飞机结冰的不确定性量化研究进展

郝云权; 赵大志; 李伟斌; 赵炜; 陈江涛

doi:10.13224/j.cnki.jasp.20210611

飞机结冰的不确定性量化研究进展

doi: 10.13224/j.cnki.jasp.20210611

郝云权^{1, 2},
赵大志¹,
李伟斌^2,, ,,
赵炜²,
陈江涛²

1.
西南石油大学理学院，成都 610500
2.
中国空气动力研究与发展中心计算空气动力研究所，四川绵阳 621000

基金项目:

四川省科技计划项目 2021YJ0526

国家数值风洞工程

详细信息

作者简介:
郝云权（1996-），男，硕士生，主要从事飞机结冰不确定量化研究。

通讯作者:
李伟斌（1985-），男，副研究员，博士，主要从事飞机结冰特性及视觉测量研究。E⁃mail：liweibin@nudt.edu.cn

中图分类号: V211.71
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出版历程
- 收稿日期: 2021-10-25

Recent advances in uncertainty quantification research of aircraft icing

HAO Yunquan^{1, 2},
ZHAO Dazhi¹,
LI Weibin^{2,
, ,},
ZHAO Wei²,
CHEN Jiangtao²

1.
School of Sciences，Southwest Petroleum University，Chengdu 610500，China
2.
Computational Aerodynamics Institute，China Aerodynamics Research and Development Center，Mianyang Sichuan 621000，China

摘要

摘要:
为深入认识影响飞机结冰的不确定性及其研究方法，从自然条件结冰、冰风洞试验、数值模拟等方面，介绍了飞机结冰不确定性来源，以蒙特卡洛法、多项式混沌法和随机配置法等为例，系统分析了各种不确定性量化方法在计算能力、求解精度等方面的优劣。考虑飞机结冰不确定性量化处于起步时期，重点综述了数值模拟中结冰条件不确定性对冰形和气动特性的影响。从结合单步法和多步法确定最佳结冰时间步长来提升结冰计算精度和效率、对其他关键部件进行结冰不确定性量化从而为更精细化的防/除冰系统的设计提供支撑，以及通过建立高精度的代理模型来代替原本复杂的数值模拟系统以应对考虑多个不确定性因素共同作用所带来的计算挑战等多个方面，全面展望不确定性量化方法及其在飞机结冰应用中的发展方向。
- 飞机结冰 /
- 不确定性量化 /
- 蒙特卡洛法 /
- 多项式混沌法 /
- 随机配置法
Abstract:
In order to deeply understand the uncertainty affecting aircraft icing and its research methods,the sources of aircraft icing uncertainty were introduced from the aspects of natural icing,ice wind tunnel test,and numerical simulation.Taking Monte Carlo method,polynomial chaos method and random configuration method as examples,the advantages and disadvantages of various uncertainty quantification methods in calculation ability and solution accuracy were systematically analyzed.Furthermore,considering the quantification of aircraft icing uncertainty at the beginning,focus was put on the influence of icing condition uncertainty on ice shape and aerodynamic characteristics in numerical simulation.Finally,single‑step and multi‑step methods were combined to determine the best ice time step to improve the accuracy and efficiency of ice calculation,to quantify the ice uncertainty of other key components to provide support for the more refined design of ice prevention/de‑icing system,and to build a high‑precision proxy model to replace the original complex numerical simulation system for meeting the computational challenges caused by the combined action of multiple uncertainties,etc.Overall prospect of uncertainty quantification method and its development direction in aircraft icing application was presented.
- aircraft icing /
- uncertainty quantification /
- Monte Carlo method /
- polynomial chaos method /
- stochastic collocation method
注释:

1) 陈越

HTML

图 1 来流条件不确定性量化流程图

Figure 1. Flow chart of uncertainty quantification of inflow conditions

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图 2 PCE方法量化冰形不确定性对气动性能的影响流程图

Figure 2. Flow chart of PCE method to quantify the effect of ice shape uncertainty on aerodynamic performance

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图 3 来流风速不确定性量化流程图

Figure 3. Flow chart of uncertainty quantification of incoming wind speed

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图 4 霜冰算例不确定性量化分析结果^[90]

Figure 4. Uncertainty quantification analysis results of frosted ice case^[90]

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图 5 混合冰算例不确定性分析结果^[90]

Figure 5. Uncertainty quantification analysis results of a mixed ice case^[90]

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图 6 明冰算例不确定性量化分析结果^[90]

Figure 6. Uncertainty quantification analysis results of a clear ice case^[90]

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图 7 2阶元模型和HAX热修正模型的全局Sobol灵敏度指数^[94]

Figure 7. Total Sobol sensitivity indexes for 2‑order metamodel and the HAX thermal correction model^[94]

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图 8 温度的2阶元模型和HAX热修正模型的全局Sobol灵敏度指数^[94]

Figure 8. Total Sobol sensitivity indexes for 2‑order metamodel of temperature and the HAX thermal correction model^[94]

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图 11 局部灵敏度：关于不确定参数冰形状对应的升力梯度^[105]

Figure 11. Local sensitivity: ice shapes corresponding to the gradient of lift with respect to the uncertain parameters^[105]

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图 12 相应角冰高度下载荷损失的径向分布^[106]

Figure 12. Radial distribution of power loss regarding the relative ice horn hight^[106]

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表 1 常见的分布类型及其对应的正交基函数

Table 1. Common distribution types and their corresponding orthogonal basis functions

	分布	定义域	多项式基
连续型	Gaussan	（ $- \infty$ ， $\infty$ ）	Hermite
	Uniform	[b₁,b₂]	Legendre
	Gamma	[0, $\infty$ ）	Laguerre
	Beta	[b₁,b₂]	Jacobi
离散型	Binomal	{0,1,…,N}	Krawtchouk
离散型	Poisson	{0,1,2,…}	Charlier

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表 2 各阶元模型的全局Sobol灵敏度指数^[94]

Table 2. Total Sobol sensitivity indexes for each metamodel^[94]

元模型	目标输出信息	HAX Sobol指数	2PP Sobol指数
1阶元模型	在 $x_{c}$ =11.36 cm处的传热系数	$k =$ 0.239	$k =$ 0.820 $k_{s} / k =$ 0.271
		$k_{s} / k =$ 0.051
		$S_{c o r r}$ =0.787
2阶元模型	在 $x_{c}$ =14.29 cm处的传热系数	$k =$ 0.239	$k =$ 0.802 $k_{s} / k =$ 0.291
		$k_{s} / k =$ 0.050
		$S_{c o r r}$ =0.787
3阶元模型	在 $x_{c}$ =27.48 cm处的传热系数	$k =$ 0.248	$k =$ 0.756 $k_{s} / k =$ 0.341
		$k_{s} / k =$ 0.052
		$S_{c o r r}$ =0.779
4阶元模型	最大结冰厚度	$k =$ 0.326	$k =$ 0.894 $k_{s} / k =$ 0.202
		$k_{s} / k =$ 0.072
		$S_{c o r r}$ =0.682
5阶元模型	结冰延伸	$k =$ 0.166	$k =$ 0.912 $k_{s} / k =$ 0.288
		$k_{s} / k =$ 0.088
		$S_{c o r r}$ =0.882

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表 3 温度影响的全局Sobol灵敏度指数^[94]

Table 3. Total Sobol sensitivity indexes for the temperature effect^[94]

元模型	目标输出信息	HAX Sobol指数	2PP Sobol指数
2阶温度元模型	最大结冰厚度	$k =$ 0.302	$k =$ 0.750 $k_{s} / k =$ 0.170 $T$ =0.162
		$k_{s} / k =$ 0.067
		$S_{c o r r}$ =0.667
		$T$ =0.039
3阶温度元模型	结冰延伸	$k =$ 0.190	$k =$ 0.681 $k_{s} / k =$ 0.255 $T$ =0.176
		$k_{s} / k =$ 0.050
		$S_{c o r r}$ =0.784
		$T$ =0.022

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表 4 MC方法和PCE方法的统计矩比较^[104]

Table 4. Comparison of statistical moments for MC and PCE methods^［104］

要素	$C_{L, m a x}$		$α_{m a x}$ /（°）		$L / D_{m a x}$
要素	MC	PCE	MC	PCE	MC	PCE
均值	0.87	0.86	9.8	9.6	16.6	16.5
方差	0.002	0.003	0.16	0.13	4.0	4.4
偏度	-0.33	-0.37	-0.5	-0.9	0.56	0.40
峰度	2.3	2.2	2.9	2.7	3.0	2.6

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