CFD modeling of a pilot-scale countercurrent spray drying tower for the manufacture of detergent powder

A steady-state, three-dimensional, multiphase computational fluid dynamics (CFD) modeling of a pilot-plant countercurrent spray drying tower is carried out to study the drying behavior of detergent slurry droplets. The software package ANSYS Fluent is employed to solve the heat, mass, and momentum transfer between the hot gas and the polydispersed droplets/particles using the Eulerian–Lagrangian approach. The continuous-phase turbulence is modeled using the differential Reynolds stress model. The drying kinetics is modeled using a single-droplet drying model, which is incorporated into the CFD code using user-defined functions (UDFs). Heat loss from the insulated tower wall to the surrounding is modeled by considering thermal resistances due to deposits on the inside surface, wall, insulation, and outside convective film. For the particle–wall interaction, the restitution coefficient is specified as a constant value as well as a function of particle moisture content. It is found that the variation in the value of restitution coefficient with moisture causes significant changes in the velocity, temperature, and moisture profiles of the gas as well as the particles. Overall, a reasonably good agreement is obtained between the measured and predicted powder temperature, moisture content, and gas temperature at the bottom and top outlets of the tower; considering the complexity of the spray drying process, simplifying assumptions made in both the CFD and droplet drying models and the errors associated with the measurements.     

Unraveling the droplet drying characteristics of crystallization‐prone mannitol – experiments and modeling

Spray‐dried mannitol is a potential lactose replacement in pharmaceutical formulations, yet the drying behavior of individual mannitol droplets within the spray chamber has not been fully understood. This work explored the drying characteristics of mannitol by employing the reaction engineering approach (REA) in data analysis. A glass filament single droplet drying technique was used to monitor the changes in droplet temperature, mass, and diameter. The drying kinetics data obtained clearly demonstrated the droplet “wet‐bulb” period, the crust formation, and the crystallization phenomena. The master activation‐energy curves developed from REA modeling responded sensitively to varying drying temperatures, which could have led to different crystallization events. The deviation of these plots from the expected norms that do not encounter a phase change was used effectively to discern the physics involved. A REA kinetic model was proposed to assist in process optimization of large‐scale spray‐drying operations. © 2017 American Institute of Chemical Engineers AIChE J, 63: 1839–1852, 2017     

Application of the reaction engineering approach (REA) for modeling of the convective drying of onion

In this study, the drying of thin layers of the “Violet de Galmi” onion (a variety mainly grown in West Africa) is presented in this article, along with the reaction engineering approach (REA) modeling for a comprehensive understanding of the drying kinetics. The experiments were conducted on a lab-scale dryer to form thin layer of cylindrical onion slice. By performing this experiment, the standard activation energy is evaluated and modeled. The model is validated by simulating the drying rates under various drying conditions. The comparison of simulation and experimental data is found to be satisfactory. This approach allows the determination of the internal characteristics of the onion for the further studies such as design of solar dryer for onion.     

Microwave drying at various conditions modeled using the reaction engineering approach

ABSTRACT

One of the most significant process intensification schemes in drying is microwave drying. Modeling the process of microwave drying is very useful. The lumped reaction engineering approach (REA) is now coupled with appropriate equations for modeling microwave heating. Here, a slight modification of the equilibrium activation energy is needed since the product temperature is higher than the ambient temperature. Unlike the diffusion-based approach, the REA drying parameters were generated from minimum number of drying runs. It has been found that the modifications lead to excellent agreements between the predicted and experimental data. The results of modeling match well with the experimental data. The overall model is accurate to describe the moisture content and temperature profiles. Comparisons with the diffusion-based approach indicate that the REA can achieve comparable or even better agreement toward the experimental data. This exercise has demonstrated that a simple combination of the lumped reaction engineering approach and the microwave energy absorption is versatile in predicting the microwave drying process accurately; thus, this worked example will be illustrative for future needed studies.     

More comprehensive 3D modeling of clay‐like material drying

Drying process plays an important role in the manufacturing of many products such as ceramic, kitchenware and building materials, some of which have complex three‐dimensional (3D) geometry. To deal with many restrictions found in literatures, a 3D numerical approach was used to describe the drying process of a porous Clay‐like material. The problem investigated involves highly coupled equations considering heat, mass, and mechanical aspects. The model is validated through the comparison of experimental measurements with simulation result. Simulation results show that increasing the initial moisture content and reducing the initial temperature have the same privilege and without significant increase in drying time, it reduces slightly the amount of maximum stress but delays the occurrence time of maximum stress. The nonuniform heat expansion induced stresses are very small in comparison to nonuniform moisture shrinkage induced stresses and can be neglected in drying simulation. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1469–1478, 2018     

Optimization of single‐zone drying of polymer solution coatings using mathematical modeling

Optimal conditions for drying polymer–solvent coatings result from a trade‐off between minimizing the residual solvent level and creating defects. This article describes an application of automated constrained optimization with a detailed mathematical drying model to find the optimal drying conditions for a prototypical coating in a single‐zone oven. The optimization process seeks oven conditions that minimize the residual solvent level for a fixed oven residence time without boiling the solvent within the coating. The optimal oven conditions include the air temperature and coating‐side and substrate‐side heat‐transfer coefficients. The conditions are constrained to physically reasonable values. According to our results, the optimal coating‐side heat‐transfer coefficient is always equal to or greater than the optimal substrate‐side heat‐transfer coefficient. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 149–165, 2000     

A composite reaction engineering approach to drying of aqueous droplets containing sucrose,maltodextrin (DE6) and their mixtures

Recently, several studies have been published on the spray drying of sucrose and other low‐molecular‐weight sugars which are typically sticky materials. Sticky materials can not be processed under normal drying conditions and may require addition of high‐molecular‐weight carbohydrates such as maltodextrin. Predicting appropriate drying conditions are however difficult due to the unavailability of drying kinetics. In this article, we have formulated the drying kinetics model using the reaction engineering approach (REA) for the drying of aqueous sucrose and aqueous maltodextrin (DE6) droplets. The relative activation energy was empirically obtained based on experimental measurements. To model the drying of droplets containing both solutes (sucrose and maltodextrin), a new “composite” REA has been established and presented here for the first time. Results demonstrated that the composite REA forms a reliable framework to model the drying of aqueous solutions of pure carbohydrates and their mixtures. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

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。     

Modeling of drying kinetics of green peas by reaction engineering approach

Modeling of particulate or thin-layer drying of materials is necessary to understand the fundamental transport mechanism and a prerequisite to successfully simulate or scale up the whole process for optimization or control of the operating conditions. Simple models with a reasonable physical meaning are effective for engineering purposes. Thin-layer drying of green peas was carried out in a fluidized bed with a newly developed slotted gas distributor. Based on the reaction engineering approach, a drying model of green peas was well established, in which relative activation energy (ΔE_v/ΔE_v,b) was correlated with reduced moisture content (X ? X_b) at a drying air temperature of 80°C. The drying kinetics of green peas was discussed in terms of activation energy. In addition, activation energy based on a simplified material surface temperature profile was recalculated to evaluate the temperature sensitivity to the model establishment.     

Comments to “Analysis of constant rate period of spray drying of slurry” by Liang et al., 2001

In the study by Liang et al. [2001. Analysis of constant rate period of spray drying of slurry. Chemical Engineering Science 56, 2205-2213] the Darcy flow of liquid through a pore system of primary particles to the surface of a slurry droplet was applied for the constant rate period. Steep primary particle concentration gradients inside droplets with a primary particle size of were observed. Unfortunately, the boundary condition at the droplet surface for the parabolic second-order PDE did not conserve the solid mass in the droplet, and the plots for the primary particle concentration profiles in the droplets were incorrect. In this letter we derive the correct boundary condition equation. Furthermore, we show that the primary particle concentration profiles inside the droplets are flat when the primary particles have a size of . We conclude that the model presented by Liang et al. is unable to predict the formation of hollow particles.     

Multiscale modeling for surface composition of spray‐dried two‐component powders

Spray drying is a primary process for manufacturing various powder products. One of the most important properties of powders is the ability to get wet. Surface chemical composition critically influences this property. Furthermore, surface composition also influences the efficiency of production as it affects the stickiness of the powder. This work is an attempt to analyze the surface compositions of spray‐dried two‐component powders produced under various conditions using an innovative multiscale modeling approach. A molecular‐level geometrical interpretation is seamlessly coupled with a continuum diffusion model. The predictions are compared with the measurements done on the protein–lactose system using X‐ray photoelectron spectroscopy. Sample calculations for the system have demonstrated that the new approach helps reveal surface formation mechanisms much better than that explained with the monoscale continuum approach. This work provides a good basis for a fruitful area of study toward surface composition‐focused powder quality control that will have a positive impact in industries. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2416–2427, 2014     

入口旋流对均一粒径液滴喷雾干燥塔影响的数值模拟

均一粒径液滴喷雾干燥塔（MDSD）在生产均匀尺寸颗粒产品中发挥着较大优势,进一步优化其干燥过程操作尤为重要。集成离散相（DPM）和反应工程法（REA）干燥方法,通过耦合分散室和主干燥室模型,本研究开发了完整的MDSD三维计算流体力学模型。并系统探究了在干燥过程中分散气旋流、热空气旋流以及二者共同旋流对颗粒运动和最终干燥效果的影响。模拟结果表明,在30°入射角下加入旋流效果最优。同时引入分散室和干燥室旋流后发现,同向旋流比反向旋流带来的干燥效果提升2%,更比无旋流操作下的干燥效果提升30%。欲达到同样的干燥效果,引入同向旋流,塔身可缩短近12%。     

A practical CFD modeling approach to estimate outlet boundary conditions of industrial multistage spray dryers: Inert particle flow field investigation

Industrial multistage spray drying systems often have limited in situ process measurements to provide sufficient information for computational fluid dynamics (CFD) simulations of the primary drying chamber. In this case study on the spray dryer at Davis Dairy Plant (South Dakota State University), uncertainties were encountered in specifying the outlet boundary conditions of the spray drying chamber with two outlets: the side outlet and the bottom outlet leading to the second stage external vibrating bed. Using the available data on the vacuum pressure of the chamber, a numerical framework was introduced to approximate suitable outlet boundary conditions for the drying chamber. The procedure involved analyzing the ratio of the airflow rate between the two outlets and using a pseudo-tracer inert particle injection analysis. The goal of this approach was to determine a suitable range of outlet vacuum pressure that will lead to realistic particle movement behaviors during the actual plant operation. The protocol developed here will be a useful tool for CFD modeling of large scale multistage spray drying systems.

Abbreviations: ARC: Australian Research Council; CFD: Computational Fluid Dynamics; FFT: Fast Fourier Transform; MCC: Micellar Casein Concentrate; PRESTO: Pressure Staggering Option; SDSU: South Dakota State University; SIMPLE: Semi???Impilicit Method for Pressure Linked Equations; WPC: Whey Protein Concentrate     

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.     

A control-relevant approach to demand modeling for supply chain management

The development of control-oriented decision policies for inventory management in supply chains has drawn considerable interest in recent years. Modeling demand to supply forecasts is an important component of an effective solution to this problem. Drawing from the problem of control-relevant parameter estimation, this paper presents an approach for demand modeling in a production-inventory system that relies on a specialized weight to tailor the emphasis of the fit to the intended purpose of the model, which is to provide forecasts to inventory management policies based on internal model control or model predictive control. A systematic approach to generate this weight function (implemented using data prefilters in the time domain) is presented and the benefits demonstrated on a series of representative case studies. The multi-objective formulation developed in this work allows the user to emphasize minimizing inventory variance, minimizing starts variance, or their combination, as dictated by operational and enterprise goals.     

Reply to the Comment by K. Jorgensen et al. to “Analysis of constant rate period of spray drying of slurry”

Previously developed model for spray drying of slurry droplets with high solid content (Liang, 2001) was revised to describe correctly a boundary condition on the outer surface of droplet on basis of the rate of liquid evaporation.     

Big data for microstructure‐property relationships: A case study of predicting effective conductivities

The analysis of big data is changing industries, businesses and research as large amounts of data are available nowadays. In the area of microstructures, acquisition of (3‐D tomographic image) data is difficult and time‐consuming. It is shown that large amounts of data representing the geometry of virtual, but realistic 3‐D microstructures can be generated using stochastic microstructure modeling. Combining the model output with physical simulations and data mining techniques, microstructure‐property relationships can be quantitatively characterized. Exemplarily, we aim to predict effective conductivities given the microstructure characteristics volume fraction, mean geodesic tortuosity, and constrictivity. Therefore, we analyze 8119 microstructures generated by two different stochastic 3‐D microstructure models. This is—to the best of our knowledge—by far the largest set of microstructures that has ever been analyzed. Fitting artificial neural networks, random forests and classical equations, the prediction of effective conductivities based on geometric microstructure characteristics is possible. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4224–4232, 2017