1. 1 Aerospace Thermal Analysis Overview G. Nacouzi ME 155B

2. 2 Thermal Analysis Summary Overview Purpose Summary of heat transfer modes Aerospace considerations: LV & SC Thermal control SC equilibrium temperature Example

3. 3 Thermal Considerations Thermal control system for launch and space vehicles needed to ensure vehicles survive environment, operate properly and meet customer requirements. –Material properties, ultimate strength are a function of temperature –Temperature gradients can cause pointing errors in space vehicles, and stresses on structure (Payload cooling, e.g., cryostat not addressed)

4. 4 Thermal Analysis Summary Review Quick review of the 3 modes of heat transfer: –Conduction, driven by material thermal conductivity k: q ~ k dT/dx –Convective (Forced and natural), driven by convective heat transfer coefficient, h: q ~ hA(  T) –Radiative, driven by surface properties & view factor F: q ~  F T 4 where  is the surface emissivity coefficient

5. 5 Aerospace Considerations Pre-launch environmental conditions: easily controlled Launch phase conditions –Launch vehicle thermal envt: Dominated by aeroheating (forced convection), other contributors include combustion chamber, plume and limited solar –SV may be subjected to limited, usually insignificant, heating envt during launch phase

6. 6 Aerospace Considerations On-orbit thermal environment –SV environment dominated by radiative (internal & external) & conduction from internally generated sources. Significant envt difference on SC, e.g., Sun heating and deep space cooling. Some molecular heating may occur depending on orbit. –Re-entry heating dominated by convective and radiative => requires ablative or high temperature, e.g., ceramics, materials

7. 7 Launch Vehicle Considerations Convective heat transfer calculations based on: Vehicle drag, i.e., skin friction coefficient, shock structures, flow regime and transition points Trajectory parameters, i.e., flight time, velocity & altitude profiles (q ~  V 3 ) Internal heat sources, i.e., combustion chamber

8. 8 Launch Vehicle Considerations Several light weight insulators are available to protect launch vehicle and maintain structure and other components below maximum allowable temperature. –Material uses include different coatings, low density ablative materials and light weight insulators –High density ablators such as carbon-carbon and carbon phenolics are used for hot nozzle operation

9. 9 Space Vehicle Thermal Considerations Thermal envt dominated by radiative transfer and internally generated heat –Main external contributors: Emission from Sun, Js. Sun assumed as a blackbody with a Temp. of 5800 K, usually a point source. Js = (P/ 4 pi a*a), where, P ~ Sun total emission = 3.856 E26 W a ~ distance from planet to Sun => Js = 1370 W/m^2 for Earth Radiation into deep space, assume 0 K

10. 10 Space Vehicle Thermal Considerations –Main external contributors (cont’d): Emission from Earth, effective Earth Temp ~ 290 K => Earth emits in the long IR region between 2 & 50 um –Wien’s law -> max ( T) ~ 2890 um K Reflection from Earth. Earth reflects some of the impinged Sun energy back into space. Fraction based on Albedo, w. Effective w ranges from 0.3 to 0.4 (instantaneous w has wider range, depending on reflecting ‘surface’)

11. 11 Space Vehicle Thermal Control Active: Requires control (& power) from S/C –Includes: Louvers (shutters), heaters, coolers, cryo. Systems Passive: Self contained system, no power input. Includes: –Geometry & structure, insulators, shields, radiating fins, phase change materials and heat pipes

12. 12 Space Vehicle Thermal Control: Heat Pipes Heat pipe contains a wick running the length of the sealed pipe which is partially filled with a fluid such as ammonia. –One end of the heat pipe is connected to a hot region, while the other end is exposed to the colder portion. –Heat causes fluid to evaporate (at hot end) and condense at cold end. Wick transports fluid back to hot end through capillary motion. Heat of vaporization used to cool hot end.

13. 13 Space Vehicle Thermal Control: Heat Pipes Evaporation Heat in Vapor Liquid Condensation Heat out Wick Heat transfer based on latent heat of vaporization

14. 14 SC Thermal Balance Jrad ~ radiated heat flux Jabs ~ absorbed heat flux A ~ Emissive or abs. Area ,  ~ absorption and emissive coefficient Note that there is a spectral dependency for , . For the Sun (  ), peak is at about 0.45 um while for Earth peak is at ~ 10 um (Wien’s law)

15. 15 SC Thermal Balance: Example Ja Jearth Js

16. 16 SC Thermal Balance: Example Heat from Sun: Js x Asun x  Sun reflected from Earth: Ja x  x Aalb Emission from Earth: Jearth *  * Aearth Heat radiated to space:   Aspace * T 4 Internal heat generation: Q Heat balance calculation: (Asun Js + Aalb Ja)*  + Aearth Jearth *  + Q =   Aspace * T 4

17. 17 SC Thermal Balance: Example T 4 = Aearth * Jearth/(Asun  ) + Q/(Asun   ) + (Asun Jsun + Aalb Ja)/(Asun  ) (  /  ) where, Area (Ax) refers to x surface involved in process, e.g., Aearth is the area of the SC that is exposed to Earth. Approach provides average temperature of SC, used only as initial estimate.

18. 18 SC Thermal Analysis Example presented a ‘zeroth’ order analysis to estimate equilibrium temperature Actual temperature distribution solved using a nodal network representing SC and accounts for all modes of heat transfer at each node. –Needed to determine local hot spots and temperature gradients