Abstract
The relative ease with which a low-pressure hydrogen stream may be heated in an electrical discharge suggests that such a system be considered in current efforts to develop thrusters for spacecraft orbit raising purposes. In this work a detailed model of a microwave discharge in flowing, low-pressure hydrogen is used to interpret and clarify experimental measurements of atom concentration, electron energy, and electron density. The radially averaged, constant-pressure model accurately reproduces the experimental data and also calculated the rates of a number of gas-heating and wall-heating processes as well as rates of energy deposition into coolant and working fluid streams. The calculated gas-heating rates indicate that the gas heating is due primarily to the thermalization of the energetic atoms produced by dissociation of H2 via excitation of theb 3∑ + u state. The calculations also indicate that the energy flux to the quartz tube is significantly influenced by Lyman and Werner band radiation and by heterogeneous atomic recombination processes and, to a much lesser degree, by electron-ion recombination processes. The fraction of power input which is ultimately transferred to the gas stream is a decreasing function of the power input and varies from 0.24 to 0.12.
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Abbreviations
- A :
-
tube cross-sectional area, m2
- C :
-
molar concentration, g-mol·m−3
- D :
-
diffusion coefficient, m2·s−1
- e 0 :
-
energy of formation of H atoms, J·g-mol−1
- f(j):
-
fractional population of vibrational levelj
- F :
-
molar feed rate, g-mol·s−1
- h :
-
enthalpy, J·kg−1; heat transfer coefficient, J·m−2·s−1·K−1
- J :
-
generalized flux
- k :
-
Boltzmann's constant, 1.3806×10−23 J·K−1; thermal conductivity, J·s−1·K−1
- k i :
-
ionization rate constant, s−1
- k d,j :
-
dissociation rate constant, m3·s−1
- k 21 :
-
recombination rate constant, m6·s−1·g-mol−2
- k 22 :
-
recombination rate constant, m6·s−1·g-mol−2
- L :
-
discharge length, m
- m :
-
atomic mass, kg
- M :
-
molar mass, kg·g-mol−1
- N A :
-
6.022 (1023) g-mol−1
- N :
-
molar flux, g-mol·m−2·s−1
- P :
-
gas pressure, Pa
- q :
-
energy flux, J·m−2·s−1
- R :
-
molar production rate, g-mol·m−3·s−1; tube radius, m; gas constant, J·g-mol−1·K−1
- r :
-
radial coordinate, m
- S :
-
energy production rate, J·m−3·s−1
- T :
-
temperature, K
- v :
-
gas velocity, m·s−1
- z :
-
axial coordinate, m
- 0:
-
feed or reference condition outside
- 1:
-
H2 inside radius of tube
- 2:
-
H2 outside radius of tube
- e :
-
electron
- i :
-
index inside
- v:
-
vibrational
- tr:
-
translational/rotational
- j :
-
index
- e :
-
coolant
- w:
-
wall
- max:
-
maximum
- α:
-
proportionality of radial diffusion rate to ionization rate
- γ:
-
heterogeneous recombination coefficient
- ε:
-
emissivity of quartz; energy of level, J·g-mol−1
- π:
-
3.14159...
- σ:
-
Stefan-Boltzmann constant
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Morin, T.J., Hawley, M.C. The efficacy of heating low-pressure H2 in a microwave discharge. Plasma Chem Plasma Process 7, 181–199 (1987). https://doi.org/10.1007/BF01019177
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DOI: https://doi.org/10.1007/BF01019177