Jens Wendelstorf:
Models
2. Physical models for the individual parts of the electric arc discharge
The details of this work can be be found in a consistent and
scientifically elaborated form in my
dissertation.
The following introduction is short, but somewhat outdated.
The computation of a specific discharge configuration requires
mathematical models of the individual discharge regions and algorithms
for the iterative linking between them:
2.1 Modelling complex chemical equilibria
For calculating the physical properties of a specific plasma gas, first
the thermodynamic properties have to be determined.
Since our applications lie in the field of
thermal plasmas, we assume [partial] local
thermodynamic equilibrium ([p]LTE). That means, local particle
densities only depend on local temperature.
However, the distinction of electron and heavy particle temperature
is often important (partial LTE). A practical implication of the pLTE is the
need to calculate the partition functions, as these are tabulated for LTE
only.
For the simple case of a single gas plasma (neutral
particles, electrons and the individual ionization states), elementary
thermodynamic data can be calculated and visualized on-line
(on-line plasma Calculator
OPLACALC
- sorry, access is limited)
.
2.2 Calculation of the transport coefficients in (partial) LTE
If the densities and thermodynamic state variables of the
respective gas mixture are known, the electric and thermal conductivities etc.
can be calculated with the help of various cross sections or interaction potentials.
The resulting transport coefficients are functions of the local temperatures (and pressure).
In particular for lamp plasmas, there is also
substantial effort needed to calculate the radiation
phenomena. State of the art is the separation in
optically thin (net emission coefficient) and optically thick
(additional heat conductivity) radiation.
2.3 Modelling the plasma column
Knowing the temperature-dependent transport coefficients, enables us to
calculate the flowing [p]LTE plasma of the arc column.
Depending upon application, continuity equation,
Navier Stokes equation and energy transfer equation have be
considered.
For a [p]LTE plasma two coupled energy balances are to be
set up. For the case of large Reynolds numbers (plasma torches)
turbulence models are needed also. At lower pressures
or currents (some lamps) some additional
transport equations have to be implemented (segregation effects).
2.4 Modelling the non equilibrium layers in front of the electrodes
The assumption of local thermodynamic equilibrium is not justified
some hundreds of micrometers in front of the electrodes.
These areas are called cathode- and anode-fall
and are forming a skin over the
surface of the electrode solid. They are responsible for the transition
from metallic solid to thermal plasma, which in general shows
substantially higher temperatures than the solid surface.
Here we have substantial effects from space charges, ionization and (ambipolar) diffusion.
2.5 Modelling of the electron emission processes
To some extend, the electron emission properties of the
hot (tungsten) cathode are modelled by the Richardson-Schottky equation.
For higher local electric fields, we have thermal field emission calculation codes
and tables, which were developed at the Institute for
Theoretical Physics that TU-Braunschweig.
2.6 Modelling of the electrode solid
In the electrode solid, we are computing thermal conduction and
current transport. However, temperature-dependent
material properties are necessary.
Additionally, the transport and high temperature chemistry of
activator substances (e.g. ThO_2) and the reactions between electrode
material and orifice gas can become important.
Perhaps, you may want to see, how these electrodes look like?
Last modified: 10.10.1998
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