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

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

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

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

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

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)

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

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

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

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

Long Duration Exposure Facility (LDEF) MLI Test Blanket

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

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

Orbit Geometry Considerations (GEO) Simple Case: Zero Degree Inclination (2D Planar Orbit) Earth Radius: RE = 6.378 x103 km Altitude (GEO) = 35.785 x103 km Rorbit = RE + GEO = 42.163 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

Orbit Geometry Considerations (LEO) Simple Case: Zero Degree Inclination (2D Planar Orbit) Earth Radius: RE = 6.378 x103 km Altitude = 150 n.mi. = 0.278 x103 km Rorbit = RE + Altitude = 6.656 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

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.

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

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

Multi Layer Insulation (MLI) Design Overview B 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).

LEO Geometric Considerations (revisited) Simple Case: Zero Degree Inclination (2D-Planar Orbit) Earth Radius: RE = 6.378 x103 km Altitude = 150 n.mi. = 0.278 x103 km Rorbit = RE + Altitude = 6.656 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

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

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

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

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

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)

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

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

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

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 = 583.7 K (exterior) Note: Gold Melting Point = 1337 K Temp. Settling Time = 3–5 hours (~580 K) Note: Maneuver Time = 4 hours max

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.

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

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 = 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.

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)

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

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)

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