Rotating detonation of coal–CH4 gas–solid mixtures: effects of annulus width and initial pressure on DDT control and cell structure

• Systematically explores annulus width and pressure effects on DDT in coal–CH₄ RDCs. • Cell size and induction length decrease with higher initial pressure and richer mixtures. • Bituminous coals produce smaller, concentrated detonation cells versus anthracite. • Provides experimental framework for scaling and DDT control in coal-based detonation engines. To achieve efficient coal-based two-phase fuel release in rotating detonation combustors (RDC), this study investigates the influence of annular gap width ( W ), initial pressure ( p 0 ), global equivalence ratio ( φ global ), and coal rank on the sub-detonation-to-detonation transition (DDT) control and cellular structure in coal-methane-oxygen gas-solid two-phase RDC. High-bandwidth pressure measurements and high-speed imaging combined with FFT/STFT and wavelet transform methods quantified time-frequency features. The soot-foil technique determined cell size λ and detonation development length L dev , compared with CEA calculations. Results show that when p ₀ exceeds 2.1 kPa, the mixture sustains stable detonation. As p ₀ increases and φ global approaches moderately fuel-rich conditions, the dominant frequency shifts higher, transient bursts weaken, and both λ and L dev decrease with tighter distributions. Different coal ranks exhibit distinct characteristics: bituminous/sub-bituminous coals yield smaller, more concentrated λ than anthracite under identical conditions, indicating volatiles enhance radical formation and shorten the ZND induction period. Based on integrated statistics and dimensionless analysis, optimal parameters are p ₀ ≥4 kPa and φ global :1.4-1.6, achieving smaller, stable λ and expanding coal-based fuel detonation applicability. These findings provide experimental evidence and methodological framework for geometric-operational similarity design and DDT control in coal-based RDCs.