平衡斜爆震波角的精确显式解
Exact explicit wave-angle solutions for equilibrium oblique detonations
- Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所）
- University of Chinese Academy of Sciences（中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对经典斜爆震模型，通过将逆问题简化为三次方程，推导出波角、分离点及下游总声速点的显式解析公式，并揭示高马赫数极限下的标度律，促进理论理解。
AI中文摘要：
平衡斜爆震极线是一个基本的气体动力学关系。该关系将偏转角、波角、流动状态和热释放联系起来。然而，波角通常通过数值迭代确定。对于经典的斜爆震模型——比热比恒定且热释放固定的量热完全气体——即使在该模型下，也没有显式公式可以根据给定的偏转角（即逆问题）确定波角。这在实际应用中很不方便。在本工作中，我们解决了经典模型下的这一逆问题，并推导出波角的显式公式。受斜激波逆关系推导的启发，斜爆震逆关系也简化为一个三次方程。热释放仅改变三次方程的系数，因此该方程仍可显式求解。我们还推导了完整的解析分支结构。我们进一步发现，分离点和下游总声速点可以分别通过求解一个三次方程和一个二次方程来显式确定。在高马赫数极限下，分离偏转和总声速偏转趋近于一个共同的极限角，而它们之间的间隔遵循特定的标度律。这些针对波角、分离点和下游总声速点的显式公式促进了对经典斜爆震模型理论的理解。
英文摘要：
The equilibrium oblique-detonation polar is a fundamental gasdynamic relation. This relation links the deflection angle, the wave angle, the flow state and the heat release. However, the wave angle is usually determined by numerical iteration. There is no explicit formula to determine the wave angle from a prescribed deflection angle, referred to as the inverse problem, even for the classical oblique-detonation model: a calorically perfect gas with a constant specific-heat ratio and a fixed heat release. This is inconvenient in practical applications. In this work, we solve this inverse problem for the classical model and derive explicit formulae for the wave angle. Inspired by the derivation of the oblique-shock inverse relation, the oblique-detonation inverse relation also reduces to a cubic equation. Heat release only changes the cubic coefficients, so the equation can still be solved explicitly. We also derive the complete analytical branch structure. We further find that the detachment point and the downstream total-sonic point can be determined explicitly by solving a cubic and a quadratic equation, respectively. We extend the explicit formulae to the two-$γ$ model and apply them to oblique-detonation calculations with equilibrium chemistry. These explicit formulae for the wave angle and critical points promote the theoretical understanding of oblique detonations and support their practical calculation.
