Non-linear evolution and acceleration of unstable fuel-lean hydrogen/air flame at ambient and cryogenic temperatures

Abstract

Hydrogen storage at cryogenic temperatures is crucial for industrial applications, yet these conditions can significantly affect flame behavior. Both Darrieus–Landau instability (DLI) and diffusional-thermal instability (DTI) can intensify at cryogenic temperature, leading to unique flame dynamics relevant to safe hydrogen usage. In this study, two-dimensional simulations are performed to assess the effects of cryogenic temperature on the non-linear evolution and acceleration of fuel-lean hydrogen/air flames. By changing the initial temperature and equivalence ratio of the unburned gas as well as the channel width, distinct flame evolution regimes driven by the interplay of DLI and DTI are identified. Specifically, for fuel-lean hydrogen/air flames, the growth rate of DLI and DTI in the linear stage increases at cryogenic temperatures. In the non-linear stage, DTI leads to the chaotic evolution of the cellular flame, which is further destabilized at cryogenic temperatures. It is found that the long-term dynamics, characterized by cell splitting, merging, and lateral movement, result from complex interactions among flow, flame stretch, and chemical reactions. Moreover, flame structure analysis shows that, compared to ambient temperatures, cryogenic temperatures significantly increase the local reaction rate. The propagation speed of fuel-lean hydrogen/air flames is further accelerated at cryogenic temperature, which is associated with the combined effects of enhanced local reaction rate and increased flame surface area, with the primary contribution from enhanced DTI and the secondary contribution from enhanced DLI. In contrast, stoichiometric and fuel-rich flames propagate in a stable single-cusp shape, with their acceleration primarily driven by DLI and flame surface area increase. The width of the channel also affects cellular flame evolution. Rather than altering reaction rates, channel geometry influences flame acceleration mainly through constraining the surface area during flame propagation. These insights contribute to our understanding of cryogenic hydrogen flame dynamics and have important implications for hydrogen safety management.

Novelty and significance Statement

The novelty of this study lies in assessing and interpreting the effects of cryogenic temperatures on fuel-lean hydrogen/air flames subjected to both Darrieus–Landau instability (DLI) and diffusional-thermal instability (DTI) for the first time. Through detailed numerical simulations, we reveal mechanisms driving the chaotic evolution and cellular structure of flame fronts under cryogenic conditions. Our quantitative analysis demonstrates the relative contributions of DLI and DTI. The research fills a critical knowledge gap by examining the role of DLI and DTI at cryogenic conditions for highly unstable fuel-lean hydrogen/air flame. The results are especially valuable for predicting and managing potential flame acceleration hazards in cryogenic hydrogen systems, where traditional ambient-temperature models may not adequately capture the underlying physics.