Asymptotic acceleration exponent of large self-wrinkling expanding flames
In plain words
A large spherical flame wrinkles by itself because the hot burned gas expands, and its radius then grows faster than steadily in time. Does this growth settle into a universal power law, and with what exponent?
Precise statement
For an outwardly propagating premixed flame subject to the Darrieus-Landau (gas-expansion) and thermo-diffusive instabilities, determine whether the radius approaches a self-similar law $R \sim t^{\alpha}$ at $R/\delta_L >\sim 1e4$, the value of $\alpha$ (field-scale correlations suggest $\alpha = 3/2$, equivalent to a fractal front dimension $7/3$), and its dependence on expansion ratio and Lewis number. An answer is $\alpha$ with uncertainty from simulations or experiments reaching the asymptotic range.
What would settle it
Large-scale simulations or large-volume experiments that reach $R/\delta_{L}$ of 1e4 or more and show a converged power law in $R(t)$.