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

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

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

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

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

The Cavity Effect – Parameters Shape Geometry

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

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

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

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

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

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

Ray Tracing – Thermal Models

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 )

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

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%

Results – Accordion

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 = 0.028 or 0.9)

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

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

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

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

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

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

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

Appendix

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

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

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. 1988 “Mathematical proof of an extended Kirchoff Law for a cavity having direction-dependent characteristics” Journal of the Optical Society of America 5(1). 141-145.

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