Thermal Analysis - spacecraft-design-lab-2019/documentation GitHub Wiki

Nomenclature:

  • alpha, absorptivity
  • eps, emissivity
  • a, albedo constant (~ 0.37)
  • sigma, Stefan Bolzmann constant
  • JS, solar heat flux (1322 W/m2 - 1414 W/m2)
  • JA, Earth Albedo heat flux (aJS)
  • JE, Earth IR emission (231 W/m2)

Battery Specs

Operating range:

  • Charge: 0 - 45 °C
  • Discharge - 20 - 60 °C

Satellite Specs

Dimensions:

  • 50mm x 50mm per face, Area = 0.0025m2, m = 0.170 kg

Thermal properties:

  • Black Paint (Chemglaze Z306): eps = 0.89, alpha = 0.95

Back of the Envelope Calculations

*Note: Satellite modeled as top and bottom faces of aluminum plate with heat flux from Sun absorbed by top face, heat flux from Earth absorbed by bottom face, and heat leaving on both faces

Thermal Equilibrium, Qin = Qout

Qin = (alpha)(A)(JS + JA + JE)= (alpha)(A)((1 + a)JS + JE)

Qout = (eps)(sigma)(2A)(T4)

Solve for T (results below)

Conditions:

  • Max Solar Flux (JS = 1414 W/m2): T = 104.97 °C
  • Min Solar Flux (JS = 1322 W/m2): T = 99.35 °C
  • Eclipse (JS = 0 W/m2): T = -57.06 °C

MATLAB Numerical Solution

  • Lumped Mass Thermal Model: dT/dt = (Qin - Qout)/mc = (Qin -(eps)(sigma)(T4)(6A))/mc
  • In sun: Qin = alpha(JS + JA + JE)A
  • In eclipse: Qin = alpha(JE)A
  • Setup: Initial temperature of 10 °C, 90 minute orbit, 30 minutes in eclipse, 60 minutes in sun (JS averaged to 1368 W/m2)
  • Results: Over 10 orbits, temperature oscillates between 10 °C and - 25 °C, see plot below

FEA Results (ANSYS)

FEA Settings:

  • ANSYS Transient Thermal Simulation
  • 90 minute orbit, 30 minute eclipse.
  • During orbit, solar flux starts at 1322 W/m^2, peaks at 1414 W/m^2 then returns down. Ramps are linear.
  • Earth albedo remains throughout.
  • Boards modeled as FR-4. Windform model created independently from published test data. Lithium polymer modeled with a general polyesterine polymer, thermal conductivity of 0.481 W/mC.
  • CAD model - 'Simplified ANSYS model.' Available in Fusion 360 repo.

See mechanical-thermal repository for a detailed description of the model as well as the model itself!

https://github.com/spacecraft-design-lab-2019/mechanical-thermal/

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