16.522, Space Propulsion
Prof.
Manuel Martinez-Sanchez
Lecture 11-12: SIMPLIFIED ANALYSIS OF ARCJET OPERATION
1. Introduction
These notes aim at providing order-of-magnitude results and at illuminating the
mechanisms involved.
Numerical precision will be sacrificed in the interest of physical
clarity.
We look first at the arc in a cooled constrictor, with no flow, expand the analysis
to the case with flow, and then use the results to extract performance parameters for
arcjets.
2. Basic Physical Assumptions
The gas conductivity model will be of the form
σ
=
o
a T
−
T
e
(
)
⎧
⎨
⎩
T
<
T
e
(
)
T
>
T
e
(
)
T
e
≈
6000
−
7000
K
(
)
a
≈
0.8
Si
/
m
/
K
(
)
(1)
The termal conductivity k of the gas will be modelled as a constant (with possibly
a different value outside the arc).
This is a fairly drastic simplification, since in H
2
and
N
2
k(T) exhibits very large peaks in the dissociation range (2000-5000K) and in the
ionization range (12000-16000K).
Because k always multiplies a temperature gradient,
the combination
d
is relevant, and so the proper choice of
Φ
T
( )
=
kdT
k
to be used is the
averaged value
k
=
1
T
2
−
T
1
kdT
T
1
T
2
∫
(2)
over the range of temperatures intended.
The arc gas is modelled as ideal, even though its molecular mass shifts strongly
and its enthalpy increases rapidly in the dissociation and ionization ranges.
In particular,
c
p
=
∂
h
∂
T
⎛
⎝
⎞
⎠
p
has strong peaks, similar to those of k(T), and, once again, we should use
temperature-averaged values for it.
The arc is assumed quasi-cylindrical, with axial symmetry and with gradients
which are much stronger in the radial than in the axial direction (similar to boundary
layers).
The flow region comprises three sub-domains:
(a) The arc itself, for
r
, corresponding to
<
R
a
x
( )
T
>
T
e
.
This is the only part carrying
current.
(b) The outer gas, not ionized and with
T
<
T
e
.
16.522, Space Propulsion
Lecture 11-12
Prof. Manuel Martinez-Sanchez
Page 1 of 18

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