SPRAY DRYING DYNAMIC MODELING WITH A MECHANISTIC MODEL

In this work we suggest the dynamic modeling of a spray dryer considered as a series of well-stirred dryers. That is, a series of dryers in which the output variables are equal to the state variables. The state equations were obtained from the heat and water mass balances in product and air. Additionally, heat and water mass balances in interface jointly with water equilibrium relation between product and air were considered. A pilot spray dryer was modeled assuming one, two, five and 20 well stirred steps. Low-fat milk with 10-20% of solids was dried at different inlet air temperatures (120-160°C), air flow rate of 0.19 kg dry air s^-1 and different feed rates (1.4 - 4.2 × 10^-4 kg dry solids s^-1). Stationary result showed that the model predicts the experimental air outlet temperature, at different inlet conditions with a maximum deviation of 6°C. The dynamic simulation reproduce the experimental one with moderate accuracy. Experimental dynamic showed that the pilot plant spray dryer has a well-stirred process behavior. The model represents a method for estimate outlet product moisture as function of the outlet air temperature. This has application for automatic control because there is not an easy way to measure on-line measure the outlet product moisture content.     

PNEUMATIC DRYING WITH SUPERHEATED STEAM: BI-DIMENSIONAL MODEL FOR HIGH SOLID CONCENTRATION

The utilization of superheated steam for pneumatic drying of solid particles makes it possible to operate with high particle concentration without the problem of phase saturation which tends to occur when hot air is utilized for drying. Normally, the operation of pneumatic dryers is analyzed through variations of unidirectional flows. For highly diluted transport conditions this is a correct assumption, but when the solid concentration is too high, the fluid dynamics is highly modified and the gas and solid velocities are distorted by solid–solid and Solid–Wall -interactions. These conditions affect the temperature distribution along the axial and the radial coordinates, which makes a bi-dimensional model analysis very important. Mathematical models have been developed for the bi-dimensional fluid dynamics of pneumatic transport. The present work applies one of these models to describe the axial and radial variation of velocities in a gas and particulate phase flow.     

HIGH-TEMPERATURE SPRAY DRYING

This paper summarizes the results of long-term studies on high-temperature spray drying performed at the Institute of Engineering Thermophysics in Kiev. Two-stage processing involving evaporation followed by drying is proposed to dewater very dilute and temperature-sensitive materials. A new calculation procedure, which accounts for the gas-particle flow pattern and process kinetics, is given along with the performance data for selected drying plants designed according to the procedure developed.     

A DYNAMIC MODEL WITH ON-LINE IDENTIFICATION FOR ROTARY SUGAR DRYING PROCESSES

A dynamic modelling methodology, which combines on-line variable estimation and parameter identification with physical laws to form an adaptive model for rotary sugar drying processes, is developed in this paper. In contrast to the conventional rate-based models using empirical transfer coefficients, the heat and mass transfer rates are estimated by using on-line measurements in the new model. Furthermore, a set of improved sectional solid transport equations with localized parameters is developed in this work to replace the global correlation for the computation of solid retention time. Since a number of key model variables and parameters are identified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.     

A DYNAMIC MODEL WITH ON-LINE IDENTIFICATION FOR ROTARY SUGAR DRYING PROCESSES

A dynamic modelling methodology, which combines on-line variable estimation and parameter identification with physical laws to form an adaptive model for rotary sugar drying processes, is developed in this paper. In contrast to the conventional rate-based models using empirical transfer coefficients, the heat and mass transfer rates are estimated by using on-line measurements in the new model. Furthermore, a set of improved sectional solid transport equations with localized parameters is developed in this work to replace the global correlation for the computation of solid retention time. Since a number of key model variables and parameters are identified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.     

VALIDATION OF A DYNAMIC MODEL FOR A DEHUMIDIFIER WOOD DRYING KILN

ABSTRACT

The validation of a dehumidifier wood drying kiln model established previously has been conducted by using the performance data for a commercial scale kiln. The good agreement between the modelled and measured performance results shows that the model can be used for the design and analysis of dehumidifier wood drying kilns.     

THE EFFECT OF HETEROGENEITY ON WOOD DRYING,PART I: MODEL DEVELOPMENT AND PREDICTIONS

ABSTRACT

A two dimensional model which can predict the effects of the anisotropy and heterogeneity on the transport phenomena which occur in wood during drying is developed. It is shown that the appropriate driving potential for moisture transport is the ratio of the moisture content to the driving potential. In its one dimensional form, die model results compare favorably with experimental measurements for drying in the radial direction. In its two dimensional form the model is used to predict drying in a direction midway between the radial and the tangential. In this case free water moves in a diagonal direction because the low density earlywood dries faster than the latewood during the early stages of drying. The result is significant gradients in moisture content, not only in the drying direction, but also in the direction parallel to the drying surface.     

DRYING MODEL WITH NON-ISOTROPIC SHRINKAGE DEFORMATION UNDERGOING SIMULTANEOUS HEAT AND MASS TRANSFER

A model of simultaneous heat and moisture transfer in a cylindrical sample was coupled with the virtual work principle applicable to a body undergoing shrinkage deformation in two dimensions. Non-constant physical and thermal properties were also incorporated in the model. Governing equations and boundary conditions were solved numerically using Galerkin's finite element method. To check the mathematical model drying experiments were carried out. A cylindrical potato was used as a drying sample. Experimental conditions were as follows: a drying temperature of 333 K, relative humidity of 5.4%, and air velocity of 1.6 m/s. We obtained the central temperature of the sample, average moisture content, and the shrinkage change in the axial and radial directions during drying. It was observed that the shrinkage coefficients in the axial and the radial directions were significantly different during air-drying. Comparison between predicted and experimental results provides satisfactory agreement.     

A NEW MODEL FOR FLUID BED DRYING

A new model is proposed which calculates fluid bed drying curves without any adaptation of the Sherwood number between panicles and gas. Even the fine-structure of experimental data, i.e. the influence of bed height and gas flow rate, is predicted reliably. This is achieved by considering backmixing of the suspension gas in the kinetic parameter and not in the driving potential. A traditional derivation with reduced driving potential fails in the comparison with experimental results.     

A NEW MODEL FOR FLUID BED DRYING

ABSTRACT

A new model is proposed which calculates fluid bed drying curves without any adaptation of the Sherwood number between panicles and gas. Even the fine-structure of experimental data, i.e. the influence of bed height and gas flow rate, is predicted reliably. This is achieved by considering backmixing of the suspension gas in the kinetic parameter and not in the driving potential. A traditional derivation with reduced driving potential fails in the comparison with experimental results.     

RADIATIVE DRYING MODEL OF POROUS MATERIALS

ABSTRACT

A transient one dimensional first principles model is developed for the drying of a porous material (paper) that includes both heat and mass transfer. All three modes of heat transfer are considered; conduction, convection and radiation. The conduction is assumed to be in one dimension, through the porous material. The convection is assumed to exist only at the surface as a boundary condition. The radiation is assumed to be a volumetric phenomenon, so that the material internally absorbs, emits, and scatters energy. The absorption and scattering coefficients are spectrally dependent. Furthermore, the material is considered to have a non-unity refractive index with diffuse surfaces. In the mass transfer it is assumed that water exists in three phases: bound, free and vapor. The results provide profiles within the material for each moisture phase, temperature, and pressure and the effect of radiation on these distributions.     

DYNAMIC MODELLING OF A DEHUMIDIFIER WOOD DRYING KILN

ABSTRACT

For the optimum design and operating information of heat pump dehu-midifier wood drying kilns, a comprehensive kiln model has been developed, which solves the fundamental balance equations for the whole system. The model is suitable for analysing the influence of design and control variables on the performance of the system as a whole. To illustrate the application of the model, the operation of a dehumidifier wood drying kiln has been analysed under typical operating conditions and kiln controls. The drying performance has been discussed in detail.     

DRYING MODEL WITH NON-ISOTROPIC SHRINKAGE DEFORMATION UNDERGOING SIMULTANEOUS HEAT AND MASS TRANSFER

A model of simultaneous heat and moisture transfer in a cylindrical sample was coupled with the virtual work principle applicable to a body undergoing shrinkage deformation in two dimensions. Non-constant physical and thermal properties were also incorporated in the model. Governing equations and boundary conditions were solved numerically using Galerkin's finite element method. To check the mathematical model drying experiments were carried out. A cylindrical potato was used as a drying sample. Experimental conditions were as follows: a drying temperature of 333 K, relative humidity of 5.4%, and air velocity of 1.6 m/s. We obtained the central temperature of the sample, average moisture content, and the shrinkage change in the axial and radial directions during drying. It was observed that the shrinkage coefficients in the axial and the radial directions were significantly different during air-drying. Comparison between predicted and experimental results provides satisfactory agreement.     

干燥过程热质传递的简化模型

对多孔介质体积平均理论进行简化,得到简化的热质传递干燥模型,用一个理论式表达模型中有效扩散系数。对香蕉片千燥的研究表明,模型的预测值与实验结果相     

食品冷冻干燥过程的模型及影响因素

在合理简化的基础上,得到了只需较少参数的冷冻干燥过程一维数学模型。通过对胡萝卜和土豆食品的冷冻干燥实验,研究了加热方式、加热搁板温度和干燥室真空度对干燥时间的影响,模型的数值解与实验值吻合良好。     

喷射工况下的二维传质模型

提出了一个计算喷射工况下塔板效率的二维传质 -混合单元模型 ,可以模拟单元液体提升量、单元间液体交换分率、液体循环分率等模型参数的变化对塔板效率的影响 ,为喷射型塔板的开发与设计提供了一定的理论依据 .     

A SEMI-THEORETICAL MODEL FOR THE DRYING OF THUMPSON SEEDLESS GRAPES

In this paper, the usefulness of a mathematical model based on equations describing the diffusional phenomena which are variable with time, is developed and discussed in relation to serve as a model for experimental data of drying of Thompson seedless grapes.

This model represents more closely the drying curves tested, than the classic diffusion model normally utilized to analize drying processes     

COMPARISON OF EXPERIMENTAL RESULTS WITH ANALYTICAL SOLUTIONS AND TWO DIHENSIONAL MODEL OF OAK DRYING IN AN EVACUATED KILN

ABSTRACT

In continuation of a series of tests, the original results of oak drying in an evacuated kiln are presented here for different plate temperatures and for various pressures in the kiln. These results include more particularly the drying curves, the evolution of temperature, of moisture and of pressure in and on the wood. They evidence the pressure and the levels of temperature occurring in the wood during the drying period.

These results also allow the development of two types of drying models a simple monodimensional model of drying curves from the analytical solutions of the equations of water diffusion in the wood and, moreover, a model, in two dimensions, of temperature, moisture and pressure fields in the wood by applying the finite element method. The boundary conditions of the second model can be fixed with precision thanks to the results of the first model. In both cases, the proposed solutions are justified by experimental results.     

CONVECTWE DRYING MODEL OF SOUTHERN PINE

ABSTRACT

A transient one dimensional first principles model is developed for the drying of a porous material (wood is used as an example) that includes both heat and mass transfer. Heat transfer by conduction and convection, mass transfer by binary gas diffusion, pressure-driven bulk flow in the gas and liquid, and diffusion of bound water are included in the analysis. The diffusive mass transfer terms are modeled using a Fickian approach, while the bulk flow is modeled assuming Darcian flow. Depending on the state (pendular or funicular) of the moisture in the wood, appropriate terms are considered in the development of the governing mass equations. The results provide distributions within the material of each moisture phase (vapor, liquid, and bound), temperature, and total pressure. Information regarding the drying rate and evaporation rate is also presented. Average distributions are obtained as a function of time, and compared with experimental data from the literature. It is observed that the total pressure within the material can be considerably above one atmosphere during the drying process.     

A MODEL FOR THIN-LAYER DRYING OF LENTILS

A procedure was developed based on a three-component physical model to simulate the drying characteristics of Laird lentils. In this model, the cotyledons were simplified as a homogeneous slab where moisture transfer was governed by a one-dimensional diffusion equation, and the hilum and seedcoat were considered as two parallel routes for moisture to escape from a seed. The simulation procedure was verified with the experimental data from thin-layer drying testing on samples of 19.0 to 24.5% initial moisture content at temperatures from 23 to 80°C and relative humidities from 5 to 70%. Using previously obtained information on the transport properties of the cotyledons, the seedcoat, and the hilum, the simulation followed the drying data closely over temperatures between 23 and 60°C.