Design of nozzle inviscid contour based on axial Mach number distribution
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摘要: 针对高超声速风洞轴对称喷管设计问题，开展了喷管扩张段无粘型面设计研究。介绍了基于预设轴线马赫数分布的直接设计方法，改进了基于面积比的轴线马赫数分布预设方法，提出了一种方便多点控制的轴线特征点分布方法。对设计喷管流场进行特征线网三角化，与数值模拟结果进行比较，并分析了影响喷管无粘型面的设计因素。表明：改进的面积比方法可以保证轴线马赫数分布预设的合理性；轴线马赫数分布、轴线上特征点分布和边界特征点数明显影响喷管无粘型面。Abstract: The supersonic inviscid contour design methods were studied for the hypersonic wind tunnel axial-symmetric nozzle. The Direct-design technique based on the axial Mach number distribution presetting was introduced, the axial Mach number distribution presetting method based on the ratio of area was improved, and a new multipoint-control characteristic point distribution method was proposed. The designed nozzle characteristic network was triangulated and compared with the numerical simulation result, and influencing factors were analyzed for the nozzle inviscid contour. Results indicate that: the feasibility of the axial Mach number distribution presetting method based on the ratio of area is guaranteed by the present improvement; the nozzle inviscid contour is significantly affected by the axial Mach number distribution, axial characteristic point distribution and the amount of characteristic points on the boundary.
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图 1 特征线推进方法 (a)往上游推进 (b)往下游推进
Figure 1. Characteristic marching method (a) march upstream (b) march downstream
图 3 基于Sivells方法预设轴线马赫数分布的特征线网
Figure 3. Characteristic network based on the Sivells’ axial Mach number distribution
图 4 不同预设方法的轴线马赫数分布(cF=3.0时)
Figure 4. Axial Mach number of different presetting methods with cF=3.0
图 5 不同预设方法的轴线马赫数分布(cF=5.57时)
Figure 5. Axial Mach number of different presetting methods with cF=5.57
图 6 轴线上马赫数大于出口马赫数时的特征线相交
Figure 6. Characteristic intersection when Mach number on axis larger then Maexit
图 7 马赫数增长过快导致的特征线相交(J点附近)
Figure 7. Characteristic intersection caused by too fast Mach number increase (near J point)
图 9 基于Sivells轴线马赫数分布预设的喷管马赫数等值线
Figure 9. Mach number contour of the nozzle designed with the Sivells’ axial Mach number distribution
图 10 基于面积比三次多项式分布预设的喷管马赫数等值线
Figure 10. Mach number contour of the nozzle designed with the cubic distribution of the ratio of area
图 11 基于面积比五次多项式分布预设的喷管马赫数等值线
Figure 11. Mach number contour of the nozzle designed with the quintic distribution of the ratio of area
图 12 基于B样条曲线马赫数预设的喷管马赫数等值线
Figure 12. Mach number contour of the nozzle designed with the B-spline Mach number distribution
图 13 不同轴线马赫数预设方法的喷管出口马赫数
Figure 13. Mach number at exit of the nozzle designed with different axial Mach number presetting methods
图 14 不同轴线马赫数预设方法的喷管出口马赫数cF=3.0
Figure 14. Mach number at exit of the nozzle designed with different axial Mach number presetting methods with cF=3.0
图 15 轴线上不同布点的特征线网和喷管型面比较
Figure 15. Comparision of characteristic networks and contours of different point distributions
图 16 不同点数的特征线网(F点附近)
Figure 16. Comparision of characteristic networks of different point numbers (near F point)
表 1 不同马赫数分布方法比较
Table 1. Comparison of different Mach number distribution methods
分布方法 计算量 可调参数 适用范围 三次多项式 低 无 短喷管 改进的三次多项式 低 a4,内部微调 短喷管 五次多项式 低 无 短喷管 面积比的多项式 中 无 长喷管 改进的面积比的多项式 中 idx，控制起点终点的马赫数增长 任意 Bezier或B样条曲线 高 dL，控制起点终点的曲线导数进而控制马赫数 任意 
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