Applicability analysis of Sivells' method in nozzle designwith high Mach number and low total pressure
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摘要:
目前高超声速轴对称型面喷管广泛采用Sivells方法进行无黏型面设计，通过求解轴对称的von Kármán动量方程进行边界层修正。该方法在常规高超声速风洞、激波风洞等的高马赫数、高总压条件下已成功应用，但鲜有在高马赫数、低总压条件下的应用研究。在低总压条件下，采用该方法设计了马赫数6、8、10、12的轴对称型面喷管，通过数值模拟分析流场结构，并进行试验验证；模拟了喷管射流流场，通过对射流流场进行结构分析，判断设计方法的适用性。研究结果表明：马赫数6、8喷管流场与设计基本一致，射流流场品质较好，适合开展风洞试验；马赫数10、12喷管流场局部过度膨胀，马赫数高于设计值，其中马赫数10喷管的射流流场品质较好，马赫数12喷管的射流流场品质下降显著且马赫数轴向梯度增大。因此，在高马赫数、低总压条件下，Sivells设计方法仍适用于马赫数6、8喷管，马赫数10喷管处于临界状态，而不适用于马赫数12喷管。
Abstract:At present, the Sivells' method is widely used for the design of the inviscid hypersonic axisymmetric nozzle contour. And then, the nozzle contour viscous correction is performed by solving the axisymmetric momentum equation. This design procedure is validated by nozzles in conventional hypersonic wind tunnels and shock wind tunnels, which are operated under high Mach number and high total pressure conditions. Meanwhile, there are few validation studies of this procedure under high Mach number and low total pressure conditions. In this study, the nozzle design procedure based on the Sivells' method is used for Mach 6, 8, 10, and 12 nozzle contour design under the low total pressure condition. Furthermore, in order to analyze nozzle flowfields, numerical simulation and wind tunnel experiment are carried out. It can be found that, the flowfields in Mach 6 nozzle and Mach 8 nozzle are consistent with expectation and the jet flowfields are so good that are suitable for test. In contrast, there are some over-expanded areas in the flowfields of Mach 10 nozzle and Mach 12 nozzle, which results in higher Mach number than expectation in those areas. The jet flowfield quality of Mach 10 nozzle is better than that of Mach 12 nozzle. It can be concluded that, under the condition of low total pressure, the Sivells' method still works well for Mach 6 nozzle and Mach 8 nozzle design. Meanwhile, the method is less effective when applied to the Mach 10 nozzle and Mach 12 nozzle design.
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Keywords:
- Sivells' method /
- high Mach number /
- low total pressure /
- nozzle flowfield /
- jet flowfield /
- axisymmetric nozzle
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图 5 马赫数10喷管马赫数等值线分布图
Fig. 5 Mach number isoline distribution diagram of Mach 10 nozzle
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图 6 马赫数12喷管马赫数等值线分布图
Fig. 6 Mach number isoline distribution diagram of Mach 12 nozzle
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图 8 Φ0.3米高超声速低密度风洞结构图
Fig. 8 Structure chart of Φ0.3 m hypersonic low density wind tunnel
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图 9 喷管轴线马赫数分布测量探针
Fig. 9 Test probe used to measure Mach Number distribution of the nozzle axis
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图 10 喷管轴线马赫数分布测量装置安装
Fig. 10 Installation of measuring equipment for Mach number distri-bution on nozzle axis
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图 11 喷管出口马赫数分布与总温的关系曲线
Fig. 11 Relationship between the pressure distribution of the nozzle exit and the total temperature
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图 12 喷管轴线马赫数分布测量结果与数值模拟结果对比
Fig. 12 Contrast between the test result of Mach Number distribution of the nozzle and the numerical simulation
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图 13 马赫数6喷管及射流马赫数等值线分布图
Fig. 13 Mach number isoline distribution diagram of Mach 6 nozzle and the jet flow
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图 14 马赫数8喷管及射流马赫数等值线分布图
Fig. 14 Mach number isoline distribution diagram of Mach 8 nozzle and the jet flow
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图 15 马赫数10喷管及射流马赫数等值线分布图
Fig. 15 Mach number isoline distribution diagram of Mach 10 nozzle and the jet flow
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图 16 马赫数12喷管及射流马赫数等值线分布图
Fig. 16 Mach number isoline distribution diagram of Mach 12 nozzle and the jet flow
表 1 马赫数6～12喷管设计参数
Table 1 Design parameters of Mach 6–12 nozzles
设计
马赫数p0/MPa T0/K 入口半径
/mm6 0.3 288 100 8 0.9 366 45 10 1.4 502 30 12 2.0 654 30 
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表 2 马赫数6～12喷管设计结果特征参数
Table 2 Characteric parameters of Mach 6–12 nozzles
设计
马赫数入口段长度
/mm喉道半径
/mm扩张段长度
/mm6 200 18.366 1344 8 90 9.203 1518 10 60 5.054 1572 12 60 2.965 1564
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表 3 喷管轴线马赫数典型参数
Table 3 Characteric parameters of nozzle axis
设计
马赫数出口中心点
马赫数轴线最高
马赫数高于出口中心点
马赫数的区域/mm6 6.188 6.293 x = 603～756，
x = 882～1249 8 8.293 8.582 x = 596～ 1518 10 10.408 11.185 x = 592～ 1572 12 12.484 14.076 x = 509～ 1564
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表 4 总压1 MPa情况下喷管轴线马赫数分布测量结果
Table 4 Mach Number distribution on the nozzle axis when the total pressure is 1 MPa
x/mm 994 1014 1064 1114 1164 1194 1214 1264 1314 1364 1414 1464 1514 1564 T0 = 773 K 12.67 12.60 12.44 12.37 12.35 12.37 12.35 12.24 11.88 11.72 11.68 11.57 11.57 11.57 T0 = 593 K 12.95 12.91 12.87 12.91 13.03 12.99 13.02 12.71 12.61 12.55 12.46 12.44 12.42 12.33
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表 5 马赫数 6～12喷管及射流流场模拟基本参数
Table 5 Simulation parameters of Mach 6–12 nozzles and freestream
设计马赫数 p0/MPa 轴线最高马赫数 T0/K 6 0.3 6.293 288 8 0.9 8.582 398 10 1.4 11.185 578 12 2.0 14.076 801
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表 6 马赫数6～12喷管及射流流场主要数值模拟结果
Table 6 Major numerical simulation result of Mach 6–12 nozzles
设计
马赫数喷管出口截面 每200 mm的
马赫数轴向梯度核心区直径/mm 马赫数最大相对偏差 6 240 0.20% 0.050 8 200 0.27% 0.090 10 168 0.37% 0.184 12 150 1.31% 0.257
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