Emittance & Absorptance for Cryo Testing

1. Emittance & Absorptance for Cryo Testing • Goal: To better understand emittance and absorptance and how they vary at cryo temperatures • Sample problem • Emittance & absorptance of non-conductors • Effects of wavelength (spectral dependencies and trends) • Effects of low temperatures • Effects of thickness (paints and films) • Honeycomb enhancements

2. Example: SIRTF Thermal Testing • SIRTF Cryo Telescope Assembly • On orbit, CTA passively cooled to 40 K by radiation to space • 40 K well below typical LN2-cooled thermal-vac chambers at 80 K • Initial plans for thermal balance test • Simulate space environment • Add helium-cooled shroud inside existing LN2-cooled thermal-vac chamber • Helium-cooled shroud at 4 K • Painted honeycomb on shroud for absorptance close to 1.0 • Concerns about test • Validity (see next chart) • Feasibility • Cost • Time SIRTF CTA (40 K) Helium-cooled shroud (4 K) (painted honeycomb) Nitrogen-cooled coldwall (80 K) Vacuum chamber walls (293 K)

3. Example: Basis for Conclusion • Emittance of paint at 4 K hard to predict • At 40 K, epaint = 0.70 ± 0.15 uncertainty (Goddard data) • No data at 4 K, but emittance much lower (at 0 K, emittance  0.00) • Even with painted honeycomb shroud, emittance at 4 K could be < 0.50 • Test vs space: too different • Tsink = 4 K vs 2.7 K (OK) • esink = 0.48 vs 1.0 (not OK) • Heat reflected back to CTA • CTA won’t get cold enough • Gradients won’t be realistic • Heat balance unpredictable • Thermal balance in 4 K shroud not meaningful • Omit 4 K shroud • Cool CTA with direct liquid helium lines • Make do with questionable thermal balance Goddard Paint Data Extrapolated From model What’s wrong with this picture?

4. Example: Revised Solution • Helium-cooled shroud gives meaningful test • Absorptivity of the paint is relative to 40 K, not 4 K • Paint’s absorptivity depends on wavelength distribution of incident radiation • Paint’s absorptivity at a given wavelength is independent of paint’s temperature • Effective absorptance = emittance of paint at 40 K = 0.70 • At 40 K, absorptance of painted honeycomb can be > 0.90 • Some variation with paint thickness and paint process • Some variation with cell size and honeycomb thickness • Use specular paint • Calorimeter uncertainties increase at cryo temperatures • Helium-cooled shroud could mimic space to within 1% • Grow shroud from 2X to 10X the area of SIRTF CTA • Additional cost for liquid helium to cool larger shroud • Concentric spheres: RadK12 = A1/[1/e1 + (A1/A2)(1/e2 – 1) 98% 99.5% 1/2 1/10

5. Spectral Intensity of a Blackbody • Planck’s Radiation Law • I(l,T) = (2phc2/l5)/(ehc/lkT – 1) • Flux (Qbb) = area under curve • Qbb,T = sT4 • s = 5.6697 X 10-8 W/m2-K4 • Curves have similar shapes • Imax is proportional to T5 • lmax is proportional to 1/T 0.004 inches lmax & Imax

6. Spectral Intensity: Log Plot lT = 1148m-K lmaxT = 2897m-K lT = 22917m-K • Everything shifts proportional to 1/T • Max power occurs at longer wavelengths at lower temperatures • Curve for a lower temperature is less than curve for a higher temperature at all wavelengths • At low temperatures, power spreads over wider range of wavelengths 98% of power

7. Absorptance = Emittance: Kirchhoff’s Law • Absorptance = emittance, if the same… • Surface • Temperature • Wavelength • Angle of incidence • al,T,q,f= el,T,q,f(rest of presentation omits effects of angle of incidence) • Total absorptance= total emittance at the same temperature • Emittance • Total hemispherical emittance • Surface at the given temperature • Absorptance • Surface is at the given temperature • Surface is surrounded by blackbody at the same temperature • Must be true, else violates the 2nd Law of Thermodynamics a + r + t = 1 a + r = 1 (opaque)

8. Conclusions So Far • Emittance varies with wavelength for real surfaces • Some surfaces have a fairly constant emittance over a range of wavelengths • Emittance at a given wavelength can also change with temperature • The blackbody intensity changes non-linearly with temperature • Increases with temperature to the 4th power • At lower temperatures, the distribution shifts towards longer wavelengths • At lower temperatures, the power spreads out more • Therefore, effective emittance changes with temperature, if… • Emittance varies with wavelength, or if… • Emittance at a given wavelength changes with temperature • For the range of wavelengths of importance at the given temperature

9. Emittance of Non-Conductors • For non-metals, el andalis essentially independent of temperature • 2-step absorption process • Surface reflectance depends on index of refraction • Reflectance = [( - 1)/( + 1)]2(normal) •  = index of refraction = 1/relative light speed ≈ [dielectric constant]½ • Volumetric absorptance sometimes limited by thickness • Dielectrics are partially transparent • Absorptance within material increases with thickness: a = 1 – e-kx • Free-standing film, or backed by metal layer • No significant difference beyond certain thickness (1 to 10 mils typically) • At low temperatures, emittance of paints and films decreases • Energy shifts to longer wavelengths • When wavelengths exceed thickness, paint or film becomes more transparent • No decrease for non-conductive substrate—if thick enough • Surfaces becomes more specular at low temperatures • As more wavelengths exceed roughness of surface and substrate 1 2

10. Spectral Emittance of a Paint • Emittance/absorptance at a given wavelength doesn’t vary with temperature • Total emittance may vary with temperature as the range of wavelengths shifts • Changing temperature of emitting source may shift the absorptance of an absorbing surface • Changing temperature of absorbing surface does not change its absorptance

11. Emittance of Non-Conductors: Films • For non-conductors, radiation transfer is more of a volumetric phenomenon • Many thin films are partially transparent • Absorptance (and emittance) varies exponentially vs thickness • Films are volume-limited • At low temperatures, wavelengths are longer and films are more transparent • Different paints or films show a decrease in emittance at different temperatures • Emittance of FEP Teflon films drops off at higher temperatures than most films or paints • Paints or OSRs are better on cryo radiators • Painted honeycomb gives highest emittance • If material is thick enough, emittance stays constant to much lower temperature • Emittance of 35-mil fused silica constant from 25 K to 300 K

12. Honeycomb Blackbodies • Open, painted honeycomb cells increase emittance or absorptance • Cavity offers several chances for absorptance • Each cavity approximates a blackbody • Absorptance still equals emittance • Not too sensitive to honeycomb geometry • Aspect ratio: cell width versus cell height • Aluminum honeycomb minimizes DT to base • At cryo temperatures, DT not a factor • Obtaining uniform paint may be driver • Recommend larger cell honeycomb • Allows thicker paint • Paint process less critical • Specular paint increases effective emittance • Diffuse paint: 0.9773125 K, 0.929180 K • Specular paint: 0.9984125K, 0.985780K Multiple bounces in a honeycomb hex cell Simplified model • Same hemispherical emittance • 100% diffuse vs 100% specular

13. Percent Power vs Wavelength for Cryo 40 mils • 1% of power at l less than 1448/T • Maximum power at l of 2897/T • Also 25%/75% split • 50% of power either side of l of 7393/T • 99% of power at l less than 22,917/T 4 mils • Typical paint thickness = 2 to 8 mils • Paint have reduced emittance when wavelengths exceed thickness • ¼” (honeycomb cell) = 6,350 microns • Cell size well beyond significant wavelength effects

14. Conclusions / Recommendations • For radiation between hot and cold surfaces, the hot surface dominates • Temperature of hot emitter determines cold non-conductor’s absorptance • Absorptance depends on distribution of incident wavelengths • Most of the incident radiation originates at the hot surface • For non-conductors, al does not vary with temperature • Total emittance varies with temperature if … • Emittance varies with wavelength • For paints and films, emittance drops off at longer wavelengths (cryo temperatures) • Thicker substrates of non-conductors will not show this effect • Emittance at a given wavelength varies with temperature • Typical non-conductors do not show such an effect • Thicker paint has higher absorptance at low temperatures • Use specular paints for honeycomb or multi-bounce blackbodies