1

Radiative Heat Trade-Offs for Spacecraft Thermal Protection

A Practical Guide to

Thermal Blanket/Multi-Layer

Insulation Design

Scott FrankeAFRL/VSSV

2

• 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

Thermal Radiation Trade-offs Overview

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):

qAB B TB4

TA4

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)

c htTd

d T

4 q

ρ = material densityσ = Stefan-Boltzmannh = material thicknessc = material heat capacitance

5

Thermal Radiation Basics: Radiation Geometries

Heat flux (W/m2) between:

Two large (infinite) plates

Small Convex Object in aLarge Cavity

q 12

T 14

T 24

1

1

1

2 1

F12 = 1 (View Factor)

q 12 1 T 14

T 24

F12 = 1

1

2

1

2

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 averageAF 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 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

Thermal Radiation Trade-offs Overview

8

Materials: Radiative Property Comparison

Material absorptivity (α) varies with temperature of source.

Polished Aluminum (15)

Anodized Aluminum (13)

9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Aluminum Silver Gold Nickel Platinum Titanium

Emmissivity

Density (lbs/in3)

Materials: Radiative Property Comparison

• Not easily found via web

– www.matweb.com 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 exposedTo 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 ofpressure on orbit negates conductivity

•Protects against orbital debris / micrometeoroids

qleak2 leak

n 1

n layers

Heat leaking through layers.

Ф = maximum heat flux encountered

Dacron filling

13

• 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

Thermal Radiation Trade-offs Overview

14

Orbit Geometry Considerations (GEO)

Simple Case: Zero Degree Inclination (2D Planar Orbit)

Earth Radius: RE = 6.378 x103 kmAltitude (GEO) = 35.785 x103 kmRorbit = RE + GEO = 42.163 x103 km

Sunlight

Umbra boundary

Umbra boundary

Orbit

Earth Surface

4.8% of the 2D GEO orbit sweeps through the Umbra

“Top-down” (North facing South) view of Earth

15

Orbit Geometry Considerations (LEO)

Simple Case: Zero Degree Inclination (2D Planar Orbit)

Earth Radius: RE = 6.378 x103 kmAltitude = 150 n.mi. = 0.278 x103 kmRorbit = RE + Altitude = 6.656 x103 km

Sunlight

Umbra boundary

Umbra boundaryOrbit

Earth Surface

40% of the equatorial orbit sweeps through the Umbra(Order of magnitude higher than GEO!!)

“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.

60o Inclined OrbitSunlight

Umbra

Orbit sweeping through Umbra << 40%

90o Polar Orbit

0% of orbit sweeps through Umbra (constant sunlight on one side)

An extreme case: 60o InclinationdT/dt lower than equatorial case

The Most Benign Case PossibledT/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 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

Thermal Radiation Trade-offs Overview

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 Overview

Assumption: Shroud modeled as thin circular plate.

External Heat flux (Ф) Sun + Albedo + Earth

Spacecraft structural members modeled as small convex object in a large cavity.

Heat leaking through MLI can not be more than heat between surfaces A and B, limited by design requirement: ΔT = 1 K.

MLI

A

A

B

Heat qAB is omnidirectional throughout shroud (assumption).

q leak q AB

qAB = f (ΔT)

Required:qleak

A

B

qAB

20

LEO Geometric Considerations (revisited)

Simple Case: Zero Degree Inclination (2D-Planar Orbit)

Earth Radius: RE = 6.378 x103 kmAltitude = 150 n.mi. = 0.278 x103 kmRorbit = RE + Altitude = 6.656 x103 km

Sunlight

Umbra boundary

Umbra boundaryOrbit

Earth Surface

40% of the equatorial orbit sweeps through the Umbra

“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

External Source Radiated Heat Flux

0 50 100 150 200 250 300 3500

500

1000

1500

TotalAlbedoSolarEarth

Planar Orbit (deg)

flu

x (

W/m

^2

)

Umbra Region:(~40% of orbit)

22

Thermal Radiation Flux Profile Explained:

Change Due to Orbit/Sun Angle

External Source Radiated Heat Flux

0 50 100 150 200 250 300 3500

500

1000

1500

TotalAlbedoSolarEarth

Planar Orbit (deg)

flux (W

/m

^2)

Umbra Region:(~40% of orbit)

2D plate model

23

0 5 10 15 200

100

200

300

400

Time (hours)

Tem

pera

ture

(K

)

15 16 17 18 19 20 21300

350

400

Time (hours)

Tem

pera

ture

(K

)

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:

T 1 K

TO = 340 K

B 1 Truss/Interior

leak .04 MLI (Gold coat)

5.67 108

kg

s3

K4

TqAB

4 B To3

qAB 4 T B To3

qAB B T24

T14

B

Shroud, A

(± 0.5 K)

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)

max qexternal

n2 leak

4 T B To3

1

qleak2 leak

n 1

qAB 4 T B To3

qleak

A

B

qAB

Ф = f (outer material, geometry)

ε leak = MLI material dependent

ε B = always 1 (worst case)

q leak q AB

qAB = f (ΔT)

Required:

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 1 1 1 367 322

Graphite Epoxy Exterior /

Nickel MLI

0.85 0.6 1 0.08 340 25

Graphite Epoxy

Exterior /

Silver MLI

0.85 0.6 1 0.05 340 15

Graphite Epoxy / Gold MLI

0.85 0.6 1 0.04 340 12

Gold Coat Ext. /

Gold MLI

0.04 0.04 1 0.04 163 5

Nickel Coat Ext. / Gold MLI

0.08 0.08 1 0.04 194 6

Anodized Aluminum Ext. /

Gold MLI

0.15 0.8 1 0.04 290 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

28Source: http://astro.estec.esa.nl/GAIA/Assets/Papers/IN_L2_orbit.pdf

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 shadowshadow

xy

z

Conclusion: Thermal Environment is stable.

Constant Radiation: Large Lissajous orbit about S-E L2

29

Thermally Stable Orbit (Worst Case for Steady State Temperature)

c htTd

d T

4 q

qS 405W

m2

q E 113.702W

m2

q A 139.71W

m2

qt 658.412W

m2

Assumption: gold foil material exterior

Solar, Albedo and Earth Fluxes calculated to be:

Total Constant Heat Flux :

Using ODE for Radiantly Heated Thin Plate:

Stead State Temperature Calculation

0 5000 1 104

1.5 104

2 104

2.5 104

3 104

0

200

400

600

Time (s)

Tem

pera

ture

(K

)

Steady State Temp = 583.7 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:

Equation above isTransformed into:

Also:

So, design parameter is:

qAB 4 T B To3

qAB B TA4

TB4

B

Shroud, A

qAB

ΔT

ToTextText

qleakqleak

qleak2 leak

n 1

q leak q AB

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

ToText

qleakqleak

Text

q 12

T 24

T 14

1

1

1

2 1 T1 = To and T2 = Text

Outside plate:Shroud exterior, Text

N shield layers (A)

Inside plate (B), To

ε1 ε2

qleak1

N 1q12

32

MLI Design Method 2

Similar to method 1 except solve for N with definite T2 and T1 known:

q12

T24

T14

1

1

1

2 1

qleak1

N 1q12 q leak q AB

qAB T 4 AB To3

N 1 T2

4T1

4

T 4 To3

1

1

1

2 1

ΔT = 1 K (Proposed sub-requirement) To = 200 K (Given requirement)T1 = 200 KT2 = 580 K (Steady state exterior temperature)ε1 = 1 (Worst case for telescope/truss surfaces)ε2 = 0.03 (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

N 1 T2

4T1

4

T 4 To3

1

1

1

2 1

Method 2:Two Parallel Plates

n2 leak

4 T B To3

1

Method 1:Small Convex Object Enclosed in Large Cavity

n = f (Heat Flux, Material)

External Temperature

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?)

0.07 1 .035 271 4

Method 1

(Gold Foil)

0.3 1 0.03 583

(not valid)

21

Method 2

(Gold Foil)

0.3 1 0.03 583 107

Method 1

(Aluminum Foil)

0.15 1 0.06 347

(Not valid?)

21

Method 2

(Aluminum Foil)

0.15 1 0.06 347 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-offs

4. http://www.swales.com/products/therm_blank.html

5. http://setas-www.larc.nasa.gov/LDEF/index.html

6. http://www.aero.org/publications/crosslink/summer2003/07.html