Yves Fortin

Experimental determination of the convective heat and mass transfer coefficients for wood drying

Abstract The knowledge of the convective heat and mass transfer coefficients is required for the characterization of the boundary conditions of the heat and mass transfer equations of a wood drying model based on water potential. A new experimental method for the determination of the convective mass transfer coefficient is presented. This method is based on the measurement of the moisture content, and indirectly the water potential, at the surface of a wood specimen at different drying times. Drying experiments were performed on red pine (Pinus resinosa Ait.) sapwood from nearly saturated to dry conditions at 56 °C, 52% relative humidity and air velocities of 1.0, 2.5 and 5.0 m s−1. The results show that the convective mass transfer coefficient is constant until the wood surface moisture content reaches about 80% and then decreases more or less gradually as the moisture content decreases further. The convective mass transfer coefficient increases with air velocity. A regression analysis shows that there is no significant improvement in considering the water potential gradient near the wood surface when the difference in water potential between the surface and the surrounding air (ψs − ψ∞) is used to determine the convective mass flux at the surface. Also, ψs − ψ∞ is more appropriate than the water vapour pressure difference (pvs − pv∞) as the responsible driving force of the moisture flux leaving the wood surface. The convective heat transfer coefficient was determined during the same experiments. A plateau is observed at high values of moisture content corresponding to the constant drying rate period.

Moisture content—water potential relationship of wood from saturated to dry conditions

SummaryThe water potential concept as applied to wood-water relations is presented. The gradient in water potential can be used as the driving force of moisture in wood in a model of drying in isothermal conditions provided the moisture content — water potential relationship is known. This relationship is established for aspen sapwood in desorption from saturated to dry conditions at 20, 35 and 50 °C for two specimen orientations. The tension plate, pressure plate and pressure membrane methods were used at high moisture contents and equilibration over saturated salt solutions was used at low moisture contents. The results obtained demonstrate that these methods can be used in combination in order to establish the relationship within the whole range of moisture contents. The equilibrium moisture contents obtained by the tension plate, the pressure plate and the pressure membrane methods for tangential desorption were slightly higher than those measured for radial desorption. The water potential increased with temperature at a given moisture content. This effect cannot be solely explained by the variation of surface tension of water with temperature.

A model of moisture movement in wood based on water potential and the determination of the effective water conductivity

SummaryA model of isothermal moisture movement in wood during drying using the gradient in water potential as the driving force is proposed. The moisture transport coefficient used in this model is the effective water conductivity. It is a function of moisture content, temperature, and direction of flow. The boundary desorption curve of the effective water conductivity function is established in the radial and tangential directions of aspen sapwood from nearly saturated to dry conditions at 20, 35, and 50 °C using the instantaneous profile method. The results show that the effective water conductivity increases exponentially with moisture content and temperature. The effect of temperature cannot be solely explained by the variation of the viscosity of water. The variation of the moisture content-water potential relationship with temperature would explain a large part of this effect. The effective water conductivity was generally higher in the radial direction than in the tangential direction in a ratio varying from 1/1 to 25/1 depending on moisture content and temperature. The flux-gradient relationship obtained at given moisture contents were found to be linear, confirming the validity of the model for the experimental conditions considered in the present work.

A global rheological model of wood cantilever as applied to wood drying

In the process of wood drying inevitable stresses are induced. This often leads to checking and undesired deformations that may greatly affect the quality of the dried product. The purpose of this study was to propose a new rheological model representation capable to predict the evolution of stresses and deformations in wood cantilever as applied to wood drying. The rheological model considers wood shrinkage, instantaneous stress–strain relationships, time induced creep, and mechano-sorptive creep. The constitutive law is based on an elasto–viscoplastic model that takes into account the moisture content gradient in wood, the effect of external load, and a threshold viscoplastic (permanent) strain which is dependent on stress level and time. The model was implemented into a numerical program that computes stresses and strains of wood cantilever under constant load for various moisture content conditions. The results indicate that linear and nonlinear creep behavior of wood cantilever under various load levels can be simulated using only one Kelvin element model in combination with a threshold-type viscoplastic element. The proposed rheological model was first developed for the identification of model parameters from cantilever creep tests, but it can be easily used to simulate drying stresses of a piece of wood subjected to no external load. It can therefore predict the stress reversal phenomenon, residual stresses and maximum stress through thickness during a typical drying process.

Modeling Superheated Steam Vacuum Drying of Wood

Abstract A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s−1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.

Moisture content-water potential relationship of red pine sapwood above the fiber saturation point and determination of the effective pore size distribution

SummaryThe pressure membrane and pressure plate techniques were used to establish the moisture content-water potential (M-ψ) relationship of red pine (Pinus resinosa Ait.) sapwood in desorption above the fiber saturation point. The moisture content-water potential relationship is required for the development of a model of drying considering the gradient of water potential as the driving force of moisture in wood. This relationship was established at 18, 56 and 85 °C for radial desorption. The results obtained demonstrate that water potential ψ increases with temperature T at a given moisture content M. There is no significant variation of ∂ψ/∂T with temperature. Also, there is no plateau at intermediate moisture contents as was the case for the M-ψ relationship of aspen sapwood established in a previous work. The effective integral and differential pore size distributions inferred from the M-ψ relationship are also presented. The largest proportion of effective pore openings was found for a radius of 0.2 μm. This value can be related to the pit membrane openings of red pine.

A Simulation Tool for the Optimization of Lumber Drying Schedules

Abstract A two-dimensional wood drying model based on the water potential concept is used to simulate the convection batch drying of lumber at conventional temperature. The model computes the average drying curve, the internal temperature and moisture content profiles, and the maximum effective moisture content gradient through board thickness. Various scenarios of conventional kiln-drying schedules are tested and their effects on drying time, maximum effective moisture content gradient, final moisture content distribution within and between boards, and energy consumption are analyzed. Simulations are performed for two softwood species, black spruce (Picea mariana (Mill.) B.S.P.) and balsam fir (Abies balsamea (L.) Mill.). The simulation results indicate that the predictive model can be a very useful tool to optimize kiln schedules in terms of drying time, energy consumption, and wood quality. Such a model could be readily combined with intelligent adaptive kiln controllers for on-line optimization of the drying schedules.

MODELING VACUUM-CONTACT DRYING OF WOOD: THE WATER POTENTIAL APPROACH

ABSTRACT A two-dimensional mathematical model for vacuum-contact drying of wood is presented. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady state conservation equation of dry air. Most of the model parameters were determined during independent experiments. The set of equations is then solved in a coupled form using the finite element method. The validation of the model is performed using experimental results obtained during vacuum-contact drying of sugar maple sapwood. The experimental and calculated data are in good agreement. Nevertheless, some discrepancies are observed which can be attributed to the boundary conditions used and to the fact that heat transfer by convection was neglected.

Determination of the effective water conductivity of red pine sapwood

Summary The instantaneous profile method was used to establish the boundary desorption curve of the effective water conductivity function of red pine (Pinus resinosa Ait.) sapwood in the radial and tangential directions from nearly saturated to dry conditions at 18, 56 and 85 °C. The results obtained demonstrate that the effective water conductivity is a function of moisture content, temperature, and direction of flow. The effective water conductivity increases by several orders of magnitude (104–105) as moisture content increases from dry to nearly saturated conditions at a given temperature. The effective water conductivity also increases by a factor varying between 10 and 50 as temperature rises from 18 to 85 °C in the moisture content range considered. The variation of the moisture content–water potential relationship with temperature can explain part of the temperature effect. The effective water conductivity was generally higher in the radial direction than in the tangential direction in a ratio varying from about 1/1 to 3/1 depending on moisture content and temperature. Finally, the flux–gradient relationships obtained at given moisture contents were found to be linear, confirming the validity of using a moisture flux equation considering the water potential gradient as the driving force for the experimental conditions considered in the present work. The knowledge of the effective water conductivity function and of the moisture content–water potential relationship allows the utilization of a two-dimensional model of moisture movement in wood during drying using the gradient in water potential as the driving force for drying at temperatures up to 85 °C.

DEVELOPMENT OF A TECHNIQUE TO DETERMINE THE 3D ELASTICITY TENSOR OF WOOD AS APPLIED TO DRYING STRESS MODELING

The objective of this study was to develop an accurate and simple method for measuring the engineering coeffi cients of the 3D elasticity tensor of wood. A method using a semi-ring extensometer (SRE) and a compression specimen (6-specimen technique) is proposed. The SRE is made of a semi-ring stainless steel blade pin-jointed to two aluminum fi xing plates, and two resistance strain gauges bonded to the top and bottom faces of the blade at mid-span position. Groups of fi ve matched compression specimens (20 mm x 20 mm x 60 mm) from black spruce wood (Picea mariana (Mill.) B.S.P.), cut in six different orientations with respect to load axis (three orthotropic directions and three diagonal directions at an angle of 45 degrees to the load axis) were used for the calibration of the SRE. A resistance strain gauge bonded directly to the wood surface was used as a reference for both the axial and transverse measurements. The validation of the technique was made with another series of specimens cut in the same six orientations. The axial strain data of the SRE were then compared to the ones obtained from a linear displacement sensor (LVDT). For the transverse directions, the SRE results in terms of Poisson’s ratios and shear moduli were compared with corresponding data obtained from the literature. Results showed that the R 2 value of the relationship between the Young’s moduli determined with the SRE and the LVDT varied from 0.88 to 0.97. The SRE technique appeared also reliable to evaluate both the Poisson’s ratios and shear moduli as the obtained values were in good agreement with the literature data. As compared to bonded strain gauges, the SRE technique is reusable, simpler and cheaper to use and its sensitivity is nearly independent of temperature.