NUMERICAL SIMULATION OF DRYING IN A CYCLONE

This work presents a complete improved mathematical model of drying in cyclone. The slip condition of the particles on the wall, the heat transfer wall-panicle and the shrinkage of the panicles during the drying process were considered. The mathematical model considers a two-dimensional turbulent gas-particle flow where the panicle phase is treated as a continuum. The momentum equations of both particle and gas phases were written in cylindrical coordinates. The discretized equations were solved by the SIMPLE algorithm. Considering the slip condition to the panicle phase and the shrinkage of the material during the drying process it was revealed a better fitness between numerical and experimental results than the previous model.     

PNEUMATIC DRYING IN DILUTED PHASE: PARAMETRIC ANALYSIS OF TUBE DIAMETER AND MEAN PARTICLE DIAMETER

ABSTRACT

In previous work on pneumatic drying presented by the authors, a mathematical model based on the conservation equations of momentum, mass and energy was proposed. This model was developed taking into account axial and radial profiles for gas and solids velocities, pressure and porosity in the drying tube. These dynamic profiles influenced the behavior of temperature in the gas and particulate phases, gas humidity and solids moisture content. In this work, this model has been used to perform a parametric analysis of the tube and panicle diameters in the pneumatic drying process. These variables were analyzed here for fixed conditions of gas and solids flowrates and initial values of temperatures, humidity and moisture content. Factorial planning was applied to the numerical solution of the mathematical model. Experimental data obtained in a pilot scale pneumatic dryer were used as the initial conditions in the simulation to specify the levels of the variables analyzed. Results on the influence of tube diameter and particle diameter on the drying process were obtained by statistical analysis of the responses generated by the factorial planning.     

MODELLING GAS-SOLID FLOW IN A PNEUMATIC-FLASH DRYER

ABSTRACT

Investigations of aerodynamics of gas-solid flow in a pneumatic-flash dryer in semiindustrial scale have been carried out. Apparatus was composed of three elements with varying cross-sectional area connected together, i.e. expanding cone, decreasing cone and a vertical pipe with constant diameter. A mathematical model of the dryer is based on the continuity equations for both gas and solid phase and on differential equations for momentum balance of the gas-solid mixture and momentum balance of the solid phase. The model has been solved by means of Gear's numerical method. The effect of various empirical correlations for the solid-wall friction factor has been shown. Distributions, resulting from the model, for pressure, gas velocity, panicle velocity, voidage and residence time of panicle along the axis of apparatus have been presented. The results of numerical calculations have been verified on the basis of measurements in pan.     

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.     

A MATHEMATICAL MODEL FOR DRYING OF SHRINKING MATERIALS

ABSTRACT

A mathematical model has been developed to describe heat and mass transfer within materials undergoing shrinkage during drying. Both heat and mass transfer equations are solved simultaneously using a numerical technique A beat pump dryer has been used to conduct experiments to validate the model. Several samples were placed in the drver and after the commencement of each drying test one sample was taken oat at rceular time interval: The bone-dry mass of each piece was also determined. This enables to determine moisture distribution within the materials. Temperatures at different locations of the material were measured with thermocouples. The predicted temperature and moisture distribution within the material agreed fairly well with the experimental results.     

DEEP LAYER MALT DRYING MODELLING

ABSTRACT

In malt production drying operation plays an important role in the total processing cost, however there are not many studies on malt drying modeling and optimization.

In this paper a deep layer malt drying mathematical model in the form of four partial differential equations is presented.

To determine drying constants, malt thin layer drying experiments at several air temperatures and relative humidities were made.

The model were validated at industrial scale. The greatest energy savings, approximately 5 5% in fuel and 7.5% in electric energy, were obtained by an additional (and increased) air recirculation, which is carried out during the last 6 hours of the drying process and a significant decrease of air flow-rate during the last 6 hours of the drying process.     

MATHEMATICAL MODELING OF CONTINUOUS DRYERS USING THE HEAT AND MASS TRANSFER PROPERTIES AND PRODUCT-AIR EQUILIBRIUM RELATION

ABSTRACT

In this work a phenomenological mathematical model that describes the continuous drying process is presented. Heat and mass transfer in gas phase, solid phase and gas-solid interface were taking in account in the model. In addition, the equilibrium and interfaces conditions were evaluated using the product sorption isotherm. Model structure is a system of four couple differential equations in conjunction with five algebraicequations. The results shown that this structure is robust with respect to heat or mass transfer controlled mechanisms. Behaviors predicted were similar with other simulators results and with the behavior reported by chemical engineering texts. The proposed mathematical model is able to use in continuous drying operation design involving heat and mass transfer properties and equilibrium relationships.     

Analysis of Freeze-Drying of Tropical Fruits

Abstract

Freeze-drying is a process recommended for drying of heat-sensitive products. Some advantages of this technique are that it allows the shrinkage and the degrading reactions in the material, which are common in conventional drying operations, to be minimized. The knowledge of drying kinetics is essential for modeling and optimization of a freeze-drying process. In this work, drying kinetics for pineapple, guava, and mango pulps were investigated using five empirical equations commonly applied for convective drying of foodstuffs. Increasing constant- and falling-rate periods were observed during the drying of such pulps. The best fittings for the drying kinetics of all the materials were obtained using the Page and Chen and Douglas equations.     

Mathematical Modeling of Drying of Liquid/Solid Slurries in Steady State One-Dimensional Flow

ABSTRACT

A mathematical model of simultaneous mass, heat and momentum transfer for two-phase flow of a gas and a solid/liquid slurry was developed. The model was applied to calculation of the drying process of coal-water slurry droplets in a gas medium in a steady one-dimensional flow. The model was based on the well-known two-stage drying process for slurry droplets. After the first period of drying, in which the evaporation rate is controlled by the gas phase resistance, the evaporating liquid diffuses through the porous shell (crust) and then, by convection, into the gas medium. Inside the dry external crust of the drop, a wet central core forms, which shrinks as evaporation proceeds. The temperature of the slurry droplet rises. The process ends when the temperature of the dry outer crust reaches the coal ignition temperature in the case of combustion or when the moisture of the particle reaches the final required moisture. The developed model was based on one-dimensional balance equations of mass, energy and momentum for the liquid/solid and gas phases. The system of governing equations was represented by first-order differential equations and solved simultaneously. The numerical solution of the governing equations was obtained using Gear's method. The model permitted calculation     

AIR DRYING OF ONION: SOME THEORETICAL CONSIDERATIONS

Abstract

The equation for the air drying of solids during a constant drying-rate period was modified to formulate a new model for describing the initial phase of onion drying, with volume shrinkage of dried particle taken into account. The model was fitted to experimental data satisfactory, and the parameters were estimated. It was shown that drying shrinkage of the onion particle, caused that initial phase of the falling drying-rate period is controlled by the external water transfer resistance. It was recommended that the Neuman-type, rather than Dirichlet-type, boundary conditions should be used for calculation of the effective diffusivity during the first phase of the falling rate period of drying of the onion.     

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.     

DRYING OF BIOMASS PARTICLES IN FIXED AND MOVING BEDS

ABSTRACT

The drying of biomass fuel particles in fixed and moving beds with hot gas or steam is considered both experimentally and theoretically. A single particle drying model is coupled with a model describing beat and moisture transfer in The gas phase of the bed. The size of the bed to reach a certain degree of drying depends mostly on the following parameters: particle size, panicle moisture content, gas inlet temperature, gas inlet moisture content and gas mass flow rate.     

INVESTIGATION ON THE INCIPIENT FLUIDIZATION AND HEAT TRANSFER IN A CENTRIFUGAL FLUIDIZED BED DRYER

Abstract

Based on the continuum theory, a physical model of gas-solid two phase flow in a centrifugal fluidized bed has been proposed. A set of governing equations to describe the fluidization state are obtained and solved numerically after some simplifying. The quantitative experimental study on the characteristics of the incipient fluidization in the centrifugal fluidized bed is performed to examine the proposed model. Gas-solid two phase heat transfer in CFB during a drying process is also conducted. The influences of bed thickness, particle diameter, physical properties of particle, rotating speed of the bed and the gas superficial velocity on heat transfer characteristics are examined. A correlation that can be used to calculate the heat transfer coefficients in the drying process in CFB is obtained.     

Rheological Behavior of Douglas-fir As Related to the Process of Drying

ABSTRACT

Large inelastic strain occurs inside a piece of lumber during drying. The strain consists of several components such as elastic, plastic, creep, shrinkage and mechano-sorptive effect. The drying behavior of the whole board is determined by the behavior of the individual components and their interactions. Whereas limited investigations have been made on those strains under moderate conditions, there is a lack of comprehensive research aimed to examine the behavior at elevated temperatures and to incorporate the various strain components into a process model. This research provides experimental data for various strain components of small wood samples and an analytical tool for evaluating the drying behavior of full-size boards.

Small test specimens of Douglas-fir were loaded tangentially in both tension and compression under constant and varying moisture conditions at different temperatures. Experiments were conducted using a small testing machine contained within a pressure vessel. The strain fields for loaded and unloaded test samples were measured using a high resolution video camera. The required moisture change at controlled temperatures was achieved by controlling the total pressure in absence of air with saturated steam. Moisture content was monitored by a quartz spring sorption balance.

The total deformation due to loading and moisture change was decomposed into instantaneous, creep, shrinkage and mechano-sorptive components. Constitutive equations for each component were developed as a function of stress, temperature, moisture, time and moisture change. These equations were incorporated into a process model to simulate the development of stress and strain in large pieces of lumber during drying.

A slicing method was used to measure the distribution of moisture and strain through the thickness of full-size boards at different stages of drying. The process model was used to predict drying stress and strain based on the measured moisture distribution and material properties. The effect of drying conditions and types of wood on the development of drying stress was demonstrated. The predicted drying strains under different drying conditions were compared with the corresponding measurements.     

DENSITIES,SHRINKAGE AND POROSITY OF SOME VEGETABLES DURING AIR DRYING

Abstract

Bulk density, particle density, shrinkage and porosity were experimentally determined at various moisture content during air drying for apple, carrot and potato cubes. A simple mathematical model was used to predict the above properties versus material moisture content. Four parameters were incorporated in the model: enclosed water density, dry solids' density, bulk density of dry solids, and volume-shrinkage coefficient. The model was fitted to experimental data satisfactorily, and the parameters were estimated. The influence of varying drying conditions was also investigated.     

CROSS-EFFECT OF HEAT AND MASS TRANSFER OF LU1KOV EQUATION: MEASUREMENT AND ANALYSIS

Abstract

This paper mainly focuses on cross-effect of heat and mass transfer of capillary porous media which A.B.Luikov set up on irreversible thermodynamics principle. On the basis of perfecting the equations of heat and mass transfer, the heat and mass transfer parameters are determined during drying processes, and thermal gradient coefficient δ and moisture gradient coefficient ξ are obtained which show the cross-effect of heat and mass transfer. Thus the fundamentals are provided for quantitative analysis of cross-effect of heat and mass transfer. The convective drying mathematical model under the first unsteady boundary condition is therefore proposed. By the application of Henry transform, the theoretical solution of unsteady drying process is given and its validity is verified     

Drying Simulation of a Solid Slab with Three Dimensional Shrinkage

ABSTRACT

A mathematical model is developed to simulate the drying of a hygroscopic porous solid. The model, based on the gradient of moisture concentration per unit volume as driving force, takes into account the migration of water within the solid by diffusion and the evaporation at the interface. A mathematical equation for diffusion in a slab with three dimensional shrinkage has been derived, assuming that the magnitude of shrinkage is equal to the volume of water evaporated. The resulting diffusion equation and the heat balance eauation for infinite thermal conductivitv were solved n;merically with temperature dependent diffusion coefficient and convective boundary conditions. The deDendence of the desorption isotherm with temperature is-also considered. corndination of all these factors in a single model provides a tool that is effective in predictinq dryinq behavior and also useful in exploring and understanding the impact of important variables on the drying process.     

Modeling of Diffusion in Capillary Porous Materials During the Drying Process

ABSTRACT

This paper presents a model of heterogenous diffusion in capillary porous materials during the process of drying. The governing heat and mass transfer equations have been established using the liquid as well as vapor flow. Two models have been presented. Model 1 does not consider the heat conduction while the model 2 has been established by considering the conduction. The developed models and the numerical solutions of the resulting differential equations can take into account the moisture and temperature dependent thermophysical properties of the product. All equations have been established in spherical coordinates but the programme written for the purpose of calculations can be used for other geometries also. Numerical calculations have been performed for gas concrete and tiles using model 1, while model 2 has been used for gas concrete only because of the lack of data for thermophysical properties of the tile. For gas concrete it was seen that conduction has only marginal effect on the drying process and the numerical predictions of the drying process were reasonably accurate.     

Two-Fluid,Two-Dimensional Model for Pneumatic Drying

Abstract

Pneumatic drying is a widely used process in the chemical industries and includes simultaneous conveying and heat and mass transfer between the particles and the heat gas. The increase in the use of this unit operation requires reliable mathematical models to predict processes in the industrial facilities. In the present study a Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a two-dimensional steady-state condition and considering axial and radial profiles for the flow variables. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle is assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The numerical procedure includes discretization of calculation domain into torus-shaped final volumes, solving conservation equations by implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm and controls over coupling of phases by IPSA (Interphase Slip Algorithm). The developed model was applied to simulate a drying process of wet PVC particles in a large-scale pneumatic dryer and to a drying process of wet sand in a laboratory-scale pneumatic dryer. The numerical solutions are compared successfully with the results of independent numerical and experimental investigations. Following the model validation, the two-dimensional distributions of the flow characteristics were examined.     

Modeling and simulation of isothermal process of natural gas pipeline drying with dehydrated air

Abstract

Ventilative drying is an essential drying method to protect natural gas pipeline from corrosion and prevent the formation of hydrate. A mathematical model describing the problem of pipelines drying with dehydrated air is developed based on the fundamental principle of mass, momentum, and species conservation in present work. To enhance the accuracy of the model, a new correlation of the evaporation rate of water in pipeline is introduced by taking interfacial resistance into account. Finite volume method (FVM) is employed to discretize the governing equations with first-order upwind scheme for mass and momentum equations and QUICK scheme for species equations. To reduce calculation load, a new solution strategy of semi-implicit method for S_m-linked equations is proposed to solve the nonlinear algebraic equations after the discretization of mathematical model. The results indicate that average absolute deviation between experimental data and the calculations are 8.8% and 8.2% for two cases, respectively. By analysis of dynamic process of the ventilative drying, it is found that the drying process takes place from the ends toward the center of the pipeline. In addition, the results also demonstrate that the nonuniform distribution of the liquid holdup may reduce the service efficiency of dehydrated air at the late period of drying process. Thus, we suggest that the drying process shifts to soak-test stage when the water vapor at the outlet reaches a minimum set value. Finally, a number of influential factors on the drying process are studied.