Download Modeling study on plasma flow and heat transfer of low power helium arcjet

st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Modeling study on plasma flow and heat transfer of low power helium arcjet
Hai-Xing Wang, Wei-Ping Sun
School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
(Corresponding author. E-mail: [email protected])
Abstract: The different construction and geometrical size of the radiation-cooled arcjet
thrusters are employed in this modeling to clarify the effect of nozzle geometry on arcjet performance parameters. The calculated temperature and velocity distributions within the arcjet
thruster are presented and analyzed. Modeling results of arcjet thruster with helium as the
propellant are found to compare favorably with the corresponding experimental data.
Keywords: Helium, Arcjet, Plasma flow and heat transfer.
1. Introduction
At present, since there are some new propulsion options
that can achieve the specific impulse higher than arcjets, it
is desirable to extend the application of arcjets to higher
specific impulse with moderate thrust. The broader use of
arcjets as enabling technologies for new space mission
application will require improvements in thrust efficiency
or an extension in specific impulse. Both of these improvements need a better understanding of the physics of
arcjet thruster flows.
In principal, arcjet is capable of operating on a variety
of different propellants such as hydrazine, ammonia, and
hydrogen. While, in recent years the experimental study
of arcjet thrusters with the helium as the propellant has
attracted wide attention. Next to hydrogen, helium has the
highest ionization energy of any atom but a smaller atomic mass than those of hydrazine, ammonia. So, on the one
hand, helium arcjet can deposited more input electric energy into the propellant due to the highest ionization energy. On the other hand, since it lacks internal vibrational
and rotational energy modes, the arcjet thrusters with helium as working gas has a higher percentage of the energy
deposited into kinetic energy of the flow. The experimental results has already shown that compared to hydrogen and hydrazine arcjet thrusters, helium arcjets have
the higher thrust efficiency[1].
Since the plasma property of helium is different from
those of other common used propellants, it is predicted
the plasma flow and heat transfer features of helium
arcjets should be different from other propellants arcjets
and further lead to different thruster performance. At the
same time, from the view point of improving design of
thruster structure, further research is needed.
The modeling study is thus conducted to investigate the
heat transfer and flow characteristics in the low-power
helium arcjet. Three arcjet thruster geometries, designed
and proposed by Institute of Mechanics, Chinese Academy of Sciences are used in this modeling to clarify the
effects of nozzle geometry on arcjet performance parameters[2]. In order to further validate the numerical code, the
experimental data reported by NASA Lewis Research
Center is also used to compare with modeling results.
2. Modeling approach
The main assumptions employed in the modelling study
are as follow. (i) the plasma flow in the arcjet nozzle is
steady, axisymmetrical, laminar and compressible; (2) the
plasma is optically thin and in the LTE (local thermodynamic equilibrium) state, and thus the thermodynamic and
transport properties are completely determined by the
local gas temperature and pressure; and (3) the swirling
velocity component is negligible in comparison with the
axial velocity component. In order to better model such a
complex flow, Lorentz body force components will be
included in the axial and radial momentum equations, and
the Joule heating, radiation loss, viscous dissipation and
pressure work will all be included in the energy equation.
Based on these assumptions, the governing equations in
the cylindrical coordinate system can be written in in a
compact flux vector formulation as follow [3,4]:
U
t
E
z
F
r
Ev
z
H
Fv
r
Hv
S
Where
U
u
v
u
E
p
F
uv
et
pu
v
uv
uv
H
v2
p
et
pv
zz
v
zz
v2
zr
Fv
rr
zr
qz
u
zr
v
qr
rr
0
0
Hv
1
r
zr
S
jr B
jz B
rr
u
zr
v
pv
0
zr
u
1
r
et
0
Ev
T
v
u
2
et
rr
qr
jz Ez
jr Er
(1)
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
electric field can be determined by Ampere’s law and
Ohm’s law. In this study, the anode-nozzle wall is included in the computational domain, so the temperature distribution along the inner surface of the anode-nozzle is
determined by the iterative computation process itself
instead of being artificially specified.
Three construction and geometrical size of the radiation-cooled arcjet thrusters are shown in Fig. 1, which are
designed and proposed by Institute of Mechanics, Chinese
Academy of Sciences. It is noted that three thrusters have
the same size of constrictor and the same diameter of
nozzle exit, while different expansion half angles and
lengths of nozzle. The boundary conditions used in this
computation are listed in Table 1.
and
p
et
zz
1
2
1
2
u
z
u
,
2
v
r
u
,
u
u
z
qz
v
r
v
r
T
Z
,
u2
v2
rr
2
;
v
r
u
u
r
zr
v
z
2
3
,
T
r
qr
Here u, v, T, ρ and p are the axial (z-) and radial (r-)
components of the velocity vector, the temperature, the
gas density and the gas pressure, respectively. Bθ, Ez, Er, jz
and jr are the azimuthal magnetic induction intensity, the
axial electric field component, the radial electric field
component, the axial current density component and the
radial current density component, respectively. The physical properties , , ,
are the temperature- and pressure-dependent specific heat ratio, viscosity, thermal
conductivity and electrical conductivity respectively, and
are calculated for each spatial point based on local temperature and pressure by using pre-compiled LTE plasma
property databases (covering the temperature range
300-30,000 K and the pressure range 10 Pa to 3×105 Pa).
Rewriting Ohm’s law by making use of Maxwell’s
equations for steady conditions, one obtains an equation
for the magnetic induction intensity in the following form
1
r r
rB
r
1
z r
rB
z
vB
r
0
uB
z
(a) Thruster A
(b) Thruster B
(2)
(c) Thruster C
Fig.1 Schematic diagram of the kW-class arcjet thrusters
under study
After Bθ has been obtained, the current density and
Table 1. Boundary conditions
Flow Field
B-C
p
extrapolated/specified
dp dn
u
 / extrapolatfrom m
ed
0
v
specified
T
specified
Magnetic
Field
B-C-I-J
rB
0
I 2
Anode
D-C
T
specified
C-I-J-F
F-G
0
0
dT dn
dT dn
Anode
Gas
J-F
rB
r cos
rB
z sin
0
Anode
0
dp dn 0
extrapolated
du dr
0
0
0
specified
extrapolated
0
extrapolated
dT dr
3. Result and discussion
Typical modeling results describing the plasma
flow and heat transfer characteristics of the helium
Gas
rB
0
dT dn
0
H-K
F-E
dT dn
H-K-B
dp dr
F-G-H
C-I-J-F
dT dn
G-H
extrapolated
K-B
diminishes from 0 to
0I 2
0
I 2
E-D
T4
dT dn
T4
arcjet are presented in Fig. 2-5 respectively. In order
to facilitate comparison, the operation conditions,
such as the mass flow rate of 18 mg/s and arc current
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
of 10 A, are fixed to the same for three thrusters.
2000
0
4 00 0
-0.001
0.004
0.006
0.008
0.01
z (m)
(a) Thruster A
r (m)
0.001
2 00 0
0
400
0
0.004
-0.001
0.005
0.006
z (m)
0.007
0.008
(b) Thruster B
r (m)
r (m)
0.001
nozzle, the dip of the temperature in the center of profile is more obvious. Such a non-monotonic temperature profile was also observed by Walker [5] in an experimental study of a helium arcjet thruster. This
phenomenon implies that fluid expands to a temperature lower than the nozzle wall and further suggests
that heat transfer from the nozzle wall is responsible
for the inverted temperature profile. The thruster C
has more uniform temperature profile than those of
thruster B and C due to the special structure of expansion portion of nozzle. It suggests that if uniform
temperature profile at the exit plane of arcjet thruster
is required in some certain conditions, the structure of
arcjet nozzle should be carefully designed.
2000
6000
0
8000
4000
-0.004
0
0.002
0.005
20
r (m)
00
0
4000
0.01
0.015
z (m)
(a) Thruster A
0.02
0.004
0.006
0.008
0.01
z (m)
0.012
r (m)
-0.002
0.014
8000
4000
-0.004
0
0.005
0.01
z (m)
2500
r (m)
Thruster A
Thruster B
Thruster C
0.015
(b) Thruster B
0.004
3000
Temperature (K)
6000
0
-0.002
(c) Thruster C
Fig.2 Computed isotherms within the partial gas flow
region in three thrusters with helium as the propellant.
Contour interval: 2,000 K.
0.03
2000
0.002
0.004
0.025
2000
6000
10000
0
8 0 00
4000
-0.004
2000
0
1500
1000
-4
-2
0
r (mm)
2
4
Fig.3 Comparison of calculated radial profiles of
plasma temperature at the thruster exit
In order to clearly show the detail of temperature
distribution within arcjet thruster, only partial gas
flow region of three thrusters are shown in Fig.2. It is
seen that gas heating and energy conversion processes
are similar generally in three thrusters, while the
temperature distributions are quite different due to the
different construction and geometrical sizes of the
nozzle. The differences of temperature distribution are
further shown in Fig. 3. It is interesting to find that the
highest temperatures of helium do not appear at the
center of the thruster exit for the cases of the thruster
A and B. With the increase of expansion half angle of
0.005
0.01
0.015
0.02
0.025
z (m)
(c) Thruster C
Fig.4 Computed axial velocity contours within the gas
flow region in three thrusters with helium as the propellant. Contour interval: 2,000 m/s.
The computed axial velocity distributions within
the thruster nozzle and thruster exit are shown in Fig.
4 and 5. Although the similar conversion processes of
the pressure energy and internal energy into the kinetic energy are found in three thrusters, the axial velocity distributions inside expansion nozzle are somewhat different. For the case of thruster A, with a
smaller expansion half angle and longer nozzle, the
maximum axial velocity at the thruster exit is lower
than that of thruster B with bigger expansion half angle and shorter nozzle. For the case of thruster C, the
expansion half angle of nozzle changes from 35°at the
3.1 mm downstream from constrictor into 8°，which
leads to the more complex flow field inside thruster
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
nozzle. It is seen from Fig. 4(c) that the axial velocity
increase very rapidly at region with expansion half
angle 35°and decrease appreciably at the transition
region between two expansion half angle. It is also
shown from Fig. 5 that contrary to temperature profiles shown in Fig. 3, the maximum of axial velocity
at the center of exit plane of thruster C is lower than
those of thruster A and B.
Axial velocity (m/s)
8000
6000
4000
Thruster A
Thruster B
Thruster C
2000
0
-4
-2
0
r (mm)
2
4
Fig.5 Comparison of calculated radial profiles of axial
velocity at the thruster exit
10000
Axial velocity (m/s)
9000
8000
7000
6000
5000
4000
36.13 mg/s
26.60 mg/s
18.13 mg/s
Predicted 36.13 mg/s
Predicted 26.60 mg/s
Predicted 18.13 mg/s
3000
2000
1000
0
-4
-2
0
r (mm)
2
3000
42.5 mg/s
26.60 mg/s
18.13 mg/s
Predicted 42.5 mg/s
Predicted 26.60 mg/s
Predicted 18.13 mg/s
Temperature (K)
2000
1500
1000
500
0
-4
-2
0
r (mm)
2
4. Conclusion
Numerical simulations have been carried out to
study the plasma flow and heat transfer characteristics
of low-power arcjet thrusters with helium as the propellant. The effects of construction and geometrical
sizes on temperature and velocity distributions inside
arcjet thruster have been examined. The temperature
and velocity profiles dependence on expansion half
angles and structures are presented and analyzed. It is
found that the thruster C with variable expansion half
angle of the nozzle present the highest temperature
and the lowest axial velocity value at center of thruster exit among three thrusters.
4
Fig.6 Comparison of predicted radial profile of axial
velocity at the exit plane with the experimental results
in [5]
2500
For the case with helium as the propellant, experimental results of low power arcjet with the almost
same geometrical structure, which is operated under
the similar parameters with this study have been reported by Walker [5]. Our predicted results for radial
profiles of the axial velocity and gas temperature at
the exit plane are thus compared with the experimental data in Ref [5]. Fig. 6 and Fig. 7 compare the
predicted radial distribution of the axial velocity and
gas temperature at the arcjet nozzle exit with corresponding experiment results presented in Ref. [5] for
the case with helium flow rates of 36.13, 26.60, 18.13
mg/s and a constant current value of 10.3 A. It is seen
that our predicted radial distribution of the axial velocity agree well with the experimental and predicted
result.
4
Fig.7 Comparison of predicted radial profile of gas
temperature at the exit plane with the experimental
results in [5]
In order to validate the reliability of numerical code
used in this study, a comparison of modeling results
with the available experimental results is conducted.
5. Reference
[1] A Rybakov, M A Kurtz and H Kurtz, et al., in
38th AIAA/ASME/SAE/ASEE Joint Propulsion
Conference & Exhibit (2002).
[2] W X Pan, X Meng, C K Wu, Proceedings of the
13th Asian Congress of Fluid Mechanics (2010).
[3] H X Wang, J Y Geng, and X Chen, et al., Plasma
Chemistry and Plasma Processing, 30, 707(2010).
[4] H X Wang, X Chen and W X Pan, et al., Plasma
Science & Technology, 12, 692 (2010).
[5] Q E Walker, "Characterization and novel applications of the helium arcjet", Stanford University,
2007.
6. Acknowledgment
This study was supported by the National Natural
Science Foundation of China (No. 50836007,
11072020, 11275021)