ef2260 thermal

Spacecraft Thermal Control

Lars Bylander

Picture Maya Heat Ltd.

Lecture contents• Radiation• Radiation heat exchange• Spacecraft thermal environments• Thermal control hardware• Conduction heat exchange• Mounting and interfaces• Thermal design analysis• Thermal design examples• Thermal testing

RadiationThe electromagnetic power spectrum is described by

Planck’s radiation law:

Radiation peak is at (know as Wien's displacement law):

310 [ ]mT

λ−2.898⋅

=

Radiation• For bulk samples and opaque films the relation

between the spectral directional hemispherical reflectance, ρλ(Φ,θ), spectral directional emittance, ελ(Φ,θ), and the spectral directional absorptance, αλ(Φ,θ), is given by Kirchoff’s first law:

αλ(Φ,θ) = ελ(Φ,θ) = 1 - ρλ(Φ,θ)

where ρλ(Φ,θ) is the reflectance at all angles from a monochromatic beam incident from the direction (Φ,θ).

The solar absorptance, αS, is defined as (where denotes the incident spectral solar

power):

And by using Kirchoff’slaw the solar absorptance can be written:

Radiation

i

i0S

i

0

P d1 P d

P dS

∞

λ λ ∞

λ λ∞0

λ

α λα = = α λ

λ

∫∫

∫

iS

1 P dS

∞

λ λ0

α = (1 − ρ ) λ∫

iPλ

Radiation• The temperature

dependant emittance, ε(T), is defined as (where denotes the temperature dependant spectral blackbody

radiant power):• And by using

Kirchoffs law the emittance can be written:

bb

bb0bb

bb 0

P (T)d( ) P (T)d

P (T)P (T)d

T

∞

λ λ ∞

λ λ∞

λ0

ε λ1

ε = = ε λλ

∫∫

∫bbP (T)

bbbb

0

( ) )P (T)dP (T)

T∞

λ λ

1ε = (1− ρ λ∫

RadiationExamples of electromagnetic power spectra:

Radiation

• The world according to a human eye

• The world according to an infrared camera

(Pictures source: Wikimedia Commons)

Radiation heat exchange• Black body radiation (Stefan-

Boltzmann's law, σ=5,670·10-8, T = surface temperature, unit is Kelvin):

• A non black body’s radiation per square meter (ε=emission coefficient):

• A non black body’s total radiation (Ae = emitting area) :

2/W mσ 4⋅ Τ ⎡ ⎤⎣ ⎦

2/W mε σ 4⋅ ⋅ Τ ⎡ ⎤⎣ ⎦

[ ]eA Wε σ 4⋅ ⋅ ⋅ Τ

Radiation heat exchange

• Absorbed power (S is the Solar constant, αS is the solar absorption, Aill is the illuminated area): [ ]S illS A Wα⋅ ⋅

Radiation heat exchange

• An object’s equilibrium temperature can be calculated by balancing the object’s absorbed and emitted power.

e S illA S Aε σ α4⋅ ⋅ ⋅ Τ = ⋅ ⋅

4 S ill

e

S AAα

ε σ⋅ ⋅

⋅ ⋅Τ =

Spacecraft thermal environments

• The illuminated area of a sphere is π·r2 and its emitting area is 4·π·r2. This results in an equilibrium temperature of:

44

SS αε σ⋅⋅ ⋅Τ =

S

Spacecraft thermal environments• Solar flux versus distance from the Sun= 1376.5 / AU2 (W/m2)

Figure from Spacecraft Thermal Control Handbook, David G. Gilmore et.al., 2002

Spacecraft thermal environments• Equilibrium temperature of a sphere having αS=ε.


Spacecraft thermal environments• Orbits around planets means albedo (reflected solar radiation) and

planet IR-radiation.• Earth IR average temperature is about -18 °C.• Note! At 1280 km altitude 310 W/m2 albedo and 175 W/m2 IR


Spacecraft thermal environments

44

SS αε σ⋅⋅ ⋅Τ =

Calculate the temperature of a sphere where:

-altitude is 1280 km

-αS=ε(T)

-in eclipse and sunlight

S(W/m2)

Albedo(W/m2)

IR(W/m2)

T(°C)

Eclipse 0 0 175 -106

Sunlight 1376 310 175 28

Thermal control hardware

• Optical Surface Reflectors (OSR)• αS= 0.08, ε=0.8


• Multi Layer Insulation (MLI)• αS= 0.03, εinsulation<=0.02

Picture from Satellite Thermal Control for Systems Engineers and ESA Integral.


• White colour, example αS= 0.17, ε=0.86• Black paint, Chemglaze, αS= 0.95, ε=0.85• Polished aluminium, αS= 0.08, ε=0.03• Solar cells, αS= 0.7 to 0.9, ε=0.76 to 0.8

Thermal control hardware• Heat pipes are used to improve heat sharing in a satellite

Conductive heat exchange• One-dimensional heat

conduction through a region (λ = thermal conductivity, xA = distance, A = cross section heat flow area, T1-T2 = temperature difference over xA):

A 1 2x ( ) [ ]AQ T T Wλ⋅= −

Conductive heat exchange

The quantity: [ ]xAA WK K

λ ⋅=

is called conduction conductance (or just conductance) and is an important quantity in thermal modelling. The inverse is called conduction thermal resistance.

Example: A 5 cm long rod with cross section area 1 cm2, made of a Aluminum alloy having thermal conductivity 185 W/m·K, has an conductance of 0.37 W/K.

Conductive heat exchange

• A thermal interface is created between e.g. an electronics box and the satellite deck it is mounted on.

• The thermal contact resistance depends on:– Surface roughness– Contact pressure– Use of fillers

Interface

Mounting and interfaces

• Example of an electronics box which:– Is painted black to

maximize radiation heat exchange

– Has mounting lugs at the bottom for conducting heat exchange



• Example of an electronics box internal thermal design with:– Printed circuit

boards mounted on heat sink modules

– Heat sinks mounted with good thermal connection to the bottom plate



• Machined surface finish has an impact on heat conduction through an interface

• Surface finish is defined as roughness average (RA) and waviness



• A filler material improves interface heat conduction

• Filler gasket consists of thermal conductive particles (e.g. AlO2) and an elastomeric binder (e.g. silicone)



• Example of thermal filler conduction resistance per cm2

versus mechanical pressure.


Thermal design analysis• Analysis is typically done using a CAD software

with a thermal solver• A model is built e.g. by adding a mesh to a

simplified mechanical model• Optical and material properties are defined• Nodes in the mesh get connected through a

conduction network• Heat loads are defined• The thermal solver calculates radiation

exchange and the heat conductance between elements

Thermal design analysis

• View factors (or form factor), is basically the fraction of radiated energy emitted by element ithat is intercepted by element j.

Thermal design analysis• View factors can be solved analytically, see e.g.:http://www.me.utexas.edu/~howell/tablecon.html

C-125: Sphere to coaxial disk.Reference: Feingold and Gupta; Naraghi and Chung (1981);

where R = r/aGoverning Equation:

•The good news is: Your CAD software will do it for you.

http://www.me.utexas.edu/~howell/referenc.html#feingold-3

http://www.me.utexas.edu/~howell/referenc.html#naraghi-4

Thermal design analysis• Example, analytic calculation of a view factor:

Two infinitely long, directly opposed parallel plates of the same finite width.

( ) ( )21 2 2 1 1 h h

w wF F− −= = + −

1

0h/w10

F1-2

2

Thermal design analysis• Example of a satellite

interior mesh. The green mesh represents a cavity in the satellite and the red mesh two electronic boxes in the cavity.

• Meshed elements are connected through a conduction network

Entity Filter Mode: Off Display Group Current Grp: INSIDE_SAT_ENCLOSURE

Thermal design analysis• The thermal solver solves the equation:

Thermal Design Examples

6-14 kW/m2

≤ 13 kW/m2

Sun

Mercury

BepiColombo with wire booms

The BepiColombospacecraft will be irradiated with two spectra, the Sun’s and Mercury’s. The spacecraft itself will radiate with a spectrum closer to the room temperature.


Reflected irradiance, ρ

Infrared emitter (e.g. Quartz glass)

Solar reflector (e.g. Silver)

Irradiance

ρThe absorption and emission coefficients be calculated from reflectance data: αλ=ελ=1-ρλ.

Typical ρλ for a OSR is shown in the graph. The high Solar reflectance and low infrared reflectance result in relatively low temperatures.

OSR


• Mimic the OSR reflectance spectra by sputter a thin film of ZrO2 on the wire booms Silver braid.

• Below is a section of the 1.5 mm diameter wire boom:

ZrO2

Silver braid

Insulator

Copper wire

Thermal design examples

A test object orbiting Mercury.

Ground track

Eclipse cone

Planet equator plane

Thermal testing

• Thermal tests are done at both unit level and on complete assembled satellites.

• Thermal tests are also done to find material properties. E.g. calorimetric tests to measure emissivity

Thermal testing of wire boom

• Testing of a wire boom at the Institute of Space Physics, Kiruna.

Solar simulator

Wire boom

Inside of walls cooled with liquid nitrogen


Wire, Twire

Tw2Tw1

Walls

4 4 4 4( ) ( )1 22 2A Aemit emitS A T T T Twire wireS w willα σ ε σ ε⋅ ⋅ = ⋅ ⋅ − + ⋅ ⋅ −

Aemit = 2·π·r·l


4 4 41 2

4 4 41 2

4 4 41 2

(2 )222 (2 )

2(2 )

2

emitS ill wire w w

S wire w w

S wire w w

AS A T T T

r lS r l T T T

T T TS

α σ ε

πα σ ε

α σ πε

⋅ ⋅ = ⋅ ⋅ − − ⇒

⋅ ⋅ ⋅⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ − − ⇒

⋅ ⋅ − −=

⋅


αS/ε Twire

(K)σ S

(W/m2)Tw1

(K) Tw2

(K) 1.6 332 5.6703

10-81350 90 90

1.5 90 200

1.3 90 263

1.3 225 225

1 263 263


Assuming Aill = 2· r ·l·cos 45º and Aemit = 2·π·r·l:

4 22 2 2

S ill S S

emit

S A S r l STA r l

α α ασ ε σ ε π σ ε π

⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅= = =

⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

T wire(°C)

Solar flux αS/ε

280 14 489 1.6270 1.5250 1.3220 1

Thermal balance tests

• Thermal balance tests are done to verify the thermal behaviour and simulation models

• Test chamber at Jaxa, Japan.

Thermal balance test of MEFISTO-S

• Thermocouple• Solar lamp• Walls liquid Nitrogen

cooled• MEFISTO-S front

Thermal testing of BepiColombo

Drawing of BepiColombo MMO (diameter about 2 m) in a test chamber.

Sun radiation

Test jigRotation table

Thermal testing of ClusterThe Cluster satellite in a space simulator test chamber at IABG outside Munich.

ef2260 thermal

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