1. Radiative Heat Trade-Offs for Spacecraft Thermal Protection
A Practical Guide to
Thermal Blanket/Multi-Layer
Insulation Design
Scott Franke
AFRL/VSSV

2. Thermal Radiation Trade-offs Overview
Thermal Radiation Basics
Properties and Relations: View Factor, absorptivity, emissivity, Stefan-Boltzmann, thin-plate ODE
Radiation Geometries: Parallel Plates, Convex Object in Large Cavity
Sources: Solar Radiation, Earth Radiation, Albedo
Materials
Radiative Comparison
Long Term Exposure Degradation
Multi-Layer Insulation (Thermal Blanket / Shroud)
Orbit Considerations
GEO, LEO, Lagrange points, Inclination
Design Examples
Design for Stabilization of Oscillating Heat Flux
@ LEO
Oscillation due to orbit: sun/shadow (umbra)
Design for Specific Temperature with Constant Heat Flux
@ Sun-Earth Lagrange (L2) point:
Stationary position relative to Earth.
Summary/Questions

3. Thermal Radiation Basics: Properties and Relations
No medium required, only “optical” transmission
Only effective heat transfer method in “empty” space
unless very low earth orbit (drag  convection  conduction)
Properties for transmission:
Absorptivity, α: ability for the surface to absorb radiation.
Emissivity, ε: ability for the surface to emit radiation.
View factor, F12: relates fraction of thermal power leaving object 1 and reaching object 2.
Used when a sink can see more than one source
Relations:
Blackbody vs. Greybody radiation
Blackbody is ideal emitter (max case): ε ≡ 1
Greybody is anything less than blackbody, 0 < ε < 1
Stefan-Boltzmann relation (any greybody):
Surface finish dependent;
want low values for both
Note: q is really area-normalized q-dot (W/m2)
σ = Stefan-Boltzmann Constant

4. Thermal Radiation Basics: Properties and Relations
Simple time ODE for radiantly heated thin plate:
In order to use such a simple equation: Assumptions.
1) Our thermal blanket/MLI behaves as a “thin plate”
2) Density is uniform
3) Temperature is same everywhere on blanket (big assumption)
Why bother then?
Because it gives us a good rough approximation without using a FEM model
Hard to model with FEM  thermal blanket irregular/unpredictable geometry
“Reliably vague” (ballpark reliability)
ρ = material density
σ = Stefan-Boltzmann
h = material thickness
c = material heat capacitance

5. Thermal Radiation Basics: Radiation Geometries
Heat flux (W/m2) between:
Two large (infinite) plates
Small Convex Object in a
Large Cavity 1 2
F12 = 1 (View Factor) 1 2
F12 = 1

6. Thermal Radiation Basics: Sources Flux (W/m2)
Solar Radiation
Sun radiates at blackbody temperature of ~5000K  Solar Constant: ~1350 W/m2
q = 1350 · α · cos(Ψ)
Ψ is angle between S/C normal to the sun
Largest heat source by far
Function of S/C attitude only
Earth Blackbody Radiation
View factor specific (how close you are to earth compared to sun)
T (Earth blackbody) = 289 K
q = σ · T4 · α · F
Function of S/C attitude AND orbit
Earth Albedo
Reflected light from sun
q = 1350 · AF · α · F · cos(θ)
Function of S/C attitude, orbit, AND season/latitude/longitude
AF = Albedo Factor ~ 0.36 on average
AF is a measure of reflectivity of Earth’s surface.
θ = Angle between S/C surface and sun
(θ is 90 degrees out of phase with Ψ)

7. Thermal Radiation Trade-offs Overview
Thermal Radiation Basics
Properties and Relations: View Factor, absorptivity, emissivity, Stefan-Boltzmann, thin-plate ODE
Radiation Geometries: Parallel Plates, Convex Object in Large Cavity
Sources: Solar Radiation, Earth Radiation, Albedo
Materials
Radiative Comparison
Long Term Exposure Degradation
Multi-Layer Insulation (Thermal Blanket / Shroud)
Orbit Considerations
GEO, LEO, Lagrange points, Inclination
Design Examples
Design for Stabilization of Oscillating Heat Flux
@ LEO
Oscillation due to orbit: sun/shadow (umbra)
Design for Specific Temperature with Constant Heat Flux
@ Sun-Earth Lagrange (L2) point:
Stationary position relative to Earth.
Summary/Questions

8. Materials: Radiative Property Comparison
Material absorptivity (α) varies with
temperature of source.
Anodized Aluminum (13)
Polished Aluminum (15)

9. Materials: Radiative Property Comparison
Not easily found via web
 some data on certain materials, emissivity is searchable

10. Materials: Degradation
10 yrs
@ Simulated
GEO
(also, LDEF)
Cosmic Rays, Solar Storms, etc. deteriorate paint over time.
Thin films used in for Multi-Layer Insulation (MLI) can also degrade over long term:
Tedlar thin film exposed
To 3 yrs simulated GEO

11. Long Duration Exposure Facility (LDEF) MLI Test Blanket

12. Materials: Multi-Layer Insulation (MLI) / Thermal Blanket
Typically Aluminized Mylar
Hubble ST: Aluminized Teflon FEP
(fluorinated ethylene propylene)
“Dacron” Polyethylene Terephthalate (PET) deposited between each sheet
Layers expand like a balloon due to lack of
pressure on orbit  negates conductivity
Protects against orbital debris / micrometeoroids
n layers
Heat leaking through layers.
Ф = maximum heat flux encountered
Dacron filling

13. Thermal Radiation Trade-offs Overview
Thermal Radiation Basics
Properties and Relations: View Factor, absorptivity, emissivity, Stefan-Boltzmann, thin-plate ODE
Radiation Geometries: Parallel Plates, Convex Object in Large Cavity
Sources: Solar Radiation, Earth Radiation, Albedo
Materials
Radiative Comparison
Long Term Exposure Degradation
Multi-Layer Insulation (Thermal Blanket / Shroud)
Orbit Considerations
GEO, LEO, Lagrange points, Inclination
Design Examples
Design for Stabilization of Oscillating Heat Flux
@ LEO
Oscillation due to orbit: sun/shadow (umbra)
Design for Specific Temperature with Constant Heat Flux
@ Sun-Earth Lagrange (L2) point:
Stationary position relative to Earth.
Summary/Questions

14. Orbit Geometry Considerations (GEO) Simple Case: Zero Degree Inclination (2D Planar Orbit)
Earth Radius: RE = x103 km
Altitude (GEO) = x103 km
Rorbit = RE + GEO = x103 km
4.8% of the 2D GEO orbit
sweeps through the Umbra
Sunlight
Umbra boundary
Umbra boundary
Earth Surface
Orbit
“Top-down” (North facing South) view of Earth

15. Orbit Geometry Considerations (LEO) Simple Case: Zero Degree Inclination (2D Planar Orbit)
Earth Radius: RE = x103 km
Altitude = 150 n.mi. = x103 km
Rorbit = RE + Altitude = x103 km
Earth Surface
Orbit
Umbra boundary
Sunlight
40% of the equatorial orbit
sweeps through the Umbra
(Order of magnitude higher than GEO!!)
Umbra boundary
“Top-down” (North facing South) view of Earth

16. LEO Inclination Concerns (more significant than GEO)
The 2D-planar orbit is a rough approximation of the sunlight geometry. Seasons (axis tilt) and inclination will change the percent of orbit that sweeps through the umbra.
0% of orbit sweeps through Umbra (constant sunlight
on one side)
Orbit sweeping through Umbra << 40%
Umbra
Sunlight
60o Inclined Orbit
90o Polar Orbit
An extreme case: 60o Inclination
dT/dt lower than equatorial case
The Most Benign Case Possible
dT/dt = 0
From these cases, one can see that the zero degree case (at solstice) for LEO has the highest dT/dt possible, and represents the worst thermal transient condition.

17. Thermal Radiation Trade-offs Overview
Thermal Radiation Basics
Properties and Relations: View Factor, absorptivity, emissivity, Stefan-Boltzmann, thin-plate ODE
Radiation Geometries: Parallel Plates, Convex Object in Large Cavity
Sources: Solar Radiation, Earth Radiation, Albedo
Materials
Radiative Comparison
Long Term Exposure Degradation
Multi-Layer Insulation (Thermal Blanket / Shroud)
Orbit Considerations
GEO, LEO, Lagrange points, Inclination
Design Examples
Design for Stabilization of Oscillating Heat Flux
@ LEO
Oscillation due to orbit: sun/shadow (umbra)
Design for Specific Temperature with Constant Heat Flux
@ Sun-Earth Lagrange (L2) point:
Stationary position relative to Earth.
Summary/Questions

18. Design for Stabilization of Oscillating Heat Flux (Typical for LEO orbit)
Given
90 minute orbit, LEO altitude, 0 degree inclination
Orbit is around earth, satellite sweeps through earth’s shadow (Umbra) periodically.
Consider Solar, Earth, and Albedo radiation flux.
Satellite is always pointed at Nadir (angular rotation rate is orbit rate)
Temperature fluctuates due to Umbra sweep but eventually achieves an average steady state. (nominal temperature, To)
Find
Thermal blanket MLI material specification and number of layers to keep satellite structural members at nominal delta T < ± 0.5 K to prevent large thermal expansion in members.
Strategy
Model MLI blanket as a thin plate
Use simple ODE

19. Multi Layer Insulation (MLI) Design OverviewB
Assumption:
Shroud modeled as thin circular plate.
Heat leaking through
MLI can not be more than heat between surfaces A and B, limited by design requirement: ΔT = 1 K.
External Heat flux (Ф)
Sun + Albedo + Earth
qleak A B
qAB
MLI
qAB = f (ΔT)
Required:
Spacecraft structural members
modeled as small convex object
in a large cavity.
Heat qAB is omnidirectional throughout shroud (assumption).

20. LEO Geometric Considerations (revisited) Simple Case: Zero Degree Inclination (2D-Planar Orbit)
Earth Radius: RE = x103 km
Altitude = 150 n.mi. = x103 km
Rorbit = RE + Altitude = x103 km
Earth Surface
Orbit
Umbra boundary
Sunlight
40% of the equatorial orbit
sweeps through the Umbra
Umbra boundary
“Top-down” (North facing South) view of Earth

21. Thermal Radiation Flux Profile for One Equatorial Orbit Based on view factor and satellite-earth angle
Umbra Region:
(~40% of orbit)

22. Thermal Radiation Flux Profile Explained: Change Due to Orbit/Sun Angle
Umbra Region:
(~40% of orbit)
2D plate model

23. Temperature Response Showing Steady State (Time ODE calculation for Thin Plate)
To ~ 340 K

24. Multi-Layer Insulation Design Computation (Droopy Eyes!)
From previous, nominal temperature for 2D orbit:
Worst case for objects inside emissivity = 1:
MLI (material dependent) emissivity:
Stefan-Boltzman Constant:
From design requirement:
Unit heat flow between two surfaces of emissivity:
(Small convex object in a large cavity depends only on small object’s emissivity)
Linearizing the above:
(see NASA contractor report 3800)
Solving for surface to surface heat flux:
TO = 340 K
(± 0.5 K) B
Shroud, A

25. MLI Design Computation Concluded
From before, surface-surface heat flux:
(known)
Worst case thermal radiation from external sources: (known)
heat leaking through MLI:
(unknown due to n)
To find n, relate qleak <= qAB:
(solve for n)
qAB = f (ΔT)
Required:
qleak A B
qAB
Ф = f (outer material, geometry)
ε leak = MLI material dependent
ε B = always 1 (worst case)

26. MLI Design Tradeoffs (LEO, equatorial)
Shroud Exterior Solar Spectrum Absorptivity
Shroud Exterior Earth Spectrum Absorptivity
Emissivity between MLI and Interior
Emissivity between layers of MLI
Steady State Temp. (K) (ΔT = 1 K)
Number of MLI layers
Worst Case 1
367
322
Graphite Epoxy Exterior /
Nickel MLI
0.85
0.6
0.08
340 25
Graphite Epoxy
Exterior /
Silver MLI
0.05 15
Graphite Epoxy / Gold MLI
0.04 12
Gold Coat Ext. /
Gold MLI
163 5
Nickel Coat Ext. / Gold MLI
194 6
Anodized Aluminum Ext. /
0.15
0.8
290 7
INPUT
OUTPUT

27. Design for Constant Heat Flux
Given
Spacecraft at Sun-Earth Lagrange L2 point
No orbit about Earth, only about the sun. No shadow sweeps.
Consider Solar heat flux only, since View Factor for Earth is negligible.
Maneuver time is about four hours, (angular rotation rate is very slow)
Temperature is constant once at desired rotated position
Find
Thermal blanket MLI material specification and number of layers to keep satellite structural members at nominal temperature of 200K.
Strategy
Model MLI blanket as a thin plate
Use simple ODE to achieve settling time within 4 hours and discover steady state temperature
Specify number of layers, material specs to get steady state temp. to 200K

28. Constant Radiation: Large Lissajous orbit about S-E L2
L2 lies 1.5 million km from Earth,
1% farther from the sun than the earth
300,000 km Lissajous Orbit
Avoids a ~13,000 km-radius Earth shadow x y z
Conclusion: Thermal Environment is stable.
Source:

29. Thermally Stable Orbit (Worst Case for Steady State Temperature)
Assumption: gold foil material exterior
Solar, Albedo and Earth Fluxes calculated to be:
Total Constant Heat Flux :
Using ODE for Radiantly Heated Thin Plate:
Steady State Temp
= K (exterior)
Note: Gold Melting
Point = 1337 K
Temp. Settling Time
= 3–5 hours (~580 K)
Note: Maneuver Time
= 4 hours max

30. Two Methods for Modeling Shroud and Contents
Method 1 (previous):
Using the method the same as for the fluctuating heat: B
Shroud, A
qAB ΔT To
Text
qleak
Equation above is
Transformed into:
Also:
So, design parameter is:
This only holds if temperatures are close to the desired nominal temperature (200 K).
See Hedgepeth, pg. 9. (NASA contractor report 3800) However, as we have seen from the steady state computation:
Text = 580 K >> 200 K !!!!
This method may not hold.

31. Two Methods For Modeling Shroud and Contents
Method 2 ( A better approximation?) :
Model as 2D planar surface
(contents surfaces) enclosed by another 2D plate (shroud surface)
Equation for heat leaking across two parallel plates with N shield layers:
Where q12 is the heat flux between plates with no shielding: B
Shroud, A
qAB ΔT To
Text
qleak
T1 = To and T2 = Text
Outside plate:
Shroud exterior, Text
N shield layers (A)
Inside plate (B), To
ε1 ε2

32. MLI Design Method 2
Similar to method 1 except solve for N with definite T2 and T1 known:
ΔT = 1 K (Proposed sub-requirement)
To = 200 K (Given requirement)
T1 = 200 K
T2 = 580 K (Steady state exterior temperature)
ε1 = (Worst case for telescope/truss surfaces)
ε2 = (Gold emissivity)
Solving these four equations gives:
Note: T2 and ε2 depend on material selected.
T2 also depends on external heat flux (Ф) from Sun and Earth, etc.

33. Differences between Method 1 and Method 2
Small Convex Object Enclosed in Large Cavity
Method 2:
Two Parallel Plates
External Temperature
n = f (Heat Flux, Material)
N = f (External Temperature, Material)
f (Heat Flux)

34. Thermal Shroud Design Results
Shroud Exterior Absorptivity
Emissivity between MLI and Interior
(Worst case)
Emissivity between layers of MLI
Exterior Steady State Temp. (K)
Number of MLI layers
Method 1
Silver (Coated?)**
0.07 1
.035
271
(valid)* 5
Method 2
Silver (Coated?) 4
(Gold Foil)
0.3
0.03
583
(not valid) 21
107
(Aluminum Foil)
0.15
0.06
347
(Not valid?) 24
*Valid = steady state temperature close to nominal
**Questionable if silver can be used as coating
Conclusion: 5 Ag layers, 107 Au layers, 24 Al layers

35. Thermal Radiation Trade-offs: Summary / Questions
Space Thermal Environment Dependencies:
Orbit Altitude (GEO, LEO, L points)
Inclination
S/C Attitude
Design Issues
Materials
Modeling (geometry, assumptions)
Given requirements or desirements (delta T, etc.)
Analytical Insight (ODE, FEM)

36. Thermal Radiation Trade-offs4. 5. 6.