Magnitude Study: a substudy to Flame Spreading Rate Study

About

Reaction Zone Test 2

• About: As a result of the failure of the first Reaciton Zone test, it was necessary to try a better Taylor expansion of the reaction zone thickness. Reaction Zone Thickness is determined by: ((-Ec+sqrt((-Ec*-Ec)+4*Ec*R*Ts_local))*Ts_local*Ts_local*R/(Ec*beta_local*(2*R*Ts_local-Ec))). These are the results.
• Relevant Graphs:

• Notes:

Reaction Zone Test

• About: The idea behind this run is that there is a reaction zone, and instead of basing the unsteady rate on the thickness of the preheated zone, it should be based on the thickness of the reaction zone. As such, a Taylor expansion on the exponential determining the extent of reaction was used to solve for the point where the reaction extent = 0
• Relevant Graphs:

• Notes:

Times Unsteady

• About: Because the n was defined only with respect to steady state values an attempt was made to use m_local times m_nonsteady in order to reduce the n which lengthens the time to full steady state burning.
• Relevant Graphs:

• Notes: Greatly reduces the flame propagation rate, too much so it seems. There was no progress with the flame across the surface in around 0.1 sec, which means it's not worth running futher.

n_coef = n_coef-0.5/n_coef

• About: Spurred by past two tests. Should cause the time to steady state beta to increase by factor of two as an averaging of half of the steady state value compared to normal model occurs.
• Relevant Graphs:

• Notes: The run did not give the desired effect, at least not quantitatively from a two cell problem. Simulation is being run on a full simulation to test. The Beta does take about twice the time to decrease, however it doesn't affect burning rate much.

Beta_init = 1e11

• About: Used to test the magnitude change in PR with a a high limit beta value.
• Relevant Graphs:

• Notes:

Beta_init = 1e10

• About: Basically the idea behind this test is that a large beta indicates a small preheated area, which should lower the flame spreading rate.
• Relevant Graphs:

• Notes: Much was learned during this run. Essentially, a high inital beta (as the beta is carried over) will lower the propagation rate due ramping up burning rate. However it's not nearly to the magnitude we need, and is approaching the physical limit for beta that makes since.
  However, the most important thing learned was that a small initial penetration zone represents a large Beta, but that within a given number of timesteps basically a fixed number, thevalues will converge on steady state values. This time to stabilization is the key, perhaps, to our solution.



M_init/2

• About: Basically the idea behind this test is that a large beta indicates a small preheated area, which should lower the flame spreading rate.
• Relevant Graphs:

• Notes: The utility of this is null, as the inital burn rate set to a lower value does not trickle down to later burn rates, which helps us not in our goal to have a steadily increasing



Baseline for comparisons

• About: Basically the idea behind this test is that a large beta indicates a small preheated area, which should lower the flame spreading rate.
• Relevant Graphs:

• Notes: Baseline. Of particular interest is how the pressure, burn rate, etc. jump almost immediately to a very high value--represents the fact that a burning cell in the model is considered "burning" at it's full capacity with the code the way it is.

Useful Maple Output

References