For a typical white dwarf density of 5108 g cm-3 and a pure carbon environment, the flame thickness is 3.7810-4 cm and the speed is 58 km s-1 (Timmes and Woosley 1992). The radius of a white dwarf is ~108 cm —a full direct numerical simulation of a supernova will need to span 12 orders of magnitude. We are interested in understanding the microphysics of flames, which will be necessary for sub-grid modeling for large calculations.

Figures 2 and 3 show two flame-vortex interaction calculations, where the direction of the vortex was varied. The calculation was setup by mapping a steady-state flame solution onto a grid with a superposed vortex given by the stream function:

(Poinsot et al. 1991). These calculations show a decrease in the nuclear energy generation rate in the regions of the flame undergoing the highest stretching, but no quenching of the flame front is observed.

A parameter study of the effects of vortex size, strength, and direction on the flame front is currently underway.

For a typical white dwarf density of 5108 g cm-3 and a pure carbon environment, the flame thickness is 3.7810-4 cm and the speed is 58 km s-1 (Timmes and Woosley 1992). The radius of a white dwarf is ~108 cm —a full direct numerical simulation of a supernova will need to span 12 orders of magnitude. We are interested in understanding the microphysics of flames, which will be necessary for sub-grid modeling for large calculations.

Figures 2 and 3 show two flame-vortex interaction calculations, where the direction of the vortex was varied. The calculation was setup by mapping a steady-state flame solution onto a grid with a superposed vortex given by the stream function:

(Poinsot et al. 1991). These calculations show a decrease in the nuclear energy generation rate in the regions of the flame undergoing the highest stretching, but no quenching of the flame front is observed.

A parameter study of the effects of vortex size, strength, and direction on the flame front is currently underway.

ASCI/Alliances Center for Astrophysical Thermonuclear Flashes

ASCI/Alliances Center for Astrophysical Thermonuclear Flashes

Direct Numerical Simulations of Flame-Vortex Interactions Direct Numerical Simulations of Flame-Vortex Interactions M. Zingale, J. C. Niemeyer, F. X. Timmes, A. C. Calder, L. J. Dursi, B. Fryxell, K. Olson, P. M. Ricker, R. Rosner, J. W. Truran, H. Tufo, P. MacNeiceM. Zingale, J. C. Niemeyer, F. X. Timmes, A. C. Calder, L. J. Dursi, B. Fryxell, K. Olson, P. M. Ricker, R. Rosner, J. W. Truran, H. Tufo, P. MacNeice

We have begun direct numerical simulations of flame-vortex interactions in order to understand quenching of thermonuclear flames. The key question is—can a thermonuclear flame be quenched? If not, the deflagration-detonation transition mechanisms for Type Ia supernovae that demand a finely tuned preconditioned region are unlikely to work. In these FLASH Code simulations, we pass a steady-state laminar flame through a vortex pair, which represents the most severe strain the flame front will encounter inside the white dwarf. We vary the speed and size of the vortex pair in order to understand the quenching process.

We have begun direct numerical simulations of flame-vortex interactions in order to understand quenching of thermonuclear flames. The key question is—can a thermonuclear flame be quenched? If not, the deflagration-detonation transition mechanisms for Type Ia supernovae that demand a finely tuned preconditioned region are unlikely to work. In these FLASH Code simulations, we pass a steady-state laminar flame through a vortex pair, which represents the most severe strain the flame front will encounter inside the white dwarf. We vary the speed and size of the vortex pair in order to understand the quenching process.

This work is supported by the Department of Energy under Grant No. B341495 to the Center for Astrophysical thermonuclear Flashes at the University of Chicago. These calculations were performed on the Nirvana Cluster at Los Alamos National Laboratory and an SGI Origin 2000 at Argonne National Laboratory with FLASH 1.61.

This work is supported by the Department of Energy under Grant No. B341495 to the Center for Astrophysical thermonuclear Flashes at the University of Chicago. These calculations were performed on the Nirvana Cluster at Los Alamos National Laboratory and an SGI Origin 2000 at Argonne National Laboratory with FLASH 1.61.

A flame propagates by balancing thermal diffusion and nuclear burning. Heat diffuses from hot ash to the cold fuel ahead of the burning front, raising its temperature to ignition. The width and speed of the burning front depends on how rapidly energy is released by nuclear burning, and how efficiently conduction can transport energy to the material ahead of the front.

A flame propagates by balancing thermal diffusion and nuclear burning. Heat diffuses from hot ash to the cold fuel ahead of the burning front, raising its temperature to ignition. The width and speed of the burning front depends on how rapidly energy is released by nuclear burning, and how efficiently conduction can transport energy to the material ahead of the front.

FLASH (Fryxell et al. 2000) was extended to include explicit thermal diffusion. The one-dimensional laminar flame speeds calculated by FLASH were compared to those computed by Timmes and Woosley (1992), and found to be in excellent agreement (see figure 1).

FLASH (Fryxell et al. 2000) was extended to include explicit thermal diffusion. The one-dimensional laminar flame speeds calculated by FLASH were compared to those computed by Timmes and Woosley (1992), and found to be in excellent agreement (see figure 1).

IntroductionIntroduction ResultsResults

Fig. 1 Comparison of the flame speeds between FLASH (blue) and Timmes and Woosley (1992) (black), for pure carbon flames.

Fig. 1 Comparison of the flame speeds between FLASH (blue) and Timmes and Woosley (1992) (black), for pure carbon flames.

Fig. 3 Time sequence of a flame vortex interaction showing the nuclear energy generation rate (ergs g -1 s-1) and the velocity field. In this simulation, the flow between the vortices moves away from the flame front. The frames are 50 picoseconds apart. The peak nuclear energy generation rate falls by ~ half-order of magnitude in the regions of highest strain.Fig. 3 Time sequence of a flame vortex interaction showing the nuclear energy generation rate (ergs g -1 s-1) and the velocity field. In this simulation, the flow between the vortices moves away from the flame front. The frames are 50 picoseconds apart. The peak nuclear energy generation rate falls by ~ half-order of magnitude in the regions of highest strain.

Fryxell et al., 2000 ApJ, in press

Timmes, F. X. & Woosley, S. E. 1992, ApJ, 396, 649

Poinsot, T., Veynante, D., & Candel, S. 1991, JFM, 228, 561.

Fryxell et al., 2000 ApJ, in press

Timmes, F. X. & Woosley, S. E. 1992, ApJ, 396, 649

Poinsot, T., Veynante, D., & Candel, S. 1991, JFM, 228, 561.

Fig. 2 Time sequence of a flame vortex interaction showing the nuclear energy generation rate (ergs g -1 s-1) and the velocity field. In this simulation, the flow between the vortices approaches the flame front. The frames are 50 picoseconds apart. The peak nuclear energy generation rate falls by ~ half-order of magnitude in the regions of highest strain.Fig. 2 Time sequence of a flame vortex interaction showing the nuclear energy generation rate (ergs g -1 s-1) and the velocity field. In this simulation, the flow between the vortices approaches the flame front. The frames are 50 picoseconds apart. The peak nuclear energy generation rate falls by ~ half-order of magnitude in the regions of highest strain.

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