# Turbulence-Flame Interactions in Type Ia Supernovae

## Abstract

The large range of time and length scales involved in type Ia supernovae (SN Ia) requires the use of flame models. As a prelude to exploring various options for flame models, we consider, in this paper, high-resolution three-dimensional simulations of the small-scale dynamics of nuclear flames in the supernova environment in which the details of the flame structure are fully resolved. The range of densities examined, 1 to 8 x 107 g cm-3, spans the transition from the laminar flamelet regime to the distributed burning regime where small scale turbulence disrupts the flame. The use of a low Mach number algorithm facilitates the accurate resolution of the thermal structure of the flame and the inviscid turbulent kinetic energy cascade, while implicitly incorporating kinetic energy dissipation at the grid-scale cutoff. For an assumed background of isotropic Kolmogorov turbulence with an energy characteristic of SN Ia, we find a transition density between 1 and 3 x 107 g cm-3 where the nature of the burning changes ualitatively. By 1 x 107 g cm-3, energy diffusion by conduction and radiation is exceeded, on the flame scale, by turbulent advection. As a result, the effective Lewis Number approaches unity. That is, the flame resemblesmore »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- Computational Research Division; Directorate

- OSTI Identifier:
- 929426

- Report Number(s):
- LBNL-302E

Journal ID: ISSN 0004-637X; ASJOAB; TRN: US200814%%152

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Name: Astrophysical Journal; Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99; ADVECTION; ALGORITHMS; DIFFUSION; EXPLOSIONS; FLAMES; KINETIC ENERGY; LAMINAR FLAMES; LEWIS NUMBER; MACH NUMBER; RADIATIONS; RESOLUTION; SUPERNOVAE; TURBULENCE; simulation, supernova, turbulence, combustion, low mach number

### Citation Formats

```
Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 50A-1148, Berkeley, CA 94720, Department of Astronomy and Astrophysics, University of California at Santa Cruz, Santa Cruz, CA 95064, Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, Aspden, Andrew J, Aspden, Andrew J, Bell, John B, Day, Marc S, Woosley, Stan E, and Zingale, Mike.
```*Turbulence-Flame Interactions in Type Ia Supernovae*. United States: N. p., 2008.
Web.

```
Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 50A-1148, Berkeley, CA 94720, Department of Astronomy and Astrophysics, University of California at Santa Cruz, Santa Cruz, CA 95064, Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, Aspden, Andrew J, Aspden, Andrew J, Bell, John B, Day, Marc S, Woosley, Stan E, & Zingale, Mike.
```*Turbulence-Flame Interactions in Type Ia Supernovae*. United States.

```
Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 50A-1148, Berkeley, CA 94720, Department of Astronomy and Astrophysics, University of California at Santa Cruz, Santa Cruz, CA 95064, Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, Aspden, Andrew J, Aspden, Andrew J, Bell, John B, Day, Marc S, Woosley, Stan E, and Zingale, Mike. Tue .
"Turbulence-Flame Interactions in Type Ia Supernovae". United States. https://www.osti.gov/servlets/purl/929426.
```

```
@article{osti_929426,
```

title = {Turbulence-Flame Interactions in Type Ia Supernovae},

author = {Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 50A-1148, Berkeley, CA 94720 and Department of Astronomy and Astrophysics, University of California at Santa Cruz, Santa Cruz, CA 95064 and Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794 and Aspden, Andrew J and Aspden, Andrew J and Bell, John B and Day, Marc S and Woosley, Stan E and Zingale, Mike},

abstractNote = {The large range of time and length scales involved in type Ia supernovae (SN Ia) requires the use of flame models. As a prelude to exploring various options for flame models, we consider, in this paper, high-resolution three-dimensional simulations of the small-scale dynamics of nuclear flames in the supernova environment in which the details of the flame structure are fully resolved. The range of densities examined, 1 to 8 x 107 g cm-3, spans the transition from the laminar flamelet regime to the distributed burning regime where small scale turbulence disrupts the flame. The use of a low Mach number algorithm facilitates the accurate resolution of the thermal structure of the flame and the inviscid turbulent kinetic energy cascade, while implicitly incorporating kinetic energy dissipation at the grid-scale cutoff. For an assumed background of isotropic Kolmogorov turbulence with an energy characteristic of SN Ia, we find a transition density between 1 and 3 x 107 g cm-3 where the nature of the burning changes ualitatively. By 1 x 107 g cm-3, energy diffusion by conduction and radiation is exceeded, on the flame scale, by turbulent advection. As a result, the effective Lewis Number approaches unity. That is, the flame resembles a laminar flame, but is turbulently broadened with an effective diffusion coefficient, D_T \sim u' l, where u' is the turbulent intensity and l is the integral scale. For the larger integral scales characteristic of a real supernova, the flame structure is predicted to become complex and unsteady. Implications for a possible transition to detonation are discussed.},

doi = {},

url = {https://www.osti.gov/biblio/929426},
journal = {Astrophysical Journal},

issn = {0004-637X},

number = ,

volume = ,

place = {United States},

year = {2008},

month = {5}

}