IMPINGING JET DRYER

In coating and gravure printing, an impinging jet nozzle with high thermal efficiency for drying of coated film was developed.

Trial production 0f 40 kinds of nozzle enables to develop a high-performance impinging jet nozzle with heat transfer coefficient 1.5 times larger than that of current slit nozzle, through measurement of heat transfer coefficient, visualizations of air flow and heat transfer, and measuremenu of jet velocity and turbulence distribution. The purpose of the trial production was to expand a range of high heat transfer and promote turbulence compared with the current nozzle.

Paying attention to mass transfer within gravure ink coated film, drying characteristic of the film was analyzed by numerical solution of a set of equations governing the drying process in which concentration dependencies 0f the diffusion coefficient and the equilibrium vapor pressure were considered.

Applying these analyses. an industrial scale dryer with excellent drying efficiency has finally been developed.     

ANALYSIS OF HEAT AND MASS TRANSFER DURING DRYING OF PAPER/BOARD

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.     

PROCESSES RELATED TO DRYING: PART II USE OF THE SAME MODEL TO SOLVE TRANSFERS BOTH IN SATURATED AND UNSATURATED POROUS MEDIA

From the mathematical formulation presented in part I, a numerical code is developed to simulate heat and: mass transfers in porous media. The aim of this· tool is to understand and to improve each process related to drying. The association of a comprehensive set of equations with a efficient 2-D computer code allows us to predict the comportment of several porous media even if submitted to severe drying conditions. A few runs have been selected with special attention paid to the effect of internal gaseous pressure:

Convective drying of softwood at high temperature illustrate the typical two-dimensional transfers that occur in an anisotropic medium.

Microwave drying of light concrete pinpoints liquid expulsion of water which is driven by the pressure due to internal heating.

Finally, appropriate physical behaviours of a bed of glass spheres allows one to deal with simple processes for which full saturation occurs.     

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.     

COMPARISON OF SUPERHEATED STEAM AND AIR OPERATED SPRAY DRYERS USING COMPUTATIONAL FLUID DYNAMICS.

In this paper a numerical simulation of a spray dryer using the computational fluid dynamics (CFD) code Fluent is described. This simulation is based on a discrete droplet model and solve the partial differential equations of momentum, heat and mass conservation for both gas and dispersed phase.

The model is used to simulate the behaviour of a pilot scale spray dryer operated with two drying media : superheated steam and air Considering that there is no risk of powder ignition in superheated steam, we choosed a rather high inlet temperature (973 K). For the simulation, drop size spectrum is represented by 6 discrete droplets diameters, fitting to an experimental droplets size distribution and all droplets are injected at the same velocity, equal to the calculated velocity of the liquid sheet at the nozzle orifice.

It is showed that the model can evaluate the most important features of a spray dryer : temperature distribution inside the chamber, velocity of gas, droplets trajectories as well as deposits on the walls. The model predicts a fast down flowing core jet surrounded by a large recirculation zone. Using superheated steam or air as a drying medium shows only slight differences in flow patterns. Except for the recirculation which is tighter in steam.

The general behaviour of droplets in air or steam are quite the same : smallest droplets are entrained by the central core and largest ones are taken into the recirculation zone. In superheated steam, the droplets penetrate to a greater extent in the recirculation zone. Also, they evaporate faster. The contours of gas temperature reflect these differences as these two aspects are strongly coupled. In both air and steam there is a “cool” zone which is narrower in steam than in air. Finally, the panicle deposit problem seems to be more pronounced in air than in steam.

Adding to the inherent interest in using superheated steam as a drying medium, the model predicts attractive behaviour for spray drying with superheated steam. In particular. under the conditions tested with the model, a higher volumetric drying rate is obtained in superheated steam.     

VACUUM DRYING OF OAKWOOD :MOISTURE STRAINS AND DRYING PROCESS

After presenting the characteristics and the data acquired in an industrial evacuated kiln, a simplified analysis of heat and mass transfers is proposed. This analysis is based on the existence of a evaporization front determining two zones in the longitudinal direction :

-a dried zone in which moisture is less than 30 %

-a wet zone in which moisture is still at its initial value.

Such a hypothesis allows to study transfers transversally first, then longitudinally. Both equation systems ore linked by conditions of continuity for mass and energy.

This study allows to determine the shapes of the temperature and pressure curves in the longitudinal direction. The linearity of the variation of the average drying velocity versus the average moisture content of the board is also proved. Finally, the modeling of mechanical phenomena thanks to a finite element program shows the rupture zones appearing during the drying process.     

UNSTEADY, TWO-DIMENSIONAL HEAT AND MASS TRANSFER IN A PACKED BED OF FINE PARTICLES WITH AN ENDOTHERMIC PROCESS

The basic differential equations controlling the temperature and concentration field in a single packed bed of fine particles were derived and solved for the general case in which unsteady, two-dimensional heat and mass transfer lakes place with an endothermic process.

The time-change of particle- and fluid-temperature and concentration of water vapor (humidity) were calculated by a numerical method which assumed that the rate of the endothermic process can be expressed by a first-order rate equation and that the fluid flowing through the bed is of the piston flow type.

The experiments were conducted for the drying of silica-gel and the two-stage dehydration reaction of natural gypsum to demonstrate the applicability of the present theoretical analysis.

It has been found that the calculated results show satisfactory agreement with the measured data within the range of the experimental conditions employed.     

CONTACT DRYIXG OF WOOD VENEER

A model for contact drying of wood veneer is presented and compared with experimental results. The model is and-dimensional and assumes that convective transport of liquid and vapor is dominant for the drying conditions examined. Model results are in good agreement with the experimental data.

A parameter study indicates that total drying time is a strong function of platen temperature and veneer thickness. The model indicates that the spacing of ventilation grooves does not affect drying rate significantly, but has a large effect on pressure buildup in the veneer. Veneer permeability shoved a similar effect--with lover permeabilities resulting in slightly slower drying, but significantly higher internal pressure.     

DEVELOPMENT AND VALIDATION OF A PROCESS SIMULATOR FOR DRYING SUBBITUMINOUS COAL

Drying subbituminous coal has never been practiced commercially. The commercial dryers built to date have been designed for drying surface moisture in conjunction with upstream coal preparation facilities. This type of drying is mainly controlled by input energy and the basis of the design is an energy balance. In drying inherent moisture from subbituminous coal, the thermal conductivity of the coal and the diffusion of molecular water within coal particles impose limitations on the process conditions. Energy input and solids residence time in the dryer have to be controlled properly for simultaneously balancing the heat and mass transfer within the coal particles. Improper control of either parameter can cause fires and explosions during the key steps of the drying process—drying and cooling

In parallel to the Anaconda coal drying pilot plant program, a cross-flow, fluid-bed coal drying/cooling process simulator was developed for: (1) understanding the drying phenomena on an individual particle basis; (2) analyzing potential risks and safety limits, and (3) designing the Anaconda pilot plant program

The development of the process simulator was based on both first principles and laboratory data and can be divided into two phases:

1 Development of a semi-mechanistic drying model for Powder River Basin subbituminous coal employing an analytical solution of the diffusion equation

2.Formulation of a fluid-bed cross-bed cross-flow dryer/cooler simulator employing simultaneous heat and mass transfer

This model was validated against process variables data taken on a 4 tph pilot plant. An operable range, or process envelope, has been developed through the pilot plant experience and the process simulation study. Based on the model predictions, an uncertainly range was defined in the design recommendations of a pioneer coal drying plant in scale-up.     

A MATHEMATICAL MODEL FOR PARALLEL FLOW DRYER FOR SLABS WITH HIGH THERMAL DIFFUSIVITY

An analytical model for the process is developed. The thermal diffusivity of the drying slabs is assumed infinite and the moisture diffusivity constant during the entire drying process.

With specified initial and boundary conditions, the mathematical model yields a two-part solution for the diffusion equation. The first part is valid for the initial drying during which the surface moisture content exceeds the value of fiber saturation. This part of the solution is used until the surface moisture content drops to the fiber saturation value. The moisture profile at the end of this period is used as the initial condition for the second period of drying which takes place under hygroscopic conditions.

Two simplifying assumptions are adapted for the hygroscopic region: 1. The dependence between the surface temperature and the moisture content is linear. 2. Constant (average) absorption heat is used during this second drying period.

For both parts of the solution, the surface moisture gradient is proportional to the local temperature difference between the drying air and the slab surface. This temperature difference can be expressed by means of a water mass balance equation for the part of the dryer between the slab in-feed and the point considered and by using the thermodynamic properties of the humid air.     

STEAM DRYLNG OF WOOD FUELS

The objective of this work is to investigate some of the important aspects in the design of a steam band dryer for wood fuels. For this purpose the drying of the material in a bench-scale fixed bed dryer has been studied.

Drying times and thermal efficiencies for experiments conducted under different conditions are compared. The investigated materials are soft-and hardwood chips and softwood bark.

The thermal efficiency, the part of the sensible heat which is used during one passage of the steam through the bed, increases with increasing mass load (mass of dry matter per unit area) and with decreasing steam mass flux. At a mass load of 30 kg/m the thermal efficiency is about 0.85 even at steam mass fluxes as high as 0.6 kg/m² s (1.2 m/s). The thermal efficiency proves to be almost independent of pressure and temperature of the steam.

Due to the very inhomogeneous materials the steam mass flow distribution was uneven. This causes a decreased thermal efficiency. When bark     

Determination of Spray-Drying Kinetics in a Small Scale

The main aim of the study presented in this article was to develop and test a method to determine spray-drying kinetics in a laboratory scale. A special measuring tunnel to obtain evaporation rate similar to the conditions observed in a spray-drying column was designed, built and tested.

Extensive studies of drying kinetics for maltodextrin were performed for different air flow rates and air temperatures. Test runs to determine repeatability of this technique showed satisfactory agreement between subsequent measurements, which confirms accuracy of the developed measuring method.

An effect of the initial moisture content on the critical moisture content was observed which is related to a decrease of the equilibrium vapor pressure over the solution and a decrease of the driving force of evaporation and drying rate of the process.

Results of the experiments proved that the generalized drying curve obtained from small-scale experiments could be used to describe spray-drying kinetics if the critical moisture content of the material is known.     

Freeze-Drying of Pharmaceutical Crystalline and Amorphous Solutes in Vials: Dynamic Multi-Dimensional Models of the Primary and Secondary Drying Stages and Qualitative Features of the Moving Interface

Dynamic and spatially multi-dimensional mathematical models of the primary and secondary drying stages of the freeze-drying of pharmaceutical crystalline and amorphous solutes in vials, are constructed and presented in this work. The models account for the removal of free and bound water and could also provide the geometric shape of the moving interface and its position. It is proved that the temperature of the moving interface can not be constant if the flux of heat flow to the sides of the vial is not zero. It is also proved that the slope of the free surface (moving interface) at the edge of the vial is always curved downward.

The numerical solution of the nonlinear partial differential equations of the models would allow model simulations that could indicate design conditions, operating conditions, and control strategies that could provide high drying rates and could lead to a series of novel experiments in freeze-drying.     

Vacuum Drying of Oak Wood

Vacuum drying, j,e drying under absolute gas pressure of about 10⊃ Pa. is an efficient means of reducing the process period and of producing good quality wood. We will examine here continuous vacuum drying where the plank surfaces are kept at a constant temperature, which remains above the boiling point, and moisture flowing to the surface is extracted from the kiln.

We have carried out an experimental study of oak drying under such conditions. The drying rate and moisture content profile of the sample (40 mm thick) are recorded during the whole drying period.

A model of continuous drying is established from general conservation equations with the main approximation that the air is rapidly extracted. The two constitutive equations of the model which describe temperature and water content fields are of a diffusive type and coupled through coefficients. The adequate boundary equation is not a convective one, but expresses a hygroscopic equilibrium between the vapour in the chamber and the wood surface. The mass diffusive coefficient can be adjusted to the drying rates through capillary pressure and bound water diffusion functions. The wood heterogeneity (seasonal growth) is the main factor of discrepancy in these functions. The simulated drying rates correspond with the experimental ones.     

MICROSCOPIC DETERMINATION OF TRANSPORT PARAHETERS IN DRYING POROUS MEDIA

The flow and distribution of liquid and vapor in the pore space of drying porous media are represented by a simple network model that incorporates the microscopic mechanisms. A method akin to Monte Carlo and molecular dynamics approaches is described for calculating from any such model the macroscopic, 'volume- averaged', or effective transport parameters: relative permeabilities for pressure-driven flow, effective diffusivities for molecular diffusion, and so on.

The method is to map representative small samples of pore space onto regular networks that have equivalent mean coordination and are made up of biconical pore segments intersecting in pore bodies, all dimensions being drawn from measured or estimated distributions. Evaporation and meniscus curvature, vapor movement by diffusion away from menisci and viscous flow toward them are described by one-dimensional local approximations. The resulting large set of ordinary differential and algebraic equations is solved by computer. Solutions from several such realizations are averaged to determine relative permeability to liquid, capillary pressure, and effective diffusivity of vapor as functions of liquid saturation and drying history. The results are to be used for interpreting, interpolating, and extrapolating experimental measurements of the same quantities.     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

TRANSPORT PROPERTIES OF CELLULAR FOOD MATERIALS UNDERGOING FREEZE-DRYING

The samples of sliced and mashed apples were freeze-dried by controlling their surface temperatures over the usual pressure range of commercial operations. The surface of sliced samples could not be maintained at above 10°C in order to prevent the frozen layer from melting, while that of mashed samples was allowed to heat up to 70°C.

Thermal conductivities and permeabilities were determined by applying the uniformly-retreating-ice front model to the dried layer of the samples undergoing freeze-drying. The values of permeability for the mashed samples were found to depend on the ice-crystallization time during freezing. The results indicated that the drying rate of sliced samples was limited by the transfer rate of water vapor flowing through the dried layer. A cellular structural model is proposed for predicting the permeability of the dried layer, based on the resistance of the cell membrane to molecular transfer of water vapor.     

RELATIONSHIP BETWEEN A SOLAR DRYING MODEL OF RED PEPPER AND THE KINETICS OF PURE WATER EVAPORATION (I)

Drying of red pepper under solar radiation was investigated, and a simple model related to water evaporation was developed. Drying experiments at constant laboratory conditions were undertaken where solar radiation was simulated by a 1000 W lamp.

In this first part of the work, water evaporation under radiation is studied and laboratory experiments are presented with two objectives: to verify Penman's model of evaporation under radiation, and to validate the laboratory experiments. Modifying Penman's model of evaporation by introducing two drying conductances as a function of water content, allows the development of a drying model under Eolar radiation.

In the second part of this paper, the model is validated by applying it to red pepper open air solar drying experiments.     

Sublimation Kinetics during Freeze-Drying of Pharmaceutical Protein Formulation

The influence of total gas pressure and shelf temperature on sublimation kinetics of BSA-based formulation in glass vial as geometrical configuration was determined with a pilot freeze-dryer in standard operating freeze-drying conditions.

The sublimation rate curves showed three different periods with a plateau corresponding to a stationary regime. These kinetics data were mainly dependent on the shelf temperature and slightly influenced by the total gas pressure. Thus, the sublimation process in our conditions was mainly governed by overall heat transfer rate from the plate and from the surroundings to the sublimation front.

Moreover, it proved that the water vapor mass transfer mechanism through the dried layer occurs by molecular diffusion in Knudsen regime.

Finally, these experimental sublimation kinetics data were found in a quite fair agreement with the set up results. They confirm the validation of previous modeling of mean product temperature profiles during the freeze-drying by using the finite element code FEMLAB in real vial geometry (2-D).     

Drying of Transformer Board

The internal insulation in shell type power transforms is usually ensured by the stacking of plates of board impregnated with oil. A board is in equilibrium with the atmosphere at a moisture content varying from seven to eight percent by weight, but, when the insulating function is required, the water content must be lower than 0.5 %. The aim of the present work is the understanding and the modelling of transformer boards drying.

The first part of this work presents experimental studies showing that the drying of transform board follows two regimes :

- a fast regime in the fim period

- a slow regime, up to 99 percent of dryness.

The effect of heating and the influence of the board thickness on the drying rate also studied. In the second part of this paper, we presnt a model capable to represent the observed kinetics of transformer board drying. This model is based on the diffusion of water vapour in the gaseous phases combined with the transfer of water vapor from the fibres to the -us phase. The due of the average global transfer coefficient can be deduced from the slope of the curve 1 f(drying time), where x