A heterogeneous three-dimensional computational model for wood drying

Abstract

An accurate and efficient heterogenous three-dimensional computational model is developed for simulating the drying of wood. The complex macroscopic drying equations comprise a coupled and highly nonlinear system of partial differential equations. Due to the heterogeneous nature of wood, the physical model parameters strongly depend upon the local pore structure of the medium, the wood density variation within growth rings and the local variations in primary and secondary system variables. In order to provide a realistic representation of this behaviour, previously determined parameters derived using sophisticated image analysis methods and homogenisation techniques are used. Results are presented for a first generation virtual board description, where the board material properties vary along the section according to the pith position that defines the radial and tangential directions. These variations are assumed fixed throughout the longitudinal direction. The development of an accurate and efficient computational model requires the consideration of a number of significant numerical issues, including the virtual board description, the mesh design, the discretisation process, accurate flux approximations, and finally the solution of a large, nonlinear system. Each of these issues will be explored in this paper for the case of low temperature drying of softwood. Nomenclature c molar concentration (mol/m 3 ) D b bound liquid diffusivity (m 2 /s) D v effective vapour diffusivity (m 2 /s) g gravitational acceleration (m/s 2 ) h enthalpy (J/kg) h heat transfer coefficient (W/m 2 /K) h 0 vap latent heat of vaporisation (J/kg) J e energy flux (J/m 2 /s) J w liquid flux (kg/m 2 /s) K eff effective thermal conductivity (W/m/K) k m mass transfer coefficient (m/s) k w relative liquid permeability K w absolute liquid permeability (m 2 ) M v molecular weight of vapour (kg/mol) n normal vector (m) N number of mesh nodes P c capillary pressure (Pa) P w liquid pressure (Pa) r flux limiter sensor S w liquid saturation (m 3 /m 3 ) t time (s) T temperature (°C) V volume (m 3 ) v w liquid phase velocity (m/s) X moisture content (kg/kg) X average moisture content (kg/kg) X fsp fibre saturation point (kg/kg) x v molar fraction of vapour (mol/mol) Greek symbols Dh w differential heat of sorption (J/kg) dt discrete time step (s) dV CV control volume volume (m 3 ) e g gaseous volume fraction (m 3 /m 3 ) k w liquid mobility (m s/kg) l w liquid dynamic viscosity (kg/m/s) q density (kg/m 3 ) q 0 wood density (kg/m 3 ) r flux limiter function / porosity (m 3 /m 3 ) 382 S.L. Truscott, I.W. Turner / Applied Mathematical Modelling 29 (2005) 381-410

Air permeability in longitudinal and radial directions of compression wood of Picea abies L. and tension wood of Fagus sylvatica L.

“…It is also a key parameter for drying behavior (Perré and Turner 2001;Perré 2004;Perré and Passard 2004) and thus it is suitable for simulating the drying process (Couture et al 1996;Truscott and Turner 2005;Ré mond et al 2006). Rapid drying of wood at moisture content (MC) above fiber saturation point (FSP) is often hindered by an inherent lack of permeability (Elustondo et al 2004;Eriksson et al 2007).…”

A hygrothermo-mechanical model for wood: part A. Poroelastic formulation and validation with neutron imaging

“…The relative liquid permeability is given as a function of the saturation degree to the power eight for the L direction and power three for the transverse directions ( Truscott 2004 ). The relative gas permeability decreases proportionally with the liquid saturation with power fi ve in the L direction and power three in transverse directions ( Truscott 2004 ). The activation energy E bw of the adsorbed water is a function of u in the hygroscopic range ( Skaar 1998 …”

“…The intrinsic liquid permeability is taken constant with a value at T = 296 K ( Zillig 2009 ). The relative liquid permeability is given as a function of the saturation degree to the power eight for the L direction and power three for the transverse directions ( Truscott 2004 ). The relative gas permeability decreases proportionally with the liquid saturation with power fi ve in the L direction and power three in transverse directions ( Truscott 2004 ).…”

Impact of Wood Species, Dimensions and Drying Temperature on Sorption Behaviour of Wood

“…Other research papers provide two-dimensional and three-dimensional computer models imitating the wood drying process (Turner, 1996;Truscott and Turner, 2005). The paper by Merakeb et al (2009) presents a model for wood sorption hysteresis, when wood undergoes moistening and drying in the environment of different parameters.…”