Entropy generation rates in acoustically perturbed hydrogen flames

Abstract

Compressible direct numerical simulations with multi-step chemistry were performed to investigate the temporal characteristics of entropy generation in two-dimensional laminar premixed hydrogen–air flames at equivalence ratios of 0.4 and 0.7, subjected to acoustic forcing over a range of frequencies (50–500 kHz) and sound pressure levels (SPL of 110–130 dB). A monopole-type acoustic source located at the inflow boundary generated pressure waves, thereby wrinkling an initially planar flame front. Higher SPL was associated with an earlier increase in entropy generation in both mixtures. Entropy generation rate was found to mark the transition from an initial linear to a non-linear regime of flame development. Beyond this transition point in the non-linear developed phase, the overall entropy evolution was relatively insensitive to variations in acoustic forcing. A stability analysis based on non-equilibrium thermodynamics suggested that all cases with the same equivalence ratio shared similar instability characteristics, indicating that the developed flame behaviour in the non-linear regime is governed primarily by inherent chemical properties, rather than by specific perturbation conditions.

Novelty and significance statement

As hydrogen and hydrogen-enriched fuels become increasingly important for future energy systems, flame instabilities, including intrinsic and acoustic types, remain a central topic in fundamental combustion research due to their strong influence on flame dynamics and stability. Advancing the understanding of their temporal evolution is essential for predictive combustion theory. Conventional approaches to identifying the transition between the linear and non-linear development regimes of intrinsic flame instabilities rely on amplitude evolution or Fourier-mode analysis and are limited by ambiguities in flame-front definitions and non-unique, wavelength-dependent transition times. This study introduces a novel entropy-based marker that provides a single temporal threshold for regime separation, enabling a more precise characterisation of flame dynamics. Unlike conventional methods restricted to planar flames, this marker is also applicable to complex flame configurations. In addition, stability theory from non-equilibrium thermodynamics is applied to assess the entropy-based stability criteria in numerical simulations of acoustically forced flames.