Download Electric Rocket Propulsion

Electric Rocket Propulsion
A. Background
Electric Propulsion-1
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Electric Propulsion - Accelerators
Electrothermal Electromagnetic
Pressure,∇p
Lorentz,
r
Fm
Electrostatic
r
Electrostatic, Fe
Accel.
Force
Electrically heat
propellant and use
nozzle expansion
Magnetic and elec.
fields accelerate
charged particles
Isp(s)
300-1,500
1,000-10,000
2,000-100,000+
Thrust
Weight
<10-3
<10-4
<10-4−10-6
Electric Propulsion-2
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
Static electric field
alone accelerates
charged particles
AE4451 Propulsion
Electrical Heating
• Current passing through
conductor heats it by
amount proportional to
its resistance
• Wire
Current
(A=C/s)
Resistance
(Ohms)
2
&
Q=J R
J
• Gas (Plasma)
Discharge
Cathode
– resistance due
V
r
r
to collisions E = −∇V
Electric Propulsion-3
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
e-
r
E
J
i+
Anode
AE4451 Propulsion
Forces on a Charged Particle
• To examine how to use electrical energy to
accelerate a propellant, consider acceleration
of a particle with mass m and charge q
r Elec.r Field Mag.r Field
du
r
r
(1)
m
= qE + q u × B + p
dt Electrostatic Lorentz Collisional Force
(
Force
q
+
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
Force (Momentum Transfer)
r
u
q +
r
Fm
r
B
r
u r
Fm
`
Electric Propulsion-4
r
E
r
Fe
)
r
B
AE4451 Propulsion
Motion of Charged Particle in E&B Fields
• How does charged particle move in electric
r
and magnetic fields
r
du q r
= E
E
• Electric field only
dt m
+
– electron lighter, higher accel.
r
• Magnetic field only
r
du q r r
= (u × B )
– particle gyrates
B
dt m
r
(centripedal accel.)
r r
u
mu × B
– radius of gyration rg = qB 2
qB
– frequency of gyration ωg =
rg
m
– No work; B and F perpendicular
Electric Propulsion-5
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Induced Magnetic Fields
• In general, current flow induces a B field
– B field induced by
linear current
– B field induced
by coil
r
J
Electric Propulsion-6
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
r
B
r
B
From Space Propulsion Analysis
and Design, Humble, Henry and
Larson, 1995
AE4451 Propulsion
Motion of Charged Particle in E&B Fields
• Crossed E and B fields
– E field accelerates
particle upward
r
– B field causes
E
acceleration
perpendicular to u
– overall result is drift
velocity normal
r r to E and B
r E×B
ud =
2
B
Electric Propulsion-7
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
r
B
heavy
r
ud
light
AE4451 Propulsion
Plasmas
• Gas composed of equal “amount” of negatively
and positively charged particles
– electrically neutral
– negative particles usually e– positive particles are positive ions
– typically most of gas molecules remain
neutral
• Momentumrequation for plasma
r r
 ∂u r r 
ρ  + u ⋅ ∇u  = −∇p + j × B
Current Density
 ∂t

(A/m2)
Electric Propulsion-8
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Induced E Fields – Hall Effect
• Electron acceleration
– lighter e- accelerate more quickly
and accommodate to flow field (most of j)
– collisional coupling (momentum) of electrons
and heavies (ions and neutrals)
is weak
r
r
r r r r B ∇pe
⇒ E =η j − u × B + j ×
−
(2)
ne e nee
plasma
resistivity (Ωm)
Induced
Hall Effect
E field due
η = mevce nee 2 to plasma accelerates heavy
particles in charge
motion
collision freq.
neutral plasma
electrons with heavies
Electric Propulsion-9
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
electron
pressure
term
AE4451 Propulsion
Electric Rocket Propulsion
B. Examples
Electric Propulsion-10
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Electrothermal Rockets
• Resistojet (1W-10kW)
– walls hotter than gas,
lower Tmax
– can combine with
chemical heating, e.g.,
hydrazine monopropellant
• Arcjet (1 kW- 10 MW)
– high Tarc>Twall
(1-4×104 K)
– must mix with
rest of gas
– very high To,
frozen flow losses in nozzle
Electric Propulsion-11
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
Insulation
arc unstable
Space Propulsion Analysis and Design,
Humble, Henry and Larson, 1995
AE4451 Propulsion
Resistojets
• Heating methods
– flow over coils of wire
– flow through hollow tubes
– flow over heated cylinder or plate
• Material limits temperature/performance
– conducting materials < 2700 K
rhenium, refractory metals/alloys (tungsten,
tantalum, molybdenum), platinum, cermets
– max Isp ~ 300 sec
• Power supply
– AC or DC
2
&
– Power = Q = V R = m
& c p ∆T
Electric Propulsion-12
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Arcjets
• Gas heated by electrical discharge (arc)
– electrically conducting gas: plasma
r
• Joule heating
from
(2)
r
r r
r r r r B ∇pe
E =η j − u × B + j ×
−
Q& = j ⋅ E = m& c p ∆T
ne e ne e
r r r r
2
= η j − j ⋅ u × B − j ⋅ ∇pe nee
Hall Effect
r r r r
normal to j
2
= η j + u ⋅ j × B − j ⋅ ∇pe nee
(
(
)
)
Resistive Work from Work from
Heating EM force pressure grad.
no work
• Nozzle and electrode erosion
– high temperature, current arc
• Isp for H2 ~1200-1500 sec
Electric Propulsion-13
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
1.8 kW Hydrazine Arcjet
• Telstar IV application
– stationkeeping
• Hot gas from catalytically
decomposed liquid
N2H4
• Heated valve
prevents N2H4
from freezing
• Isp~570 sec
• τ~230 mN
(~40mg/s)
Electric Propulsion-14
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
Space Propulsion Analysis and Design,
Humble, Henry and Larson, 1995
AE4451 Propulsion
Arcjet with Applied Magnetic Field
• High current density in arc
tends to destroy electrodes
• Add soleniod B Field
– adds azimuthal drift
velocity to arc
– improves azimuthal
symmetry of gas
temperature
– reduces local electrode
heating, reduces erosion
– needed for high powers
(≥100 kW)
• Microwave discharge
– alternate to arc heating
Electric Propulsion-15
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
Space Propulsion Analysis and Design,
Humble, Henry and Larson, 1995
AE4451 Propulsion
Electromagnetic Propulsion Systems
• Use applied or induced magnetic fields to
produce acceleration of propellant
– high currents/
powers required
to produce
significant
induced fields
– high power available
only (normally) in
pulsed operation
Space Propulsion Analysis and Design,
Humble, Henry and Larson, 1995
Electric Propulsion-16
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Pulsed Plasma Thruster
• Propellant produced by vaporizing solid
material with discharge
• B field induced by discharge also acts to
accelerate vaporized propellant
• Advantage of simplicity
• Acceleration
force
~ j2
(discharge current)
Space Propulsion Analysis and Design,
Humble, Henry and Larson, 1995
Electric Propulsion-17
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Magnetoplasmadynamic (MPD) Thrusters
• Resemble arcjets
• Lower flow densities to
attain higher exhaust
velocity
• Diffuse discharge,
low erosion
• Self field requires high J
• Applied B field
– allows higher V
at lower discharge
currents
– increase accel.
– larger Hall effect
Self-Field MPD Thruster
Applied-Field MPD Thruster
Electric Propulsion-18
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
Space Propulsion Analysis and Design,
Humble, Henry and Larson, 1995
AE4451 Propulsion
MPD Thrusters (con’t)
• Most efforts focused on applications with
exhaust velocities (Isp) greater than arc jets
• Typically require higher powers than currently
available on in-space vehicles
• Exhaust speed ue ∝ j 2 m
&
– limited by erosion
and oscillations at high j
Electric Propulsion-19
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Hall Thruster
•
•
Hall effect most noticeable at
low particle densities
Stationary Plasma Thruster
(SPT)
– developed in Russia
– 10’s kW
– axial current flow
across radial B
generates azimuthal
electron flow
– induced (axial) Hall E
accelerates ions
– also called “gridless”
(neutral) ion thruster
– 1500-2000 s Isp with >50%
efficiency using Xe and no
oscillations like MPD
Electric Propulsion-20
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
Space Propulsion Analysis and Design,
Humble, Henry and Larson, 1995
AE4451 Propulsion
Electrostatic Thrusters
• Ion engine example
• Near vacuum required
• Ion source
– usually electron
A
bombardment
plasma
– also ion contact:
propellant flowing
through hot porous
tungsten
– field emission: charged
spray droplets/particles
• Electrons added to
neutralize exhaust
– thermionic emitters
Electric Propulsion-21
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
Accelerator
L
Space Propulsion Analysis and Design,
Humble, Henry and Larson, 1995
AE4451 Propulsion
Electrostatic Thruster Performance
• Maximum exhaust velocity (Isp)
q
theoretically limited by voltage ue = 2 m (Vexit − Vinlet )
difference across accelerator
∆V ( volts) m
= 13,800
for singly ionized
MW
s
• High thrust requires high mass
flowrates and therefore current j = nque accelerator electrode
spacing
(and number, n) densities
32
4ε o 2q ∆V
Child-Langmuir
• Ion current limited
jmax =
2
Law
9
m L
by space-charge
permittivity ε = 8.854 × 10 −12 Farad
– field from lots of ions
of free space o
meter
32
overcomes applied
∆
V
(
volts
)
Amps
−8
jmax = 5.44 × 10
E field
2
2
m
(
)
MW
L
m
for singly ionized
AE4451 Propulsion
Electric Propulsion-22
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
Electrostatic Thruster Thrust
τ = m& ue = jA(m q )ue A=cross-sectional area flow
• Maximum thrust
m
4ε o
τ max = jmax A ue =
q
9
τ max = (8ε o
for circular cross-section
τ max = (2π
of diameter, D
2q ∆V
m 2q
A
∆V
2
m L
q m
9 )A ∆V 2 L2
32
9 )ε o (D L ) ∆V
2
−12
2
(
)
= 6.18 × 10 D L ∆V in Newtons
2
2
• High τ requires high ∆V and aspect ratio
– space charge⇒D/L ~1
D
L
– use many small ion beams to
get more thrust
Electric Propulsion-23
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Electrostatic Thruster Thrust
• For fixed specific impulse
τ max
τ max
A
4
=
9ε o
I sp = ue
2q ∆V 3 2 m
A I sp
2
m Laccel q
∝ mq
– best propellant for high thrust
• heavy molecules (particles)
• xenon (Xe) good choice (MW=131.3)
Electric Propulsion-24
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Electrostatic Thruster Power
Power = I ∆V = jA ∆V
• Electrical energy converted to kinetic
energy with some efficiency
1 2
ηconv I ∆V = m& ue
2
• Must also account for energy used to
create ions – ionization losses
– given by ionization potential for atom
times current
m&
Pion loss = ε I I = ε I q
m
Electric Propulsion-25
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Electron Bombardment Xe+ Engine Example
• Operating conditions
– ∆V=700 V, L=2.5 mm, 2200 holes (grids)
each with D=2.0 mm
– MW(Xe)=131.3, εI(Xe)=12.08 eV
• Determine
– τ,
– u.e, Isp
–m
– power required including ionization loss
Electric Propulsion-26
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
AE4451 Propulsion
Solution
τ max = 6.18 × 10
−12
(D L ) ∆V
(2 / 2.5) 700
2
2
2
2
= 6.18 × 10
= 1.94 × 10−6 N / grid
τ max ,total = 2200 grids (1.94 × 10−6 N / grid ) = 4.3mN
−12
ue = 13,800 ∆V MW m s = 13,800 700 131.3 m s
ue = 31,860 m s ⇒ I sp = 3248 s
m& = τ ue = 1.34 × 10−4 g s
−27
m
=
1
.
67
×
10
MW kg
P = Pexhaust + Pion loss = m& 2u + ε I q m& m
= 2.19 × 10−25 kg
= 67.9W + 1.18W
q = 1.602 × 10−19 C
2
e
P = 69.1W
Electric Propulsion-27
Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.
maximum effic. =67.9/69.1
= 98.3%
for singly ionized molec.
AE4451 Propulsion