# An Overview of Theoretical, Numerical and Experimental Studies on Clean Energy and Combustion
## 3 Combustion Dynamics and Modeling  
Combustion modeling under varying conditions can provide critical insights into flame behavior, which could inform the system design requirements. [PERSON] et al. [6] conducted thorough numerical simulations to investigate how an equivalence ratio can affect the detonation characteristics and performance of methane-oxygen combustion in rotating detonation rocket engines (RDREs). They showed that increasing the equivalent ratio reduces the number of detonation waves while boosting specific impulse, a trend that correlates with the enhanced reactivity observed by [PERSON] et al. [7] in ammonia-air flames with higher cracking ratios.  
In a different context, [PERSON] and [PERSON] [8] examined the high-gravity combustion characteristics of propane-air in a channel with backward-facing steps (in an ultra-compact combustor) utilizing large eddy numerical simulations.  
Analyzing their simulation result, they concluded that the centrifugal forces double the flame propagation speed by triggering Rayleigh-Taylor and Kelvin-Helmholtz instabilities, which enhance mixing and reduce combustion time--an effect that resonates with the turbulence-driven flame enhancements noted by [PERSON] et al. [9] in methane-oxygen rocket flames. [PERSON] et al. [10] further explored the flame stabilization by simulating lean premixed methane flames piloted by rich premixed flames, showing that the pilot flame adjusts stretch and heat transfer to anchor the main flame closer to the wall, a mechanism that could inform the micro-combustion stability challenges addressed by [PERSON] et al. [11].  
Micro-scale combustion introduces additional complexities, as reviewed by [PERSON] et al. [12], who highlighted phenomena such as flashback, quenching diameter and flames with repeated extinctions and ignition (FREI) cycles, which [PERSON] et al. [11] substantiated through simulations of premixed methane-air combustion in micro-channels, noting that higher inlet velocities stabilize flames while lower velocities trigger FREI modes influenced by equivalence ratio and channel size.  
[PERSON] et al. [13] utilized numerical simulations to investigate the impact of thermal gas on the boundary layer flame flashback in channels. They demonstrated that thermal gas expansion globally modifies flow in narrow channels but remains localized in widerones, challenging the model critical gradient assumptions while aligning with [PERSON] and [PERSON] [8] in emphasizing the role of flow-flame interactions under confinement.  
Modeling efforts to reduce computational costs are advanced by [PERSON] and [PERSON] [14], who compared different species selection methods, including the principal component analysis (PCA), directed relation graphs (DRGs), the global pathway selection (GPS) and the manifold-informed species selection methods, to reduce the complexity of the chemical mechanisms describing complex hydrocarbon fuel combustion. They suggested that these approaches effectively capture key species across the oxidation stages, with sensitivity to variance and target species as also implied in parametric sensitivities in [PERSON] et al. [6].  
Building on this, [PERSON] et al. [15] developed a hybrid chemistry framework using neural networks to model the low-temperature oxidation of n-heptane, coupling it with foundational chemistry to achieve acceptable accuracies at reduced computational expense. Such a strategy could enhance the detonation simulations of [PERSON] et al. [6] or the micro-flame analyses of [PERSON] et al. [11].