# 不同声带长度的声门管内流场数值模拟Numerical Simulation of the Glottal Flow Field with Different Lengths of Vocal Cord

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In order to investigate the distribution of pressure field in the glottal duct with different vocal cord lengths, three different glottal models were established by using finite element analysis method. Five different glottal diameters (0.01 cm, 0.02 cm, 0.04 cm, 0.08 cm, 0.16 cm) and three kinds of subglottal pressure (500 pa, 1000 pa, 1500 pa) were set up in the model respectively. The pressure distribution is obtained by numerical simulation of the flow field by ANSYS Fluent. The experimental results show that the longer glottal length will reduce the pressure drop at the en-trance of the glottal, which helps make it easier to create vibration of the vocal folds and reduces the phonation threshold pressure, and provide reference for further study of the vocal mechanism of human vocal cords and the repair of damaged vocal cords.

1. 引言

2. 声带建模与边界条件

2.1. 声带几何模型

Figure 1. Vocal cord simulation model

2.2. 网格划分与边界条件

Figure 2. Vocal cord mesh model

3. 声门管流场分析基本理论

3.1. 连续性方程

$\frac{\partial \rho }{\partial t}+\frac{\partial \left(\rho {v}_{x}\right)}{\partial x}+\frac{\partial \left(\rho {v}_{y}\right)}{\partial y}+\frac{\partial \left(\rho {v}_{z}\right)}{\partial z}=0$ (1)

$\frac{\partial {v}_{x}}{\partial x}+\frac{\partial {v}_{y}}{\partial y}+\frac{\partial {v}_{z}}{\partial z}=0$ (2)

3.2. Navier-Stokes方程

$\begin{array}{l}\rho \left(\frac{\partial {v}_{x}}{\partial t}+{v}_{x}\frac{\partial {v}_{x}}{\partial x}+{v}_{y}\frac{\partial {v}_{x}}{\partial y}+{v}_{z}\frac{\partial {v}_{x}}{\partial z}\right)=-\frac{\partial p}{\partial x}+\mu \left(\frac{{\partial }^{2}{v}_{x}}{\partial {x}^{2}}+\frac{{\partial }^{2}{v}_{x}}{\partial {y}^{2}}+\frac{{\partial }^{2}{v}_{x}}{\partial {z}^{2}}\right)\\ \rho \left(\frac{\partial {v}_{y}}{\partial t}+{v}_{x}\frac{\partial {v}_{y}}{\partial x}+{v}_{y}\frac{\partial {v}_{y}}{\partial y}+{v}_{z}\frac{\partial {v}_{y}}{\partial z}\right)=-\frac{\partial p}{\partial y}+\mu \left(\frac{{\partial }^{2}{v}_{y}}{\partial {x}^{2}}+\frac{{\partial }^{2}{v}_{y}}{\partial {y}^{2}}+\frac{{\partial }^{2}{v}_{y}}{\partial {z}^{2}}\right)\\ \rho \left(\frac{\partial {v}_{z}}{\partial t}+{v}_{x}\frac{\partial {v}_{z}}{\partial x}+{v}_{y}\frac{\partial {v}_{z}}{\partial y}+{v}_{z}\frac{\partial {v}_{z}}{\partial z}\right)=-\frac{\partial p}{\partial z}+\mu \left(\frac{{\partial }^{2}{v}_{z}}{\partial {x}^{2}}+\frac{{\partial }^{2}{v}_{z}}{\partial {y}^{2}}+\frac{{\partial }^{2}{v}_{z}}{\partial {z}^{2}}\right)\end{array}$ (3)

3.3. SST k-ω模型方程

$\begin{array}{l}\frac{\partial }{\partial t}\left(\rho {u}_{i}\right)+\frac{\partial }{\partial {x}_{i}}\left(\rho {u}_{i}{u}_{j}\right)=-\frac{\partial p}{\partial {x}_{i}}+\frac{\partial }{\partial {x}_{j}}\left(\Gamma \frac{\partial {u}_{i}}{\partial {x}_{j}}\right)+{S}_{i},\left(i=1,2,3\right)\\ \frac{\partial }{\partial t}\left(\rho k\right)+\frac{\partial }{\partial {x}_{i}}\left(\rho k{u}_{j}\right)=\frac{\partial }{\partial {x}_{j}}\left({\Gamma }_{k}\frac{\partial k}{\partial {x}_{j}}\right)+{\stackrel{˜}{G}}_{k}-{Y}_{k}+{S}_{k}\\ \frac{\partial }{\partial t}\left(\rho \omega \right)+\frac{\partial }{\partial {x}_{j}}\left(\rho \omega {u}_{j}\right)=\frac{\partial }{\partial {x}_{j}}\left({\Gamma }_{\omega }\frac{\partial \omega }{\partial {x}_{j}}\right)+{G}_{\omega }-{Y}_{\omega }+{D}_{\omega }+{S}_{\omega }\end{array}$ (4)

4. 实验结果与分析

Table 1. Vocal cord length of 0.108 cm

Table 2. Vocal cord length of 0.308 cm

(i) (ii) (iii) (a) (i) (ii) (iii) (b) (i) (ii) (iii) (c) (i) (ii) (iii) (d) (i) (ii) (iii)(e)

Figure 3. Surface pressure distribution of vocal cords corresponding to different vocal cords lengths. (a) 0.01 cm and (b) 0.02 cm, (i) 0.108 cm, (ii) 0.308 cm, (iii) 0.908 cm; (c) 0.04 cm and (d) 0.08 cm, (i) 0.108 cm, (ii) 0.308 cm, (iii) 0.908 cm; (e) 0.16 cm, (i) 0.108 cm, (ii) 0.308 cm, (iii) 0.908 cm

Table 3. Vocal cord length of 0.908 cm

5. 结论

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