# Three-dimensional numerical simulations of Rayleigh-Taylorunstable flames in type Ia supernovae

## Abstract

Flame instabilities play a dominant role in accelerating the burning front to a large fraction of the speed of sound in a Type Ia supernova. We present a three-dimensional numerical simulation of a Rayleigh-Taylor unstable carbon flame, following its evolution through the transition to turbulence. A low Mach number hydrodynamics method is used, freeing us from the harsh time step restrictions imposed by sound waves. We fully resolve the thermal structure of the flame and its reaction zone, eliminating the need for a flame model. A single density is considered, 1.5x107 gm/cc, and half carbon/half oxygen fuel--conditions under which the flame propagated in the flamelet regime in our related two-dimensional study. We compare to a corresponding two-dimensional simulation, and show that while fire-polishing keeps the small features suppressed in two dimensions, turbulence wrinkles the flame on far smaller scales in the three-dimensional case, suggesting that the transition to the distributed burning regime occurs at higher densities in three dimensions. Detailed turbulence diagnostics are provided. We show that the turbulence follows a Kolmogorov spectrum and is highly anisotropic on the large scales, with a much larger integral scale in the direction of gravity. Furthermore, we demonstrate that it becomes more isotropicmore »

- Authors:

- Publication Date:

- Research Org.:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)

- Sponsoring Org.:
- USDOE Director. Office of Science. Office of AdvancedScientific Computing Research. Mathematical Information and ComputationalSciences Division, Supernoval Science Center DE-FC02-01ER41176; NationalAeronautics and Space Administration NAG5-12036

- OSTI Identifier:
- 862068

- Report Number(s):
- LBNL-56966

Journal ID: ISSN 0004-637X; ASJOAB; R&D Project: K11101; TRN: US200602%%39

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

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Volume: 632; Journal Issue: 2pt1; Related Information: Journal Publication Date: 09/20/2005; Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CARBON; COMBUSTION; DIMENSIONS; FLAMES; HYDRODYNAMICS; MACH NUMBER; OXYGEN; SIMULATION; SOUND WAVES; STATISTICS; SUPERNOVAE; TURBULENCE; VELOCITY; supernovae white dwarfs hydrodynamics numericalmethods

### Citation Formats

```
Zingale, M, Woosley, S E, Rendleman, C A, Day, M S, and Bell, J B.
```*Three-dimensional numerical simulations of Rayleigh-Taylorunstable flames in type Ia supernovae*. United States: N. p., 2005.
Web.

```
Zingale, M, Woosley, S E, Rendleman, C A, Day, M S, & Bell, J B.
```*Three-dimensional numerical simulations of Rayleigh-Taylorunstable flames in type Ia supernovae*. United States.

```
Zingale, M, Woosley, S E, Rendleman, C A, Day, M S, and Bell, J B. Fri .
"Three-dimensional numerical simulations of Rayleigh-Taylorunstable flames in type Ia supernovae". United States. https://www.osti.gov/servlets/purl/862068.
```

```
@article{osti_862068,
```

title = {Three-dimensional numerical simulations of Rayleigh-Taylorunstable flames in type Ia supernovae},

author = {Zingale, M and Woosley, S E and Rendleman, C A and Day, M S and Bell, J B},

abstractNote = {Flame instabilities play a dominant role in accelerating the burning front to a large fraction of the speed of sound in a Type Ia supernova. We present a three-dimensional numerical simulation of a Rayleigh-Taylor unstable carbon flame, following its evolution through the transition to turbulence. A low Mach number hydrodynamics method is used, freeing us from the harsh time step restrictions imposed by sound waves. We fully resolve the thermal structure of the flame and its reaction zone, eliminating the need for a flame model. A single density is considered, 1.5x107 gm/cc, and half carbon/half oxygen fuel--conditions under which the flame propagated in the flamelet regime in our related two-dimensional study. We compare to a corresponding two-dimensional simulation, and show that while fire-polishing keeps the small features suppressed in two dimensions, turbulence wrinkles the flame on far smaller scales in the three-dimensional case, suggesting that the transition to the distributed burning regime occurs at higher densities in three dimensions. Detailed turbulence diagnostics are provided. We show that the turbulence follows a Kolmogorov spectrum and is highly anisotropic on the large scales, with a much larger integral scale in the direction of gravity. Furthermore, we demonstrate that it becomes more isotropic as it cascades down to small scales. Based on the turbulent statistics and the flame properties of our simulation, we compute the Gibson scale. We show the progress of the turbulent flame through a classic combustion regime diagram, indicating that the flame just enters the distributed burning regime near the end of our simulation.},

doi = {},

journal = {Astrophysical Journal},

issn = {0004-637X},

number = 2pt1,

volume = 632,

place = {United States},

year = {2005},

month = {1}

}