A correction method of icing testing scaling law with dynamic effects
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摘要: 结冰相似准则是将飞行条件转换为试验参数的重要理论方法，然而现有的相似准则多基于小水滴结冰过程而提出，其在应用于大水滴的相似转换时会出现较大偏差。针对这一现状，开展考虑水滴动力学特性的结冰相似准则研究。首先，基于ONERA相似准则，融入关于水滴变形破碎和飞溅动力学特性的相似参数，提出了修正的结冰相似准则；其次，基于这两种相似准则，采用数值模拟的方法计算获得了修正前后的收集系数，并对比验证了修正方法的有效性；最后，分析两种修正方法得到的试验参数随尺寸缩比的变化情况，给出了所修正的相似准则在结冰试验中的应用建议。结果表明，本文修正方法提高了局部收集系数的吻合度，降低了收集系数平均误差和撞击极限误差，且应用该准则得到的缩比试验参数在结冰风洞的设计范围之内。该修正方法可以为过冷大水滴结冰风洞试验相似变换提供指导。Abstract: The icing scaling law is an important theoretical method for converting flight conditions into test conditions. But existing icing scaling laws are mostly based on small droplets, which can cause large errors when applied to scaling transformations of large droplets. In response to this situation, research on icing scaling law considering the dynamics of droplets was carried out. Firstly, based on the ONERA scaling laws, the scaling parameters of the droplet deformation/breakup and splash were incorporated, and the modified icing scaling law was proposed. Secondly, based on these two scaling laws, the numerical simulation method was used to calculate the collection coefficient before and after the correction. The validity of the correction method was verified. Finally, the variation of the test parameters obtained by the two correction methods with the size reduction ratio was analyzed. The application of the scaling law in the icing test was given. The results show that the proposed method improves the coincidence of the local collection coefficient and reduces the average error of the collection coefficient and the impact limit. In addition, the scaling test parameters are within the design range of the icing wind tunnel. These correction methods can provide guidance for scaling transformations in supercooled large droplets ice wind tunnel test.
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图 1 参考条件与缩比条件的局部收集系数对比
Fig. 1 Comparison of local collection coefficient reference condition and scaling condition
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图 2 流场速度比与模型尺寸缩比的关系
Fig. 2 The relationship between the flow field velocity and the scale of the model dimension
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图 3 水滴直径比与模型尺寸缩比的关系
Fig. 3 The relationship between the droplet diameter and the scale of the model dimension
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图 4 液态水含量比与模型尺寸缩比的关系
Fig. 4 The relationship between the liquid water content and the scale of the model dimension
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图 5 结冰时间比与模型尺寸缩比的关系
Fig. 5 The relationship between the freeze time and the scale of the model dimension
表 1 影响结冰过程的变量的量纲
Table 1 The dimension of the variable that affects the icing process
Variable Xb Xs ρa μa σ Dimension L4T-2 L0.75T-0.25 ML-3 ML-1T-1 MT-2 
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表 2 参考试验条件参数
Table 2 Parameters of reference condition
Parameter Case 1 Case 2 l/m 1 1 p/Pa 70 121 54 048 V/(m·s-1) 49.3 80.1 d/μm 75 160 LWC/(g·m-3) 0.5 0.5 t/min 20 10 T/℃ -20 -20
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表 3 缩比试验条件参数(Case 1)
Table 3 Parameters of scaling condition (Case 1)
Parameter Without correction πb correction πs correction l/m 0.5 0.5 0.5 p/Pa 101 325 101 325 101 325 V/(m·s-1) 41.0 93.5 50.6 d/μm 57.1 41.7 52.7 LWC/(g·m-3) 0.78 1.17 0.86 t/min 7.74 2.26 5.66 T/℃ -19.8 -20.8 -20.0
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表 4 缩比试验条件参数(Case 2)
Table 4 Parameters of scaling condition (Case 2)
Parameter Without correction πb correction πs correction l/m 0.5 0.5 0.5 p/Pa 101 325 101 325 101 325 V/(m·s-1) 58.5 146.3 131.6 d/μm 136.0 96.0 99.9 LWC/(g·m-3) 0.83 1.31 1.24 t/min 4.15 1.01 1.23 T/℃ -19.6 -21.8 -21.3
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表 5 修正前后相似准则误差
Table 5 The errors of scaling law before and after correction
Case Scaling law Errors of collection coefficient Errors of impacting limit Case 1 Without correction 13.1% 6.2% πb correction 2.3% 6.1% πs correction 9.5% 6.1% Case 2 Without correction 11.4% 17.4% πb correction 0.3% 10.2% πs correction 1.8% 10.1%
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