Effect of fuel stratification length scale on thermodiffusively unstable lean hydrogen flames

Abstract

Lean premixed hydrogen flames are highly susceptible to thermodiffusive instabilities, which generate complex cellular structures and enhance propagation speed. In practical combustors, incomplete premixing introduces spatial variations in local equivalence ratio upstream of the flame. This work investigates how the length scale of inlet fuel stratification affects the structure and propagation of lean laminar hydrogen flames using direct numerical simulations with detailed chemistry and transport. Controlled sinusoidal perturbations of fuel mass fraction are imposed at moderate amplitude, leading to local equivalence-ratio variations of $\varphi \simeq 0.45-0.55$ in the flame region. Seven stratification wavelengths, from $\lambda =15.4{\delta }_f$ to $133.3{\delta }_f$, are examined at constant density-weighted global equivalence ratio. Additional unity-Lewis-number simulations separate geometrical effects from differential transport. The results reveal a strongly scale-dependent response. In unity-Lewis-number flames, stratification organises the front at the imposed wavelength and monotonically increases flame surface area and propagation speed with wavelength. With differential diffusion, large wavelengths ($\lambda \gtrsim 40{\delta }_f$) produce a similar large-scale organisation, with rich channels forming forward bulges and lean channels recessed cusps, while thermodiffusive cells remain superimposed. This increases flame surface area and global propagation speed. At smaller wavelengths ($\lambda \lesssim 29{\delta }_f$), composition gradients interfere with intrinsic thermodiffusive cellular dynamics, reducing flame surface area and propagation speed relative to the perfectly premixed reference. These findings identify stratification length scale as a key parameter controlling the interaction between moderate mixture inhomogeneity and thermodiffusive instability in lean hydrogen flames.