Arcjet nozzle having improved electrical-to-thrust conversion efficiency and high voltage operation

An arcjet thruster is disclosed which has an electrically conductive anode body having an anode cavity therein which defines a nozzle symmetrical about a central axis. The anode cavity has a tandemly arranged divergent recombination portion and a divergent expansion portion. The expansion portion has a greater rate of divergence than the recombination portion. The anode body further preferably comprises a cylindrical constrictor portion upstream and in tandem with the recombination portion. An electrically conductive cylindrical cathode body is coaxially arranged and spaced from the anode body by a gap. An electrical current source connected to the cathode and the anode produces an electrical arc across the gap. A vortex flow of propellant gas is fed through the gap and through the nozzle to produce thrust. The vortex flow of propellant gas pushes the arc through the constrictor into one of the divergent portions of the nozzle. The recombination and expansion portions merge at a transition being between a divergence of 5 and 15 degrees and within a diameter ratio range of the transition to the constrictor of about 1.5 to 4.0. The divergent recombination portion causes a portion of the ionized and disassociated propellant gas passing therethrough to recombine, recovering frozen flow losses prior to entering the expansion portion and increasing the overall energy conversion efficiency of the thruster.

The present invention generally relates to electrothermal propulsion 
devices and more specifically to an improved arcjet thruster. 
Typical arcjet thrusters utilize an electrical arc to heat a flowing 
propellant as it passes through an arc chamber shaped generally as a 
convergent/divergent nozzle. The conventional thruster typically has a 
hollow anode body having a cavity therethrough which defines the nozzle. 
Coaxially aligned with and spaced from the nozzle is a cylindrical 
cathode. The anode and cathode are usually made of tungsten or other high 
temperature metal alloy. 
Typical arcjet thrusters are disclosed in U.S. Pat. Nos. 3,603,089 and 
3,425,223 and are also described in "Physics of Electric Propulsion", by 
Robert G. Jahn, McGraw Hill, pages 90 to 130. Improved efficiency arcjet 
thrusters are disclosed in U.S. Pat. Nos. 4,800,716 and 4,882,465, and 
4,926,632 assigned to the assignee of the present invention. 
A simplified example of a conventional arcjet thruster is schematically 
illustrated in cross-section in FIG. 1. This arcjet thruster 10 has a 
generally hollow anode body 12 which defines therein a divergent nozzle 
14. Nozzle 14 is symmetrical about a central axis 16. Coaxially aligned 
and spaced upstream of the anode body 12 is a cylindrical cathode 18 which 
has a generally conical cathode tip 20. This tip is spaced from the anode 
body 12 by a gap 22. 
A propellant gas 24 is fed in a vortex flow into nozzle 14 through gap 22, 
past a nozzle throat 26 and a constrictor portion 28, and then expanded 
through a divergent portion 30 of the nozzle 14 to produce thrust. 
Simultaneously, an electrical potential is applied between the cathode 18 
and the anode body 12 to produce an arc 32 across the gap 22. The arc 32, 
emanating from the cathode, is pushed through the throat 26 and through 
the cylindrical constrictor 28 by the flowing propellant so that the 
downstream end of the arc 32 attaches to the anode body 12 in the 
divergent portion 30 of nozzle 14. Thus the constrictor 28 serves to 
elongate the arc, prolonging the arc contact time with the propellant. 
This increases the heat transfer between the arc 32 and the propellant 24 
passing through the constrictor 28. 
The constrictor length is chosen based on the particular arcjet 
application. In some applications, the constrictor may not be desired. In 
this case the constrictor would effectively have a zero length. 
The vortex flow of the propellant through the constrictor 28 into the 
divergent portion 20 of the nozzle produces a central low density region 
along the axis 16 through the constrictor 28 which tends to stabilize the 
arc 32. In addition, the vortex flow of the propellant 24 through the 
constrictor 28 is preferably laminar adjacent the surface of the 
constrictor 28. This laminar flow of propellant effectively insulates the 
portion of the anode body 12 adjacent the constrictor 28. This minimizes 
the heat transfer to the anode body 12 by the arc in the region of the 
constrictor. 
Basically, the high temperature and the electromagnetic fields of the 
electrical arc 32 cause thermal excitation, ionization and partial 
disassociation of the propellant 24 as it flows through the throat, the 
constrictor, and into the divergent portion of the nozzle 14. The ionized 
and disassociated propellant 24 is then expanded in the divergent portion 
30 to produce thrust. The efficiency with which the electrical energy of 
the arc 32 is converted to kinetic energy in the arcjet thruster 10 is 
partially limited by the energy which is transferred from the arc to the 
molecules of the gas in disassociation and ionization of the propellant 
gas as it passes through the arc in the throat and through the constrictor 
28. 
A portion of this energy may be regained by recombination and reassociation 
of the ions and neutral species. However, recombination and deionization 
occurs slowly in comparison to the propellant transit time through the 
nozzle and therefore occurs downstream of the nozzle. Accordingly, the 
energy utilized in disassociation and ionization of the propellant gas is 
effectively lost. This loss is generally termed a frozen flow loss. The 
frozen flow losses limit the obtainable efficiency in conventional arcjet 
thruster designs to about 30 percent efficiency. 
Various attempts have been considered and tried to regain frozen flow 
losses and thus improve the efficiency of arcjet thrusters. One attempt is 
illustrated in FIG. 2. In this simplified sectional view of an arcjet 
thruster 40 designed by Gianninni Corporation, it was thought that if the 
entire arc 32 could be constrained within the constrictor 42, and a mixing 
chamber effectively produced therein, the frozen flow losses could be 
recovered. In this prior art design, constrictor 42 included an enlarged 
mixing chamber section 44 terminating in a throat 46. The arc 32 attached 
to the anode body 12 inside the enlarged portion 44. The mixing chamber 44 
provided an increased residence time for the gas as it passed through the 
constrictor 42 which allowed partial recombination and hence recovery of 
some of the frozen flow losses. 
However, as arc attachment resided in the mixing chamber 44, substantial 
heat was transferred to the anode wall, netting very little or no 
improvement in the overall efficiency. 
Thus there is still a continued need for an improved efficiency arcjet 
thruster which minimizes the inherent losses, recovers frozen flow losses, 
and maximizes the effective electrical to thrust energy conversion 
efficiency. 
Accordingly, it is an object of the present invention to provide an 
improved efficiency arcjet thruster having reduced frozen flow losses. 
It is another object of the present invention to provide an arcjet thruster 
having an increased lifetime. 
It is a still further object of the present invention to provide an 
improved performance arcjet thruster operating with a high voltage for a 
given power level. 
The arcjet thruster in accordance with the present invention is a thruster 
having a convergent/divergent nozzle. The divergent part of the nozzle has 
a divergent recombination portion in tandem with a divergent expansion 
portion to permit recovery of frozen flow losses and conversion thereof to 
useful thrust. The expansion portion has a greater rate of divergence than 
the recombination portion. The transit of the vortex flow of ionized 
propellant gas passing through the throat and/or constrictor is delayed in 
the recombination portion of the divergent nozzle to allow for 
recombination to take place and heat to be released to the gas in the form 
of kinetic energy. In other words, the recombination portion allows ionic, 
dissociative, and rotational energy modes to relax into translational 
modes which can then be converted to thrust in the nozzle. Thus some of 
the frozen flow losses are recovered prior to the gas entering the 
divergent expansion portion of the nozzle. 
It has been found that the transition between the recombination portion and 
the expansion portion must occur in a specific region downstream of the 
constrictor. 
This transition region of the nozzle is bounded axially by a nozzle 
diameter equal to about 1.5 times the constrictor diameter and a nozzle 
diameter equal to about 4.0 times the constrictor diameter, and by a 
divergence angle from the constrictor of between about 5 degrees and about 
15 degrees. 
The shape of the transition may be gradual or sharp. For example, a smooth 
shape may be used so long as the transition occurs within the region 
defined above, substantial recombination will occur resulting in a 
substantial increase in efficiency. 
One preferred arrangement having conical recombination and expansion 
portions is basically a bi-angle divergent nozzle. It creates a high 
pressure region in the recombination portion which enhances ion 
recombination and hence recovery of frozen flow losses. An increase in 
overall efficiency of about 7 percent has been achieved. 
The expansion portion has a cone half angle of between 20 and 40 degrees. 
The recombination portion has a cone half angle of between 5 and 15 
degrees. In addition, the ratio of diameters between the transition of the 
recombination and expansion portion and the constrictor or throat is 
preferably between about 1.5 and 4.0. In one optimized preferred 
embodiment the cone angles are seven degrees for the recombination portion 
and 20 degrees for the expansion portion. 
The arcjet thruster in accordance with the present invention also results 
in an arc voltage which is substantially higher than that of comparable 
conventional arcjet nozzle designs operating with the same power and flow 
inputs. This permits arcjet operation at a substantially lower current 
level for the same applied voltage which in turn implies increased arcjet 
lifetime, smaller overall system size, and better reliability.

One preferred embodiment of the arcjet thruster in accordance with the 
present invention is schematically illustrated in FIG. 3. The arcjet 
thruster 50 includes an electrically conductive anode body 52 having an 
anode cavity 54 therein which defines a convergent/divergent nozzle 56 
symmetrical about a central axis 58. In this embodiments, the anode cavity 
54 has a convergent portion 59 and a tandemly arranged conical divergent 
recombination portion 60 and a divergent conical expansion portion 62. 
Optionally, and as illustrated in FIG. 3, the anode cavity 54 may further 
include a cylindrical constrictor portion 64 upstream of and merging with 
recombination portion 60 coaxially with axis 58. The constrictor portion 
64 effectively constitutes a nozzle throat having a length "L". The length 
"L" is preferably about equal to the constrictor diameter "D". 
A cathode body 66, having a generally cylindrical shape, is coaxially 
positioned along the axis 58 and spaced from the convergent portion 59 of 
the anode body 52 by a gap 68. Cathode 66 preferably includes a generally 
conical pointed tip 70. An electrical current supplying means such as a DC 
power supply 72 is electrically connected to the cathode body 66 and to 
the anode body 52 to produce an electrical arc 74 across the gap 68. A 
vortex flow of propellant gas 76 is injected, preferably tangentially, 
along cathode tip 70 through gap 68 and radially and tangentially into the 
constrictor 64. The vortex flow of propellant 76 pushes one end of the arc 
74 downstream through the constrictor 64 causing the arc to diffusely 
attach to the anode 52 in either the recombination portion 60 or the 
divergent expansion portion 62 depending upon the supply pressure of the 
propellant 76. As previously described, the arc heats, disassociates and 
at least partially ionizes the propellant gas 76 as the gas passes through 
the constrictor 64. 
The expansion portion 62 has a greater rate of divergence (.theta..sub.2) 
than that of the recombination portion 60 (.theta..sub.1). The expansion 
portion 62 and recombination portion 60 are conically shaped in FIG. 3. It 
is to be understood that these portions need not be conical so long as the 
expansion portion has a rate of divergence greater than that of the 
recombination portion. 
The divergence of the recombination portion 60, being less than that of the 
divergent expansion portion 56, i.e., .theta..sub.1 .theta..sub.2, causes 
a temporary delay in the pressure reduction and the expansion of the 
ionized and disassociated propellant 76. This delay creates a relatively 
high pressure region in the divergent recombination portion 60 of the 
nozzle which permits a partial recombination of the ionized and neutral 
species of the propellant gas 76. A comparison of recombination rates at 
various pressures is shown in FIG. 5. This Figure illustrates that the 
delay at a relatively high pressure permits at least a partial recovery of 
frozen flow losses back into the gas. 
In other words, as the ions and neutral species recombine in the 
recombination portion 60, heat is returned to the gas which then is 
available to be converted to thrust as the gas expands through the 
divergent expansion portion 62 of the nozzle 56. Thus the portion of the 
propellant which recombines in the recombination portion 60 increases the 
overall energy conversion efficiency of the propellant gas 76 flowing 
through the nozzle 56 of the arcjet thruster 50. The attainable overall 
efficiency has been demonstrated, with the present invention, to increase 
from 33 to over 37 percent over the baseline nozzle having simply a 
straight divergence of 20 degrees. 
The specific impulse of the propellant gas for different power/flow rates, 
when utilized in the thruster in accordance with the present invention, is 
illustrated in FIG. 4. The specific impulse attained with hydrazine in the 
arcjet thruster in accordance with one preferred embodiment of the present 
invention, is illustrated by biangle nozzle curve 80. The specific impulse 
attributable to the prior art nozzle having a divergence cone angle of 20 
degrees, illustrated in FIG. 1 is shown by the baseline curve in FIG. 4. 
As can readily been seen, the specific impulse of the thruster in 
accordance with the present invention is about 10 to 20 seconds greater 
than that of the prior art nozzle at the power to flow ratios of 3.2 to 
3.8, which are of particular interest in thrusters of less than 2.5 Kw. 
The phenomenon believed to be responsible for the increase in efficiency 
observed is illustrated in FIG. 5. The energy normally lost as frozen flow 
can be recovered if the proper environment is created to accelerate the 
recombination and relaxation rates or to increase the time available for 
recovery and minimize the heat losses to the thruster anode walls. 
Recombination rates increase significantly at higher pressures. For 
example, at a pressure of one atmosphere, the recombination rate is about 
four times that of the same gas at half the pressure. In the thruster 
shown in FIG. 3, the recombination region 60 provides a relatively high 
pressure divergent region in which recombination and recovery of frozen 
flow energy can take place. 
The dimensional relationships between the divergent expansion portion and 
the recombination portion are important to an arcjet thruster having this 
improved efficiency. These relationships are broadly illustrated in the 
enlarged partial sectional view of FIG. 6. 
The transition 78 between the expansion portion 62 and the recombination 
portion 60 must occur within a transition region 84. The transition may be 
sharp, as in the biangle design, or may be a smooth curve, so long as the 
transition is within this transition region. In addition, the 
recombination and expansion portions may be conical as shown or a curved, 
trumpet shaped. 
The transition region 84 is directly related to the constrictor diameter D. 
The region 84 is axially bound by an upstream location equal to about 1.5 
D and a downstream location equal to about 4.0 D and between divergence 
angles of about 5 degrees and 15 degrees originating at the constrictor 
exit 86. 
In the conical configurations illustrated in FIGS. 3 and 6 it has been 
found that the overall efficiency is optimal when the recombination 
portion 60 has a cone half angle (.theta..sub.1) of between about 5 
degrees and 15 degrees and the expansion portion has a cone half angle 
(.theta..sub.2) of between 20 degrees and about 40 degrees. The diameter 
of the circular mouth 80 of the nozzle 56 preferably has a ratio with 
respect to the constrictor portion within a range of about 30 to 250. 
More specifically, the optimum efficiency for N.sub.2 H.sub.4 propellant 
maybe obtained with a .theta..sub.1 equal to about 7 degrees and 
.theta..sub.2 equal to about 20 degrees. Finally, it has been found that 
the length L of the constrictor portion 64 is optimum when it is about 
equal to the diameter of the constrictor portion 64 
The design of the nozzle according to the present invention which allows 
for recovery of frozen flow energy in a divergent recombination region 
with a relatively slow rate of propellant expansion just downstream of the 
nozzle throat or constrictor, followed by an expansion region of much 
higher rate of expansion produces a substantially higher overall 
electrical to kinetic energy conversion efficiency over previous designs 
of arcjet nozzles. Furthermore, the nozzle design results in arcjet 
electrical operation at an arc voltage substantially higher than that of 
conventional arcjet nozzle designs operating with the same power and flow 
rate inputs. 
For example, referring again to FIG. 4, a 1.7 Kw nozzle according to the 
present invention utilized an applied voltage of 176 volts and a current 
of 9.7 amps. In contrast, the conventional 1.7 Kw nozzle as shown in FIG. 
1 utilized a voltage of 126 volts with a current of 13.5 amps. 
Accordingly, in the case of the arcjet thruster of the present invention 
the current level is reduced by over 25 percent with the same power and 
flow rate inputs. This illustrates the potential for reduction of the 
cathode and anode erosion rates commonly present in conventional 
constricted arcjet thrusters. This has important arcjet life and also 
arcjet system level benefits. For example, the power supply may be 
smaller, the size and mass of electrical cabling may be reduced, and so 
forth. 
While the invention has been described above with reference to specific 
embodiments thereof, it is apparent that many changes, modifications and 
variations can be made without departing from the inventive concept 
disclosed herein. Accordingly, it is intended to embrace all such changes, 
modifications and variations that fall within the spirit and broad scope 
of the appended claims. All patent applications, patents and other 
publications cited herein are incorporated by reference in their entirety.