The Rarefaction Paradigm: A Unifying Thermodynamic Topology of Jet, Rocket, and Ion Propulsion via Active Exergy Sinks

This manuscript introduces a paradigm-shifting unification of aerospace propulsion by redefining engines fundamentally as active topological exergy sinks. While classical momentum theory treats propulsion as a downstream reactive consequence, this work mathematically proves that primary physical causality resides in the localized rarefaction field (ΔP). By rigorously combining Navier-Stokes integral formulations with Second-Law exergy balances, we introduce a novel dimensionless metric—the Propulsive Rarefaction Number (Rp)—which uniquely classifies all propulsive systems from scramjets to chemical rockets. Under typical turbofan cruise conditions, rarefaction dictates 68–82% of flow availability (Rp ≫ 1). High-fidelity Monte Carlo simulations (N=10⁴) and Sobol' global sensitivity mapping confirm that topological suction governs over 75% of thrust variance. This deterministic framework is robustly validated via Bayesian Uncertainty Quantification (UQ) against cycle-scaled EASA certification data for the CFM56-5C, achieving an exceptional 0.2% predictive error. Beyond classical aerodynamics, this causal isomorphism resolves boundary-layer ingestion (BLI) paradoxes, predicting realistic power-saving coefficients of 7–12%. Crucially, we demonstrate that this topological rarefaction framework extends universally: mapping fluid pressure deficits (ΔP) directly to both thermodynamic vacuum expansion in chemical rockets and electrostatic potential deficits (ΔV) in ion/plasma thrusters. All derivations, statistical protocols, and reproducible Python models are entirely self-contained.本手稿提出了一种颠覆范式的航空推进统一理论，将发动机从本质上重新定义为主动拓扑㶲阱。传统动量理论将推进视为下游的被动反应结果，而本工作通过数学推导证明，物理因果的本源在于局域稀疏场（ΔP）。本研究通过严格结合纳维-斯托克斯（Navier-Stokes）积分形式与热力学第二定律㶲平衡方程，提出了一种全新的无量纲指标——推进稀疏数（Propulsive Rarefaction Number，Rp），该指标可唯一对从超燃冲压发动机到化学火箭的所有推进系统进行分类。在典型涡扇发动机巡航工况下，稀疏效应主导了68%至82%的流动可用能，此时Rp≫1。高保真蒙特卡洛（Monte Carlo）模拟（样本量N=10⁴）与Sobol全局灵敏度映射分析证实，拓扑抽吸主导了超过75%的推力方差。本确定性框架通过贝叶斯不确定性量化（Bayesian Uncertainty Quantification，UQ），对照CFM56-5C发动机的循环缩放欧洲航空安全局（EASA）认证数据进行了稳健验证，预测误差仅为0.2%，性能优异。突破传统空气动力学范畴，该因果同构理论解决了边界层吸入（BLI）悖论，并预测出符合实际的7%至12%的节能系数。尤为关键的是，本研究证明该拓扑稀疏框架具有普适性：可将流体压力亏缺（ΔP）直接对应至化学火箭的热力学真空膨胀过程，以及离子/等离子体推力器的静电势亏缺（ΔV）。所有推导过程、统计流程与可复现的Python模型均完全自给自足，无需外部依赖。