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Elizabeth P. Hicks

Publications and source records attributed to Elizabeth P. Hicks.

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Rayleigh-Taylor Unstable Flames: Thin and Thick

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.

physics.flu-dyn

Rayleigh-Taylor Unstable Flames: the Effect of Two-Mode Coupling

In the classical Rayleigh-Taylor (RT) instability, initial conditions are forgotten and the growth of the mixing layer becomes self-similar when short wavelength modes couple to generate longer wavelength modes. In this paper, we explore how adding a reaction at the unstable interface affects this inverse cascade in wavenumber ("inverse k-cascade"). We simulate a 2D, Boussinesq, premixed model flame perturbed by a large amplitude primary mode ($k_1$) and a smaller amplitude secondary mode ($k_2$). Early on, the modes are uncoupled and the flame propagates as a metastable traveling wave. Once the secondary mode has grown large enough, the modes couple. The traveling wave is destabilized and the flame front bubbles rapidly grow. This inverse k-cascade, driven by two-mode coupling, ultimately generates a long wavelength mode with wavenumber GCD$(k_1,k_2)$, where GCD is the greatest common divisor. We identify five distinct flame growth solution types, and show that the flame may stall, develop coherent pulsations, or even become a metastable traveling wave again depending on GCD$(k_1,k_2)$. Finally, we compare our results with two-mode coupling in ablative and classical RT and show that all three systems may follow the same mode coupling dynamics.

physics.flu-dyn