Numerical Determination of Diffusion Coefficients in Wood Using Data From CT-Scanning

Authors

  • John Eriksson
  • Håkan Johansson
  • Jonas Danvind

Keywords:

Calibration, CT-scanning, diffusion coefficient, parameter identification, wood drying

Abstract

The radial moisture diffusion coefficient in Fick's law for a sample of Norway spruce (Picea abies) under isothermal drying conditions was determined in a parameterization of Arrhenius' equation type. Using X-ray CT-scanning, the wood density and moisture content distributions were obtained in the radial direction for the wood sample. An optimization scheme, based on finite element computation, was then applied to find the parameter values such that the difference between observed and computed moisture content was minimized. The combined numerical and experimental technique was developed to reduce known disadvantages of similar approaches, and a specific algorithm to determine diffusion coefficients was presented. A comparison of the calibrated diffusion coefficient with those given in the literature showed a good fit. The computed moisture content based on the obtained diffusion coefficient and the observed moisture content agreed well. Finally, the effect of measurement errors on the computed material parameter was found to be small.

References

Chen, Y., E. T. Chong, and D. M. Wetzel. 1996. A numerical analysis to evaluate the moisture-dependent diffusion coefficient on moisture movement during drying. Wood Fiber Sci.28:338-345nDanvind, J. 2003. Measuring strain and moisture content in a cross section of drying wood using Digital Speckle Photography and X-ray Computerised Tomography. In Proc. 13th International Symposium on Nondestructive Testing of Wood, 19-21 August, 2002, Berkeley Campus, University of California, CA.nDanvind, J., and T. Morén. 2004. Using X-ray CT-scanning for moisture and displacement measurements in knots and their surroundings. In Proc. 5th COST ACTION E15, Advances in Drying of Wood, NAGREF/Forest Research Institute, 22-24 April, Greece.nDanvind, J., J. Eriksson, and H. Johansson. 2004. Calibration of a constitutive model for diffusive moisture transport in wood using data from X-ray CT-scanning and Digital Speckle Photography. In Proc. 5th COST ACTION E15, Advances in Drying of Wood, NAGREF/Forest Research Institute, 22-24 April, Greece.nEriksson, J. 2004. Study of moisture flow and moisture-induced distortions in sawn boards and laminated timber products. Lic. Thesis, Department of Structural Engineering and Mechanics, Chalmers University of Technology, Gothenburg, Sweden.nEriksson, K., D. Estep, P. Hansbo, and C. Johnson. 1996. Computational Differential Equations, Studentlitteratur, Lund, Sweden.nHukka, A. 1999. Diffusion and mass transfer coefficient of Nordic softwoods, Holzforschung53:534-540.nJohansson, H., and K. Runesson. 2005. Parameter identification in constitutive models via optimization with a posteriori error control. Int. J. Num. Methods Eng.62(10): 1315-1340.nKeey, R. B., T. A. G. Langrish, and J. C. F. Walker. 2000. Kiln drying of lumber. Springer, Berlin, GermanynKleiber, M., H. Antúnez, T.D. Hien, and P. Kowalczyk. 1997. Parameter sensitivity in nonlinear mechanics: Theory and finite element computations. John Wiley and Sons, New York, NY.nKoc, P., M. Houška, and B. Štok. 2003. Computer aided identification of the moisture transport parameters in spruce wood, Holzforschung57:533-538.nKoponen, H. 1984. Dependences of moisture diffusion coefficients of wood and wooden panels on moisture content and wood properties. Paperi ja Puu12:740-745.nLiu, J. Y., W. T. Simpson, and S. P. Verrill. 2001. An inverse moisture diffusion algorithm for the determination of diffusion coefficient, Drying Tech.19(8):1555-1568nLuenberger, D. G. 2003. Linear and nonlinear programming. Kluwer Academic, London, UK.nMahnken, R. 1998. Theoretiche und numeriche aspekte zur parameteridentifkation und modellierung bei metallischen werkstoffen. Report nr. f 98/2, Institut fuer Mechanik und Numeriche Mechanic, University of Hannover, Hannover, Germany.nOlek, W., and J. Weres. 2001. The inverse method for diffusion coefficient identification during water sorption in wood. In Proc. 3rd European COST E15 Workshop on Wood Drying, 11-13 June, Finland.nRosenkilde, A., and J. Arfvidsson. 1997. Measurement and evaluation of moisture transport coefficients during drying of wood. Holzforschung51(4):372-380.nSimpson, W. T., and J. Y. Liu. 1997. An optimisation technique to determine red oak surface and internal moisture transfer coefficients during drying. Wood Fiber Sci.29: 312-318nWadsö, L. 1993. Studies of water vapor transport and sorption in wood. Ph.D. thesis, Report TVBM-1013, Building Materials, Lund University, Lund, Sweden.n

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Published

2007-06-05

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Research Contributions