february 1, 2005hyperion erau 1 thermal analysis of a radiation shield for antimatter rocketry...

February 1, 2005 HYPERIONERAU

1

Thermal Analysis of a Radiation Shield for Antimatter Rocketry Concepts

Jon Webb

Embry Riddle Aeronautical University


2

Agenda

• Why Hyperion

• Rocket Principles

• Why antimatter

• Velocity Profile and Fundamentals

• Thermal Considerations


3

Why fly so fast in space?

Space flight takes to long!


4

Microgravity Environment

Skeletal and Muscular atrophycan make it impossible toreturn to the surface of Earth!


5

Cosmic Radiation

Radiation in space is lethal!!


6

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


7

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


8

Chemical Rocketry

• LO/LH2


9

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


10

What is antimatter (positrons)

• Produces photons isotropically• Produces photons back to back• 0.511 MeV per photon


11

How do we propel a S/C


12

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


13

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


14

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


15

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


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


17

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)


18

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


19

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


20

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.


21

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


22

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


23

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


24

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


25

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


26

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


27

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


28

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


29

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


30

Convective Cooling

LH2 Properties

- Cp = 10,000 J/ (kg.K)- h = 210 W/(m2.K)- TLH2 = 16 K- Tshld = 3300 K


31

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


Po

wer

(M

W)

Power


32

LH2 Mass Flow Rate

3.

4.

5.

22

LHshieldpLH TTC

Qm

pLH C

hAm 2

s

kgxAmLH 021.02


33

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


Mas

s F

low

Rat

e (k

g/s

)

Mass Flow Rate


34

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


35

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


36

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


37

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


38

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


39

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


40

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


41


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


42


Positron Mass Vs. Burnout Velocity

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25


Po

sitr

on

Mas

s (m

icro

-gra

ms)

Series1


43


• 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


44


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


IML

EO

/H2

Mas

s (M

t)

IMLEO

H2 Mass

f

isp M

MgIV ln


45


Mass of Positrons Vs. dV

0

20

40

60

80

100

120

140

0 5 10 15 20 25


Mas

s o

f P

osi

tro

ns

(mic

ro-g

ram

s)

e+ mass


46

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


Bu

rn T

ime

(min

ute

s)

Series1


47

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


48

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


49

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


50

Concluding Remarks

• Antimatter offers extraordinary propulsion capabilities

• Unfortunately thermal challenges are quite daunting

• Production and storage are a whole different challenge


51

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


52

Questions or Comments

• ????


53

Backup Slides


54

Propulsion Systems

Goal is to obtain highest Isp


55

Antiprotons

• Statistically complicated• Produces massive particles


56

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


57

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


58

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


59

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


60

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


61

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


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

february 1, 2005hyperion erau 1 thermal analysis of a radiation shield for antimatter rocketry...

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