cycles of intermittency. The equilibrium activation energy (ΔE _v,b ), an important parameter for REA approach, is evaluated according to the corresponding drying air temperature and humidity in each drying section. The results of modeling suggest the L-REA works well with the experimental data. The simplicity of the L-REA is obvious and is hoped to be used in an industrial setting more readily. The L-REA can be used for sustainable processing in industries to assist in energy audit and management.     

A Parametric Study of Spray Drying of a Solution in a Pulsating High-Temperature Turbulent Flow

Spray drying of a concentrated common salt (NaCl) solution carried out in the intense oscillating high-temperature turbulent flow field generated in the tailpipe of a pulse combustor was simulated. Simulation of such transport process problems is especially crucial since the environmental conditions are too hostile for detailed and reliable measurements. The momentum, heat, and mass transfer processes between the gas and droplet phases during drying were simulated using a computational fluid dynamic solver. The simulated profiles of flow field, temperature, and humidity of gaseous phase, and particle trajectories in a drying chamber are presented and discussed. The effects of gas temperature, pulse frequency and amplitude, and gas mass flow rate on the transient flow patterns, droplet trajectories, and overall dryer performance were investigated. Different turbulence models were also tested. Simulation results show that the flow field and droplet drying conditions vary widely during a single pulsating period. Very short drying times and very high drying rate characterize pulse combustion spray drying. Thus, pulse combustion drying can be applied to drying of fine droplets of highly heat-sensitive materials although the jet temperature initially is extremely high.     

A Parametric Study of Spray Drying of a Solution in a Pulsating High-Temperature Turbulent Flow

Spray drying of a concentrated common salt (NaCl) solution carried out in the intense oscillating high-temperature turbulent flow field generated in the tailpipe of a pulse combustor was simulated. Simulation of such transport process problems is especially crucial since the environmental conditions are too hostile for detailed and reliable measurements. The momentum, heat, and mass transfer processes between the gas and droplet phases during drying were simulated using a computational fluid dynamic solver. The simulated profiles of flow field, temperature, and humidity of gaseous phase, and particle trajectories in a drying chamber are presented and discussed. The effects of gas temperature, pulse frequency and amplitude, and gas mass flow rate on the transient flow patterns, droplet trajectories, and overall dryer performance were investigated. Different turbulence models were also tested. Simulation results show that the flow field and droplet drying conditions vary widely during a single pulsating period. Very short drying times and very high drying rate characterize pulse combustion spray drying. Thus, pulse combustion drying can be applied to drying of fine droplets of highly heat-sensitive materials although the jet temperature initially is extremely high.     

Superheated Steam Drying of Single Wood Particles: Modeling and Comparative Study with Hot Air Drying

A deterministic model is developed to describe the superheated steam drying process of single wood particles. A comparison between calculated data and experimental observations infers that the moisture‐dependent effective diffusivity is suitable to be used for beechwood material drying. To reduce the computational cost of the deterministic drying model, a semi‐empirical model is proposed within the framework of a reaction engineering approach (REA). The validity of the proposed model is checked by comparing against experimental data from literature. The experimental drying behavior may fairly be reflected by the reduced model. Due to the simplicity and predictive ability of the REA model, this semi‐empirical model can be implemented to describe heat and mass transfer between a population of single particles and a drying agent in dryer models.