Transcript Thermal Shroud Design - University of Colorado Boulder
Radiative Heat Trade-Offs for Spacecraft Thermal Protection
A Practical Guide to Thermal Blanket/Multi-Layer Insulation Design
Scott Franke AFRL/VSSV
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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
• @ Sun-Earth Lagrange (L2) point: • Stationary position relative to Earth.
Heat Flux Summary/Questions
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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.
• Used when a sink can see more than one source Surface finish dependent; want low values for both View factor, F 12 : relates fraction of thermal power leaving object 1 and reaching object 2.
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 TB 4 TA 4 Note: q is really area-normalized q-dot (W/m 2 ) σ = Stefan-Boltzmann Constant
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Thermal Radiation Basics: Properties and Relations
• Simple time ODE for radiantly heated thin plate: c h d d t T T
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q ρ = material density σ = Stefan-Boltzmann h = material thickness c = material heat capacitance • 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)
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Thermal Radiation Basics: Radiation Geometries
Heat flux (W/m 2 ) between: Two large (infinite) plates 1 2 q 12 T 1 4 T 2 4 1 1 1 2 1 F 12 = 1 (View Factor) Small Convex Object in a Large Cavity 1 2 q 12 1 T 1 4 T 2 4 F 12 = 1
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Thermal Radiation Basics: Sources Flux (W/m 2 )
• • • Solar Radiation – Sun radiates at blackbody temperature of ~5000K Solar Constant: ~1350 W/m 2 – – – – 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 · T 4 · 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)
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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
• @ Sun-Earth Lagrange (L2) point: • Stationary position relative to Earth.
Heat Flux Summary/Questions
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Materials: Radiative Property Comparison
Material absorptivity (α) varies with temperature of source.
Anodized Aluminum (13) Polished Aluminum (15)
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Materials: Radiative Property Comparison
0.4
0.3
0.2
0.1
0 0.9
0.8
0.7
0.6
0.5
• Not easily found via web – www.matweb.com
some data on certain materials, emissivity is searchable Emmissivity Density (lbs/in3) Aluminum Silver Gold Nickel Platinum Titanium
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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
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Long Duration Exposure Facility (LDEF) MLI Test Blanket 11
•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 qleak 2 leak n 1 n layers
Materials: Multi-Layer Insulation (MLI) / Thermal Blanket
Heat leaking through layers.
Ф = maximum heat flux encountered Dacron filling
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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
• @ Sun-Earth Lagrange (L2) point: • Stationary position relative to Earth.
Heat Flux Summary/Questions
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Orbit Geometry Considerations ( GEO ) Simple Case: Zero Degree Inclination (2D Planar Orbit)
Earth Radius: R
E
= 6.378 x10 Altitude (GEO) = 35.785 x10 3 3 km km R
orbit
= R
E
+ GEO = 42.163 x10 3 km 4.8% of the 2D GEO orbit sweeps through the Umbra
Umbra boundary
Sunlight
Umbra boundary
Earth Surface Orbit “Top-down” (North facing South) view of Earth
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Orbit Geometry Considerations ( LEO ) Simple Case: Zero Degree Inclination (2D Planar Orbit)
Earth Radius: R
E
= 6.378 x10 3 Altitude = 150 n.mi. = 0.278 x10 3 km km R
orbit
= R
E
+ Altitude = 6.656 x10 3 km Earth Surface Orbit Sunlight
Umbra boundary
40% of the equatorial orbit sweeps through the Umbra (Order of magnitude higher than GEO!!) “Top-down” (North facing South) view of Earth
Umbra boundary 15
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. Orbit sweeping through Umbra
<<
40% Umbra 0% of orbit sweeps through Umbra (constant sunlight on one side) Sunlight 60 o Inclined Orbit An extreme case: 60 o Inclination dT/dt lower than equatorial case dT/dt = 0 90 o Polar Orbit The Most Benign Case Possible 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 .
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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
• @ Sun-Earth Lagrange (L2) point: • Stationary position relative to Earth.
Heat Flux Summary/Questions
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• •
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, T o )
•
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 18
Multi Layer Insulation (MLI) Design Overview A B A
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 MLI q
AB =
f (ΔT) Required:
q
leak
A
q
AB
B Spacecraft structural members modeled as small convex object in a large cavity.
Heat q
AB
is omnidirectional throughout shroud (assumption).
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LEO Geometric Considerations (revisited) Simple Case: Zero Degree Inclination (2D-Planar Orbit)
Earth Radius: R
E
= 6.378 x10 3 Altitude = 150 n.mi. = 0.278 x10 3 km km R
orbit
= R
E
+ Altitude = 6.656 x10 3 km Orbit Earth Surface
Umbra boundary
40% of the equatorial orbit sweeps through the Umbra Sunlight
Umbra boundary
“Top-down” (North facing South) view of Earth
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1500
Thermal Radiation Flux Profile for One Equatorial Orbit Based on view factor and satellite-earth angle
External Source Radiated Heat Flux 1000 500 Umbra Region: (~40% of orbit) 0 0 50 Total Albedo Solar Earth 100 150 200 Planar Orbit (deg) 250 300 350
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Thermal Radiation Flux Profile Explained: Change Due to Orbit/Sun Angle
2D plate model External Source Radiated Heat Flux 1500 1000 500 0 0 50 Total A lbedo Solar Earth 100 Umbra Region: (~40% of orbit) 150 200 Planar Orbit (deg) 250 300 350
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400 300 200 100 0 0
Temperature Response Showing Steady State (Time ODE calculation for Thin Plate)
5 10 Time (hours) 15 20 400 T o ~ 340 K 350 300 15 16 17 18 Time (hours) 19 20 21
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Multi-Layer Insulation Design Computation (Droopy Eyes!)
From previous, nominal temperature for 2D orbit: T
O
= 340 K Worst case for objects inside emissivity = 1:
B
MLI (material dependent) emissivity:
leak 1 .04
Truss/Interior MLI (Gold coat)
Stefan-Boltzman Constant:
5.67
10
8
kg s
3
K
4 From design requirement: T (± 0.5 K) Unit heat flow between two surfaces of emissivity: (Small convex object in a large cavity depends only on small object’s emissivity) Shroud, A Linearizing the above: B (see NASA contractor report 3800) Solving for surface to surface heat flux: qAB B T2 4 T1 4
T qAB 4
B
To
3
qAB 4
T
B
To
3
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MLI Design Computation Concluded
From before, surface-surface heat flux: (known)
qAB 4
T
B
To
3 Worst case thermal radiation from external sources: (known) q
AB =
f (ΔT) max qexternal heat leaking through MLI: (unknown due to n) To find n, relate q leak <= q AB : (solve for n) qleak 2 leak n 1
n
2
leak 4
T
B
To
3
1
Ф
= f (outer material, geometry) Required:
q
leak
A
q
AB
ε leak = MLI material dependent ε B = always 1 (worst case) B
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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 / Graphite Epoxy Exterior Nickel MLI 1 0.85
Graphite Epoxy Exterior / Silver MLI Graphite Epoxy / Gold MLI 0.85
0.85
Gold Coat Ext. / Gold MLI Nickel Coat Ext. / Gold MLI 0.04
0.08
/ Anodized Aluminum Ext. Gold MLI 0.15
1 0.6
0.6
0.6
0.04
0.08
0.8
1 1 1 1 1 1 1 1 0.08
0.05
0.04
0.04
0.04
0.04
367 340 340 340 163 194 290 322 25 15 12 5 6 7 INPUT OUTPUT
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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
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Constant Radiation: Large Lissajous orbit about S-E L2
z y x 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
Conclusion: Thermal Environment is stable.
Source: http://astro.estec.esa.nl/GAIA/Assets/Papers/IN_L2_orbit.pdf
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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 : W m 2 qt W 658.412
m 2 W m 2 W m 2 Using ODE for Radiantly Heated Thin Plate: c h d d t T T 4 q Stead State Temperature Calculation Steady State Temp = 583.7 K (exterior) 600 Note: Gold Melting Point = 1337 K 400 200 Temp. Settling Time = 3–5 hours (~580 K) 0 0 5000 1 10 4 1.5
10 4 Time (s) 2 10 4 2.5
10 4 3 10 4 Note: Maneuver Time = 4 hours max
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Two Methods for Modeling Shroud and Contents Method 1 (previous):
Using the method the same as for the fluctuating heat: qAB B TA 4 TB 4 Shroud, A Equation above is Transformed into: Also: qAB 4 T B To 3 qleak 2 leak n 1 So, design parameter is: q leak T ext B T o q AB ΔT q leak T ext 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: T ext = 580 K >> 200 K !!!!
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This method may not hold.
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: q leak T ext qleak 1 N 1 q12 Outside plate: Shroud exterior, T ext Where q 12 is the heat flux between plates with
no shielding
: q 12 T 2 4 T 1 4 1 1 1 2 1 T 1 = T o and T 2 = T ext ε 1 ε 2 Shroud, A B q AB ΔT T o q leak T ext N shield layers (A) Inside plate (B), T o
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MLI Design Method 2
Similar to method 1 except solve for N with definite T2 and T1 known: q12 T2 4 T1 4 1 1 1 2 1 qleak 1 N 1 q12 qAB T 4 AB To 3 N Solving these four equations gives: 1 T 4 T2 4 To 3 1 1 T1 4 1 2 1 ΔT = 1 K (Proposed sub-requirement) T o = 200 K (Given requirement) T 1 = 200 K T 2 ε 1 ε 2 = 580 K (Steady state exterior temperature) = 1 (Worst case for telescope/truss surfaces) = 0.03 (Gold emissivity) Note: T 2 T 2 and ε 2 depend on material selected.
also depends on external heat flux (Ф) from Sun and Earth, etc.
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Differences between Method 1 and Method 2
Method 1: Small Convex Object Enclosed in Large Cavity
n 2
leak 4
T
B
To
3
1
n = f (Heat Flux, Material) Method 2: Two Parallel Plates External Temperature N 1 T 4 T2 4 To 3 1 1 T1 4 1 2 1 N = f (External Temperature, Material) f (Heat Flux)
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Thermal Shroud Design Results
Method 1 Silver (Coated?)** Method 2 Silver (Coated?) Method 1 (Gold Foil) Method 2 (Gold Foil) Method 1 (Aluminum Foil) Method 2 (Aluminum Foil) Shroud Exterior Absorptivity 0.07
0.07
0.3
0.3
0.15
0.15
1 1 Emissivity between MLI and Interior (Worst case) Emissivity between layers of MLI Exterior Steady State Temp. (K) Number of MLI layers 1 .035
5 1 1 1 .035
0.03
0.03
271 (valid)* 271 583 (not valid) 583 4 21 107 0.06
0.06
347 (Not valid?) 347 21 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
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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)
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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
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