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