Distributed Flames in Type Ia Supernovae
IntroductionIn a previous paper (referred to here as paper I, see also here) we used three-dimensional simulations to examine the interaction of turbulence with a thermonuclear carbon-burning flame at a variety of Karlovitz numbers. It was shown that at a Karlovitz number of approximately 230, the flame presented a completely different mode of burning where turbulent mixing dominated species and thermal diffusion - a distributed flame was observed.
TheoryDamkohler (1940), by analogy with laminar flames, predicted that the turbulent flame speed and width in this so-called small-scale turbulence regime should follow the relations
for D_{T} and τ_{nuc} are the turbulent diffusion coefficient and nuclear burning time scale respectively. In this study, we start with the high Karlovitz number case from paper I, and investigate the predictions made by Damkohler by moving to larger and larger domains keeping the Karlovitz number fixed, effectively increasing the Damkohler number. Both s_{T} and l_{T} are predicted to scale with Da^{1/2}.
Simulations
The fuel density in each case was 10^{7} g/cm^{3}. A total of five cases were simulated, the details of which are summarized in the table below:
Slices of density (top) and burning rate (bottom) are shown for all seven cases above, (a)-(g) left-to-right. In each case the domain size increases by a factor of 8 in each direction. As the turbulent width is predicted to grow with Da^{1/2}, the flame gets relatively thiner compared to the domain width. The burning rate appears to decrease but due to the greater volume of fluid burning, the global burning rate greatly increases. Any questions should be directed to Andy Aspden. ReferencesA. J. Aspden, J. B. Bell, S. E. Woosley, "Distributed Flames in Type Ia Supernovae", Astrophysical Journal, 710, 1654-1663, February 2010. [ApJ] [pdf] S. E. Woosley, A. R. Kerstein, V. Sankaran, A. J. Aspden and F. Ropke "Type Ia Supernovae: Calculations of Turbulent Flames Using the Linear Eddy Model", Astrophysical Journal, 704, pp.255-273, October 10, 2009. [ApJ] A. J. Aspden, J. B. Bell, M. S. Day, S. E. Woosley, M. Zingale, "Turbulence-Flame Interactions in Type Ia Supernovae", Astrophysical Journal, 689, pp.1173-1185, December 20, 2008. [ApJ] [pdf] [pdf2] A. J. Aspden, J. B. Bell, and S. E. Woosley "Distributed Flames in Type Ia Supernovae" accepted for publication in the Astrophysical Journal. G. Damkohler, "Der Einfluss der Turbulenz auf die Flammengeschwindigenkeit in Gasgemishcen", Z. Elektrochem, 46, 1940. |