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Thermal Systems 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
© 2009 David L. Akin - All rights reservedhttp://spacecraft.ssl.umd.edu
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Thermal Systems 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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Thermal Systems 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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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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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 = Isπ r2
€
Qout = 4π r 2σT 4
€
Isπ r2 = 4π r2σT 4 ⇒ Is = 4σT 4
€
Teq =Is4σ
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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Effect of Distance on Equilibrium Temp
Mercury
PlutoNeptuneUranus
SaturnJupiter
Mars
Earth
Venus
Asteroids
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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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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Thermal Systems 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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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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Incident Radiation on Non-Ideal BodiesKirchkoff’s Law for total incident energy flux on solid
bodies:
where– α =absorptance (or absorptivity)– ρ =reflectance (or reflectivity)– τ =transmittance (or transmissivity)
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QIncident =Qabsorbed+Qreflected +Qtransmitted
€
Qabsorbed
QIncident
+Qreflected
QIncident
+Qtransmitted
QIncident
=1
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α ≡Qabsorbed
QIncident
; ρ ≡Qreflected
QIncident
; τ ≡Qtransmitted
QIncident
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
U N I V E R S I T Y O FMARYLAND
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 total surface area)
• For equilibrium, set equal
€
Qin = Isαπ r2
€
Qout = 4π r 2εσT 4
€
Isαπ r2 = 4π r 2εσT4 ⇒ Is = 4 ε
ασT 4
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Teq =αεIs4σ
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(ε = “emissivity” - efficiency of surface at radiating heat)
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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Effect of Surface Coating on
ε = emissivity
α =
abs
orpt
ivit
y
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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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 =εσA T 4 −Tenv4( )
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Isα As + Pint =εσArad T4 − Tenv
4( )
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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Example: AERCam/SPRINT
• 30 cm diameter sphere• α=0.2; ε=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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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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AERCam/SPRINT Analysis (Free Space)
• As=0.0707 m2; Arad=0.2827 m2
• Free space, no sun
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Pint = εσAradT4 ⇒ T =
200W
0.8 5.67 ×10−8 Wm2°K 4
0.2827m2( )
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= 354°K
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Thermal Systems 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
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Isα As + Pint = εσAradT4 ⇒ T =
Isα As + PintεσArad
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= 362°K
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Thermal Systems 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
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Pint =εσArad 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
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Isα As + Pint =εσArad T4 − Tenv
4( )⇒ T =Isα As + PintεσArad
+ Tenv4
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= 391°K
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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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 = !"AT 4 ! A =Q
!"T 4
A =140
(0.8)(5.67! 10!8)(295)4= 0.41 m2
Thermal Systems 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 + !AIs = "#AT 4 ! A =Q
"#T 4 " !Is
A =140
(0.8)(5.67! 10!8)(295)4 " 0.2(1394)= 2.2 m2
Thermal Systems 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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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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Sitting on a Planetary Surface
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IsTb
Th
Th
Thermal Systems 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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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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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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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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Emissivity Variation with MLI Layers
Ref: D. G. Gilmore, ed., Spacecraft Thermal Control Handbook AIAA, 2002
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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MLI Thermal Conductivity
Ref: D. G. Gilmore, ed., Spacecraft Thermal Control Handbook AIAA, 2002
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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Effect of Ambient Pressure on MLI
Ref: D. G. Gilmore, ed., Spacecraft Thermal Control Handbook AIAA, 2002
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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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
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Q = −KAdTdx
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
U N I V E R S I T Y O FMARYLAND
3D Conduction
General differential equation for heat flow in a solid
whereg(r,t)=internally generated heatρ=density (kg/m3)
c=specific heat (J/kg°K)K/ρc=thermal diffusivity
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∇ 2Tr r ,t( ) +
g(r r ,t)K
=ρcK∂T
r r ,t( )∂t
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Thermal Systems 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
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Qin = −KATi − Ti−1Δx
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Qout = −KATi+1 −TiΔx
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Qout −Qin =ρcK
Ti( j +1) − Ti( j)Δt
… …
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Thermal Systems 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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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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Heat Pipe Schematic
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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Shuttle Thermal Control Components
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Thermal Systems DesignENAE 697 -Space Human Factors and Life Support
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Shuttle Thermal Control System
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