﻿ 圆弧面动态空气喷涂数值模拟
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 浙江大学学报(工学版)  2018, Vol. 52 Issue (12): 2406-2413  DOI:10.3785/j.issn.1008-973X.2018.12.019 0

### 引用本文 [复制中英文]

dx.doi.org/10.3785/j.issn.1008-973X.2018.12.019
[复制中文]
CHEN Wen-zhuo, CHEN Yan, ZHANG Wei-ming, HE Shao-wei, LI Bo, JIANG Jun-ze. Numerical simulation for dynamic air spray painting of arc surfaces[J]. Journal of Zhejiang University(Engineering Science), 2018, 52(12): 2406-2413.
dx.doi.org/10.3785/j.issn.1008-973X.2018.12.019
[复制英文]

### 作者简介

orcid.org/0000-0003-0980-5166.
E-mail：voldemort@yeah.net.

### 通信联系人

orcid.org/0000-0002-1624-3846.
E-mail: yansohucom@sohu.com
.

### 文章历史

Numerical simulation for dynamic air spray painting of arc surfaces
CHEN Wen-zhuo , CHEN Yan , ZHANG Wei-ming , HE Shao-wei , LI Bo , JIANG Jun-ze
Department of Petroleum, Army Logistics University, Chongqing 401331, China
Abstract: A paint deposition model was established comprising a two-phase spray flow field model and an impinging and sticking model based on the Euler-Euler approach. The control domain for spray painting of the outer and inner arc surfaces and a plane surface were divided into moving region and stationary region, where the calculation meshes were generated, respectively. The spring smoothing model coupled with the region remeshing model was adopted to achieve the dynamic change of the meshes in the moving regions. Based on the finite volume method, the model was discretized by the second order upwind scheme and the discretized equations were solved by the PC-SIMPLE algorithm. The results of the spray field simulation show that the spray flow field is flattened in Y direction and spreads along the X direction by the impact of the air stream provided by the fan holes, and the spray field slightly tilts back away from the spray gun due to the motion of the spray gun. The results of the paint thickness distribution show that the maximum value of the film thickness distribution on the outer arc surface is smaller than that on the flat plane, while that on the inner arc surface is bigger than that on the flat plane; the film width on the inner arc surface is larger than that on the flat plane, while that on the outer arc surface is smaller than that on the flat plane. The simulated results are in good agreement with the experiments, which verifies the feasibility of the proposed models for the numerical simulation of dynamic spray painting.
Key words: arc surface    spray painting    two-phase flow    computational fluid dynamics (CFD)    dynamic mesh model    numerical simulation

1 喷涂成膜模型 1.1 喷雾流场模型 1.1.1 两相流基本控制方程

1）质量守恒方程为

 $\frac{{\partial {\alpha _q}{\rho _q}}}{{\partial t}} + {\nabla} \cdot ({\alpha _q}{\rho _q}{{{v}}_q}) = 0.$ (1)

2）动量守恒方程为

 $\begin{split}&\frac{\partial }{{\partial t}}\left( {{\alpha _q}{\rho _q}{{{v}}_q}} \right) + \nabla \cdot ({\alpha _q}{\rho _q}{{{v}}_q}{{{v}}_q}) = \\ &\quad - {\alpha _q}\nabla p + \nabla \cdot {\tau _q} + {\alpha _q}{\rho _q}{{g}} + {F^{{\text{td}}}}\!\!\!\!\!\!{_{q}} + {{{F}}_q} . \end{split}$ (2)

 ${{{F}}_{\rm{d}}} = 0.75{{\rm{C}}_{\rm{D}}}{\alpha _q}{\rho _q}\left| {{{{v}}_p} - {{{v}}_q}} \right|\left( {{{{v}}_p} - {{{v}}_q}} \right).$ (3)

1.1.2 湍流模型

 ${\mu _{\rm{t}}} = \rho {{\rm{C}}_\mu }\frac{{{k^2}}}{\varepsilon }.$ (4)

 $\begin{split}& \frac{\partial }{{\partial t}}\left( {{\rho _{\rm{m}}}k} \right) + \nabla \cdot \left( {{\rho _{\rm{m}}}{{{v}}_{\rm{m}}}k} \right) =\\ & \quad\nabla \cdot \left( {\frac{{{\mu _{{\rm{t,m}}}}}}{{{\sigma _k}}}\nabla k} \right) + {G_{k,{\rm{m}}}} - {\rho _{\rm{m}}}\rho + {\varPi _{{k_{\rm{m}}}}}\end{split}$ (5)
 $\begin{split} \frac{\partial }{{\partial t}}&\left( {{\rho _{\rm{m}}}\varepsilon } \right) + \nabla \cdot \left( {{\rho _{\rm{m}}}{{{v}}_{\rm{m}}}\varepsilon } \right) = \nabla \cdot \left( {\frac{{{\mu _{{\rm{t,m}}}}}}{{{\sigma _\varepsilon }}}\nabla \varepsilon } \right) + \\ &\frac{\varepsilon }{k}\left( {{{\rm{C}}_{{\rm{1\varepsilon }}}}{G_{k,{\rm{m}}}} - {{\rm{C}}_{2\varepsilon }}{\rho _{\rm{m}}}\varepsilon } \right) + {\varPi _{{\varepsilon _{\rm{m}}}}}. \end{split}$ (6)

1.2 碰撞黏附模型 1.2.1 液相沉积模型

 ${\dot m_{\rm{s}}} = {\alpha _{\rm{d}}}{\rho _{\rm{d}}}{v_{{\rm{dn}}}}A.$ (7)

 ${\dot {{q}}_{\rm{s}}} = {\dot m_{\rm{s}}}{{{v}}_{\rm{d}}}.$ (8)
1.2.2 液膜控制方程

 $\frac{{\partial h}}{{\partial t}} + {\nabla _{\rm{S}}} \cdot (h \cdot {{{v}}_{\rm{l}}}) = \frac{{{{\dot m}_{\rm{s}}}}}{{{\rho _{\rm{l}}}}}.$ (9)

 $\frac{{\partial h{{{v}}_{\rm{l}}}}}{{\partial t}} + {\nabla _{{{\rm S}}}} \cdot (h{{{v}}_{{l}}}{{{v}}_{{l}}}) = - \frac{{h{\nabla _{\rm{S}}}{{{p}}_{\rm{1}}}}}{{{\rho _{\rm{l}}}}} + \frac{3}{{2{\rho _{\rm{l}}}}}{{{\tau}} _{{\rm{fs}}}} - \frac{{3{\nu _{\rm{l}}}}}{h}{{{{ v}}}_{\rm{l}}} + \frac{{{{\dot {{q}}}_{\rm{s}}}}}{{{\rho _{\rm{l}}}}}.$ (10)

2 动态喷涂成膜CFD模拟 2.1 动网格模型

 图 1 喷嘴移动导致的网格动态变化 Fig. 1 Mesh dynamic change due to nozzle’s motion
2.2 动态喷涂成膜模拟计算 2.2.1 动态喷涂控制域及其计算网格

 图 2 喷枪空气喷嘴的三维模型 Fig. 2 3D geometric model of the air spray gun’s nozzle

 图 3 平面动态喷涂控制域划分 Fig. 3 Division of control domain for dynamically spray painting flat wall

 图 4 圆弧面动态喷涂控制域划分示意图 Fig. 4 Division of control domain for spray painting arc surfaces with moving paint nozzle
2.2.2 模拟条件和参数设定

2.3 计算结果与分析 2.3.1 喷雾流场

 图 5 圆弧面外壁轴向动态喷涂液相速度分布 Fig. 5 Velocity distribution of liquid phase of axially spray painting the outer arc surface with moving paint nozzle

 图 6 圆弧面内壁轴向动态喷涂液相速度分布 Fig. 6 Velocity distribution of liquid phase of axially spray painting inner arc surface with moving paint nozzle
2.3.2 涂膜厚度分布

 图 7 圆弧面内、外壁涂膜厚度分布云图 Fig. 7 Film thickness distribution contours on outer and inner arc surfaces

 图 8 外壁轴向喷涂的截面涂膜厚度 Fig. 8 Sectional film thickness of axial external spray painting
2.3.2 涂膜厚度分布

 图 9 不同形面的涂膜平均厚度分布 Fig. 9 Average film thicknesses on different surfaces

3 动态喷涂实验与分析

 图 10 平面喷涂涂膜厚度模拟结果与实验结果 Fig. 10 Simulated and measured film thickness results for spray painting flat wall

 图 11 圆弧面轴向喷涂涂膜厚度模拟结果与实验结果 Fig. 11 Simulated and measured film thickness results for axially spray painting arc surfaces
4 结　论

（1）在扇面控制孔气流的冲击下，喷雾流场在Y方向被压扁，在X方向扩张. 由于喷枪的移动，喷雾流场向喷枪移动的后方略微倾斜.

（2）圆弧面内壁、外壁轴向喷涂涂膜厚度分布与平面喷涂涂膜厚度分布有一定的差别：圆弧面内壁喷涂的最大涂层厚度（74.5 μm）大于平面喷涂（67.7 μm），外壁喷涂的最大平面喷涂涂层厚度（61.9 μm）小于平面喷涂；圆弧面内壁喷涂的涂膜宽度（23.2 cm）大于平面喷涂（20.0 cm），外壁喷涂的涂膜宽度（21.2 cm）也大于平面喷涂.

（3）通过对比试验和仿真得到的喷雾图形和涂层厚度分布，证实了本研究所建立的喷涂成膜模型用于研究圆弧面喷涂喷雾流场特性是可行的.

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