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Wood Science and Technology

, Volume 51, Issue 4, pp 701–719 | Cite as

A relevant and robust vacuum-drying model applied to hardwoods

  • Adam L. RedmanEmail author
  • Henri Bailleres
  • Patrick Perré
  • Elliot Carr
  • Ian Turner
Original

Abstract

A robust mathematical model was developed to simulate the heat and mass transfer process that evolves during vacuum-drying of four commercially important Australian native hardwood species. The hardwood species investigated were spotted gum (Corymbia citriodora), blackbutt (Eucalyptus pilularis), jarrah (Eucalyptus marginata), and messmate (Eucalyptus obliqua). These species provide a good test for the model based on their extreme diversity between wood properties and drying characteristics. The model uses boundary condition data from a series of vacuum-drying trials, which were also used to validate predictions. By using measured diffusion coefficient values to calibrate empirical formula, the accuracy of the model was greatly improved. Results of a sensitivity analysis showed that the model outputs provide excellent agreement with experimental observation despite the large range of species behaviour and variation in wood properties. This study confirms that the drying rate is significantly improved as a direct result of the enhanced convective and diffusive transfer along the board thickness. Contrary to softwood, it appears that longitudinal migration provides only a secondary effect. Not only is the model able to predict the heat and mass transfer behaviour of a range of hardwood species, it is also flexible enough to predict the behaviour for both conventional and vacuum-drying scenarios. The outcomes of this work provide the hardwood industry with a well-calibrated predictive drying tool that can be used to optimise drying schedules.

Keywords

Moisture Content Wood Property Hardwood Species Fibre Saturation Point Average Moisture Content 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

Latin letters

cp

Specific heat (J kg−1 K−1)

c

Molar concentration (mol m−3)

\(\overline{{{\overline{\mathbf{D}}}}}\)

Diffusivity tensor (m2 s−1)

FSP

Fibre saturation point

g

Gravitational acceleration (m s−2)

h

Specific enthalpy (J kg−1)

h

Heat transfer coefficient (W m−2 K−1)

J

Flux expression

K

Intrinsic permeability (m2)

\(\overline{{{\overline{\mathbf{K}}}}}\)

Absolute permeability tensor (m2)

\(\overline{{{\overline{\mathbf{k}}}}}\)

Relative permeability tensor

k

Boltzmann’s constant

ka

Air permeability (m2)

km

Mass transfer coefficient (m s−1)

kr

Relative permeability

L

Characteristic length (m)

M

Molecular weight (kg mol−1)

MC

Moisture content

ΔP

Pressure difference (Pa)

\(\bar{P}\)

Average pressure (Pa)

P

Pressure (Pa)

q

External heat transfer coefficient (W m−2 °C−1)

R

Gas constant (J mol−1 K−1)

S

Volume saturation

t

Time (s)

T

Temperature (K)

v

Mass velocity vector (m s−1)

ν

Poisson’s ratio

Vg

Green volume (m3)

x

Molar fraction (mol/mol)

X

Moisture content (dry basis) (kg kg−1)

Greek symbols

ε

Volume fraction

λ

Thermal conductivity (W m−1 K−1)

ρ

Intrinsic averaged density (kg m−2)

ρ0

Wood density (kg m−2)

σ

Surface tension (N m−1)

σ(T)

Surface tension at temperature T (N m−1)

μ

Dynamic viscosity of air (Pa s)

φ

Phase potential

ϕ

Porosity (m3 m−3)

χ

Depth scalar (m)

ω

Mass fraction

Superscripts and subscripts

a

Air

b

Bound

c

Capillary

e

Enthalpy

eff

Effective property

fsp

Fibre saturation point

g

Gas phase

l

Liquid

s

Solid phase

v

Vapour phase

ν

Vapour phase at boundary

w

Liquid phase

Value outside the boundary layer in the free stream

Notes

Acknowledgements

The substantial contributions of CentraleSupelec, Université Paris-Saclay, Queensland University of Technology (QUT), Forest and Wood Products Australia (FWPA) and the Queensland Government Department of Agriculture and Fisheries (DAF), to the undertaking of this collaborative project are gratefully acknowledged. Authors Turner and Carr wish to acknowledge that this research was partially supported by the Australian Research Council (ARC) via the Discovery Project DP150103675 and DECRA project DE150101137, respectively. Thank you to the reviewers for their comments and suggestions that led to an improved final version of the paper.

Supplementary material

226_2017_908_MOESM1_ESM.docx (50 kb)
Supplementary material 1 (DOCX 50 kb)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Science and Engineering FacultyQueensland University of Technology (QUT)BrisbaneAustralia
  2. 2.Agri-Science Queensland, Department of Agriculture and FisheriesQueensland GovernmentSalisburyAustralia
  3. 3.LGPM, CentraleSupelecUniversité Paris-SaclayChâtenay-MalabryFrance
  4. 4.Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS)Queensland University of Technology (QUT)BrisbaneAustralia

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