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
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
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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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
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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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
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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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
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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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
Effect of Distance on Equilibrium Temp
Mercury
PlutoNeptuneUranus
SaturnJupiter
Mars
Earth
Venus
Asteroids
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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
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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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
Effect of Shape on Black Body Temps
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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
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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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
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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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
Effect of Surface Coating on Temperature
$ = emissivity
! =
abs
orpt
ivit
y
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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
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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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
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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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
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( )
'
(
) ) ) )
*
+
, , , ,
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= 354°K
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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
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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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
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
'
( ) )
*
+ , ,
14
= 391°K
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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
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
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
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
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
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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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
Sitting on a Planetary Surface
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IsTb
Th
Th
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
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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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
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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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
Emissivity Variation with MLI Layers
Ref: D. G. Gilmore, ed., Spacecraft Thermal Control Handbook AIAA, 2002
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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
MLI Thermal Conductivity
Ref: D. G. Gilmore, ed., Spacecraft Thermal Control Handbook AIAA, 2002
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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
Effect of Ambient Pressure on MLI
Ref: D. G. Gilmore, ed., Spacecraft Thermal Control Handbook AIAA, 2002
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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
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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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
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( )$t
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Final Project Discussion And Thermal DesignENAE 697 - Space Human Factors and Life Support
U N I V E R S I T Y O FMARYLAND
Simple Analytical Conduction Model• Heat flowing from (i-1) into (i)
• Heat flowing from (i) into (i+1)
• Heat remaining in cell
TiTi-1 Ti+1
!
Qin = "KATi " Ti"1#x
!
Qout = "KATi+1 "Ti#x
!
Qout "Qin =#cK
Ti( j +1) " Ti( j)$t
… …
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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
• 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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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
Heat Pipe Schematic
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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
Shuttle Thermal Control Components
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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
Shuttle Thermal Control System
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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
ISS Radiator Assembly
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