fastrac thermal model analysis by millan diaz-aguado
TRANSCRIPT
FASTRAC Thermal Model Analysis
By Millan Diaz-Aguado
Overview
• Sun/Shade and Line of Sight• Heat Flux (Earth, Albedo, Sun)
– Heat Flux Earth and Albedo and View Factor
• Simple Example (Thin Disk)• Two Square Parallel Surfaces
– Conduction through the Solar Panel– Radiation to the Structure– Radiation to EMI
• Future work and Conclusions
Eclipsed vs. Light
• Find the position of the Sun (Julian Date) and the satellite, and calculate the angle between them (Θ).
• If θ1 +θ2 > Θ then there is Line of Sight
Eclipsed vs. Light
• Example: i=45º Ω=45º ω=0 h=300km on July 21st 2005
Environmental Heat Flux• Solar Heat Flux ( W/m2 )
q=1350 α cos(ψ)– Where ψ is the angle between the normal of the
spacecraft surface and the Sun and α is the aborptivity of the surface
• Earth Blackbody Radiationq=σ (T)4 α F – Where σ is the Stefan-Boltzmann constant, T is the
temperature of Earth’s blackbody, and F is the view factor• Earth Albedo
q=1350 AF α F cos (θ)– Where θ is the angle between the spacecraft surface and
the Sun, AF is the Albedo Factor (~at 90 min orbit)
Albedo Factor
Inclination0-30
Inclination30-60
Inclination60-90
Hot Case 0.28 0.31 0.28
Cold Case 0.11 0.16 0.16
View Factor
• Shape factor for different angles between the normal of the surface of the spacecraft and its position vector h/R=0.047
• Interpolate data if angle lays between the given data
Heat Flux for a Orbiting Thin Germanium Circular Disk
• Altitude 300km, i=0º, α = 0.81
Temperature for Thin Disk• To calculate the surface temperature we use a simple ODE for radiated thin
plate
• Where ρ is the density, ε is the emissivity, h is the width and T is the temperature of the thin plate
qTTdt
dhc 4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
100
200
300
400
500
600
700
Time (hours)
Tem
pera
ture
(K
elvi
n)
Thermal Model of Two Parallel Plates
• Plate 1 is facing the Earth
• Plate 2 is facing away from the Earth
• Radiation patterns will be different
• View Factor is different as the plates are square
cs
cs
r
rn
/
/
cs
cs
r
rn
/
/
Fse=.98
ε=.85
α=.81
Width=175 μm
C=0.093 W-hr/(Kg-°C)
ρ=5260 Kg/m³
Surface Heat Flux
A) Plate 1 B) Plate 2
Surface Temperatures
A) Plate 1 B) Plate 2
Conductance Through the Solar Panel
34
34
23
23
12
1214 k
x
k
x
k
x
A
qtt
23x 34x
1 2 3 4
k12 k23 k34
12x
• The Solar Panel is assumed to have a multilayer wall
• The temperature of the inner aluminum surface is calculated by:
• Where t1 is the temperature of the outer surface, k is the thermal conductivity, Δx is the thickness and q/A is the heat flux
1t
4t
Radiation Between Two Parallel Surfaces
• Radiation between the solar panel with side panel and EMI boxes
• Where T is the surface temperature, ε is the emissivity and σ is the Stefan-Boltzmann
1
1
T
1 2
2
2
T4/1
21412
1/1/1
A
qTT
Buffed Aluminum Side Panel
A) Plate 1 B) Plate 2
EMI Golden Anodized Aluminum
A) Plate 1 B) Plate 2
Conclusion and Future Work
• Conduction:– Between aluminum side panel and EMI box– Between solar panel and aluminum side panel– Between structural elements
• Thruster tank• Four other sides of the hexagon, top and bottom
sides• Inner Heat Production
– Subsystems and Thruster• Rotation of the satellite• MLI