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摘要:
针对高超飞行器计算流体力学(CFD)仿真中网格不确定度评估缺乏工程实用方法的难点问题，提出一种便于工程实际应用的CFD数据不确定度评估方法。所提方法采用Richardson插值实现高超飞行器用网格不确定度量化评估，同时建立高超飞行器仿真网格绘制规范，进而对4套网格计算得到的气动力结果进行了网格不确定度评估和分析。分析结果表明：所提方法在马赫数为4.95和7.95时，小迎角（低于8°）范围内，对乘波体飞行器气动力系数的网格不确定度评估性能良好。同时，湍流模型对所提方法影响不明显，故该高超飞行器所用CFD网格不确定度评估技术具有良好的工程适用性，对其他飞行器网格不确定度评估有一定的借鉴和指导价值。
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关键词:
- 乘波体 /
- 不确定度评估 /
- Richardson模型 /
- 高超飞行器 /
- 计算流体力学
Abstract:Addressing the challenge of the lack of practical engineering methods for grid uncertainty assessment in computational fluid dynamics (CFD) simulations of hypersonic vehicles, this paper proposes a CFD data uncertainty assessment method that is convenient for practical engineering applications. The method utilizes Richardson interpolation to quantitatively assess grid uncertainty for hypersonic vehicles, and establishes a grid drawing specification for hypersonic vehicle simulations. Subsequently, grid uncertainty assessment and analysis are conducted on aerodynamic results obtained from four sets of grid calculations. The analysis results indicate that the proposed method performs well in assessing grid uncertainty for aerodynamic coefficients of waverider vehicles within a small angle of attack (below 8°) at Mach numbers of 4.95 and 7.95. Additionally, the turbulence model has an insignificant impact on this grid uncertainty assessment method. Therefore, the CFD grid uncertainty assessment technology used for hypersonic vehicles exhibits good engineering applicability and provides valuable reference and guidance for grid uncertainty assessment in other aircraft.
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图 1 高超飞行器用CFD网格不确定度评估流程
Figure 1. Flow of CFD grid uncertainty evaluation for hypersonic aircraft
图 3 Ma=4.95时乘波体头部压力流场随网格量变化
Figure 3. Pressure flow field at head of wave rider at Ma=4.95 as function of grid size
图 4 Ma=4.95时升力系数随网格量变化
Figure 4. Lift coefficient variation with grid quantity at Ma=4.95
图 5 Ma=4.95时俯仰力矩系数随网格量变化
Figure 5. Pitch moment coefficient variation with grid quantity at Ma=4.95
图 6 Ma=4.95时阻力系数随网格量变化
Figure 6. Resistance coefficient variation with grid quantity at Ma=4.95
图 7 Ma=4.95时激波阻力系数随网格量变化
Figure 7. Shock drag coefficient variation with grid quantity at Ma=4.95
图 8 Ma=4.95时摩擦阻力系数随网格量变化
Figure 8. Variation of friction resistance coefficient with grid quantity at Ma=4.95
图 10 Ma=4.95时俯仰力矩系数不确定度
Figure 10. Uncertainty in the pitch moment coefficient at Ma=4.95
图 12 Ma=7.95时乘波体头部压力流场随网格量变化
Figure 12. Pressure flow field at head of wave rider at Ma=7.95 as function of grid size
图 13 Ma=7.95时升力系数随网格量变化
Figure 13. Lift coefficient variation with grid quantity at Ma=7.95
图 14 Ma=为7.95时俯仰力矩系数随网格量变化
Figure 14. Pitch moment coefficient variation with grid quantity at Ma=7.95
图 15 Ma=7.95时阻力系数随网格量变化
Figure 15. Resistance coefficient variation with grid quantity at Ma=7.95
图 16 Ma=7.95时激波阻力系数随网格量变化
Figure 16. Shock drag coefficient variation with grid quantity at Ma=7.95
图 17 Ma=7.95时摩擦阻力系数随网格量变化
Figure 17. Variation of friction resistance coefficient with grid quantity at Ma=7.95
图 19 Ma=7.95时俯仰力矩系数不确定度
Figure 19. Uncertainty in the pitch moment coefficient at Ma=7.95
表 1 飞行器的计算条件
Table 1. Calculation conditions for aircraft
计算条件 来流马赫数 单位雷诺数Re/107 m−1 力矩系数参考长度L /m 气动系数参考面积Sref /m2 参考点XG 迎角/（°） 条件1 4.95 6.416 0.33529 0.0024914 0 0、2、6、8 条件2 7.95 3.016 0.33529 0.0024914 0 0、2、6、8 
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表 2 4套网格规模
Table 2. Scale of four grid sets
网格 网格量Ni 网格的特征尺度hi H1 1196800 0.009418700 H2 2196736 0.007692616 H3 4409728 0.006098121 H4 16825344 0.003902522
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表 3 Ma为4.95时H2计算结果与试验结果对比
Table 3. Comparison between H2 calculation results and experimental results at Ma=4.95
结果对比 升力系数
斜率 $ C_{L}' $纵向压心系数XP 迎角为2° 迎角为6° 迎角为8° 试验结果 0.18005 0.61811 0.62077 0.62209 计算结果 0.17945 0.60110 0.60930 0.61080
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表 4 Ma为7.95时H2计算结果与试验结果对比
Table 4. Comparison between H2 calculation results and experimental results at Ma=7.95
结果对比 升力系数
斜率 $ C_{L}' $纵向压心系数XP 迎角为2° 迎角为6° 迎角为8° 试验结果 0.14430 0.59129 0.59871 0.60118 计算结果 0.14153 0.58680 0.59670 0.59920
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