Rayleigh-Taylor Unstable Flames: Thin and Thick

Abstract

A Rayleigh-Taylor (RT) unstable flame is a thin burning interface sandwiched between heavy fuel and light ash layers. RT unstable flames play an important role in complex systems like novel aviation turbine engines, storage facilities for alternative fuels and refrigerants and Type Ia supernovae. Simulations of these systems must use subgrid models of RT flame behavior, but choosing the subgrid model is difficult because RT unstable flames have characteristics of both the classical RT instability and turbulent combustion. In this paper, we investigate whether the flame structure of RT unstable flames can be described using ideas from turbulent combustion theory. We use a large parameter study of Boussinesq model flames and direct measurements of the internal flame structure to show that RT unstable flames can be thickened by their own self-generated turbulence, but that the structure of these thickened flames differs from turbulent flames. Finally, we discuss the implications for modelling RT unstable flames in practical applications.

Figures (11)

• Figure 1: p-flame temperature profiles for the values of $p$ used in this study and the limiting profile as $p \rightarrow \infty$ (see Appendix \ref{['appendix:plimits']}).
• Figure 2: This figure compares the theoretical turbulent combustion regime diagram (panel a, adapted from peters2000) to a measured regime diagram based on experiments and DNS (panel b, adapted from skiba2018). In the measured regime diagram, boundaries drawn with dashed lines aren't well constrained, but are plausible.
• Figure 3: The time-averaged flame speed vs. the time-averaged normalized flame width for all of the simulations. Each point is a separate simulation. Points with the same color have the same $p$. Points with the same shape have the same $Pr$. Multiple simulations with different resolutions are shown for each $(p, Pr)$ parameter combination. Flames are classified as thin (thick) if their normalized flame width is less than (greater than) 1. Flames are classified as fast (slow) if their flame speed is greater than (less than) predicted by the RT flame speed model. This figure shows a transition from thin+fast flames to thick+slow flames.
• Figure 4: This figure shows that the transition from thin (bluer, smaller dots) to thick (redder, larger dots) occurs going towards low $p$ and $Pr$.
• Figure 5: This figure shows how the normalized flame width depends on $Re$ (panel a), the diffusivity ratio $D_T/\kappa$ (panel b), and $Da$ (panel c). None of these parameters collapse the flame width data well.