Final Project Discussion - University Of...

Final Project Discussion And Thermal DesignENAE 697 - Space Human Factors and Life Support

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

Final Project Discussion• Final Report Discussion• Thermal Systems Design Overview

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© 2011 David L. Akin - All rights reservedhttp://spacecraft.ssl.umd.edu

http://spacecraft.ssl.umd.edu

http://spacecraft.ssl.umd.edu



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

– Internal power generation– Environmental temperatures

• Conduction• Thermal system components

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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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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 total heat 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 total surface area)

• For equilibrium, set equal

• 1 AU: Is=1394 W/m2; Teq=280°K

!

Qin = Is" r2

!

Qout = 4" r 2#T 4

!

Is" r2 = 4" r2#T 4 $ Is = 4#T 4

!

Teq =Is4"#

$ %

&

' (

14

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Effect of Distance on Equilibrium Temp

Mercury

PlutoNeptuneUranus

SaturnJupiter

Mars

Earth

Venus

Asteroids

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Shape and Radiative Equilibrium• A shape absorbs energy only via illuminated faces• A shape radiates energy via all surface area• Basic assumption made is that black bodies are

intrinsically isothermal (perfect and instantaneous conduction of heat internally to all faces)

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Effect of Shape on Black Body Temps

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

bodies:

! where– ! =absorptance (or absorptivity)– " =reflectance (or reflectivity)– # =transmittance (or transmissivity)

!

QIncident =Qabsorbed+Qreflected +Qtransmitted

!

Qabsorbed

QIncident

+Qreflected

QIncident

+Qtransmitted

QIncident

=1

!

" #Qabsorbed

QIncident

; $ #Qreflected

QIncident

; % #Qtransmitted

QIncident

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Non-Ideal Radiative Equilibrium • Assume a spherical black body of radius r• Heat in due to intercepted solar flux

• Heat out due to radiation (from total surface area)

• For equilibrium, set equal

!

Qin = Is"# r2

!

Qout = 4" r 2#$T 4

!

Is"# r2 = 4# r 2$%T4 & Is = 4 $

"%T 4

!

Teq ="#Is4$

%

& '

(

) *

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($ = “emissivity” - efficiency of surface at radiating heat)

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Effect of Surface Coating on Temperature

$ = emissivity

! =

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°K for space)

• Also take into account power used internally

!

Prad ="#A T 4 $Tenv4( )

!

Is" As + Pint =#$Arad T4 % Tenv

4( )

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Example: AERCam/SPRINT• 30 cm diameter sphere• !=0.2; $=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 = "#AradT4 $ T =

200W

0.8 5.67 %10&8 Wm2°K 4

'

( )

*

+ , 0.2827m2( )

'

(

) ) ) )

*

+

, , , ,

14

= 354°K

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AERCam/SPRINT Analysis (Free Space)• As=0.0707 m2; Arad=0.2827 m2

• Free space with sun

!

Is" As + Pint = #$AradT4 % T =

Is" As + Pint#$Arad

&

' (

)

* +

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 ="#Arad T4 $ Tenv

4( )% T =200W

0.8 5.67 &10$8 Wm 2°K 4

'

( )

*

+ , 0.2827m2( )

+ (280°K)4

'

(

) ) ) ) )

*

+

, , , , ,

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= 384°K

!

Is" As + Pint =#$Arad T4 % Tenv

4( )& T =Is" As + Pint#$Arad

+ Tenv4

'

( ) )

*

+ , ,

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= 391°K

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EVA Thermal Equilibrium• Human metabolic workload = 100 W• Suit electrical systems = 40 W• Total heat load = 140 W

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Q = �σAT 4 ⇒ A =Q

�σT 4

A =140

(0.8)(5.67× 10−8)(295)4= 0.41 m2



EVA Thermal Equilibrium with Sun• Human metabolic workload = 100 W• Suit electrical systems = 40 W• Total internal heat load = 140 W

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Q + αAIs = �σAT 4 ⇒ A =Q

�σT 4 − αIs

A =140

(0.8)(5.67× 10−8)(295)4 − 0.2(1394)= 2.2 m2



Sublimation• Water heat of sublimation = 46.7 kJ/mole• @ 18 gm/mole = 2594 W-sec/gm• Mass flow for 140 W = 0.54 gm/sec• per hour = 194 gm/hr• 8 hr total EVA time = 1.55 kg of water• @ 2 EVA/day and 180 days = 559 kg of water

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Sitting on a Planetary Surface

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IsTb

Th

Th



Radiative Insulation• Thin sheet (mylar/kapton with

surface coatings) used to isolate panel from solar flux

• Panel reaches equilibrium with radiation from sheet and from itself reflected from sheet

• Sheet reaches equilibrium with radiation from sun and panel, and from itself reflected off panel

Is

Tinsulation Twall

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Multi-Layer Insulation (MLI)• Multiple insulation

layers to cut down on radiative transfer

• Gets computationally intensive quickly

• Highly effective means of insulation

• Biggest problem is existence of conductive leak paths (physical connections to insulated components)

Is

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Emissivity Variation with MLI Layers

Ref: D. G. Gilmore, ed., Spacecraft Thermal Control Handbook AIAA, 2002

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MLI Thermal Conductivity


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Effect of Ambient Pressure on MLI


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1D Conduction• Basic law of one-dimensional heat conduction

(Fourier 1822)

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

!

Q = "KAdTdx

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3D ConductionGeneral differential equation for heat flow in a solid

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

!

" 2T ! r ,t( ) +g(! r ,t)

K=#cK$T ! r ,t( )$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 = "KATi " Ti"1#x

!

Qout = "KATi+1 "Ti#x

!

Qout "Qin =#cK

Ti( j +1) " Ti( j)$t

… …

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• Time-marching solution

where

• For solution stability,

Finite Difference Formulation

! =k

"Cv

= thermal di!usivityd =!!t

!x2

Tn+1i

= Tn

i + d(Tn

i+1 ! 2Tn

i + Tn

i!1)

!t <!x2

2!

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Heat Pipe Schematic

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Shuttle Thermal Control Components

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Shuttle Thermal Control System

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ISS Radiator Assembly

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