逆特征线法的适用性分析

刘传振; 孟旭飞; 白鹏

doi:10.13224/j.cnki.jasp.20220761

逆特征线法的适用性分析

doi: 10.13224/j.cnki.jasp.20220761

中国航天空气动力技术研究院，北京 100074

基金项目: 国家自然科学基金（12271266）

详细信息

作者简介:
刘传振（1989-），男，高级工程师，博士，主要从事乘波体设计方面的研究

通讯作者:
白鹏（1973-），男，研究员，博士，主要从事高超声速气动布局设计方面的研究。E-mail：backleon60@163.com

中图分类号: V211.5
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- 被引次数: 0
出版历程
- 收稿日期: 2022-10-02
- 网络出版日期: 2024-03-04

Applicability of inverse method of characteristics

China Academy of Aerospace Aerodynamics，Beijing 100074，China

摘要

摘要:
使用逆特征线法（iMoC）由给定激波形状求解轴对称流场，并研究其适用性。比较左右特征线交织和左特征线流线交织推进这两种推进方式，发现使用逆向左特征线和流线交织的方法求未知解点，操作比较简单，而且稳定性更好。将激波形状分为凹曲线和凸曲线，分别分析逆特征线法的适用性：对于凹激波形状，结合斜激波关系式证明，使用逆特征线法一般是可以求解波后流场的；对于凸激波形状，当激波角沿轴向减小过多时会发生左行特征线交叉，导致逆特征线法不适用，并进而提出在不适用的凸激波形状段，可以使用一段膨胀流代替。最后结合计算流体力学技术验证本文的方法和结论，为推进逆特征线法在乘波体和进气道设计中的应用提供理论支撑。
- 逆特征线法 /
- 轴对称 /
- 激波 /
- 膨胀流 /
- 计算流体力学
Abstract:
The inverse method of characteristics (iMoC) was employed to simulate the axisymmetric flow behind a predefined shock wave. Its applicability was also analyzed. Firstly, two marching schemes in iMoC were compared: by the interaction of the left-running and right-running characteristic lines and the interaction of the left-running characteristic line and stream line. It was found that the scheme of interacting the left-running characteristic line and stream line was simpler and more stable. The applicability of iMoC was then analyzed for the concave and convex shock shape, respectively. It was proved that iMoC can compute the flow behind the concave shock wave based on the oblique shock relations. For the convex shock wave, when the shock wave angle declined too much along the axial coordinate, the clusters of left-running characteristic lines may interact, leading to the failure of marching in iMoC. Furthermore, an expansion flow can be placed to deal with the infeasible segment on the convex shock wave. The computational fluid dynamics techniques were applied to verify this method and analysis result. This study provides a theoretical support to propel the application of iMoC in waverider and inward inlet design.
- inverse method of characteristics /
- axisymmetric /
- shock wave /
- expansion flow /
- computational fluid dynamics

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图 1 逆向左特征线和右特征线交织的网格单元^[5,20]

Figure 1. Mesh element intersected by left-running and right-running characteristic lines^[5,20]

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图 2 逆向左特征线和流线交织的网格单元^{[19, 21]}

Figure 2. Mesh element intersected by left-running characteristic line and stream line^{[19, 21]}

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图 3 逆特征线法计算网格

Figure 3. Computational mesh using iMoC

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图 4 激波依赖区域的补足

Figure 4. Complement of shock-dependent area

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图 5 不连续的激波角

Figure 5. Discontinuous shock wave angle

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图 6 局部的膨胀流场区域

Figure 6. Local area of expansion flow

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图 7 膨胀流的求解

Figure 7. Solution of expansion flow

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图 8 凹激波流场的网格和压力分布

Figure 8. Mesh and pressure distribution of flows with concave shock wave

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图 9 iMoC和CFD计算的凹激波流场马赫数对比

Figure 9. Mach number comparison of flows with concave shock wave simulated using iMoC and CFD

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图 10 凹激波流场沿物面的压力对比

Figure 10. Comparison of pressure distribution along wall boundary in flows with concave shock

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图 11 凸激波流场

Figure 11. Flow with convex shock wave

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图 12 凸激波流场的激波形状局部对比

Figure 12. Part comparison of shock wave shape in flow with convex shock

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图 13 iMoC和CFD计算的凸激波流场马赫数对比

Figure 13. Mach number comparison of flows with convex shock wave simulated using iMoC and CFD

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图 14 凸激波流场沿物面的压力对比

Figure 14. Comparison of pressure distribution along wall boundary in flows with convex shock wave

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表 1 凹激波曲线的B样条控制点

Table 1. Control points of B-spline for concave shock curve

坐标控制点
P₀ P₁ P₂ P₃ P₄ P₅

x 0 0.2 0.4 0.6 0.8 1.0
r 0 0.06 0.12 0.20 0.30 0.40

下载: 导出CSV

表 2 凸激波曲线的B样条控制点

Table 2. Control points of B-spline for convex shock curve

坐标控制点
P₀ P₁ P₂ P₃ P₄ P₅

x 0.0 0.2 0.4 0.6 0.8 1.0
r 0.0 0.08 0.10 0.20 0.32 0.40

下载: 导出CSV

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