Review of Important Terms
• White Dwarf• Chandrasekhar Limit• Type Ia Supernovae• Flame Bubble– Self-Similarity
• Deflagration• Breakout• GCD Model
Project Objectives
• Determine the fractional mass burned during deflagration.
• Analyze the evolution of the flame bubble.
• Compare the results against other models and simulations.
Preliminary ResultsFor the following conditions:
Initial Mass: 1.360 solar massesInitial Radius: 2,500 kilometers
• Breakout occurs in about 1.2 seconds.• Fractional burnt mass is generally too high.• Breakout velocities are around 2,600 km /s.• Maximum velocity is attained shortly before
breakout.• Bubble self-similarity appears to be supported.
Preliminary Results: Bubble-Self Similarity
• We saw the near-independence of breakout velocity from bubble conditions.
• This seemed to justify our spherical assumption for the model.
Comparison to 3-D Simulation Results
• Dr. Fisher asked me to compare my model to David’s simulation.
• Initial Conditions of Simulation– Progenitor Mass: 1.366 solar masses– Progenitor Radius: ≈ 2,000 km– Initial Bubble Radius: 16 km– Initial Bubble Offset: 40 km
Recalibrating the Model’s Bubble Radius
• Initially, the simulation had a greater fractional burnt mass.
• This was a consequence of the resolution of the simulation.
• To start with the same fractional burnt mass, the model’s bubble radius had to be changed to 24 km.
Observations
• There is relatively good agreement with the simulation’s velocities.
• The area and volume diverge from the simulation over time.
• The model area and volume obey power laws.• There is a significant discrepancy between the
fractional burned mass of the model and simulation.
Testing the Spherical Geometry of the Simulation
• The above equation is satisfied if the geometry of the bubble is spherical.
•We concluded that the simulation’s bubble was non-spherical.
Comparing to the Tabular Results
• The model’s code also has a routine to read in data about the progenitor instead of calculating it.
• However, the same general behavior as the semi-analytic model was observed.
• There was also a greater discrepancy in the fractional mass burnt.
Varying the Coefficient of Drag
• Dr. Fisher hypothesized that the coefficient of drag might be too high in the model.
• I was instructed to repeatedly halve the coefficient of drag and see if we could obtain the simulation’s fractional burnt mass.
• This is also affected by the Reynolds number, which describes turbulence.
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