斜激波总压损失率极小值理论解与物理意义

史爱明; Earl H DOWELL

doi:10.7527/S1000-6893.2018.22517

航空学报 >

2018 , Vol. 39 >Issue 12: 122517 - 122517

DOI: https://doi.org/10.7527/S1000-6893.2018.22517

流体力学与飞行力学

斜激波总压损失率极小值理论解与物理意义

史爱明 ,
Earl H DOWELL

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1. 西北工业大学航空学院 NPU-Duke空气动力与气动弹性联合实验室, 西安 710072;
2. 杜克大学普拉特工学院NPU-Duke空气动力与气动弹性联合实验室, 达勒姆 27708-0300

收稿日期: 2018-07-06

修回日期: 2018-07-26

网络出版日期: 2018-10-19

基金资助

国家自然科学基金（10602046）；航空科学基金（20071453015）；中国博士后科学基金（20060401013）；CFD前沿技术（2015-F-016）

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Theoretical solutions and physical significances for minimum ratio of total pressure loss by oblique shock

SHI Aiming ,
Earl H DOWELL

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1. NPU-Duke Topic Group for Aerodynamics and Aeroelasticity, School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China;
2. NPU-Duke Topic Group for Aerodynamics and Aeroelasticity, Pratt School of Engineering, Duke University, Durham 27708-0300, United States

Received date: 2018-07-06

Revised date: 2018-07-26

Online published: 2018-10-19

Supported by

National Natural Science Foundation of China (10602046); Aeronautical Science Foundation of China (20071453015); China Postdoctoral Science Foundation (20060401013); Advanced Technology for CFD(2015-F-016)

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摘要

以法向马赫数作为激波强度表征量，对斜激波关系式进行重新推导，得到了穿过激波总压损失率极小值的理论解。控制方程表达式为激波角对物面角的线性函数。依据斜激波总压损失率极小值解析公式，首先，绘制了针对超声速流总压损失率应用的楔形角-激波角-马赫数的斜激波效率图。其次，通过生成斜激波三维总压损失率等值线图，呈现了总压损失率在楔形角-激波角-特征马赫数空间上的分布规律。此外，利用斜激波效率图，揭示了等总压损失率条件下马赫数与激波角的对称双解现象。

关键词： 激波; 马赫数; 激波强度; 总压损失率; 斜激波效率图

本文引用格式

史爱明 , Earl H DOWELL . 斜激波总压损失率极小值理论解与物理意义[J]. 航空学报, 2018 , 39(12) : 122517 -122517 . DOI: 10.7527/S1000-6893.2018.22517

Abstract

Theoretical solutions for the minimum ratio of total pressure loss are derived based on the oblique shock relation and a definition of the strength by using normal Mach number for an oblique shock. First, the governing equation for the minimum ratio of total pressure loss is formulated as a linear function of the shock angle and the corresponding deflection angle. Second, based on the analytical formulae, a new oblique shock efficiency diagram regarding the deflection angle, the shock angle and the upstream Mach number is generated. For applications of the total pressure loss, the line for minimum ratio of total pressure loss is mapped on the diagram. Then a three-dimensional contour graph is proposed to study the distribution on ratio of total pressure loss in terms of the deflection angle, the shock angle and the characteristic Mach number. Third, according to the oblique shock efficiency diagram, solutions for the upstream Mach number and the corresponding shock angle are obtained. For the same ratio of total pressure loss, these solutions have symmetrical double values properties in their domain.

Key words： shock waves; Mach number; shock strength; ratio of total pressure loss; oblique shock efficiency diagram

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