Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Li, Jing, Luo, Changtong
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: 气动热实验数据的泛函学习方法研究, G6443147872
OpenAlex ID: W7214038287