Dynamics of an autocatalytic reaction front: effects of imposed turbulence and buoyancy-driven flows

Abstract

Thin flame dynamics in a turbulent flow remains debated, with various parameterizations proposed for the typical flame propagation velocity. According to the classical Damköhler's model based on Huygens' principle, a flame front should advance at a constant velocity normal to the interface between reactants and products, with a turbulent acceleration induced by the wrinkling and surface increase of the interface. However, combustion experiments often deviate from this model due to intertwined thermal and turbulent effects, complicating flame acceleration characterization. In this study, we use an autocatalytic reaction that generates a thin reactive front in an aqueous medium, enabling clearer isolation of turbulence effects. Using oscillating grids to generate turbulence in a closed tank, we examine two configurations: a single-grid setup with a spatially decaying turbulence and a dual-grid system with in the middle, a nearly homogeneous, isotropic turbulence. Particle Image Velocimetry and Laser Induced Fluorescence measurements capture both the velocity field and the front propagation, revealing two different regimes: the expected Huygens' propagation regime, but also a reactive mixing regime, where the turbulent advection of the products inside the reactants initiates multiple, dispersed reaction locations. Additionally, we show that even the small density difference between reactants and products plays a crucial role in the front dynamics. This work advances our understanding of autocatalytic fronts in turbulence, emphasizing the critical interplay between chemical kinetics and flow dynamics.

Figures (21)

• Figure 1: Evolution of the turbulent front propagation rate $S_{T}/S_{L}$ as a function of the turbulent intensity rate $u'/S_{L}$ found by Shy et al.shy1996ashy1996b.
• Figure 2: Snapshots of the front propagation in a 15$\times$100 mm tube seen from the side at different times, starting with reaction initiation at $t=0$. In this experiment, $[H_{3}AsO_{3}]_{0} = 0.05$ mol/l, $[IO_{3}^{-}]_{0}=0.017$ mol/l ($R=3$) and the initial pH was set to $pH_{i}$ = 8.6. The front is visualized with fluorescein, a pH-sensitive dye that fluoresces in the reactants where $pH > 4$.
• Figure 3: Experimental apparatus in the one-grid configuration. In the photo (a), the anode, connecting the positive pole of the generator to the top of the tank, is highlighted in blue and the cathode, connecting the negative pole of the generator to the bottom of the tank, is highlighted in red. In the sketch (b), the dual mount system for PIV and LIF synchronized cameras is illustrated.
• Figure 4: Grid dimensions.
• Figure 5: Evolution of $u_{RMS}(y)$ non-dimensionalized by the grid velocity $fA$ in % along the vertical direction. The position $y=0$ is here located at the lowest position of the grid. The dashed line corresponds to $CA^{1/2}M^{1/2}(y-y_{0})^{-1}$ and the circles are the experimental measurements for $f=6$ Hz and $A=10$ mm. The shaded area shows ±1 standard deviation across the $\Vec{x}$-direction.