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Thermal Analysis of a Radiation Shield for Antimatter Rocketry Concepts Jon Webb Embry Riddle Aeronautical University. Agenda. Why Hyperion Rocket Principles Why antimatter Velocity Profile and Fundamentals Thermal Considerations. Why fly so fast in space?. Space flight takes to long!. - PowerPoint PPT Presentation
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February 1, 2005 HYPERIONERAU
1
Thermal Analysis of a Radiation Shield for Antimatter Rocketry Concepts
Jon Webb
Embry Riddle Aeronautical University
February 1, 2005 HYPERIONERAU
2
Agenda
• Why Hyperion
• Rocket Principles
• Why antimatter
• Velocity Profile and Fundamentals
• Thermal Considerations
February 1, 2005 HYPERIONERAU
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Why fly so fast in space?
Space flight takes to long!
February 1, 2005 HYPERIONERAU
4
Microgravity Environment
Skeletal and Muscular atrophycan make it impossible toreturn to the surface of Earth!
February 1, 2005 HYPERIONERAU
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Cosmic Radiation
Radiation in space is lethal!!
February 1, 2005 HYPERIONERAU
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Rocket Principles
• Specific Impulse is the fuel efficiency of a rocket engine
• As fuel energy density increases so does Specific Impulse and delta V
• The equation for Specific Impulse is:
g
cI sp
February 1, 2005 HYPERIONERAU
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Rocket Principles
• Thrust is a force
• Thrust is the time rate change of propellant momentum
• Momentum is the mass of fuel ejected multiplied by the exhaust velocity
February 1, 2005 HYPERIONERAU
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Chemical Rocketry
• LO/LH2
February 1, 2005 HYPERIONERAU
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Fuel Energy Density
Fuels Energy Release J/kg Converted Mass Fraction
Chemical
LO/LH 1.35 x 107 1.25 x 10-10
Atomic Hydrogen 2.18 x 108 2.40 x 10-9
Metastable Helium 4.77 x 108 5.30 x 10-9
Nuclear Fission238U 8.20 x 1013 9.10 x 10-4
Nuclear Fusion
DT (0.4/0.6) 3.38 x 1014 3.75 x 10-3
CAT-DT (1.0) 3.45 x 1014 3.84 x 10-3
D3He (0.4/0.6) 3.52 x 1014 8.90 x 10-3
pB11 (0.1/0.9) 7.32 x 1013 8.10 x 10-4
Matter-Antimatter 9.00 x 1016 1
February 1, 2005 HYPERIONERAU
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What is antimatter (positrons)
• Produces photons isotropically• Produces photons back to back• 0.511 MeV per photon
February 1, 2005 HYPERIONERAU
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How do we propel a S/C
February 1, 2005 HYPERIONERAU
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Shield Design (Rad. Lengths)
Absorbed Energy Vs. Radiation Lengths
0
20
40
60
80
100
120
0 1 2 3 4 5
Radiation Lengths (#)
Ab
sorb
ed E
ner
gy
(% o
f in
cid
ent
ener
gy)
Series1
February 1, 2005 HYPERIONERAU
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Shield Design
• Made of Tungsten
• Melting point of 3600 K
• Density of 19.3 gm/cm3
• Radiation length is 0.35 cm
• 5 radiation lengths thick
• Roughly 1.75 cm thick
February 1, 2005 HYPERIONERAU
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Shield Design (Dimension)
Shield Area Vs. Shield Radius
0
1
2
3
4
5
6
7
8
9
10
0 100 200 300 400 500 600
Shield Area (m^2)
Shi
eld
Rad
ius
(m)
Series1
February 1, 2005 HYPERIONERAU
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Shield Design (Mass)
Shield Mass Vs. Inner Area (5 rad lengths)
0
20
40
60
80
100
120
140
160
180
200
0 100 200 300 400 500 600
Shield Area (m^2)
Sh
ield
Mas
s (M
t)
Series1
February 1, 2005 HYPERIONERAU
16
Momentum Attenuation
• Compton Scattering• Brehmstralling• Photo-electric Effect- photons/electrons ejected at
random angles- Might reduce
momentum/cosine average
• Monte-Carlo analysis is being developed to research effects
electron
Atom
February 1, 2005 HYPERIONERAU
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Thermal Problem
• Energy is lost as heat in the tungsten shield
• We must find a way to dissipate the heat in order to augment the thrust
• We must find a way to regain the energy lost from the heat to augment efficiency (Isp)
February 1, 2005 HYPERIONERAU
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Shield Thermal Loading
Shield Inner Area Vs. Thermal Loading (Constant 3300 K)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600
Shield Area (m^2)
Th
erm
al E
ner
gy
(GJ)
Series1
February 1, 2005 HYPERIONERAU
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Radiative Cooling
• For highest Isp we must find the steady state condition where blackbody radiation equals input energy.
• This will severely limit the thrust
Eradiated
E thermal , P thrust
February 1, 2005 HYPERIONERAU
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Radiative Cooling
• View Factors must be examined
• The extreme limits of the pi/2 to –pi/2 shield may re-radiate energy into the other side of the shield.
February 1, 2005 HYPERIONERAU
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Radiative Cooling
• We may want to consider making the shield flat and very large, or decrease the angular limits of the shield.
• Annihilate e+ inside shield
February 1, 2005 HYPERIONERAU
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Radiative Cooling
22
2cos
DR
R
D
AP
R
R
22
1sinDR
R
All Values in Radians
minmax sinsincos
max
min
cos1
cos
d
22
2cos
DR
R
February 1, 2005 HYPERIONERAU
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Radiative Cooling
Shield Radius Vs. Cosine Average (Large Shield)
0.6368
0.63682
0.63684
0.63686
0.63688
0.6369
0.63692
0.63694
0.63696
0 2 4 6 8 10 12
Shield Radius (m)
Co
sin
e A
vera
ge
Series1
February 1, 2005 HYPERIONERAU
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Radiative Cooling
Shield Radius Vs. Cosine Average (Small Shield)
0.585
0.59
0.595
0.6
0.605
0.61
0.615
0.62
0.625
0.63
0.635
0.64
0 0.2 0.4 0.6 0.8 1 1.2
Shield Radius (m)
Co
sin
e A
vera
ge
Series1
February 1, 2005 HYPERIONERAU
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Radiative Cooling
Flat Shield Radius Vs. Mass
0
20
40
60
80
100
120
0 2 4 6 8 10 12
Shield Radius (m)
Sh
ield
Mas
s (M
t)
Series1
February 1, 2005 HYPERIONERAU
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Radiative Cooling
1. 7.
2.
3. 8.
4.
5.
6.
4TAq 2mcq
42 TAmc 42 TAcm
42
2TA
cm
2
42
c
TAm
cmF 2
cos
c
TAF
4cos
February 1, 2005 HYPERIONERAU
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Radiative CoolingRadiated Power Vs. Shield Inner Area
0
200
400
600
800
1000
1200
0 100 200 300 400 500 600
Shield Inner Area (m^2)
Rad
iate
d P
ower
(M
W)
Series1
February 1, 2005 HYPERIONERAU
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Radiative Thrust
Shield Inner Area Vs. Thrust (Radiative Cooling)
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600
Shield Area (m^2)
Th
rust
(N
)
Series1
February 1, 2005 HYPERIONERAU
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Convective Cooling
• Use liquid Hydrogen or Ammonia to absorb excess heat
• Allow fluid to expand across the shield to produce thrust with a decreased Isp
February 1, 2005 HYPERIONERAU
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Convective Cooling
LH2 Properties
- Cp = 10,000 J/ (kg.K)- h = 210 W/(m2.K)- TLH2 = 16 K- Tshld = 3300 K
February 1, 2005 HYPERIONERAU
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Convective Power Transfer
1. 2. 2LHshield TThAQ 2
689640m
WxAQ
Energy Transfer Rate to LH2 Vs. Shield Inner Area
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Shield Inner Area (m^2)
Po
wer
(M
W)
Power
February 1, 2005 HYPERIONERAU
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LH2 Mass Flow Rate
3.
4.
5.
22
LHshieldpLH TTC
Qm
pLH C
hAm 2
s
kgxAmLH 021.02
February 1, 2005 HYPERIONERAU
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LH2 Mass Flow Rate
Mass Flow Rate Vs. Shield Inner Area
0
2
4
6
8
10
12
0 100 200 300 400 500 600
Shield Inner Area (m^2)
Mas
s F
low
Rat
e (k
g/s
)
Mass Flow Rate
February 1, 2005 HYPERIONERAU
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Convective Thrust from LH2
6.
7.
9.
10.
222 HHH VxmF
22
2
LHH m
EV
22 2 LHshieldpH TTCV
s
mVH 32.81042
22 2 Hshieldpp
H TTCC
AhF
February 1, 2005 HYPERIONERAU
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Convective Thrust from LH2
Thrust due to expanding Hydrogen Vs. Shield Area
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500 600
Shield Area m^2
Th
rust
(kN
)
Thrust
February 1, 2005 HYPERIONERAU
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Shield Thrust to Weight Ratio
Acceleration Vs. Shield Area
0.48
0.485
0.49
0.495
0.5
0.505
0 200 400 600 800 1000 1200
Shield Area (m^2)
Acc
eler
atio
n (
m/s
^2)
Series1
February 1, 2005 HYPERIONERAU
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Convective Specific Impulse
11.
12.
13.
14.
222
cosHshieldp
peeT TTC
C
AhcmF
gm
FI
LHspH
22
g
TTCI
Hshieldp
spH
222
sIHsp
8262 gmm
FFI
eeLH
eeHsp
2
2
February 1, 2005 HYPERIONERAU
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Specific Impulse vs. Shield Temp.
Specific Impulse vs. Shield Temperature
0
200
400
600
800
1000
1200
0 1000 2000 3000 4000 5000 6000
Shield Temperature (K)
Sp
ecif
ic I
mp
uls
e (s
)
Series1
February 1, 2005 HYPERIONERAU
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Thrust Augmentation
• Shield Mass: 170 Mt• 10 Shields• Shield Area: 10,000m2
• Thrust: 1.70 MN• Isp: 826 seconds
5 rad. lengths
10 sub-shields
February 1, 2005 HYPERIONERAU
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Convective Case Study 1
• MS/C = 40 Mt
• F = 1.70 MN• A = 10,000 m2
• P = 6,896 MW
• Msh = 170 Mt
• Md = 210 Mt
• Mdote+ = 7.662 x 10-8 kg/s
• MdotH2 = 210 kg/s
February 1, 2005 HYPERIONERAU
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Convective Case Study 1
Initial Mass in Low Earth Orbit/Hydrogen Propellant Mass Vs. dV (400 Mt Payload)
0
500
1000
1500
2000
2500
3000
0 5 10 15 20 25
Change in Velocity (km/s)
IML
EO
/Hyd
rog
en M
ass
(Mt)
IMLEO
Liquid Hydrogen Mass
f
isp M
MgIV ln
February 1, 2005 HYPERIONERAU
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Convective Case Study 1
Positron Mass Vs. Burnout Velocity
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20 25
Change in Velocity (km/s)
Po
sitr
on
Mas
s (m
icro
-gra
ms)
Series1
February 1, 2005 HYPERIONERAU
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Convective Case Study 2
• MS/C = 40 Mt
• F = 261.9 kN• A = 1130.4 m2
• P = 780 MW
• Msh = 19.2 Mt
• Md = 66.113 Mt
• Mdote+ = 4.33 x 10-9 kg/s
• MdotH2 = 23.7 kg/s
February 1, 2005 HYPERIONERAU
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Convective Case Study 2
Initial Mass in Low Earth Orbit/H2 Propellant Mass Vs. dV (400 Mt Payload)
0
100
200
300
400
500
600
700
800
900
0 5 10 15 20 25
Change in Velocity (km/s)
IML
EO
/H2
Mas
s (M
t)
IMLEO
H2 Mass
f
isp M
MgIV ln
February 1, 2005 HYPERIONERAU
45
Convective Case Study 2
Mass of Positrons Vs. dV
0
20
40
60
80
100
120
140
0 5 10 15 20 25
Change in Velocity (km/s)
Mas
s o
f P
osi
tro
ns
(mic
ro-g
ram
s)
e+ mass
February 1, 2005 HYPERIONERAU
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Convective Case Study
Burn Time Vs. Burnout Velocity
0
20
40
60
80
100
120
140
160
180
200
0 5 10 15 20 25
Change in Velocity (km/s)
Bu
rn T
ime
(min
ute
s)
Series1
February 1, 2005 HYPERIONERAU
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Further Convective Work
• Combine case studies into 3-D graphs (dV vs. IMLEO/H2/e+ mass vs. shield mass/radius/area)
• Research energy/heat deposition as a function of thickness plus H2 gaps
• Increase SA without increasing mass
February 1, 2005 HYPERIONERAU
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Electrical Power Production
• Another option is to use a working fluid that can be expanded through a turbine to produce electricity
• This would allow for low thrust missions and provide the spacecraft with electricity for its subcomponents
February 1, 2005 HYPERIONERAU
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Tri-Modal Operation
• Lastly the engine could be cooled with LH2 when large thrust is needed and operate in a radiative mode to slowly accelerate S/C in interplanetary space.
• When the engine is in a radiative mode, electricity can be produced
February 1, 2005 HYPERIONERAU
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Concluding Remarks
• Antimatter offers extraordinary propulsion capabilities
• Unfortunately thermal challenges are quite daunting
• Production and storage are a whole different challenge
February 1, 2005 HYPERIONERAU
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Concluding Remarks
• Advantages warrant serious look
• Possible high Isp uses as a thermal rocket by increasing the shield surface area
• Best method is to use the reflecting shield
February 1, 2005 HYPERIONERAU
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Questions or Comments
• ????
February 1, 2005 HYPERIONERAU
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Backup Slides
February 1, 2005 HYPERIONERAU
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Propulsion Systems
Goal is to obtain highest Isp
February 1, 2005 HYPERIONERAU
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Antiprotons
• Statistically complicated• Produces massive particles
February 1, 2005 HYPERIONERAU
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Flight TimesMinumum Rendezvous Times Vs. Isp for a 5000 kg Spacecraft (dm/dt = 50 mg/s)
0
50
100
150
200
250
0 20 40 60 80 100 120 140 160 180
Isp (thousand seconds)
Tra
nsfe
r T
ime (
weeks)
0 0.002 0.004 0.006 0.008 0.01 0.012
<cos(theta)>
Mercury
Venus
Mars
Jupiter
Series5
February 1, 2005 HYPERIONERAU
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Flight TimesMinimum Rendezvous Time Vs. Isp for a Spacecraft of 5000 kg (dm/dt = 50 mg/s)
0
50
100
150
200
250
300
350
400
450
500
0 20 40 60 80 100 120 140 160 180
Isp (thousand seconds)
Tra
nsfe
r T
ime (
mo
nth
s)
0 0.002 0.004 0.006 0.008 0.01 0.012
<cos(theta)>
Saturn
Uranus
Neptune
Pluto
Series5
February 1, 2005 HYPERIONERAU
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Flight TimesMinimum Rendezvous Times Vs. Isp for a Spacecraft of 50 mT (dm/dt = 50 mg/s)
0
50
100
150
200
250
0 5 10 15 20 25 30 35
Isp (million seconds)
Tra
nsfe
r T
ime (
days)
0 0.5 1 1.5 2 2.5
<cos(theta)>
Mercury
Venus
Mars
Jupiter
Series5
February 1, 2005 HYPERIONERAU
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Flight TimesMinimum Rendezvous Time Vs. Isp for a Spacecraft of 50 mT (dm/dt = 50 mg/s)
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30 35
Isp (million seconds)
Tra
nsfe
r T
ime (
days)
0 0.5 1 1.5 2 2.5
<cos(theta)>
Saturn
Uranus
Neptune
Pluto
Series5
February 1, 2005 HYPERIONERAU
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Lunar Flight TimesLunar Rendezvous Time and Propellant Mass Vs. <cos (theta)>for a spacecraft of 10 mT
dm/dt = 50 mg/s
0
10
20
30
40
50
60
0 0.002 0.004 0.006 0.008 0.01 0.012
<cos(theta)>
Tra
nsfe
r T
ime (
days)
0
50
100
150
200
250
Pro
pellan
t M
ass (
kg
)
Moon Trip Time
Propellant Mass
February 1, 2005 HYPERIONERAU
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Lunar Flight TimesLunar Rendezvous Time Vs. <cos(theta)> and Propellant Mass for a 10 mT spacecraft, dm/dt
= 50 mg/s
0
10
20
30
40
50
60
70
80
90
0 0.5 1 1.5 2 2.5
<cos(theta)>
Tra
nsfe
r T
ime (
ho
urs
)
0
2
4
6
8
10
12
14
16
18
Pro
pellan
t M
ass (
kg
)
Lunar Trp Time
Propellant Mass
February 1, 2005 HYPERIONERAU
62
Interstellar Flight Times
Mrocket Mprop Velocity Tt (years) To (years)400 Mt 53.9 Mt 0.10 c 45.7 45.5400 Mt 170 Mt 0.50 c 9.59 8.41400 Mt 360 Mt 0.98 c 5.12 1.65