Numerical Modeling Technique to Predict the Dielectric Properties of Wood

Microwave processing of wood involves many complicated physical phenomena. The process includes absorption of the electromagnetic energy, transport of the generated heat, shape and dimension changes of the wood, phase changes in water, water transport through the wood material, etc. In order to optimize and control this process, the understanding of the various phenomena involved is needed. This understanding is achieved by experimental measurements and by building models which describe the various processes. The aim of this paper is to present a numerical model technique which simulates the dielectric behavior of wood at the microwave frequencies and predicts its dielectric properties which are relevant to microwave heating. Wood is a very complex material with poor thermal conductivity. Therefore, during microwave heating the internal temperatures can reach values which are high above the boiling point of water at room conditions. Also, since wood is not a very permeable material, due to the microwave heating characteristic to heat from interior to exterior, the internal pressure increases according to the saturated pressure of water vs. temperature. As wood is structurally composed of fibers, rays, vessels and so on, its dielectric permittivity is different in various directions and strongly depends on density, moisture content, temperature and pressure. To predict the dielectric properties of such complex configuration, a general method for calculating the permittivity of any mixture of different materials was approached. The main idea is to consider a three dimensional box divided into a mesh of small cells (each cell having the specific dielectric properties) and calculate the dielectric permittivity of the equivalent structure in a sophisticated manner through the exact solution of Laplace equation. Based on this method, an efficient solver which calculates the effective dielectric permittivity of any three dimensional structure of dielectric materials was developed. However, to estimate the dielectric permittivity of different wood configurations (different densities and moisture contents), a numerical model for describing the 3-D wood structure was developed and introduced into solver. The general 3-D wood model (Fig. 1) was constructed by making the following assumption: the fibers have uniform size and square shape in the cross section, the vessels are cylindrical and the arrangement of the cells is regular. Figure 1: 3-D wood model 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 120 electric field lines 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 120 electric field lines Tangential Longitudinal