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.     

In-Plane Diffusivity of Moisture in Paper

Any nonuniformity in local moisture content of paper which develops during drying because of locally nonuniform drying rates provides a driving force for in-plane diffusion of moisture, which in turn acts to reduce this moisture nonuniformity. As no data have appeared for the in-plane diffusivity of moisture during desorption from paper over the range of conditions existing during papermachine drying, an investigation was undertaken to obtain this information.

Moisture diffusivity was determined to he a very strong function of the extent and state of water in the sheet, increasing exponentially with paper moisture content. The presence or absence of liquid water at the sheet boundary would effect moisture difiusivity when there is water in the pores but the direction of moisture transport in paper was found to be of overriding importance. In-plane moisture diffusivity is very much greater than that in the thickness direction, indicating that the non-isotropic nature of paper structure is a key factor. A microscale view of the mechanism of moisture transport in the thickness and in-plane directions was developed, consistent with the enormous difference in effect of moisture content on diffusivity in the two directions.     

CONTRIBUTIONS OF T. K. SHERWOOD AND ASSOCIATES TO THE FIELD OF DRYING (Part 3, Final)

ABSTRACT

Any nonuniformity in local moisture content of paper which develops during drying because of locally nonuniform drying rates provides a driving force for in-plane diffusion of moisture, which in turn acts to reduce this moisture nonuniformity. As no data have appeared for the in-plane diffusivity of moisture during desorption from paper over the range of conditions existing during papermachine drying, an investigation was undertaken to obtain this information.

Moisture diffusivity was determined to he a very strong function of the extent and state of water in the sheet, increasing exponentially with paper moisture content. The presence or absence of liquid water at the sheet boundary would effect moisture difiusivity when there is water in the pores but the direction of moisture transport in paper was found to be of overriding importance. In-plane moisture diffusivity is very much greater than that in the thickness direction, indicating that the non-isotropic nature of paper structure is a key factor. A microscale view of the mechanism of moisture transport in the thickness and in-plane directions was developed, consistent with the enormous difference in effect of moisture content on diffusivity in the two directions.     

Modeling Shrinkage Response to Tensile Stresses in Wood Drying: I. Shrinkage-Moisture Interaction in Stress-Free Specimens

This article reports on the wood shrinkage during drying in relationship with the temperature and moisture content. All tests were performed perpendicular to the grain on small clear wood specimens of green Western hemlock while drying at 40, 60, and 80°C to 17, 11, and 5% final moisture contents. Overall, wood dimensional changes and moisture loss phenomena were successfully analyzed and interpolated. The shrinkage strain followed a nonlinear pattern with the moisture loss being the driving force and exhibited good correlation with the square value of moisture content in tangential, and linear moisture values could be used to describe shrinkage in radial direction. Both shrinkage intersection points and end of capillary water values increased with temperature; the distinction between the two values could not be made at all times. A nonlinear function containing two regression coefficients (α and β) was found to be a good interpolation of the moisture loss experimental data. Further analyses revealed that β is independent of both target moisture content and temperature, whereas α appears to be influenced by both variables. The correlation between shrinkage and moisture loss rate is intended to be used as a stress prediction tool.     

Computer model of drying behaviour of ceramic green bodies with particular reference to moisture content dependent properties

A numerical model was developed to predict the drying behavior of ceramic green bodies. Resolution of the simultaneous heat and mass transfer equations involved finite elements and the Backward Euler method. Based on experimental data, the model uses equivalent moisture diffusivity, water activity, thermal conductivity and heat capacity as input parameters which depend on moisture content. In particular, the equivalent moisture diffusivity is a key parameter controlling water transport from the body interior to the surface. A simple method was used to estimate the effect of shrinkage on drying rate during the initial drying stage. Predictions of the internal moisture distribution, drying rate and surface temperature as a function of time gave good agreement to experiment for green bodies of alumina paste. External conditions of convection coefficient and relative humidity are shown to sensitively control drying rate and surface temperature evolution during the constant rate period.     

DRYING GRANULAR POROUS MEDIA: GRAVITATIONAL EFFECTS IN THE ISENTHALPIC REGIME AND THE ROLE OF DIFFUSION MODELS

In this paper we have examined the influence of gravity on the moisture transport process during the isenthalpic drying period, and we have considered the use of diffusion models both to predict saturation pro- files and to extract apparent diffusivities from experi- mental data. For granular or unconsolidated porous media, the one-dimensional moisture transport process can be characterized by two dimensionless groups that account for capillary forces, gravitational forces and viscous forces. Detailed numerical solutions of the saturation transport equation indicate under what circumstances the diffusion model can be used with confidence, and under what circumstances the diffusion model can be used to predict saturation profiles even though it is an incorrect representation of the moisture transport process. In addition to exploring the predictive capabilities of the diffusion model, we have     

DRYING GRANULAR POROUS MEDIA: GRAVITATIONAL EFFECTS IN THE ISENTHALPIC REGIME AND THE ROLE OF DIFFUSION MODELS

In this paper we have examined the influence of gravity on the moisture transport process during the isenthalpic drying period, and we have considered the use of diffusion models both to predict saturation pro- files and to extract apparent diffusivities from experi- mental data. For granular or unconsolidated porous media, the one-dimensional moisture transport process can be characterized by two dimensionless groups that account for capillary forces, gravitational forces and viscous forces. Detailed numerical solutions of the saturation transport equation indicate under what circumstances the diffusion model can be used with confidence, and under what circumstances the diffusion model can be used to predict saturation profiles even though it is an incorrect representation of the moisture transport process. In addition to exploring the predictive capabilities of the diffusion model, we have     

Mass Transfer in the Celery Slice: Effects of Temperature, Moisture Content, and Density on Water Diffusivity

Statistical tests were applied to determine the effects of temperature, moisture content, density, and porosity of material on the effective moisture diffusion coefficient during convective drying of root celery. In biological materials with colloidal capillary-porous structure (like root celery), which shrink considerably during drying and show high heterogeneity, the effective water diffusion coefficient depends not only on material temperature and moisture content, but also on its density. It was found that statistical tests can be applied to predict which independent variables should describe the water diffusivity in colloidal capillary-porous materials. A mathematical model of the effective water diffusion coefficient in root celery was formulated as Arhenius-type equation with moisture content of the raw material, its temperature and density as independent variables.     

MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING

Non-linear partial differential equations are presented for two dimensional heat and mass transfer within a single grain kernel during drying. In this model, the moisture evaporation inside the kernel is considered. The moisture is assumed to diffuse to the outer boundary of the kernel in liquid form and evaporate on the surface of the kernel. The influence of temperature and moisture content on grain properties is also considered in the simulation. The Non-linear partial differential equations are solved using the finite element method and simulation data is verified on a thin layer dryer for wheat kernels. The comparison shows that the simulated results have a high accuracy with average relative error of about 5%. The results of the finite element analysis can be used for grain quality evaluation, drying simulation studies and stress analysis of grain kernel.     

A Numerical Simulation for Solving the Dippusion Equations in the Drying of Hardware Timber

A numerical simulation is described for solving the thermal conduction and mass diffusion equations in boards of hardwood timber, and the Einite-volume method used here has been applied to the drying of Eucalypt timber, an Australian hardwood. The predictions of the variation in the average moisture content with time agree well with both ex~erimental data from the literature and analvtical solutions of the-diffusion equation. The nume ical simulation treats the boundary conditions more accurately than the analytical solutions when the moisture movement is two dimensional, as it is through the cross-section of a timber board. This feature makes the simulation useful when describing the drying process under intermittent drying conditions. These conditions are encountered in the drying of timber in solar kilns, and this simulation may be used to predict the distributions of temperature andmoisture content inboards of timber which are being dried intermittently inside conventional kilns. The numerical simulation for intermittent drying has shown, inthe example studied here, chat the same overall change in average moisture concentration can be achieved with 12-hour active drying and 12-hour relaxationperiodaas forcontinuousdryingbyincreasingthedry-bulb temperature by 10°C for this timber. In spite of the higher dry-bulb temperature used in the active drying period of intermittent drying. the moisture concentration profiles within the board are predicted to be more uniform than with continuous drying, because the internal moisture diffusion process continues during the relaxation period. These mare uniform moisture concentration profiles in intermittent drying are likely to result in lower stress levels within the timber than with continuous drying.     

MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING

ABSTRACT

Non-linear partial differential equations are presented for two dimensional heat and mass transfer within a single grain kernel during drying. In this model, the moisture evaporation inside the kernel is considered. The moisture is assumed to diffuse to the outer boundary of the kernel in liquid form and evaporate on the surface of the kernel. The influence of temperature and moisture content on grain properties is also considered in the simulation. The Non-linear partial differential equations are solved using the finite element method and simulation data is verified on a thin layer dryer for wheat kernels. The comparison shows that the simulated results have a high accuracy with average relative error of about 5%. The results of the finite element analysis can be used for grain quality evaluation, drying simulation studies and stress analysis of grain kernel.     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

Mass Transfer in the Celery Slice: Effects of Temperature,Moisture Content,and Density on Water Diffusivity

Abstract

Statistical tests were applied to determine the effects of temperature, moisture content, density, and porosity of material on the effective moisture diffusion coefficient during convective drying of root celery. In biological materials with colloidal capillary-porous structure (like root celery), which shrink considerably during drying and show high heterogeneity, the effective water diffusion coefficient depends not only on material temperature and moisture content, but also on its density. It was found that statistical tests can be applied to predict which independent variables should describe the water diffusivity in colloidal capillary-porous materials. A mathematical model of the effective water diffusion coefficient in root celery was formulated as Arhenius-type equation with moisture content of the raw material, its temperature and density as independent variables.     

A Simulation of Wet Pocket Lumber Drying

In general, wood containing wet pockets is difficult to dry and to ensure uniformity of moisture content at the end of the drying process. Large variations of final moisture content and severe case hardening are common problems associated with the drying of wet wood. In order to devise optimal strategies for drying wood containing wet pockets, it is necessary to understand its complex moisture movement mechanisms and therefore predict drying times and final moisture content. Sub-alpine fir dimension lumber was used in this research because of its inherent issues related to wet pockets.

A two-dimensional mathematical drying model for wood containing wet pockets was developed. An effective diffusion coefficient (D_eff) was utilized in the model and heat and mass transfer equations were solved using a control volume approach. The difficulties involved in the simulation of the drying process of wet pocket lumber are due to the differences in moisture content and physical properties between wet and normal wood. Thus, an adjustable D_eff based on the moisture content (for both below and above fiber saturation point) was used during the simulation.

Four drying runs involving green unsorted sub-alpine fir lumber were carried out in a 3-ft laboratory kiln and in an 8-ft pilot kiln. The results of the simulations were in agreement with the results obtained through the drying experiments.     

Modeling of Moisture and Temperature Changes of Wheat during Drying in a Triangular Spouted Bed Dryer

A mathematical model of temperature and wheat moisture content distribution inside a triangular spouted bed dryer was developed. The model is based on analysis of heat and mass transfer inside the dryer. In addition to that, an empirical bulk density model has been developed for wheat and included in the drying simulation. A laboratory-scale triangular spouted bed (TSB) dryer was used to dry wheat grain to validate the model. The dryer was divided into three sections, namely spouting, downcomer, and fountain. A series of drying runs were conducted to record moisture and temperature profile. There were two distinct regions observed during wheat drying. A constant rate period was observed during the initial drying stage and the falling rate period took place at the later drying stage. Initial moisture content and operating drying temperature governed the timing of transition from constant rate period to falling rate period. The model can be used to accurately predict the moisture content of wheat during drying. The temperature prediction inside the TSB dryer was less accurate, especially at high temperatures due to heat losses in the experimental dryer. Further studies are needed to improve the accuracy of this model, especially with regard to the temperature prediction.     

Breakage and Mass Transfer Models During Drying of Rough Rice

A breakage model was investigated for thin-layer drying of rough rice. The breakage model developed can predict the percentage of head rice (E/E_o) as an exponential function of the grain moisture. Experimental data of the rice moisture content during drying were fitted with a theoretical model of the drying process to obtain the parameters. Experimental data of percentage head rice and moisture content were fitted to obtain the parameters of breakage model. Both functions were used together to obtain a drying-breakage model. This model allows us to predict the drying time required to achieve a rice moisture content desired and to estimate the head rice yield percentage for this moisture content.     

Modeling conventional drying of wood: Inclusion of a moving evaporation interface

A one-dimensional mathematical model is presented that accounts for a moving evaporation interface in simulating the coupled heat and mass transfer during convective drying of wood. In the model proposed, the only mechanism considered in water transport within wood is diffusion. Additionally, the transport of moisture is dominated by the gradient of the moisture content. The controlling equations were established from Whitaker’s volume averaging laws and solved numerically with the finite volume method. The simulation results for the density of vapor and the volume rate of evaporation indicate that the migrating moisture was mainly in the form of gas under conditions of lower moisture content. The evaporation interface moved at approximately constant speed and the evaporation rate of the interface decreased with time. Finally, the core temperature and average moisture content in wood were successfully simulated.     

Stress and Failure Prediction for the Drying, Tempering, and Cooling of Extruded Durum Semolina

This work presents a method to predict the stress and breakage that is caused by the drying of hygros-copic materials. Stresses were predicted for a viscoclasic cylinder with the properties of extruded durum semolina, or pasta noodles. The stresses were calculated as functions of the transient moisture and tem-perature gradients in the material which were predicted for the combined processes of drying, tempering,and cooling. The time and radial position of failure were predicted based on failure data for extruded semolina.

Isotherm data for extruded durum semolina were obtained for temperatures from 40 to 60°C and for relative humidities from 75 to 95%. The results were fit with a modified form of Henderson's equation.Thermal conductivities were measured for temperatures from 30 to 50°C and a moisture range of 12 to 27% (dry basis).

A drying model based on the principles of irreversible thermodynamics; (Fortes, 1978; Fortes and Okos, 1981a, 1981b) was used to successfully predict drying curves for a range of experimental conditions. Transient moisture and temperature profiles were calculated numerically, and a receding evapora-tion front was predicted to exist. Drying was predicted to be a coupled liquid, vapor, and heat transport phenomena.

The drying data were used in a stress analysis of a Maxwell viscoelastic cylinder to predict trends in stress development under various contiitions of combined drying, tempering, and cooling. High temperature-high humidity drying, HTHH, (lOO°C, 65% RH) was compared with low temperature-low humidity drying, LTLH, (53°C, 13% RH). The HTHH drying offered definite advantages in terms of reduced product breakage susceptibility. The reasons for those advantages were increased failure strength and a decreased moisture gradient at the end of drying. In a five-stage drying process, the cooling stage was shown to have a significant impact on the predicted levels of stress and on the strength of the extruded material. Analysis of the model suggested that gradual temperature and humidity transitions from stage to stage in multistage processes were important to product quality.     

THE EFFECT OF HETEROGENEITY ON WOOD DRYING, PART II: EXPERIMENTAL RESULTS

Experimental measurements of drying rate, moisture distribution, surface moisture content, and temperature distribution are reported for softwood dried in the radial, tangential, and mixed (between radial and tangential) directions. The effects of both the heterogeneous and the anisotropic structure of wood are observed. The drying curves for tangential drying exhibit two distinct transition points - one when the surface reaches the fiber saturation point and one when the surface becomes completely dry. These transitions are not observed consistently for drying in the radial and mixed directions. For mixed drying, as a result of anisotropy, the drying rate is always higher at the side of the sample to which the growth rings point at die surface. Measurements of the surface mass transfer coefficient indicate that the theoretical value which is analogous to the convective heat transfer coefficient agrees well with that measured experimentally at both very high and very low values of the surface moisture content. At intermediate values of the moisture content the ratio of the experimental to the theoretical convective mass transfer coefficient can be as low as 0.20. The model discussed in Part I predicts results that are in good qualitative agreement with the experimental results presented in this paper.     

Transport in deformable food materials: A poromechanics approach

A comprehensive poromechanics-based modeling framework that can be used to model transport and deformation in food materials under a variety of processing conditions and states (rubbery or glassy) has been developed. Simplifications to the model equations have been developed, based on driving forces for deformation (moisture change and gas pressure development) and on the state of food material for transport. The framework is applied to two completely different food processes (contact heating of hamburger patties and drying of potatoes). The modeling framework is implemented using total Lagrangian mesh for solid momentum balance and Eulerian mesh for transport equations, and validated using experimental data. Transport in liquid phase dominates for both the processes, with hamburger patty shrinking with moisture loss for all moisture contents, while shrinkage in potato stops below a critical moisture content.