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Emittance & Absorptance for Cryo Testing Goal: To better understand emittance and absorptance and how they vary at cryo temperatures Sample problem Emittance.

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Presentation on theme: "Emittance & Absorptance for Cryo Testing Goal: To better understand emittance and absorptance and how they vary at cryo temperatures Sample problem Emittance."— Presentation transcript:

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 SIRTF Cryo Telescope Assembly –On orbit, CTA passively cooled to 40 K by radiation to space –40 K well below typical LN 2 -cooled thermal-vac chambers at 80 K Initial plans for thermal balance test –Simulate space environment –Add helium-cooled shroud inside existing LN 2 -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 Example: SIRTF Thermal Testing Vacuum chamber walls (293 K) Nitrogen-cooled coldwall (80 K) Helium-cooled shroud (4 K) (painted honeycomb) SIRTF CTA (40 K)

3 Example: Basis for Conclusion Goddard Paint Data Extrapolated From model Emittance of paint at 4 K hard to predict –At 40 K,  paint = 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 –T sink = 4 K vs 2.7 K(OK) –  sink  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 What’s wrong with this picture?

4 Helium-cooled shroud gives meaningful test 1. 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 2. 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 3. 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: RadK 12 = A 1 /[1/  1 + (A 1 /A 2 )(1/  2 – 1) Example: Revised Solution 1 / 10 1/21/2 98% 99.5%

5 Spectral Intensity of a Blackbody Planck’s Radiation Law –I(,T) = (2  hc 2 / 5 )/(e hc/ kT – 1) Flux (Q bb ) = area under curve Q bb,T =  T 4  = 5.6697 X 10 -8 W/m 2 -K 4 Curves have similar shapes –I max is proportional to T 5  max is proportional to 1/T max & I max 0.004 inches

6 Spectral Intensity: Log Plot 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 max T = 2897  -K T = 1148  -K T = 22917  -K 98% of power

7 Absorptance = Emittance: Kirchhoff’s Law Absorptance = emittance, if the same… –Surface –Temperature –Wavelength –Angle of incidence   =   (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 2 nd Law of Thermodynamics  +  +  = 1  +  = 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 4 th 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 For non-metals,  and  is essentially independent of temperature 2-step absorption process 1.Surface reflectance depends on index of refraction  Reflectance = [(  - 1)/(  + 1)] 2 (normal)   = index of refraction = 1/relative light speed ≈ [dielectric constant] ½ 2.Volumetric absorptance sometimes limited by thickness  Dielectrics are partially transparent  Absorptance within material increases with thickness:  = 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 Emittance of Non-Conductors 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  T to base  At cryo temperatures,  T 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:0.9773 125 K, 0.9291 80 K –Specular paint:0.9984 125 K, 0.9857 80 K Multiple bounces in a honeycomb hex cell Simplified model Same hemispherical emittance 100% diffuse vs 100% specular

13 Percent Power vs Wavelength for Cryo 1% of power at less than 1448/T Maximum power at of 2897/T –Also 25%/75% split 50% of power either side of of 7393/T 99% of power at less than 22,917/T 40 mils 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,  does not vary with temperature Total emittance varies with temperature if … 1.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 2.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

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