Altuğ Okan, MSc
22 Oct 2014, TÜBİTAK UZAY
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Thermal Analysis & Design
Copyright © 2014 by TUBITAK UZAY. All rights reserved.
OUTLINE
• Course Objectives• Introduction to Thermal Design and
Thermal Control Subsystem• Heat Transfer Basics• Hands-on exercise
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
2
COURSE OBJECTIVES
The participants will;• be aware of necessity of thermal control• learn heat transfer basics• perform basic thermal analysis
including trade-offs related to satellite configuration
• discuss analysis results with each other.
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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• First artificial satellite Sputnik was launched by Russians in 4 October 1957.
• Hermetic satellite, air inside and had no clue about space environment. • Spacecraft environment
– Vacuum– Temperature Extremes (From solar max to radiation to almost absolute Zero temperature) – Radiation– ...
• Most effective space environment effect is the orbital heat fluxes under vacuum conditions.
• Temperature of each component in the spacecraft must be within defined, tolerable limits which could be handled by Thermal Control Subsystem
INTRODUCTION
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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• Environmental Heat Loads– Solar Flux (1326 – 1417 W/m2 depending on seasons)– Albedo (Reflected portion of the incoming Solar Flux, typically
%30 of Solar)– Earth Infrared Emission (IR Emission of the Earth at 255K =
~240W/m2)• Heat Dissipation
– Batteries– Other Electronic Equipments
• Radiation to Space– Infrared emission from exterior surfaces of spacecraft
SPACECRAFT THERMAL ENVIRONMENT
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Aim;QSun + QAlb + QEarth + Qinternal – QSpace = 0
where• QSpace is radiation of spacecraft exterior surfaces
to deep space with 4th power of each external surfaces.
• Deep space temperature is about 4 K (~269°C) and behaves as heat sink and black body (perfect absorption/emission)
Finally; • The temperatures of any spacecraft equipment
shall stay within allowable limits after heat in and out is balanced.
• The system enabling this requirement is the Thermal Control Subsystem of the spacecraft.
ENERGY BALANCE
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Thermal Design
and Analysis
Mathematical
Model
Thermal Control Subsystem
Thermal vacuum/bala
nce tests
INTRODUCTION – Thermal Design & Thermal Control
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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• Heat transfer mechanisms– Conduction– Convection– Radiation
• Conduction is the way of heat transfer within spacecraft subsystems/equipment.
• Convection is negligible in space, but used in launch vehicle – spacecraft coupling during launch.
• Radiation is the major heat transfer mechanism for balancing heat in space. It is also good way of heat transfer within spacecraft subsystems/equipment for high temperature differences.
HEAT TRANSFER BASICS
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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One dimensional heat flow (x-> ) [Fourier, 1822]
Qx= -k*A*(dT/dx)
Qx : Heat flux in x-axis (W) ,k : conduction coefficient (W/(m*K)) ,A : conductance area (m2) ,T : temperature (K) ,x : Distance in x direction.i j
Qi,j= Qx
dxdTAkQx
HEAT CONDUCTION
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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i jQi,j
Ki,j
ij,
c,,
j,i TTL
AkQ
ji
jiji
Conduction Heat Transfer Equation
• All materials greater than 0 K transfers heat via thermal radiation• In electromagnetic spectrum, thermal radiation covers 0.1 100 m
of wavelength
• Black body is the ideal body that emits and absorbs all the energy in all wavelengths and defined by Boltzmann rule:
E = T4
: Stefan-Boltzmann constant( = 5.6696*10-8 W/(m2*K4) ),T : Surface temperature (K).
In reality, there is no ideal surface (black body) emitting/absorbing 100% of its energy.
THERMAL RADIATION - Basics
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Real Surfaces, (Emissivity) = Ereal surf / Eblack
surfEreal surf= T4
Total Energy transfer
THERMAL RADIATION – Real Surfaces
Reflected, (*E)
Incoming flux, E
Absorbed, (*E)
Transmitted, (*E)
+ + = 1
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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View Factor (Radiation Exchange Factor for ideal surfaces; ε=1 )
Radiation Exchange Factor (for real surfaces where ε<1)
THERMAL RADIATION – View and Radiation Exch. Factors
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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j,irij,i A
ji j
Qi,j
i,j
i
44,, ijji
riji TTAQ
Qi,j
wherei,j : Radiation Exchange Factor between surfaces i and j
THERMAL RADIATION – Radiation Exchange
Radiative Heat Transfer Equation
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Energy Balance
Time Dependent Energy Equation
tTCp q
zTk
zyTk
yxTk
x
HEAT TRANSFER EQUATION (1/2)
QSun + QAlb + QEarth + Qinternal – QSpace = 0
Conduction and Radiation Terms
In Orbit Temperatures of all the satellite
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Small Satellite Engineering and Design
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Discretized Energy Equation
HEAT TRANSFER EQUATION (2/2)
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where• m = mass [ kg ]• Cp = Specific Heat [ J/(kg*K) ]• = num. coefficient [=1 fully-implicit, =0 fully-
explicit] • Qi = heat flux coming to note i• N = number of nodes in the satellite• n = time at t; n+1 is the time at t+t
1ni
N
j
41ni
41njj,i
N
j
1ni
1njj,i
ni
1ni
i QTTRTTKtTTCm
ip
N
j
ni
N
j
4ni
4njj,i
ni
njj,i QTTRTTK)1(
Temperature Requirement of Typical Spacecraft Equipment
THERMAL DESIGN REQUIREMENTS - Temperatures
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Equipment NO min (C) Op. min (C) Op. max (C) NO max (C)
Optical Imager 0 13 23 40Battery 0 0 30 30OB Computer -30 0 50 60Other Electronics -30 -20 50 60
Solar Panels -100 -100 100 100
Antennas -50 -50 100 100NO: Non-OperatingOp: Operating
Critical Equipment1. The batteries must operate at preferably between 15°C and 25°C to
increase lifetime.2. Optical imager optics must operate in very narrow temperature
bandwidth (±5°C or less) for less thermal distortion.
Rule of Thumb 1Keep everything simple: the more you increase the complexity, the harder you analyze and solve problems
Set up your model with isothermal nodes for each equipment instead of Finite Element modeling with many meshes
Use worst hot and worst cold cases to stay within temperature limits
Always prefer commercial off the shelf coatings and materials to keep the energy balance at moderate temperatures.
TRADE OFF
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Small Satellite Engineering and Design
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Rule of Thumb 2Radiation from exterior surfaces is the key for thermal design.
Choose appropriate coatings/tapes to keep satellite in moderate temperatures
TRADE OFF
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Equipment αs εIR Remarks
Optical Solar Reflector 0.08 0.80 Solar flux rejector, Preferred for cooling
First surface mirror 0.14 0.05 Preferred for keeping warmMLI* 0.31- 0.6 0.85-0.96 Radiatively decouples from
environmentBlack Paint 0.95 0.90 Preferred for heat rejection inside
s/cWhite Paint 0.20 0.85 Preferred for coolingSolar Cells 0.70 0.70 Used in solar panel modeling*: effective emissivity <
0.04
Rule of Thumb 3Use appropriate thermal control hardware for specific thermal problems
TRADE OFF
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Thermal Hardware FunctionMLI Decouples radiative heat exchangeOptical Solar Reflector Rejects heat
Radiator Used for emitting heat to space
Heat Pipe Acts as very high conductive material and allows to carry heat from heat source to radiators
Paints / Coatings Cooling or keeping the energy depending on α/εHeaters Helps to increase tepmerature of specific equipment or regionThermostat Help to control heaters Sensors Measures temperatures
Hands-on Exercise
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Typical Thermal Design and Analysis requires • specific modelers and pre/post processors• many details & iterations = time and
effort
Hand calculation is an option but takes too much time
Therefore, we set up affordable simple satellite model for Hands-on Exercise
• 2- node satellite model (Platform and Payload)
• Averaged input and output (steady-state solution)
• Thermal data, orbital fluxes and all calculations in Excel spreadsheet
HANDS-ON EXERCISE CHALLANGES
THERMAL MATHEMATICAL MODEL – Node Definition
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Node Item1 Platform
2 Payload
3 Space
Given in the Nodes tab of the Excel sheet
THERMAL MATHEMATICAL MODEL – Heat Loads
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Environmental Heat Loads
Given in the Heat Loads tab of the Excel sheet
Internal Heat Generation
Assumptions• Steady-state orbital fluxes (averaged) on
each surface for worst hot and worst cold conditions
• Only environmental loads on Node 1 (since Node 2 is the payload and should be thermally stable and independent of orbital heat fluctuations for thermal stability ; α =ε << 1 )
• 3 axis-stabilized• +X axis is the velocity vector• +Z axis indicated the Earth
THERMAL MATHEMATICAL MODEL – Links
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Given in the Conduction and Radiation Links tab of the Excel sheet
Links Formula
K1,2 k x Ac / l
1,3 σ x Ar x ε x F1,2
Discretized heat equation given in Slide 15:
is simplified to Steady-State 1D heat transfer problem
Q1,2 = Q2 = K1,2*(T2-T1) and Q1,3 = (Q1+Q2) = R1,3*(T14-T3
4)
which are calculated in the Results tab of the Excel sheet
THERMAL MATHEMATICAL MODEL – Calculations
22 Oct 2014ISNET/TUBITAK UZAY Workshop on
Small Satellite Engineering and Design
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Q1,2
Q1,3
1ni
N
j
41ni
41njj,i
N
j
1ni
1njj,i
ni
1ni
i QTTRTTKtTTCm
ip
N
j
ni
N
j
4ni
4njj,i
ni
njj,i QTTRTTK)1(