### 斜激波总压损失率极小值理论解与物理意义

1. 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 出版日期:2018-12-15 发布日期:2018-10-19
• 通讯作者: 史爱明 E-mail:sam@nwpu.edu.cn
• 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）

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

SHI Aiming1, Earl H DOWELL2

1. 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:2018-07-06 Revised:2018-07-26 Online:2018-12-15 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)

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.