RDE Detonation Engine V-Type Dual-Channel 20° Inclination-A CDEQ Engineering Solution to Minimize Algorithm Dependency via Physical Geometry

RDE Detonation Engine V-Type Dual-Channel 20° Inclination: A CDEQ Engineering Solution to Minimize Algorithm Dependency via Physical Geometry

中文:RDE爆震发动机V型结构单边20°-用物理结构彻底消灭控制算法的终极定解

Trusted Timestamp : TSA-01-20260331284165969

Author: Jiang Wenjia (Shenzhen, China)

ORCID: 0009-0000-3850-7286

Correspondence: jiangwenjiaszx@outlook.com

Abstract

· Problem: Rotating Detonation Engine (RDE) operates at microsecond-scale detonation waves (tens of kHz). Traditional closed-loop control suffers from insurmountable time-scale mismatch: sensor/actuator/controller response (ms) >> plant dynamics (μs). High-frequency real-time algorithms are physically doomed to lag.

· Solution: This paper, based on the CDEQ framework (Cross-Domain Cyber-Dynamic Equilibrium Regulation Framework), proposes a V-type dual-channel nozzle with a 20° half-angle (40° total opening). The fixed geometry forces natural self-synchronization of the two detonation channels under normal operating conditions, liberating the flight control system from microsecond-scale phase correction.

· Clarification: “Eliminating algorithm dependency” refers specifically to high-frequency real-time feedback algorithms. Low-frequency controls (macro-state monitoring, mode switching, fault protection) remain necessary and present.

· Theoretical basis: The optimal coupling condition is given by the golden-section equation cosθ − sinθ = 0.618, yielding a theoretical optimum of 19.1°. Engineering rounding to 20° incurs <0.5% performance loss (axial thrust ~6% reduction, lateral coupling ~34.2%, coupling ratio ~0.364 – within the stable window at the edge of chaos).

· Validation: Full-range (0°–50°) sweep shows that only 20° passes the GCVT-10 (Global Convergence Validation Theorem) engineering acceptance criterion (10 consecutive steps with deviation <10%) without requiring high-frequency algorithm intervention.

· Conclusion: The 20° V-type structure significantly reduces dependency on real-time control algorithms for dual-channel RDE synchronization,  providing a verifiable, reproducible hardware path.

KEY PAPER (Full Theory & Proofs):

A Flower's Smile, V-Functions Arise: Answering Lyapunov's Centennial Question

DOI: 10.5281/zenodo.18927653

A Paradigm Shift in Control Theory

CDEQ V1.2 The Countable Foundation of Stability

DOI: 10.5281/zenodo.18939385

CDEQ V1.3 Mathematical Proof of the PCTT-CW Penta-Cyclic Clockwise Topological Theorem

DOI: 10.5281/zenodo.18988669

CDEQ V1.4: Mathematical Proof of the CENHE-LEX Nonary Central Holding Equilibrium Theorem

DOI: 10.5281/zenodo. 19023440

CDEQ V1.5 GCVT-10 Global Convergence Validation Theorem

DOI: 10.5281/zenodo. 19055969

For the complete mathematical foundation, rigorous derivations, and general solution to Lyapunov's century-old problem — see the key paper above.