﻿ 林带冬季相疏透度与透风系数的换算
 林业科学  2013, Vol. 49 Issue (11): 83-88 PDF
DOI: 10.11707/j.1001-7488.20131111
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#### 文章信息

Ren Yu, Wang Zhigang, Yang Donghui

Conversion of Porosity and Permeability of Shelter Belts with Winter Facies

Scientia Silvae Sinicae, 2013, 49(11): 83-88.
DOI: 10.11707/j.1001-7488.20131111

### 作者相关文章

1. 中国林业科学研究院荒漠化研究所 北京 100091；
2. 中国林业科学研究院沙漠林业实验中心 磴口 015200；
3. 包钢第一中学 包头 150200

Conversion of Porosity and Permeability of Shelter Belts with Winter Facies
Ren Yu1, Wang Zhigang2, Yang Donghui3
1. Institute of Desertification Studies, Chinese Academy of Forestry Beijing 100091;
2. Experimental Center for Desert Forestry, Chinese Academy of Forestry Dengkou 015200;
3. Baogang No.1 High School Baotou 150200
Abstract: In order to get more accurate forest winter facies porosity and permeability conversion formula, the physical mechanism of the resistance formation was used to deduce an approximate conversion formula of cylindrical fence porosity and permeability with different rows of trees, for revealing the consistency and the numerical variation rule of windbreak effect and the physical mechanism with different row numbers. The results showed that with the shelterbelt with the same porosity, the less the row number, the smaller the permeability, and the better the windbreak effect. With geometry similarity approaching as the principle, approximate conversion relationships between the forest winter phase permeability α, and porosity β were developed: single belt α=β0.7, two belt α=β0.6, for multiple belts α=β0.55, which was more actual than the belt simulation formula α=β0.4 which ignores rows and seasonal aspect effects, and assumes the ratio of length and height close to 1. The new relationships conduced to accurately understanding and applying windbreak effect principle and structure design of forest shelter belts.
Key words: winter facies    porosity    permeability

1 平板风障的疏透度与透风系数

$\alpha = \frac{\beta }{{\sqrt {1 - \beta + {\beta ^2}} }}。$

2 林带的疏透度与透风系数

2.1 上方封闭假设下的疏透度与透风系数

${\rm{2}}(1 - {\beta ^{1/2}})\frac{1}{2}\rho \frac{{{a^2}{v_0}^2}}{{{\beta ^{2/2}}}} =(1 - {\alpha ^2})\frac{1}{2}\rho {v_0}^2$

$\alpha = \frac{{{\beta ^{1/2}}}}{{\sqrt {2 - 2{\beta ^{1/2}} + {\beta ^{2/2}}} }}。$

$\alpha = \frac{{{\beta ^{1/3}}}}{{\sqrt {3 - 3{\beta ^{1/3}} + {\beta ^{2/3}}} }}。$

n行木栅疏透度β与透风系数α的关系式

 $\alpha = \frac{{{\beta ^{1/n}}}}{{\sqrt {n - n{\beta ^{1/n}} + {\beta ^{2/n}}} }}。$ (5)

n行木栅透风系数公式可以看出，当n逐渐加大时，α逐渐收敛。林带可以看做行数很多的木栅。

n趋于无穷大时，$\alpha = \frac{{{\beta ^{1/n}}}}{{\sqrt {n - n{\beta ^{1/n}} + {\beta ^{2/n}}} }}。$的极限:

$\mathop {\lim }\limits_{n \to \infty } {\beta ^{1/n}} = 1，$

$\mathop {\lim }\limits_{n \to \infty }(n - n{\beta ^{1/n}})= \mathop {\lim }\limits_{n \to \infty } n(1 - {\beta ^{1/n}})= \mathop {\lim }\limits_{n \to \infty } \frac{{1 - {\beta ^{1/n}}}}{{1/n}}。$

x=1/n，有$\mathop {\lim }\limits_{n \to \infty }(n - n{\beta ^{1/n}})= \mathop {\lim }\limits_{x \to 0} \frac{{1 - {\beta ^x}}}{x} = \mathop {\lim }\limits_{x \to 0} \frac{{(1 - {\beta ^x})'}}{{x'}} = \mathop {\lim }\limits_{x \to 0} \frac{{ - {\beta ^x}\ln \beta }}{1} = - \ln \beta$(洛必达法则)。则有

$\mathop {\lim }\limits_{n \to \infty } \alpha = \mathop {\lim }\limits_{n \to \infty } \frac{{{\beta ^{1/n}}}}{{\sqrt {n - n{\beta ^{1/n}} + {{({\beta ^{1/n}})}^2}} }} = \frac{1}{{\sqrt { - \ln \beta + 1} }} = \frac{1}{{\sqrt {1 - \ln \beta } }}。$

2.2 自由逃逸假设下的疏透度与透风系数

$\alpha = {\alpha _1}^2 = {({\beta _1}/\sqrt {1 - {\beta _1} + {\beta _1}^2})^2} = \frac{{{\beta _1}^2}}{{1 - {\beta _1} + {\beta _1}^2}}，$

n行木栅$\alpha = {\alpha _1}^n = {({\beta _1}/\sqrt {1 - {\beta _1} + {\beta _1}^2})^n}$，$\beta = {\beta ^{1/n}}$，$\alpha = {\alpha _1}^n = {({\beta ^{1/n}}/\sqrt {1 - {\beta _1} + {\beta _1}^2})^n}$化简得$\alpha = \beta /{(1 - {\beta ^{1/n}} + {\beta ^{2/n}})^{n/2}}$。

$\begin{array}{l} \mathop {\lim }\limits_{n \to \infty } \ln y = \mathop {\lim }\limits_{n \to \infty } [n\ln(1 - {\beta ^{1/n}} + {\beta ^{2/n}})] = \ \mathop {\lim }\limits_{n \to \infty } \frac{{\ln(1 - {\beta ^{1/n}} + {\beta ^{2/n}})}}{{1/n}} = \mathop {\lim }\limits_{x \to 0} \frac{{\ln(1 - {\beta ^x} + {\beta ^{2x}})}}{x} = \ \mathop {\lim }\limits_{x \to 0} \frac{{ - {\beta ^x}\ln \beta + 2{\beta ^{2x}}\ln \beta }}{{1 - {\beta ^x} + {\beta ^{2x}}}} = \ln \beta，\ \mathop {\lim }\limits_{n \to \infty } y = \beta， \end{array}$

2.3 上方封闭、自由逃逸假设与实验换算公式的对比

2.4 换算公式的近似简化

3 讨论与结论 3.1 林带冬季相透风系数换算的物理机制

3.2 冬季相与夏季相透风系数的比较

3.3 林带内树木排列方式对透风系数的影响

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