1. Origami-Inspired Variable Emissivity Surfaces: Models and Applications
Rydge Mulford – PhD Candidate - Brigham Young University

2. Variable Emissivity - Application
Spacecraft experience varying thermal environments
Radiators are sized to reject the maximum heat load, resulting in non- ideal radiator heat loss for a large portion of the mission’s lifetime

3. Variable Emissivity - Application
A radiator capable of varying its thermal radiative properties would reject the ideal amount of heat to the environment at all times
High Emissivity Reject as much heat as possible
Low Emissivity Hold in as much heat as possible

4. The Cavity Effect - Definition
Reflections inside a cavity create an increase in apparent absorptivity
Cavities concentrate emitted energy over the cavity opening, increasing the apparent emissivity of the cavity

5. The Cavity Effect - Parameters
Apparent radiative properties are dependent on several parameters
All parameters must match for a model to correctly predict the apparent radiative properties of a cavity
Surface Properties
Reflection

6. The Cavity Effect – Parameters
Shape
Geometry

7. The Cavity Effect - Parameters
Heating Condition / Boundary Condition
Collimated Irradiation
Diffuse Irradiation
Constant Wall Heat Flux
But how do we utilize the cavity effect?

8. The Cavity Effect - Origami
Origami tessellations control cavity aspect ratio through actuation
But what are the apparent radiative properties?

9. The Cavity Effect – Literature Review
Substantial research has been completed for the apparent radiative properties of a variety of basic shapes
Analytical
Experimental
Ray Tracing
Four analytical approaches have been developed

10. The Cavity Effect – Literature Review
The approaches are valid, but none of the published cavity effect shapes apply to origami tessellations. =

11. Research Objective
Determine the apparent emissivity of three origami tessellations, considering specular, isothermal surfaces

12. Ray Tracing - Approach
Ray Tracing is well suited for complicated geometries
The most straightforward approach for an isothermal cavity
Apparent Emissivity
Apparent Absorptivity

13. Ray Tracing – Thermal Models

14. Tessellations – Accordion and Modified V
Easy to fold, similar to infinite V-groove
Modified V-groove
Maintains a constant projected surface area while actuating
Two geometry parameters for control (W/D and )

15. Tessellations – Miura-Ori
Benefits
Linear actuation results in 3D movement
Three geometry parameters for control (β, L1/L2 , )

16. Results – Infinite V-groove
An infinite V-groove was created by placing mirrors on the open ends of a finite V-groove
Numerical results for an infinite V-groove match Sparrow’s analytical solution to within 0.5%

17. Results – Accordion

18. Results – Accordion: Ray Independence
All cases showed a convergence of 0.2% or less. The extreme cases are shown here (L/S = 1 or 5 and emissivity = or 0.9)

19. Results – Accordion: Error
Error results are complete for emissivity = The standard deviation of five repeated measurements increases with L/S ratio
Emissivity – 0.028

20. Results – Modified V-groove
Tailored control of apparent emissivity behavior is possible with geometry parameters
Modifying the side length ratio of the Modified V-groove changes the overall behavior of the apparent emissivity
Emissivity – 0.028
Emissivity – 0.117

21. Results – Modified V-groove
At low emissivities, the modified V-groove exhibits different behavior as compared to the standard V-groove. This diminishes with larger emissivites
The D/W ratio improves the fully-actuated apparent emissivity
Emissivity – 0.6

22. Results – Miura-Ori: Length Ratio
The length ratio has very little impact on apparent emissivity

23. Results – Miura-Ori: Beta Angle
The Beta angle has the largest impact on apparent emissivity behavior
As the parallelogram becomes more square the apparent emissivity increases with smaller angles

24. Results – Miura-Ori: Emissivity
The emissivity lowers or raises the curves but does not change the behavior over actuation

25. Acknowledgements and References
This research was made possible by a NASA Space Technology Research Fellowship (Grant Number NNX15AP494)

26. Appendix

27. The Cavity Effect – Literature Review
Shape
Specular
Collimated Irradiation
Geometry
Surface Properties
Diffuse Irradiation
Same as Constant T model
Temperature Profile
Constant Heat Flux
Constant Surface Temperature
Internal Heat Generation
Diffuse
Shape
Specular
Collimated Irradiation
Geometry
Surface Properties
Diffuse Irradiation
Same as Constant T model
Temperature Profile
Constant Heat Flux
Constant Surface Temperature
Internal Heat Generation
Diffuse
Each shape requires 10 solutions to be fully characterized
6 of the 10 solutions have been developed for most basic shapes
But have all possible shapes been studied?
Local, Directional Apparent Emissivity
Vs.
Cavity, Integrated Apparent Emissivity

28. Ray Tracing – Emissivity Thermal Model
From the definition of Qemit
Plug into apparent emissivity equation
Using the original energy balance and equating thermal model to ray tracing results gives:
Rearrange to give apparent emissivity

29. Ray Tracing – Absorptivity Thermal Model
Assuming opaque
Final Expression
From definition of apparent reflectivity
From Ohwada[1] we learn that apparent absorptivity and apparent emissivity are equivalent for an isothermal cavity
[1] - Ohwada, Y “Mathematical proof of an extended Kirchoff Law for a cavity having direction-dependent characteristics” Journal of the Optical Society of America 5(1)

30. Results – Accordion
Apparent emissivities below the intrinsic surface value are a result of rays escaping from the “Apparent End Surface”