Thermal Systems Design - UMD

Thermal Systems DesignPrinciples of Space Systems Design

U N I V E R S I T Y O F

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Thermal Systems Design

• Fundamentals of heat transfer• Radiative equilibrium• Surface properties• Non-ideal effects

– Internal power generation– Environmental temperatures

• Conduction• Thermal system components

© 2003 David L. Akin - All rights reservedhttp://spacecraft.ssl.umd.edu



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Classical Methods of Heat Transfer

• Convection– Heat transferred to cooler surrounding gas, which creates

currents to remove hot gas and supply new cool gas– Don’t (in general) have surrounding gas or gravity for

convective currents

• Conduction– Direct heat transfer between touching components– Primary heat flow mechanism internal to vehicle

• Radiation– Heat transferred by infrared radiation– Only mechanism for dumping heat external to vehicle



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Ideal Radiative Heat TransferPlanck’s equation gives energy emitted in a

specific frequency by a black body as afunction of temperature

• Stefan-Boltzmann equation integratesPlanck’s equation over entire spectrum

†

Prad =sT 4

†

elb =2phC0

2

l5 exp -hC0

lkTÊ

Ë Á

ˆ

¯ ˜ -1

È

Î Í

˘

˚ ˙

(Don’t worry, we won’tactually use this equationfor anything…)

†

s = 5.67x10-8 Wm2 °K 4

(“Stefan-BoltzmannConstant”)



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Thermodynamic Equilibrium

• First Law of Thermodynamics

heat in -heat out = work done internally• Heat in = incident energy absorbed• Heat out = radiated energy• Work done internally = internal power used

(negative work in this sense - adds to totalheat in the system)

†

Q -W =dUdt



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Radiative Equilibrium Temperature

• Assume a spherical black body of radius r• Heat in due to intercepted solar flux

• Heat out due to radiation (from totalsurface area)

• For equilibrium, set equal

• 1 AU: Is=1394 W/m2; Teq=280°K

†

Qin = Isp r 2

†

Qout = 4p r 2sT 4

†

Isp r 2 = 4p r2sT 4 fi Is = 4sT 4

†

Teq =Is

4s

Ê

Ë Á

ˆ

¯ ˜

14



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Effect of Distance on Equilibrium Temp

050

100150200250300350400450500

0 10 20 30 40Distance from Sun (AU)

Blac

k Bo

dy E

quili

briu

m T

empe

ratu

re

(°K)



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Shape and Radiative Equilibrium

• A shape absorbs energy only via illuminatedfaces

• A shape radiates energy via all surfacearea

• Basic assumption made is that black bodiesare intrinsically isothermal (perfect andinstantaneous conduction of heat internallyto all faces)



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Effect of Shape on Black Body Temps

0

100

200

300

400

500

600

700

0.1 1 10 100Distance from Sun (AU)

Blac

k Bo

dy E

quili

briu

m T

empe

ratu

re

(°K)

Spherical Black BodyAdiabatic Black WallDouble-Sided Wall



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Incident Radiation on Non-Ideal BodiesKirchkoff’s Law for total incident energy flux on solid

bodies:

where– a =absorptance (or absorptivity)– r =reflectance (or reflectivity)– t =transmittance (or transmissivity)

†

QIncident = Qabsorbed+ Qreflected + Qtransmitted

†

Qabsorbed

QIncident

+Qreflected

QIncident

+Qtransmitted

QIncident

=1

†

a ≡Qabsorbed

QIncident

; r ≡Qreflected

QIncident

; t ≡Qtransmitted

QIncident



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Non-Ideal Radiative Equilibrium Temp

• Assume a spherical black body of radius r• Heat in due to intercepted solar flux

• Heat out due to radiation (from totalsurface area)

• For equilibrium, set equal

†

Qin = Isap r2

†

Qout = 4p r 2esT 4

†

Isap r 2 = 4p r 2esT4 fi Is = 4 ea

sT 4

†

Teq =ae

Is

4s

Ê

Ë Á

ˆ

¯ ˜

14

(e = “emissivity” -efficiency of surface atradiating heat)



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Effect of Surface Coating on Temperature

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Teq=560°K (a/e=4)Teq=471°K (a/e=2)Teq=396°K (a/e=1)Teq=333°K (a/e=0.5)Teq=280°K (a/e=0.25)

Black Ni, Cr, Cu Black Paint

White Paint

Optical Surface Reflector

PolishedMetals

AluminumPaint

e = emissivity

a =

abs

orpt

ivit

y



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Non-Ideal Radiative Heat Transfer• Full form of the Stefan-Boltzmann equation

where Tenv=environmental temperature (=4°Kfor space)

• Also take into account power used internally

†

Prad =esA T 4 -Tenv4( )

†

Isa As + Pint =esArad T 4 - Tenv4( )



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Example: AERCam/SPRINT• 30 cm diameter sphere• a=0.2; e=0.8• Pint=200W• Tenv=280°K (cargo bay

below; Earth above)• Analysis cases:

– Free space w/o sun– Free space w/sun– Earth orbit w/o sun– Earth orbit w/sun



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AERCam/SPRINT Analysis (Free Space)

• As=0.0707 m2; Arad=0.2827 m2

• Free space, no sun

†

Pint = esAradT 4 fi T =200W

0.8 5.67 ¥10-8 Wm2°K 4

Ê

Ë Á

ˆ

¯ ˜ 0.2827m2( )

Ê

Ë

Á Á Á Á

ˆ

¯

˜ ˜ ˜ ˜

14

= 354°K



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AERCam/SPRINT Analysis (Free Space)

• As=0.0707 m2; Arad=0.2827 m2

• Free space with sun

†

Isa As + Pint = esAradT 4 fi T =Isa As + Pint

esArad

Ê

Ë Á

ˆ

¯ ˜

14

= 362°K



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AERCam/SPRINT Analysis (LEO Cargo Bay)

• Tenv=280°K• LEO cargo bay, no sun

• LEO cargo bay with sun

†

Pint =esArad T 4 - Tenv4( ) fi T =

200W

0.8 5.67 ¥10-8 Wm 2°K 4

Ê

Ë Á

ˆ

¯ ˜ 0.2827m2( )

+ (280°K)4

Ê

Ë

Á Á Á Á Á

ˆ

¯

˜ ˜ ˜ ˜ ˜

14

= 384°K

†

Isa As + Pint =esArad T 4 - Tenv4( ) fi T =

Isa As + Pint

esArad

+ Tenv4

Ê

Ë Á Á

ˆ

¯ ˜ ˜

14

= 391°K



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Radiative Insulation• Thin sheet (mylar/kapton with

surface coatings) used toisolate panel from solar flux

• Panel reaches equilibrium withradiation from sheet and fromitself reflected from sheet

• Sheet reaches equilibrium withradiation from sun and panel,and from itself reflected offpanel

Is

Tinsulation Twall



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Multi-Layer Insulation (MLI)• Multiple insulation

layers to cut down onradiative transfer

• Gets computationallyintensive quickly

• Highly effectivemeans of insulation

• Biggest problem isexistence ofconductive leakpaths (physicalconnections toinsulatedcomponents)

Is



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1D Conduction

• Basic law of one-dimensional heatconduction (Fourier 1822)

whereK=thermal conductivity (W/m°K)A=areadT/dx=thermal gradient

†

Q = -KA dTdx



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3D Conduction

General differential equation for heat flow ina solid

whereg(r,t)=internally generated heatr=density (kg/m3)c=specific heat (J/kg°K)K/rc=thermal diffusivity

†

— 2T r r ,t( ) +g(r r ,t)

K=

rcK

∂T r r ,t( )∂t



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Simple Analytical Conduction Model

• Heat flowing from (i-1) into (i)

• Heat flowing from (i) into (i+1)

• Heat remaining in cell

TiTi-1 Ti+1

†

Qin = -KA Ti - Ti-1

Dx

†

Qout = -KA Ti+1 -Ti

Dx

†

Qout -Qin =rcK

Ti( j +1) - Ti( j)Dt

… …



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Heat Pipe Schematic



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Shuttle Thermal Control Components



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Shuttle Thermal Control System Schematic



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ISS Radiator Assembly

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