LIFE Chamber Chemical Equilibrium Simulations with Additive Hydrogen, Oxygen, and Nitrogen Page: 4 of 32
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also be an issue, however, for this study, Tantalum is assumed to be in such low quantities that
it can be assumed negligible.
There will be some particles that do hit the walls, and assuming no wall reactions take
place, there will be a lower bound limiting temperature for deposition on the walls based upon
input mass rate, chamber surface area, and species evaporation rates. The purpose of this
study was to determine what the limits are for Carbon and Lead evaporation rates, and to
determine if it is possible to form compounds with Lead or Carbon before the evaporation limit
is reached, that would stay gaseous and not collect on the walls of the chamber at cooler
3. Setup Analysis/Modeling
3.1 Limitations and Evaporations Rates
In order to better gauge the scope of this simulation it is necessary to know the
constraints of the code used. The Cantera equilibrium solver minimizes the free energy in the
gas phase only; therefore, any reaction that would normally take place when a component is in
a liquid or solid phase cannot be modeled by this simulation. The results from simulations
where this occurs must then be considered non-physical. In addition to only being valid in the
gas phase, Cantera will consider all the components that it is given to always be in the gas
phase so it is thus important to know the limiting temperatures for all species that would
collect on the walls, and under what conditions. For the temperature range of 300-5000K, at
densities around 4-- the only species that will collect on the walls are Carbon, Lead, and
Tantalum. Because of the minute amounts of Tantalum in the target composition used in this
simulation it can be neglected, however evaporation limit calculations were still performed for
all three species. The evaporation limit, as defined in this context, is the temperature at which
the rate of input mass of an atomic species is equal to the evaporation rate of atoms from the
surface. The evaporation rate is given by (1):
W (9) 1OA-B--.slogT+c (3.1)
Where constants A, B, and C are given by Table 3.1 (1):
Cabn14.06 38570 0.3056
10.69 9600 0.9242
13.00 40210 0.8947
Table 3.1: Constants in the Equation for the Rate of Evaporation for Carbon, Lead, and
Hence, for a given input mass rate for each component, an evaporation rate can be found if the
surface area inside the chamber is known. An equilibrium evaporation temperature can then be
solved for iteratively (See Appendix A.2.1 for MatLab code). Assumptions made in this
calculation are 2.5m radius spherical chamber, ideal gas behavior, and a shot rate of 10
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DeMuth, J A & Simon, A J. LIFE Chamber Chemical Equilibrium Simulations with Additive Hydrogen, Oxygen, and Nitrogen, report, September 3, 2009; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc1014961/m1/4/: accessed January 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.