ASC / Alliances Center
for Astrophysical Thermonuclear Flashes

Problem 5: Quenching. What happens when Le>1?

We repeated some shear flow computations for Lewis number Le = 4. In the homogenized (small wavelengths) limit, increasing the Lewis number does not affect the critical velocity. At larger wavelengths, a lower velocity is needed to quench flame with Le > 1.

The preliminary plot below is based on single initial band width W > 6; in fact linear dependence U_cr(W) is still in question for large wavelingths and Le > 1. Nevertheless, U_cr(W) is linear for small L.

Critical velocity of the shear as function of initial band width

Reaction rate for for flame with Le = 1

Flame parameters: W = 6, L = 8, U = 5.

Time: t = 3.6.

Note that the reaction occurs everywhere along the interface. This is not the case for flames with Le = 4, where most of the burning happens in the high curvature regions (see below). quicktime movie (1.0M),

Flame with the mplitude of shear above critical.

Quicktime movie: temperature (1.1M),
Quicktime movie: concentration (1.2M),
Quicktime movie: reaction (1.0M).

Flame with the amplitude of shear below critical.

Quicktime movie: temperature (1.0M),
Quicktime movie: concentration (1.1M),
Quicktime movie: reaction (0.9M).

Problem 1: Burning in Shear Flow, Le=1, KPP
Problem 2: Burning in Cellular Flow, Le=1, KPP
Problem 3: Quenching by Shear Flow, Le=1, step function reaction
Problem 4: Quenching by Cellular Flow, Le=1, step function reaction
Problem 5: Quenching by Shear Flow, Le>1, step function reaction