Uncertainty quantification analysis in hypersonic aerothermodynamics due to freestream
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摘要:
通常的CFD计算都是确定性的，然而复杂工程数值模拟中必然存在误差与不确定度，分析与辨识其不确定度来源，对不确定度进行量化分析，对数值模拟可信度评估有重要意义。在高超声速飞行器气动热计算中，为获得更加可靠的气动热数据和鉴定影响气动热预测的关键因素，对返回舱开展了气动热不确定度量化分析和敏感性分析。首先选取来流速度、来流温度、壁面温度和来流密度4个不确定性输入变量，并且假定来流速度变化范围为±120 m/s（±2%），来流温度、壁面温度和来流密度变化范围为±10%。然后采用拉丁超立方抽样法生成样本，再通过热化学非平衡数值模拟方法进行气动热计算，最后分别运用基于非嵌入式多项式混沌（NIPC）的方法和基于Sobol指数的方法开展不确定度量化和敏感性分析。结果表明，在给定的输入变量不确定度的条件下，壁面热流不确定度不小于15.9%，在驻点和肩部存在峰值分别约为19.8%（0.087 MW/m2）和17.3%（0.076 MW/m2）；相比而言，在给定变化范围内壁面热流对来流密度和来流速度更为敏感，来流温度和壁面温度对热流变化不产生明显影响。
Abstract:The CFD calculation is usually deterministic. However, errors and uncertainties always exist in the numerical simulation of complex engineering. Analysis and identification of source of uncertainty, and quantification of uncertainty play important roles in assessing the credibility of simulation results. Uncertainties are generally ubiquitous in highly complex aerospace systems. To obtain more reliable aerothermodynamics prediction, the uncertainty quantification and sensitivity analysis were carried out for the returning capsule hypersonic reentry flight. First, four uncertainty input variables (freestream velocity, freestream temperature, wall temperature and freestream density) were selected, whose variation ranges are ±120 m/s (±2%), ±10%, ±10% and ±10% respectively. And the samples were generated by Latin hypercube Design. Then, the thermochemical non-equilibrium numerical simulation method was used to calculate the aerodynamic heat. Finally, methods based on non-intrusive polynomial chaos(NIPC) and Sobol index were applied to uncertainty quantification and sensitivity analysis. The results show that the wall heat flux is not less than 15.9% under the given condition of uncertainty input variable uncertainty, and the peak value of the stagnation and shoulder are about 19.8% (0.087 MW/m2) and 17.3% (0.076 MW/m2) respectively. The uncertainty of heat flux is more sensitive to freestream density and velocity, and meanwhile freestream temperature and wall temperature variations almost have no impact on heat flux.
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图 2 ELECTRE标模几何与网格示意图
Figure 2. Schematic of geometry and computational mesh of ELECTRE vehicle
图 3 ELECTRE标模壁面热流分布
Figure 3. Heat flux distribution on wall surface of ELECTRE vehicle
图 4 ELECTRE标模驻点线温度分布
Figure 4. Temperature distribution along stagnation line of ELECTRE vehicle
图 5 Apollo返回舱几何与网格示意图
Figure 5. Schematic of geometry and computational mesh of Apollo returning capsule
图 7 基准状态平动温度与压力分布
Figure 7. Translational temperature and pressure contours for baseline case
图 8 Apollo返回舱驻点线温度分布
Figure 8. Temperature distribution along stagnation line of Apollo returning capsule
图 10 壁面热流不确定度和输入变量Sobol指数分布
Figure 10. Uncertainty of wall heat flux and Sobol index distribution of input variable
图 11 驻点和肩部各输入变量对总体不确定度的相对贡献
Figure 11. Relative importance of each input variable on overall uncertainty at stagnation and shoulder
表 1 基准状态流动条件
Table 1. Flow condition of baseline state
参数 高度/km u∞/
(m·s-1)T∞/K ρ∞/
(kg·m-3)YN/YO 数值 67.3 6 040 225 9.8×10-5 0.77/0.23 
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表 2 输入变量不确定度
Table 2. Uncertainties of input variable
参数 不确定度 u∞ ±120 m/s(±2%) T∞ ±10% Tw ±10% ρ∞ ±10%
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表 3 不确定度量化结果
Table 3. Results of uncertainty quantification
量化结果 驻点SR=0 肩部SR=1 817 mm 平均值μR/(MW·m-2) 0.220 1 0.223 0 标准差σR/(MW·m-2) 0.022 3 0.019 5 2-σ区间 (0.176 4，0.263 8) (0.184 8，0.261 2) 不确定度/% 19.8 17.3
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表 4 驻点和肩部各输入变量Sobol指数
Table 4. Sobol index of each input variable at stagnation and shoulder
Sobol指数 驻点SR=0 肩部SR=1 817 mm u∞ 0.286 7 0.268 1 T∞ 0.032 5 0.000 3 Tw 0.031 2 0.003 4 ρ∞ 0.758 0 0.729 5
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