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1. 总参陆航部 装备发展办公室, 北京 100012;
2. 北京航空航天大学 航空科学与工程学院, 北京 100191

Simulation of heating control law of electro-thermal deicing of helicopter rotor blade
Fu Jianping1, Zhuang Weiliang2, Yang Bo2, Chang Shinan2
1. Equipment Development Office, Army Aviation Department, Beijing 100012, China;
2. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:The work mechanism of the electro-thermal anti/deicing system is very complex as it is related to the coupled heat transfer between the electro-thermal and the external heat flux, i.e., the convective heat transfer and phase transition heat transfer, and the data available is extremely limited. In order to explore the mechanism of the heat transfer of the electro-thermal anti/deicing mode, a two-dimensional electro-thermal deicing model was established based on the Messinger model and improved enthalpy method. The heat transfer between the icing surface and air flow, phase changes of melting and icing were coupled in the current model. The control volume method was used to discretize the differential equations, and the methods of TDMA (tri-diagonal matrix algorithm) & ADI (alternating direction implicit) were used to solve the linear equations, and then the temperature distribution on the deicing surface was finally obtained as well as the heat transfer mechanism was presented. The effects of the electric heating method and the heating flux on the temperature distribution were analyzed in different icing conditions. The results show that high efficient utilization of the electro-thermal deicing system and the flight safety guarantee can be achieved by adjusting the heat flux density and distribution and the control law of heating time properly.
Key words: phase-change heat transfer     electro-thermal deicing     numerical simulation     electro-heating control law     heat flux

 图 1 电热除冰系统加热器示意图Fig. 1 Electro-thermal deicing system schematic diagram

1) 系统各层材料物性参数(密度、导热系数、比热容等)不随温度变化;

2) 冰(水)层及固体各层之间接触良好,忽略接触热阻;

3) 蒙皮附近一定厚度的冰层融化后冰层脱落,这个厚度一般大于蒙皮表面的粗糙度,本文取为0.15mm;

4) 采用改进的焓法模型来模拟积冰的融化过程,即积冰融化的相变过程发生在很小的温度间隔内(0.02℃).

1) 外表面对流换热为

2) 内表面对流换热为

3) 计算域左右边界为绝热边界条件：

2 方程求解 2.1 外表面结冰热质平衡方程求解

TDMA基于高斯消元法,特别适合求解由导热型微分方程离散得到的代数方程组构造的系数矩阵.

P1，Q1可以由左端点的离散方程来确定:

 图 2 直角坐标系下的网格系统Fig. 2 Grid system in the Cartesian coordinate

ke,kw,kn,ks分别是控制体界面上的当量导热系数,用调和平均法确定.

TP,TN和TS是第n轮迭代待求解的未知值;而TE,TW是第n－1轮迭代已解出的已知值,将aETE(n－1)及aWTW(n－1)并入常数项b中,于是式(23)就成为

 图 3 块迭代法示意图Fig. 3 Schematic block iterative method
3 算例分析 3.1 计算条件

 t∞/℃ H/km V∞/(m/s) P/kPa Α/ (°) MVD/μm LWC/(g/m3) -10 4.56 131.66 57.3 5.4 15 0.6 -20 6.69 172.17 42.9 4.2 15 0.3 -30 1.52 129.05 84.4 2.3 15 0.2
 注：MVD—水滴平均容积直径；LWC—液态水含量.

 名称 厚度/mm 导热系数/(W/(m·K)) 热容/(J/(kg·K)) 密度/(kg/m3) 结构底层 2.13 115 963 2800 内绝热层 1.87 0.38 963 1760 加热层 0.26 13.2 448 8250 外绝热层 0.28 0.38 964 1760 磨损层 0.56 23.4 502 7750 水 0.55 4174 1000 冰 2.45 2102 919.5

 加热条编号 起始位置/mm 终止位置/mm A -9.50 9.50 B 9.60 34.90 C -34.90 -9.60 D 35.00 60.30 E -60.30 35.00 F 60.40 98.50 G -98.50 -60.40

 控制律编号 热流密度/(kW/m2) 加热时间/s 冷却时间/s 1 10 10 20 2 20 10 20 3 20 20 20 4 40 20 90

 控制律编号 A B C D E F G 1 40 40 40 40 40 40 40 2 40 30 30 20 20 10 10 3 40 30 30 20 20 20 20
3.2 计算结果及分析

 图 4 模拟冰形Fig. 4 Simulated ice shape

1) 加热规律对驻点处温度变化的影响.

 图 5 加热热流密度10kW/m2加热10s冷却20sFig. 5 Heat flux 10kW/m2 heating 10s cooling 20s
 图 6 加热热流密度20kW/m2加热10s冷却20sFig. 6 Heat flux 20kW/m2 heating 10s cooling 20s
 图 7 加热热流密度20kW/m2加热20s冷却20sFig. 7 Heat flux 20KW/m2 heating 20s cooling 20s
 图 8 加热热流密度40kW/m2加热20s冷却90sFig. 8 Heat flux 40kW/m2 heating 20s cooling 90s

2) 加热热流密度对除冰表面温度的影响.

 图 9 加热时间段结束时除冰表面温度Fig. 9 Ice surface temperature at the end of the heating period
4 结 论

1) 设计合理的加热热流密度及其分布,不仅可以加快相应时间,减少系统总能量消耗,更可以使除冰表面温度分布更加均匀,避免了局部温度过高造成的能量浪费,使系统更高效地工作.

2) 在确定加热热流密度的前提下,应合理设 计加热、冷却时间,使系统既能有效工作,又尽可能地节省能量.

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#### 文章信息

Fu Jianping, Zhuang Weiliang, Yang Bo, Chang Shinan

Simulation of heating control law of electro-thermal deicing of helicopter rotor blade

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(9): 1200-1207.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0551