﻿ 分体冷却变压器的有限元二维热学模型仿真与分析
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 山东大学学报(工学版)  2017, Vol. 47 Issue (6): 63-69  DOI: 10.6040/j.issn.1672-3961.0.2017.570 0

### 引用本文

WEI Bengang, GUO Ruochen, HUANG Hua, WANG Zhen, LIU Pengcheng, ZHANG Yuying, LI Kejun, LOU Jie. Simulation and analysis of two dimensional temperature field of the discrete cooling system transformer based on the finite element method[J]. Journal of Shandong University (Engineering Science), 2017, 47(6): 63-69. DOI: 10.6040/j.issn.1672-3961.0.2017.570.

### 文章历史

1. 国网上海市电力公司电力科学研究院, 上海 200437;
2. 山东大学电气工程学院, 山东 济南 250061

Simulation and analysis of two dimensional temperature field of the discrete cooling system transformer based on the finite element method
WEI Bengang1, GUO Ruochen2, HUANG Hua1, WANG Zhen2, LIU Pengcheng2, ZHANG Yuying2, LI Kejun2, LOU Jie2
1. Electric Power Research Institute, State Grid Shanghai Municipal Electric Power Company, Shanghai 200437, China;
2. School of Electrical Engineering, Shandong University, Jinan 250061, Shandong, China
Abstract: Discrete cooling transformers were mainly applied when building underground substations in urban cities, but there was little research about the heat radiation of discrete cooling transformers. The finite element method was used to simulate the temperature field of discrete transformer, and 2D model was established in FLUENT.The temperature field data from simulation were compared with filed measured ones to testify the validity of the 2D model. The influence of environment temperature and pipe wall thickness was analyzed to provide references to optimum structure.
Key words: discrete cooling    transformer    two dimensional model    the finite element method    temperature field
0 引言

1 分体式变压器的结构及传热分析 1.1 上下分体式变压器的结构

 图 1 220 kV上下分体冷却变压器 Figure 1 Split type cooling transformer of 220 kV
1.2 变压器热源

 $P = {P_0} + {P_k},$ (1)

 $q = P/V,$ (2)

1.3 散热方式及热传递过程

(1) 绕组和铁芯内部产生的热能, 通过热传导传到其表面, 绕组和铁芯表面和周围变压器油存在温度差, 以对流的方式将热能传递至变压器油[13];

(2) 变压器油温度升高, 密度变小, 油会向上流动, 通过与地上散热器连接的管道, 在管道内以热传导的方式散出一些热量, 之后热油进入地上的散热器;

(3) 地上的散热器通过热辐射以及空气的自然对流将热量散出;

(4) 内部的变压器油经过散热器后, 温度降低, 密度变大, 在重力的作用向下流动, 经过管道流入地下的变压器主体, 从而完成整个热循环过程[14-15]

2 热学模型的建立与仿真计算

 图 2 变压器散热示意图 Figure 2 Radiating of transformers

(1) 质量守恒方程

 $\frac{{\partial \rho }}{{\partial \tau }} + \frac{{\partial \rho u}}{{\partial x}} + \frac{{\partial \rho v}}{{\partial y}} + \frac{{\partial \rho w}}{{\partial z}} = 0。$ (3)

(2) 动量守恒方程

 $\rho \frac{{\partial u}}{{\partial \tau }} + u\frac{{\partial u}}{{\partial x}} + v\frac{{\partial u}}{{\partial y}} + w\frac{{\partial u}}{{\partial z}} = {F_x} - \frac{{\partial P}}{{\partial x}} + \eta \left( {\frac{{{\partial ^2}u}}{{\partial {x^2}}} + \frac{{{\partial ^2}u}}{{\partial {y^2}}} + \frac{{{\partial ^2}u}}{{\partial {z^2}}}} \right),$ (4)
 $\rho \frac{{\partial v}}{{\partial \tau }} + u\frac{{\partial v}}{{\partial x}} + v\frac{{\partial v}}{{\partial y}} + w\frac{{\partial v}}{{\partial z}} = {F_y} - \frac{{\partial P}}{{\partial y}} + \eta \left( {\frac{{{\partial ^2}v}}{{\partial {x^2}}} + \frac{{{\partial ^2}v}}{{\partial {y^2}}} + \frac{{{\partial ^2}v}}{{\partial {z^2}}}} \right),$ (5)
 $\rho \frac{{\partial w}}{{\partial \tau }} + u\frac{{\partial w}}{{\partial x}} + v\frac{{\partial w}}{{\partial y}} + w\frac{{\partial w}}{{\partial z}} = {F_z} - \frac{{\partial P}}{{\partial z}} + \eta \left( {\frac{{{\partial ^2}w}}{{\partial {x^2}}} + \frac{{{\partial ^2}w}}{{\partial {y^2}}} + \frac{{{\partial ^2}w}}{{\partial {z^2}}}} \right)。$ (6)

(3)能量守恒方程

 $\frac{{\partial t}}{{\partial \tau }} + u\frac{{\partial t}}{{\partial x}} + v\frac{{\partial t}}{{\partial y}} + w\frac{{\partial t}}{{\partial z}} = \frac{\lambda }{{\rho {c_p}}}\left( {\frac{{{\partial ^2}t}}{{\partial {x^2}}} + \frac{{{\partial ^2}t}}{{\partial {y^2}}} + \frac{{{\partial ^2}t}}{{\partial {z^2}}}} \right),$ (7)

 ${E_b} = \sigma {T^4} = {C_0}{\left( {\frac{T}{{100}}} \right)^4},$ (8)

 ${q_1} = - {\rm{ \mathsf{ λ} }}\frac{{{\rm{d}}t}}{{{\rm{d}}r}} = \frac{\lambda }{r}\;\frac{{{t_1} - {t_2}}}{{{\rm{ln}}\left( {{r_1}/{r_2}} \right)}},$ (9)

 ${{\mathit{\Phi }}_1} = 2\pi rl{q_1} = \frac{{2\pi \lambda l\left( {{t_1}-{t_2}} \right)}}{{\ln \left( {{r_2}/{r_1}} \right)}},$ (10)

 ${q_2} = h{\rm{\Delta t, }}$ (11)

 ${{\mathit{\Phi}} _2} = {q_2}A = Ah\Delta t,$ (12)

2.1 模型简化

 图 3 两个相对面试验测温点分布图 Figure 3 Distribution of temperature measuring points abouttwo opposite sides

2.2 热学计算假设

(1) 当发热与散热达到热平衡时, 铁芯、低压绕组、高压绕组以及油流的温度、速度分布不随时间变化, 变压器油的初始状态是稳态;

(2) 设定材料的密度、导热系数、比热都为常数;

(3) 单位热源均匀分布, 且为常数;

(4) 每一次模拟状态下, 外部环境的温度为常数。

2.3 边界条件

 ${N_u} = C{\left( {{G_r} \cdot {P_r}} \right)^n} = C{R_a^n},$ (13)
 ${P_r} = \frac{{{C_p} \cdot \mu }}{\lambda },$ (14)
 ${G_r} = \frac{{g\beta \Delta \theta {\rho ^2}{l^3}}}{{{\mu ^2}}},$ (15)
 ${N_u} = \frac{{h \cdot l}}{\lambda } = C{\left[ {\left( {\frac{{{C_p} \cdot \mu }}{\lambda }} \right)\left( {\frac{{g\beta \Delta \theta {\rho ^2}{l^3}}}{{{\mu ^2}}}} \right)} \right]^n},$ (16)

3 仿真及试验 3.1 仿真计算及简要分析

 图 4 变压器温度云图 Figure 4 Nephogram of transformer temperature

3.2 现场试验

 图 5 试验现场变压器 Figure 5 Transformer at field experiment

 图 6 xy面试验测温点分布图 Figure 6 Distribution of temperature measuring points onthe xy coordinate plane

3.3 仿真值与试验值对比

4 油管壁厚对变压器温度的影响

 图 7 变压器内部温度随油壁厚度变化曲线 Figure 7 The changing curve of transformer internal temperaturewith oil wall thickness

5 环境温度对变压器温度的影响

 图 8 变压器温度随环境温度变化曲线 Figure 8 Changing cure of transformer temperature with environment temperature

6 结论

(1) 鉴于变压器基本呈对称分布, 可采用二维热学模型进行分体冷却变压器的有限元温度场分布研究;

(2) 变压器油管壁厚对变压器内部温度影响呈现随壁厚增大, 先增大后减小, 再增大再减小的非线性变化规律;

(3) 环境温度对变压器内部温度影响很大, 并呈现线性关系。

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