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Title: DISTRIBUTED FLAMES IN TYPE Ia SUPERNOVAE

Abstract

At a density near a few x10{sup 7} g cm{sup -3}, the subsonic burning in a Type Ia supernova (SN) enters the distributed regime (high Karlovitz number). In this regime, turbulence disrupts the internal structure of the flame, and so the idea of laminar burning propagated by conduction is no longer valid. The nature of the burning in this distributed regime depends on the turbulent Damkoehler number (Da{sub T}), which steadily declines from much greater than one to less than one as the density decreases to a few x10{sup 6} g cm{sup -3}. Classical scaling arguments predict that the turbulent flame speed s{sub T} , normalized by the turbulent intensity u-check, follows s{sub T}/u-check = Da{sub T}{sup 1/2} for Da{sub T} {approx}< 1. The flame in this regime is a single turbulently broadened structure that moves at a steady speed, and has a width larger than the {integral} scale of the turbulence. The scaling is predicted to break down at Da{sub T} {approx} 1, and the flame burns as a turbulently broadened effective unity Lewis number flame. This flame burns locally with speed s{sub l}ambda and width l{sub l}ambda, and we refer to this kind of flame as a lambda-flame.more » The burning becomes a collection of lambda-flames spread over a region approximately the size of the {integral} scale. While the total burning rate continues to have a well-defined average, s{sub T}{approx}u-check, the burning is unsteady. We present a theoretical framework, supported by both one-dimensional and three-dimensional numerical simulations, for the burning in these two regimes. Our results indicate that the average value of s{sub T} can actually be roughly twice u-check for Da{sub T} {approx}> 1, and that localized excursions to as much as 5 times u-check can occur. We also explore the properties of the individual flames, which could be sites for a transition to detonation when Da{sub T} {approx} 1. The lambda-flame speed and width can be predicted based on the turbulence in the star (specifically the energy dissipation rate epsilon*) and the turbulent nuclear burning timescale of the fuel tau {sup T}{sub nuc}. We propose a practical method for measuring s{sub l}ambda and l{sub l}ambda based on the scaling relations and small-scale computationally inexpensive simulations. This suggests that a simple turbulent flame model can be easily constructed suitable for large-scale distributed SNe flames. These results will be useful both for characterizing the deflagration speed in larger full-star simulations, where the flame cannot be resolved, and for predicting when detonation occurs.« less

Authors:
;  [1];  [2]
  1. Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 50A-1148, Berkeley, CA 94720 (United States)
  2. Department of Astronomy and Astrophysics, University of California at Santa Cruz, Santa Cruz, CA 95064 (United States)
Publication Date:
OSTI Identifier:
21394409
Resource Type:
Journal Article
Journal Name:
Astrophysical Journal
Additional Journal Information:
Journal Volume: 710; Journal Issue: 2; Other Information: DOI: 10.1088/0004-637X/710/2/1654; Journal ID: ISSN 0004-637X
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ABUNDANCE; COMPUTERIZED SIMULATION; ENERGY LOSSES; EXPLOSIONS; HYDRODYNAMICS; INTEGRALS; LEWIS NUMBER; NUCLEAR REACTIONS; NUCLEOSYNTHESIS; ONE-DIMENSIONAL CALCULATIONS; SUPERNOVAE; THREE-DIMENSIONAL CALCULATIONS; TURBULENCE; WHITE DWARF STARS; BINARY STARS; DIMENSIONLESS NUMBERS; DWARF STARS; ERUPTIVE VARIABLE STARS; FLUID MECHANICS; LOSSES; MECHANICS; SIMULATION; STARS; SYNTHESIS; VARIABLE STARS

Citation Formats

Aspden, A J, Bell, J B, and Woosley, S E. DISTRIBUTED FLAMES IN TYPE Ia SUPERNOVAE. United States: N. p., 2010. Web. doi:10.1088/0004-637X/710/2/1654.
Aspden, A J, Bell, J B, & Woosley, S E. DISTRIBUTED FLAMES IN TYPE Ia SUPERNOVAE. United States. https://doi.org/10.1088/0004-637X/710/2/1654
Aspden, A J, Bell, J B, and Woosley, S E. Sat . "DISTRIBUTED FLAMES IN TYPE Ia SUPERNOVAE". United States. https://doi.org/10.1088/0004-637X/710/2/1654.
@article{osti_21394409,
title = {DISTRIBUTED FLAMES IN TYPE Ia SUPERNOVAE},
author = {Aspden, A J and Bell, J B and Woosley, S E},
abstractNote = {At a density near a few x10{sup 7} g cm{sup -3}, the subsonic burning in a Type Ia supernova (SN) enters the distributed regime (high Karlovitz number). In this regime, turbulence disrupts the internal structure of the flame, and so the idea of laminar burning propagated by conduction is no longer valid. The nature of the burning in this distributed regime depends on the turbulent Damkoehler number (Da{sub T}), which steadily declines from much greater than one to less than one as the density decreases to a few x10{sup 6} g cm{sup -3}. Classical scaling arguments predict that the turbulent flame speed s{sub T} , normalized by the turbulent intensity u-check, follows s{sub T}/u-check = Da{sub T}{sup 1/2} for Da{sub T} {approx}< 1. The flame in this regime is a single turbulently broadened structure that moves at a steady speed, and has a width larger than the {integral} scale of the turbulence. The scaling is predicted to break down at Da{sub T} {approx} 1, and the flame burns as a turbulently broadened effective unity Lewis number flame. This flame burns locally with speed s{sub l}ambda and width l{sub l}ambda, and we refer to this kind of flame as a lambda-flame. The burning becomes a collection of lambda-flames spread over a region approximately the size of the {integral} scale. While the total burning rate continues to have a well-defined average, s{sub T}{approx}u-check, the burning is unsteady. We present a theoretical framework, supported by both one-dimensional and three-dimensional numerical simulations, for the burning in these two regimes. Our results indicate that the average value of s{sub T} can actually be roughly twice u-check for Da{sub T} {approx}> 1, and that localized excursions to as much as 5 times u-check can occur. We also explore the properties of the individual flames, which could be sites for a transition to detonation when Da{sub T} {approx} 1. The lambda-flame speed and width can be predicted based on the turbulence in the star (specifically the energy dissipation rate epsilon*) and the turbulent nuclear burning timescale of the fuel tau {sup T}{sub nuc}. We propose a practical method for measuring s{sub l}ambda and l{sub l}ambda based on the scaling relations and small-scale computationally inexpensive simulations. This suggests that a simple turbulent flame model can be easily constructed suitable for large-scale distributed SNe flames. These results will be useful both for characterizing the deflagration speed in larger full-star simulations, where the flame cannot be resolved, and for predicting when detonation occurs.},
doi = {10.1088/0004-637X/710/2/1654},
url = {https://www.osti.gov/biblio/21394409}, journal = {Astrophysical Journal},
issn = {0004-637X},
number = 2,
volume = 710,
place = {United States},
year = {2010},
month = {2}
}