Payload Thermal Issues & Calculations

1. Payload Thermal Issues & Calculations Ballooning Unit, Lecture 3 Thermal Issues

2. Thermal Requirements • All payload components can function properly only within particular temperature ranges • Operating temperature range (narrowest) • In this temperature range the component will perform to within specified parameters • Non-Operation temperature range (wider) • Component will not perform within specs, but will do so when returned to operating temperature range • Survival temperature range (widest) • If this range is exceeded component will never return to proper operation • Thermal requirements constitute specifying these ranges for all components Thermal Issues

3. Thermal Control Plan • Systems and procedures for satisfying the thermal requirements • Show that thermal system (i.e. heaters, insulation, surface treatment) is sufficient to avoid excursions beyond survival temperature range • Show critical components remain mostly in the operating temperature range • Specify mitigation procedures if temperature moves to non-operating range (e.g. turn on heaters) Thermal Issues

4. Determining Temperature Ranges • Start with OEM (original equipment manufacturer) datasheet on product • Datasheets usually specify only operating temperature range • Definition of “operating” may vary from manufacturer to manufacturer for similar components • Look for information on how operating parameters change as a function of temperature • Your operating requirement may be more stringent than the manufacturer • Find similar products and verify that temperature ranges are similar • Search for papers reporting results from performance testing of product • Call manufacturer and request specific information Thermal Issues

5. Survival Temperature Range • Survival temperature range will be the most difficult to quantify • Range limits may be due to different effects • Softening or loss of temper • Differential coefficients of expansion can lead to excessive shear • Contact manufacturer and ask for their measurements or opinion • Estimate from ranges reports for similar products • Measure using thermal chamber Thermal Issues

6. Heat Transfer • The payload will gain or lose heat energy through three fundamental heat transfer mechanisms • Convection is the process by which heat is transferred by the mass movement of molecules (i.e. generally a fluid of some sort) from one place to another. • Conduction is the process by which heat is transferred by the collision of “hot” fast moving molecules with “cold” slow moving molecules, speeding (heating) these slow molecules up. • Radiation is the process by which heat is transferred by the emission and absorption of electromagnetic waves. Thermal Issues

7. Convection • Requires a temperature difference and a working fluid to transfer energy Qconv = h A ( T1 – T2 ) • The temperature of the surface is T1 and the temperature of the fluid is T2 in Ko • The surface area exposed to convection is given by A in m2 • The coefficient h depends on the properties of the fluid. • 5 to 6 W/(m2 Ko ) for normal pressure & calm winds • 0.4 W/(m2 Ko ) or so for low pressure • In the space environment, where air pressure is at a minimum, convection heat transfer is not very important. Thermal Issues

8. Conduction • Requires a temperature gradient (dT/dx) and some kind of material to convey the energy Qcond = k A ( dT / dx) • The surface area exposed to conduction is given by A in m2 • The coefficient k is the thermal conductivity of the material. • 0.01 W/(m2 Ko ) for styrofoam • 0.04 W/(m2 Ko ) for rock wool, cork, fiberglass • 205 W/(m2 Ko ) for aluminium • Need to integrate the gradient over the geometry of the conductor. • Q = k A ((T1-T2)/L) for a rod of area A and length L • Q = 4 k r (r + x) ((T1-T2)/x) for a spherical shell of radius r and thickness x Thermal Issues

9. Radiation • Requires a temperature difference between two bodies, but no matter is needed to transfer the heat Qrad =   A ( T14 – T24) • The Stefan-Boltzmann constant, , value is 5.67 x 10-8 W/m2 K4 • The surface area involved in radiative heat transfer is given by A in m2 • The coefficient  is the emissivity of the material. • Varies from 0 to 1 • Equal to the aborptivity (  )at the same wavelength • A good emitter is also a good absorper • A good reflector is a bad emitter • In the space environment, radiation will be the dominant heat transfer mechanism between the payload & environment Thermal Issues

10. Emissivity & Absorptivity 1 • Kirchoff’s Law of Thermal Radiation: At thermal equilibrium, the emissivity of a body (or surface) equals its absorptivity • A material with high reflectivity (e.g. silver) would have a low absorptivity AND a low emissivity • Vacuum bottles are “silver” coated to stop radiative emission • Survival “space” blankets use the same principle • Kirchoff’s Law requires an integral over all wavelengths • Thus, some materials are described as having different absorptivity and emissivity value. Thermal Issues

11. Emissivity & Absorptivity 2 • Manufacturers define absorption and emission parameters over specific (different) wavelength ranges • Solar Absorptance ( s ): absorptivity for 0.3 to 2.5 micron wavelengths • Normal Emittance ( n ): emissivity for 5 to 50 micron wavelengths • The Sun, Earth and deep space are all at different temperatures and, therefore, emit power over different wavelengths • A blackbody at the Sun’s temperature (~6,000 Ko) would emit between about 0.3 and 3 microns and at the Earth’s temperature (~290 Ko) would emit between about 3 and 50 microns • For space we want to absorb little of the Sun’s power and transfer much of the payload heat to deep space. • Want a material with low s and high n . • Sherwin Williams white paint has s of 0.35 and n of 0.85 Thermal Issues

12. Qrad Ts Qin Qcond T2 T1 Steady State Solution • In a steady state all heat flows are constant and nothing changes in the system • Sum of all heat generators is equal to the sum of all heat losses ( Qin = Qout ) • Example flow of heat through a payload box wall • Assume vacuum so no convection • Input heat ( Qin ) generated by electronics flows through wall by conduction and is then radiated to space. Qcond = Qin or kA ( T1 – T2 ) / L = Qin (1) Qrad = Qin or A (T24 – Ts4 ) = Qin (2) • Use eq. 2 to determine T2 and then use eq. 1 to determine T1 • But real systems are never this simple Thermal Issues

13. Balloon Environment is Complex Qsun+Qalbedo+QIR+Qpower = Qr,space+Qr,Earth+Qc • Multiple heat sources • Direct solar input (Qsun), Sun reflection (Qalbedo), IR from Earth (QIR), Experiment power (Qpower) • Multiple heat sinks • Radiation to space (Qr,space), Radiation to Earth (Qr,Earth), Convection to atmosphere (Qc) • Equation must be solved by iteration to get the external temperature • Then conduct heat through insulation to get internal temperature Thermal Issues

14. Solar Input Is Very Important • Nominal Solar Constant value is 1370 W / m2 • Varies ~2% over year due to Earth orbit eccentricity • Much larger variation due to solar inclination angle • Depends upon latitude, time of year & time of day • Albedo is reflection of sun from Earth surface or clouds • Fraction of solar input depending on surface conditions under payload ATIC-02 data showing effects of daily variation of sun input Thermal Issues

15. Other Important Parameters • IR radiation from the Earth is absorbed by the payload • Flux in range 160 to 260 W/m2, over wavelength range ~5 to 50 microns, depending on surface conditions • Radiation is absorbed in proportion of Normal Emittance ( n ) • Heat is lost via radiation to Earth and deep space • Earth temperature is 290 Ko and deep space is 4 Ko • There is also convective heat loss to the residual atmosphere • Atmosphere temperature ~260 Ko • For a 8 cm radius, white painted sphere at 100,000 feet above Palestine, TX on 5/21 at 7 am local time with 1 W interior power: Qsun = 9.5 W, Qalbedo = 3.7 W, QIR = 1.6 W Qr,Earth = 0.1 W, Qr,Space = 15.3 W, Qconv = 0.4 W Thermal Issues

16. Application for BalloonSat • Can probably neglect heat loss due to convection and radiation to Earth • Simplifies the equation you need to solve • Need to determine if the solar inclination angle will be important for your payload geometry • e.g. a sphere will absorb about the same solar radiation regardless of time of day and latitude • Spend some time convincing yourself that you know values for your payload surface s and n and your insulation k. • Biggest problem will be to estimate albedo and Earth IR input • Use extremes for albedo and IR to bracket your temperature range Thermal Issues

17. References • “HyperPhysics” web based physics concepts, calculators and examples by Carl R. Nave, Department of Physics & Astronomy, Georgia State University • Home page at http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#hph • Thermodynamics at http://hyperphysics.phy-astr.gsu.edu/hbase/heacon.html#heacon • Heat Transfer at http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html#c1 • Vacuum Flask at http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/vacfla.html#c1 • Thermal Conductivity Table at http://hyperphysics.phy-astr.gsu.edu/hbase/tables/thrcn.html#c1 • Table of Solar Absorptance and Normal Emmittance for various materials by Dr. Andrew Marsh and Caroline Raines of Square One research and the Welsh School of Architecture at Cardiff University. • http://www.squ1.com/index.php?http://www.squ1.com/materials/abs-emmit.html • Sun, Moon Altitude, Azimuth table generator from the U.S. Naval Observatory • http://aa.usno.navy.mil/data/docs/AltAz.html Thermal Issues