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摘要:
冰晶在压气机内部发生融化，容易造成叶片结冰，深入分析冰晶融化特性对研究压气机冰晶结冰规律具有重要意义。基于压气机一维气动特性，提出一种冰晶融化率的快速计算方法，并进行验证。以某大涵道比涡扇发动机的低压压气机为研究对象，分析冰晶粒径和环境温度对等粒径球形冰晶融化特性的影响。结果表明：冰晶粒径增加导致冰晶融化的起始位置有向低压压气机后面级移动的趋势，冰晶粒径减小或环境温度增加导致冰晶融化速率增大。在此基础上突破等粒径球形冰晶假设，分别考虑冰晶形状和粒径分布，并分析非球形冰晶的球形度和球形冰晶的粒径分布对冰晶融化特性的影响。结果表明：球形度在一定范围内对冰晶融化率有影响，当球形度在0.710～0.958之间时，随着球形度的增大，冰晶融化率减小；相比球形度，非球形冰晶的等效直径对冰晶融化率的影响更为显著；当冰晶的平均体积直径(MVD)不变时，粒径分布的不同导致压气机内同一位置的冰晶融化率偏差最大可达0.205；对于MVD相同而变异系数不同的粒径分布，其融化特性曲线前半部分由小粒径组分冰晶的融化占主导，变异系数较大的分布对应的融化率相对较高，后半部分由大粒径组分冰晶的融化占主导，变异系数较小的分布对应的融化率相对较高。
Abstract:The melting of ice crystals in the compressor leads to ice formation on the blades. It is of great significance to analyze the ice crystal melting characteristics to study the ice crystal icing in the compressor. Based on the one-dimensional aerodynamic characteristics of the compressor, a rapid method for calculating the ice crystal melting ratio was developed and validated. A low-pressure compressor of a turbofan engine with a large bypass ratio was selected to study the influence of ice crystal size and ambient temperature on the ice crystal melting characteristics at the same particle size. The results show that the initial position of ice crystal melting tends to move to the rear stage of the low-pressure compressor with the increase in ice crystal size, and the decrease in ice crystal size or the increase in ambient temperature leads to the increase in ice crystal melting ratio. On this basis, the hypothesis of spherical ice crystals with equal particle size is broken through, and the influence of sphericity of non-spherical ice crystals and the particle size distribution of spherical ice crystal on the melting characteristics were analyzed by considering ice crystal shape and particle size distribution. The results demonstrate that the sphericity has an effect on the ice crystal melting ratio within a certain range. When the sphericity is between 0.710 and 0.958, the ice crystal melting ratio decreases with the increase in sphericity. Compared with the sphericity, the equivalent diameter of non-spherical ice crystals has a more significant effect on the ice crystal melting ratio. When the mean volume diameter (MVD) of the ice crystal is constant, the difference in particle size distribution leads to the maximum deviation of 20.5% in the ice crystal melting ratio at the same position in the compressor. For the particle size distributions with the same MVD but different coefficients of variation, in the front half of the ice crystal melting characteristic curve, the melting of small-sized ice crystals is dominant, and the particle size distribution with a larger coefficient of variation has a relatively higher melting ratio. However, in the latter part, the melting of large-sized ice crystals is dominant, and the particle size distribution with a smaller coefficient of variation has a relatively higher melting ratio.
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Key words:
- compressor /
- melting characteristic /
- ice crystal melting ratio /
- sphericity /
- Langmuir distribution
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图 5 某大涵道比涡扇发动机低压压气机
Figure 5. Low-pressure compressor of turbofan engine with large bypass ratio
图 6 巡航阶段不同粒径冰晶融化特性
Figure 6. Ice crystal melting characteristics for different particle sizes at cruising phase
图 7 下降阶段不同粒径冰晶融化特性
Figure 7. Ice crystal melting characteristics for different particle sizes at descent phase
图 9 不同球形度冰晶融化特性
Figure 9. Ice crystal melting characteristics for different sphericities
图 10 不同纵横比冰晶融化特性
Figure 10. Ice crystal melting characteristics for different aspect ratios
图 11 多粒径冰晶群融化过程示意图
Figure 11. Melting process of ice crystals with multiple particle sizes
图 12 MVD=7 μm时，不同组分冰晶融化特性
Figure 12. Ice crystal melting characteristics for different components when MVD = 7 μm
图 13 MVD =7 μm时，不同粒径分布的融化特性
Figure 13. Melting characteristics for different particle size distributions when MVD = 7 μm
图 14 MVD =10 μm时，B分布的粒径组分
Figure 14. Proportion of components for B distribution whenMVD = 10 μm
图 15 不同粒径分布的冰晶融化特性
Figure 15. Ice crystal melting characteristics for different particle size distributions
表 1 巡航阶段计算工况
Table 1. Cases for cruising phase
工况 H /m T /K d /μm IWC/(g·m−3) CP01 10700 ISA +10 3 2 CP02 10700 ISA +10 5 2 CP03 10700 ISA +10 8 2 CP04 10700 ISA +10 11 2 CP05 10700 ISA +10 25 2 CP06 10700 ISA +20 3 2 CP07 10700 ISA +20 5 2 CP08 10700 ISA +20 8 2 CP09 10700 ISA +20 11 2 CP10 10700 ISA +20 25 2 
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表 2 下降阶段计算工况
Table 2. Cases for descent phase
工况 H/m T/K d/μm IWC/(g·m−3) DP01 4700 ISA +10 3 2 DP02 4700 ISA +10 5 2 DP03 4700 ISA +10 8 2 DP04 4700 ISA +10 11 2 DP05 4700 ISA +10 25 2 DP06 4700 ISA +20 3 2 DP07 4700 ISA +20 5 2 DP08 4700 ISA +20 8 2 DP09 4700 ISA +20 11 2 DP10 4700 ISA +20 25 2
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表 3 不同球形度计算工况
Table 3. Cases for different sphericities
工况 a/μm b/μm E dp /μm Φ Φ⊥ NS5-1 5.724 5.724 1 5.724 1 NS5-2 7.5 2.22 0.296 5.724 0.958 0.582 NS5-3 10 1.25 0.125 5.724 0.915 0.327 NS5-4 15 0.555 0.037 5.724 0.710 0.145 NS5-5 20 0.3125 0.015 5.724 0.555 0.081 NS8-1 8.013 8.013 1 8.013 1 NS8-2 10.5 3.11 0.296 8.013 0.958 0.582 NS8-3 14 1.75 0.125 8.013 0.915 0.327 NS8-4 21 0.777 0.037 8.013 0.710 0.145 NS8-5 28 0.4375 0.015 8.013 0.555 0.081 NS11-1 11.447 11.447 1 11.447 1 NS11-2 15 4.44 0.296 11.447 0.958 0.582 NS11-3 20 2.5 0.125 11.447 0.915 0.327 NS11-4 30 1.11 0.037 11.447 0.710 0.145 NS11-5 40 0.625 0.015 11.447 0.555 0.081
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表 4 不同纵横比计算工况
Table 4. Cases for different aspect ratios
工况 a/μm b/μm E dp/μm Φ Φ⊥ NS1 3 0.5 0.17 3.3471 0.956 0.397 NS2 3 1.0 0.33 4.5428 0.909 0.630 NS3 3 3.0 1.0 5.7235 0.763 1.029 NS4 3 4.5 1.5 6.5518 0.655 0.899 NS5 3 6.0 2.0 7.2112 0.577 0.816 NS6 3 9.0 3.0 8.2548 0.472 0.713 NS7 3 18.0 6.0 10.4004 0.320 0.566
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表 5 MVD=7 μm的Langmuir分布
Table 5. Langmuir distributions for MVD = 7 μm
占比/% 粒径/μm B分布 C分布 D分布 E分布 5 3.92 2.94 2.17 1.61 10 5.04 4.27 3.64 3.08 20 5.88 5.39 4.97 4.55 30 7.00 7.00 7.00 7.00 20 8.19 8.82 9.59 10.36 10 9.24 10.57 12.18 14 5 10.43 12.67 15.54 18.97
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表 6 Langmuir分布的变异系数
Table 6. Coefficient of variation for Langmuir distribution
B分布 C分布 D分布 E分布 0.22 0.33 0.46 0.61
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表 7 MVD =5 μm的Langmuir分布
Table 7. Langmuir distributions for MVD = 5 μm
占比/% 粒径/μm B分布 C分布 D分布 E分布 5 2.8 2.1 1.55 1.15 10 3.6 3.05 2.6 2.2 20 4.2 3.85 3.55 3.25 30 5 5 5 5 20 5.85 6.3 6.85 7.4 10 6.6 7.55 8.7 10 5 7.45 9.05 11.1 13.55
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表 8 MVD =10 μm的Langmuir分布
Table 8. Langmuir distributions for MVD = 10 μm
占比/% 粒径/μm B分布 C分布 D分布 E分布 5 5.6 4.2 3.1 2.3 10 7.2 6.1 5.2 4.4 20 8.4 7.7 7.1 6.5 30 10 10 10 10 20 11.7 12.6 13.7 14.8 10 13.2 15.1 17.4 20 5 14.9 18.1 22.2 27.1
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表 9 MVD =15 μm的Langmuir分布
Table 9. Langmuir distributions for MVD = 15 μm
占比/% 粒径/μm B分布 C分布 D分布 E分布 5 8.4 6.3 4.65 3.45 10 10.8 9.15 7.8 6.6 20 12.6 11.55 10.65 9.75 30 15 15 15 15 20 17.55 18.9 20.55 22.2 10 19.8 22.65 26.1 30 5 22.35 27.15 33.3 40.65
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