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
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)
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
– esink = 0.48 vs 1.0
(OK)
(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?
Example: Revised Solution
• 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
98%
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
99.5%
– Concentric spheres: RadK12 = A1/[1/e1 + (A1/A2)(1/e2 – 1)
1/
2
1/
10
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
lmax & Imax
0.004 inches
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
Absorptance = Emittance: Kirchhoff’s Law
• Absorptance = emittance, if the same…
– Surface
a+r+t=1
a + r = 1 (opaque)
– 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
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
Emittance of Non-Conductors
•
For non-metals, el and al is essentially independent of temperature
•
2-step absorption process
1.
2.
•
•
Surface reflectance depends on index of refraction

Reflectance = [( - 1)/( + 1)]2

 = index of refraction = 1/relative light speed ≈ [dielectric constant]½
(normal)
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)
1
2
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
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
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
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
Multiple
bounces in a
honeycomb
hex cell
• 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:
– Specular paint:
0.9773125 K, 0.929180 K
0.9984125 K, 0.985780 K
Simplified model
• Same hemispherical emittance
• 100% diffuse vs 100% specular
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
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 …
1.
2.
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