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Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
Thermal Systems Design
• Fundamentals of heat transfer• Radiative equilibrium• Surface properties• Non-ideal effects
– Internal power generation– Environmental temperatures
• Conduction• Thermal system components
© 2002 David L. Akin - All rights reservedhttp://spacecraft.ssl.umd.edu
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
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
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
Ideal Radiative Heat Transfer
Planck’s equation gives energy emitted in a specific frequency by a black body as a function of temperature
• Stefan-Boltzmann equation integrates Planck’s equation over entire spectrum
€
Prad =σT 4
€
eλb =2πhC0
2
λ5 exp−hC0
λkT
⎛
⎝ ⎜
⎞
⎠ ⎟ −1
⎡
⎣ ⎢
⎤
⎦ ⎥
(Don’t worry, we won’t actually use this equation for anything…)
€
σ =5.67x10−8 Wm2°K 4
(“Stefan-Boltzmann Constant”)
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
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
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
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 =Isπr2
€
Qout =4πr2σT 4
€
Isπr2 =4π r2σT4 ⇒ Is =4σT4
€
Teq =Is
4σ
⎛
⎝ ⎜
⎞
⎠ ⎟
14
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
Effect of Distance on Equilibrium Temp
0
50
100
150
200
250
300
350
400
450
500
0 10 20 30 40
Distance from Sun (AU)
Black Body Equilibrium Temperature
(°K)
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
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)
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
Effect of Shape on Black Body Temps
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
Incident Radiation on Non-Ideal Bodies
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
€
α ≡Qabsorbed
QIncident
; ρ ≡Qreflected
QIncident
; τ≡Qtransmitted
QIncident
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
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 =4πr2εσT 4
€
Isαπr2 =4πr2εσT4 ⇒ Is =4εα
σT 4
€
Teq =αε
Is
4σ
⎛
⎝ ⎜
⎞
⎠ ⎟
14
( = “emissivity” - efficiency of surface at radiating heat)
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
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
Polished Metals
Aluminum Paint
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
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
( )
€
Isα As+Pint =εσArad T4 −Tenv4
( )
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
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
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
AERCam/SPRINT Analysis (Free Space)
• As=0.0707 m2; Arad=0.2827 m2
• Free space, no sun
€
Pint = εσAradT4 ⇒ T =
200W
0.8 5.67 ×10−8 W
m2°K 4
⎛
⎝ ⎜
⎞
⎠ ⎟ 0.2827m2( )
⎛
⎝
⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟
14
= 354°K
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
AERCam/SPRINT Analysis (Free Space)
• As=0.0707 m2; Arad=0.2827 m2
• Free space with sun
€
Isα As + Pint = εσAradT4 ⇒ T =
Isα As + Pint
εσArad
⎛
⎝ ⎜
⎞
⎠ ⎟
14
= 362°K
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
AERCam/SPRINT Analysis (LEO Cargo Bay)
• Tenv=280°K
• LEO cargo bay, no sun
• LEO cargo bay with sun
€
Pint =εσArad T4 −Tenv4
( )⇒ T =200W
0.8 5.67×10−8 Wm2°K4
⎛
⎝ ⎜
⎞
⎠ ⎟ 0.2827m2( )
+(280°K)4
⎛
⎝
⎜ ⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟ ⎟
14
=384°K
€
Isα As+Pint =εσArad T4 −Tenv4
( )⇒ T =Isα As+Pint
εσArad
+Tenv4
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
14
=391°K
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
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
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
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
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
1D Conduction
• Basic law of one-dimensional heat conduction (Fourier 1822)
whereK=thermal conductivity (W/m°K)A=areadT/dx=thermal gradient
€
Q=−KAdTdx
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
3D Conduction
General 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
€
∇ 2Tr r ,t( )+
g(r r ,t)K
=ρcK
∂Tr r ,t( )
∂t
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
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
Δx
€
Qout =−KATi+1 −Ti
Δx
€
Qout −Qin =ρcK
Ti( j +1)−Ti( j)Δt
… …
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
Heat Pipe Schematic
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
Shuttle Thermal Control Components
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
Shuttle Thermal Control System Schematic
Thermal Systems DesignPrinciples of Space Systems Design
U N I V E R S I T Y O F
MARYLAND
ISS Radiator Assembly