﻿ 木材微波预处理圆柱形谐振腔理论模拟与设计
 林业科学  2014, Vol. 50 Issue (3): 117-122 PDF
DOI: 10.11707/j.1001-7488.20140316
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#### 文章信息

Luo Yongfeng, Li Xi, Li Xianjun, Chen Hongbin, Chai Yuan

Mathematical Simulation and Design of Cylindrical Cavity of Microwave Pretreatment Equipment Used for Wood Modification

Scientia Silvae Sinicae, 2014, 50(3): 117-122.
DOI: 10.11707/j.1001-7488.20140316

### 作者相关文章

1. 中南林业科技大学理学院 长沙 410004;
2. 中南林业科技大学材料科学与工程学院 长沙 410004

Mathematical Simulation and Design of Cylindrical Cavity of Microwave Pretreatment Equipment Used for Wood Modification
Luo Yongfeng1, Li Xi1, Li Xianjun2, Chen Hongbin1, Chai Yuan2
1. School of Sciences, Central South University of Forestry and Technology Changsha 410004;
2. School of Material Science and Engineering, Central South University of Forestry and Technology Changsha 410004
Abstract: Based on the Maxwell electromagnetic field equations and the heat and mass transfer mechanism of wood, a heat and mass transport and a electromagnetic field distribution model for wood microwave pretreatment were developed to simulate the effect of the microwave feeding mode and cylindrical resonant cavity radius on the temperature uniformity and microwave energy utilization efficiency using finite element analysis software (Comsol Multiphysics), and the optimizational parameters for the cylindrical resonant cavity was achieved. The results showed that: 1) the effect of microwave feeding mode and the radius of the cylindrical resonant cavity on the temperature uniformity within wood and microwave energy utilization efficiency was significant. 2) Compared with the other microwave feeding mode, the temperature distribution uniformity within wood and microwave energy utilization efficiency was the highest(up to 87.48%)when the microwave radiation with 3 waveguides feeding is used to heat wood. 3) The temperature coefficient variation and microwave energy utilization efficiency basically decreased and then increased with the increasing the radius of the cylindrical resonant cavity, and the optimizational radius for the cylindrical resonant cavity was in the range from 0.186 m to 0.211 m.
Key words: wood microwave pretreatment    resonant cavity radius    temperature distribution    energy utilization efficiency

1 模型构建

1.1 电磁场与微波能量分布模型

 $\nabla \times \vec E{\rm{ = }} - \frac{{\partial \vec B}}{{\partial t}};$ (1)
 $\nabla \times \vec H{\rm{ = }}\vec J + \frac{{\partial \vec D}}{{\partial t}};$ (2)
 $\nabla \cdot \vec B{\rm{ = }}0;$ (3)
 $\nabla \cdot \vec D{\rm{ = }}{\rho _c}$。 (4)

 $\nabla \times \vec E\left( {\vec r} \right) = i\omega \mu \vec H\left( {\vec r} \right);$ (5)
 $\nabla \times \vec H\left( {\vec r} \right) = \left( {\sigma - i\omega \varepsilon } \right)\vec E\left( {\vec r} \right) = - i\omega {\varepsilon ^*}\vec E\left( {\vec r} \right)$。 (6)

 $\nabla \left( {\vec E \cdot \frac{{\nabla {\varepsilon ^*}}}{{{\varepsilon ^*}}}} \right) + {\nabla ^2}\vec E + {k^2}\vec E = 0$。 (7)

 ${\nabla ^2}\vec E + {k^2}\vec E = 0$。 (8)

 $k = \alpha + i\beta ;$ (9)
 $\alpha = \frac{{2\pi f}}{c}\sqrt {\frac{{\varepsilon '\left( {\sqrt {1 + {{\tan }^2}\delta } + 1} \right)}}{2}} ;$ (10)
 $\beta = \frac{{2\pi f}}{c}\sqrt {\frac{{\varepsilon '\left( {\sqrt {1 + {{\tan }^2}\delta } - 1} \right)}}{2}}$。 (11)

 $\tan \delta = \frac{{\varepsilon ''}}{{\varepsilon '}}$。 (12)

 $n \times \left[ {{{\vec E}_1}\left( {\vec r} \right) - {{\vec E}_2}\left( {\vec r} \right)} \right] = 0;$ (13)
 $n \times \left[ {{{\vec H}_1}\left( {\vec r} \right) - {{\vec H}_2}\left( {\vec r} \right)} \right] = 0$。 (14)

 $\frac{{\partial \vec E\left( {\vec r} \right)}}{{\partial r}} = i{\mu _0}\omega \vec H\left( {\vec r} \right)$。 (15)

 $E = {A_1}{e^{ikr}} + {B_1}{e^{ - ikr}}$。 (16)

 $Q = \frac{1}{2}\omega {\varepsilon _0}\varepsilon ''\vec E \cdot {\vec E^*}$。 (17)

1.2 热迁移模型

 $\rho {C_p}\frac{{\partial T}}{{\partial t}} = \nabla \cdot \left( {{k_T}\nabla T} \right) + Q$。 (18)

 $t = 0,T = {T_{ini}},0 \le r \le R;$ (19)
 $\begin{array}{*{20}{l}} {t > 0, - {k_T}\frac{{\partial T}}{{\partial r}} = h\left( {T - {T_a}} \right) + }\\ {{L_{vap}}k'm\left( {{C_{w,s}} - {C_{equi}}} \right),r = R} \end{array}$ (20)

1.3 质迁移模型

 $\frac{{\partial {C_w}}}{{\partial t}} = \nabla \left( {{D_w}\nabla {C_w}} \right)$。 (21)

 $t = 0,{C_w} = {C_{w,ini}},0 \le r \le R;$ (22)
 $t > 0, - {D_w}\frac{{\partial C}}{{\partial x}} = k{'_m}\left( {{C_{w,s}} - {C_{equi}}} \right),r = R$。 (23)
2 结果与讨论

λ=0.23[1-0.72×(25-T)/100]W·m-1-1;C=2 650×(1+T/100)0.2J·kg-1-1

2.1 馈入方式对木材内温度分布均匀性和微波能量利用效率的影响

 图 1 不同馈入方式木材内温度空间分布 Fig. 1 The temperature distribution within wood heated by microwave with different radiation methods

 图 2 不同馈入方式木材内中央截面温度分布 Fig. 2 The central section temperature distribution within wood heated by microwave with different radiation methods

 图 3 馈入方式对温度变异系数和能量利用效率的影响 Fig. 3 The effect of microwave radiation methods on the temperature variation coefficient and microwave energy utilization efficiency

2.2 谐振腔半径对木材内温度分布均匀性和微波能量利用效率的影响

 图 4 不同谐振腔半径木材内中央截面的温度分布 Fig. 4 The central section temperature distribution within wood heated by microwave with different resonant cavity dimension
 图 5 谐振腔半径对温度变异系数和能量利用效率的影响 Fig. 5 The effect of the radius for the microwave resonant cavity on the temperature variation coefficient and microwave energy utilization efficiency

3 结论

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