Effects of gravity on lean hydrogen/air flame instability: From linear scaling law to nonlinear morphology evolution

Abstract

The instability characteristics of lean hydrogen/air flames have attracted considerable research attention, yet the effect of gravity remains insufficiently understood. In this study, time-resolved two-dimensional simulations with detailed chemistry and transport are conducted to investigate the influence of gravity-induced Rayleigh-Taylor (RT) instability on the linear growth rate of disturbances and nonlinear morphology evolution of cellular flame fronts at different length scales. In the linear regime, a parametric study is performed across various equivalence ratios, initial temperatures and pressures; in each case, the dispersion relation is calculated for various gravity levels. The influence of gravity is most pronounced under ultra-lean, low-temperature, and high-pressure conditions, and a universal scaling law between gravity sensitivity and the Froude number is established. In the nonlinear regime, gravity has opposite effects on the large-scale and small-scale structures of lean hydrogen flames. On the one hand, gravity inhibits the splitting of small-scale cellular structures through a baroclinic torque mechanism; on the other hand, it promotes the development of large-scale finger-like structures, thereby increasing the total surface area and the global consumption speed of the flame. The effects of gravity on the probability distributions of cell size, displacement speed, Karlovitz number, and local curvature are also analyzed. The results and findings of the present study should advance the fundamental understanding of hydrogen flame dynamics under varying gravity conditions and provide insight for relevant applications, including fire safety and space propulsion.

Figures (13)

• Figure 1: Computational setup and boundary conditions. $L_x$ and $L_y$ denote the domain lengths used for the linear (nonlinear) regime analyses. The flame front is illustrated with a single harmonic perturbation.
• Figure 2: Dispersion relations for Case R1 (varying $\phi$, top row), Case R2 (varying $T_u$, middle row) and Case R3 (varying $P_u$, bottom row). The influence of gravity is more pronounced at lower equivalence ratios, lower unburned temperatures and higher pressures.
• Figure 3: The relationship between the global gravity-sensitivity parameter $\eta$ and the Froude number $Fr$ under various conditions. The solid line represents a power-law fit for all cases.
• Figure 4: Snapshots of the dynamic evolution and splitting of cellular structures for a flame at $\phi=0.4$. The temporal evolution highlights the cell breakup process under different gravity conditions: (a) $g=-10g_0$, with splitting at $t/\tau_f=4.72$; (b) $g=0g_0$, with splitting at $t/\tau_f=4.81$; and (c) $g=10g_0$, with splitting at $t/\tau_f=5.09$.
• Figure 5: Temporal evolution of single-cell splitting under zero-gravity ($g=0$) conditions. (a) flame front morphology, (b) displacement velocity $S_d^*/S_L$, (c) heat release rate (HRR) normalized by the maximum HRR of a one-dimensional flame, and (d) Karlovitz number. Results at six selected times are shown in different colors, with red representing the earliest time and black the latest. The vertical axis in (a) is reversed for improved presentation.