Thermal Control Systems! Space System Design, MAE 342, Princeton University!

Robert Stengel

Copyright 2016 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/MAE342.html 1

!! Thermal design overview!!Conduction, convection, and radiation!! Types of thermal control!! Thermal analysis!! Thermal testing

Heat Sources

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Thermal Design Task

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Distribution and uniformity of proper temperatures

Thermal Design Environments•! Pre-launch (shipping, on pad)•! Launch and transfer orbit•! Mission characteristics–!On orbit

•! Diurnal variations•! Seasonal variations•! Mission life variations•! Surface property degradation

–!On planetary surface•! Sun exposure•! Shadow

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Thermal Design Constraints•! Equipment utilization philosophy•! Design margin philosophy•! Failure mode philosophy•! Power system margin•! Mass budget•! Temperature specifications•! Sun/shadow duty cycle•! Equipment redundancy

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Typical Temperature Requirements•! Maximum & minimum operational/non-

operational temperatures•! Maximum diurnal swing•! Maximum gradients•! Survival/safe state temperature•! Allowable rate of change•! Control requirements of sub-systems

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7!"#$"#%&&'&&#

Conduction and Convection

Heat transfer resulting from fluid flow

Heat transfer from conduction within material

q = h!T : Heat flux density, W/m2

[thermal power/unit area = (thermal energy change/unit time)/unit area]h : Heat transfer coefficient, W/m2 -K

!T : Temperature difference, K

q = hconv!T : hconv = Convection coefficient

q = !l"T :

! = Conductivity coefficientl = Conductive path length

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Thermal RadiationElectromagnetic radiation to/from/across space

Integrated over all wavelengths

q =! SB "hotThot4 #$ coldTcold

4( )! SB = Stefan-Boltzmann coefficient

= 5.67 %10#8 W/ m2 -K4( )" ,$ = Emissivity/absorptivity, &1

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Planck’s Law

! =" at a given wavelength (Kirchoff's Law)! # " if peak emission and absorption wavelengths are different

For a given material

Solar Illumination

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Distance, AU Planet Average Solar Intensity, JS, W/m2

Planet Albedo, %

0.39 Mercury 9145 6-10

0.72 Venus 2697 60-76

1 Earth 1349 31-39

1.52 Mars 605 15

5.2 Jupiter 51 41-52

9.54 Saturn 16 42-76

19.19 Uranus 4 45-66

30.07 Neptune 2 35-62

39.46 Pluto 1 16-40

PSun = 3.856 !1026 W

JSun = PSun 4"rSun2 = 3.856 !1026 6.957 !108 m( )#$ %&

2

= 7.355 !108 W/m2 @ solar surface

Thermal Radiation Absorbed and Emitted by Earth

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Qin = !RE2 1" #( )JSEarth

# = 0.35, Albedo, %/100

Qout = 4!RE2"TE

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TE : Earth average temperature

Qout =Qin

TE = 250 KWong

Average Solar Radiation Absorbed by Earth

Average Earth-Emitted Radiation

Earth’s Radiative Equilibrium Temperature

Sunshine

Earthshine

Fairing Inner Surface Maximum Temperatures

12Wong

Aerothermal Heating after Fairing Jettison

13Wong

Radiative Heating from Rocket Plume and Engine Nozzle

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Stowed Solar Arrays

Need for Thermal Control•! Maintain proper operating temperatures

for–!Electronics–!Sensors & actuators–!Propulsion & propellant systems–!Payload instruments–!Mechanical devices

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Thermal Control Types•! Passive

–! Coatings and paints–! Thermal isolation–! Heat sinks–! Convective heat pipes–! Phase Change Materials

•! Active–! Circulating heat pumps–! Heaters–! Thermoelectric devices–! Thermal louvers

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Coatings and Paint•! Incident energy distribution–!Absorptivity (!)–!Reflectivity (")

•! Specular (mirror-like)•! Diffuse

–!Transmittance through coating (#)

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! + " +#( ) = 1Transmittance and Reflectance of "-in

clear glass

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Wong

Spacecraft Thermal Balance

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Ai : Projected spacecraft area for ith effect, m2

Ji : Radiation intensity for ith effect, W/m2

Q : Internally dissipated power, Wa : Planet's albedo, %/100

F : Albedo visibility factor, %/100! : Angle between local vertical and Sun's rays

Tav4 = 1

! AsurfAprJ pr + " Jsol Asol + aFAalb( ) +Q#$ %& '#$ %&

surf : "Wetted" surface area of spacecraftpr : Planetary radiation

alb : Albedosol : Solar

Altitude vs. Visibility Factor (Earth)

Fortescue

Emissivity and Absorptivity of Surfaces

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Fortescue

Absorptivity increases over time due to UV degradation and contamination

Thermal Isolation•! Choose materials to reduce

conduction•! Choose surface to reduce radiation•! Multi-Layer Insulation (MLI), e.g.,

–! Facing space: conductive black Kapton, or brown Kapton over aluminum or silver (2nd-surface mirror)

–! Inner layers: double-sided aluminized Mylar, polyester mesh

–! Facing spacecraft: double-sided aluminized Kapton

•! MLI attached to spacecraft with Velcro and tape, grounded to spacecraft

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Heat “Sinks”•! Materials with high thermal

conductivity and low density adjacent to high heat sources

•! Connected to cooling elements, e.g., fins, pins, heat pipes (or “slugs”) for heat transfer

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Material Density, ", lb/in3 Conductivity, k, W/in-°C

k/"

Aluminum 0.098 4.8 49

AlBeMet (metal matrix composite)

0.075 5.3 71

Beryllium 0.067 3.8 57

Copper 0.323 9 28Wong

Convective Heat Pipe

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!! Liquid-vapor transition!! Natural capillary

circulation within a wick

Qmax =Awickleff

!"Hv

#2$ro

%&'

()*

Awick : cross-sectional arealeff : effective length! : wick permeability" : liquid-phase density

Maximum heat transport rate in zero “g”

Hv : latent heat of vaporization! : liquid-phase dynamic viscosity

" : surface tensionro : effective pore radius of wick

Constant Conductance Heat Pipes

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Heat pipes carry excess heat to radiators

Solid-Liquid Phase Change Material

•! Increased thermal capacity required for periodic loads

•! Latent heat released during solid-liquid change

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Active Heat Pumps•! ~ Air conditioning, residential heating and

cooling•! Use of compressor, pumping, refrigerant, and

expansion

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Heater Locations on a Communications Satellite

•! North-South transponder panels•! Batteries•! Reflector gimbals and hinges•! Solar array deployment system•! GN&C system

–! Earth sensor assembly–! Sun sensor detector–! Sun sensor electronics–! Inertial measurement unit

•! Propulsion system–! Hydrazine/oxidizer tanks–! Propulsion lines–! Thruster valves–! Liquid apogee engine injector

27Wong

Heater Hardware•! Heater Element

–! Cupro-nickel or Inconel dissipating element•! Mechanical Thermostat

–! On-off control for deployment mechanism damper heaters

•! On-Board Computer (OBC)–! Maintains on-off control–! Maintains allowable temperatures

•! Control Thermistor–! Input to OBC

•! Field Effect Transistor Electrical Switch–! High-voltage switching

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Wong

Radioisotope Heating Units•! Typically a few grams of PU238 or another

radioisotope•! Simplify thermal control, as they give known amount

of heat continuously for decades•! Cassini-Huygens contained 82 RHUs plus 3 RTGs

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Radiative Fins on Cassini-Huygens Radioisotope Thermoelectric Generator

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Thermal Louvers

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Messenger Thermal Louvers

Louvers vary emissivity of a radiator in response to temperature

RosettaThermal Louvers

GOES Thermal Control Sub-System

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Thermal Analysis•! Thermal Mathematical Model (TMM)

–! Closed-form idealizations–! Finite element/difference software–! Steady state (thermal equilibrium)–! Transient response–! Cycling

•! Thermal network models–! Nodes

•! Elements that can be characterized by a single temperature

•! Energy storage devices–! Conductors

•! Energy transport–! Energy sinks

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Thermal Mathematical Model•! Conduction, Convection, and Radiation•! Identification of Isothermal Nodes:–!Temperature–!Thermal capacity–!Heat dissipation–!Conductive interfaces–!Radiative interfaces

•! Surrounding nodes•! Free space

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Rosetta

Conductive Heat ExchangeConductive heat flow rate

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Qc =!Al

"T :! = Conductivity coefficientA = Cross-sectional area

l = Conductive path length

!T =Qc1hc

: hc = Thermal conductance

Temperature difference between path ends

!T =Qc1h1

+ 1h2

+ 1h3

+!"#$

%&'=Qc

1hc

hc =h1h2h3!

h1 + h2 + h3 +!= Effective heat conductance

Temperature difference, many serial paths

Conductive Heat Exchange

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!T =Qc

1h1

+ 1h2

+ 1h3

+!"#$

%&'=Qc

1hc

Temperature difference, many serial paths

hc =

h1h2h3!h1 + h2 + h3 +!

Effective heat conductance

Conductive heat transfer from ith to jth nodeQcij

= hcij Ti !Tj( ); i = 1,n; j = 1,n

Radiative Heat Exchange

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Radiative heat transfer from ith to jth nodeQrij

= AiFij! ij"hij Ti4 #Tj

4( ); i = 1,n; j = 1,n

Ai : Area of surface iFij : Radiative view factor of surface j as seen from surface i

! ij : Effective emittance of i on j

For the ith interior node

Fijj=1

k

! ; k = # of surrounding surfaces

View Factor for Two Surfaces

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I1 = I0 cos!1 : I0 = Radiation intensity normal to A1

Differential radiation from $A1 falling on $A2

!Qr12=I0 !A1 cos"1( ) !A2 cos"2( )

s2

View Factor for Two Surfaces

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Total radiation from A1 falling on A2

Qr12= I0

cos!1 cos!2s2

dA1 dA2A2"

A1"

Total radiation from A1

Qrtotal= 2!A1I0 cos" sin" d"

0

! /2

# = !A1I0

F12 =Qr12

Qrtotal

= 1A1

cos!1 cos!2"s2

dA1 dA2A2#

A1#

View factor from A1 to A2

View Factor for Two Surfaces

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AiFij =cos!i cos! j

"sij2 dA1 dA2

Aj#

Ai#

View factor # area for general nodes

AiFij = AjFji

Consequently

Effective Emittance Between Surfaces

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! ij =! i! j

! i + ! j " ! i! j

If surfaces are effectively “black”! ij = 1

Specular emittance is complexFor two, parallel, diffuse surfaces

Calculation of Nodal Temperatures

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Heat balance for ith of n nodes

Qneti=Qexti

+Qinti! " i# AspaceiTi

4 ! hcij Ti !Tj( ) +# AiFij" ij Ti4 !Tj4( )$% &'

j=1

n

(

Qexti! AprJ pr! i +" Jsol Asol + aFAalb( )

miCidTi t( )dt

=Qnetit( )

mi : Mass of node iCi : Specific heat of node i

Time variation of ith nodal temperature is solution to n nonlinear ODEs

Calculation of Nodal Temperatures

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Linearize the ODEs

miCidTi t( )dt

= miCi

d Tinom t( ) + !Ti t( )"# $%dt

& miCi

d Tinom t( )"# $%dt

+miCi

d !Ti t( )"# $%dt

=QnetiTi t( )( ) =Qneti

Tinom t( ) + !Ti t( )"# $% &QnetiTinom t( )"# $% +

dQnetiTinom t( )"# $%dTi

!Ti t( )

Perturbation responses and quasi-steady-state can be found using

miCi

d !Ti t( )"# $%dt

=dQneti

Tinom t( )"# $%dTi

!Ti t( )

(Vector-matrix form)

mC[ ]!!x t( ) = F!x t( ); !!x t( ) = mC[ ]"1F!x t( )

Thermal Design Example !(Sec. 11.5, Fortescue)

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Spherical Upper-Atmosphere Satellite

Thermal Testing•! Levels of thermal test

–! Black box components–! Sub-system module–! Complete spacecraft

•! Types of Test–! Functional–! Thermal cycling–! Thermal balance–! Deployment–! Life

•! Test objectives–! Verify the thermal design in simulated environment–! Validate the thermal model–! Workmanship screening

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Wong

Thermal-Vacuum Testing

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Next Time:!Communications!

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SSuupppplleemmeennttaall MMaatteerriiaall

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Heat Pumps

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