M1 Thermal Control

1
M1 Thermal Control

• Dr. Nathan Dalrymple
• Space Vehicles Directorate
• Air Force Research Laboratory

2
Agenda

• Requirements
• Thermal response of mirror
• Mirror thermal environment
• Modeling
• Step response trade study
• Control strategies
• Predictive
• Reactive
• Future plans

3
Requirements

• Function Mitigate mirror seeing

seeing
4
Prior Work
Seeing depends upon mirror surface temperature
and surface wind speed. Subcooled mirrors give
better seeing performance.
Ref Racine, Rene, Mirror, dome, and natural
seeing at CFHT, PASP, v. 103, p. 1020, 1991.
Iye, M. Noguchi, T. Torii, Y. Mikama, Y.
Ando, H. "Evaluation of Seeing on a 62-cm
Mirror". PASP 103, 712, 1991
5
Error Budgets
Exact values are not fixed, but change as the
error budgetas a whole is updated.
6
IR Handbook Seeing Analysis
Strong/weak cutoff 2 rad
Ref Gilbert, Keith G., Otten, L. John, Rose,
William C., Aerodynamic Effects in The Infrared
and Electro-Optical Systems Handbook, v. 2,
Frederick G. Smith, Ed., SPIE Optical Engineering
Press, 1993.
7
IR Handbook Seeing Analysis (cont.)
Layer thickness (mks units)
L upstream heated length (m) DT average
temperature difference over upstream length
(C) V wind speed (m/s)
Assume If DT lt 0 then buoyancy term does not
contribute to layer thickness.
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Convection Types and Loci
Wind is good.
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Diffraction-Limited Error Budget
Blue contours rms wavefront error (nm)
l 500 nm
Acceptable operating range, assuming no AO
correction. AO correction will extend the green
range.
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Seeing-Limited Error Budget
Blue contours 50 encircled energy (arcsec)
l 1600 nm
Acceptable operating range
11
Coronal Error Budget
Blue contours 50 encircled energy (arcsec)
l 1000 nm
Acceptable operating range
12
An Alternate View
For a particular DT, V combination, read over on
the vertical axis to find seeing
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Requirements Summary

• Our goal is to keep the mirror surface
  temperature in the green zone, approximately-2
  lt TM1 Te lt 0 C.
• Wind flushing helps reduce the sensitivity to
  TM1.

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Thermal Response of M1

• Mirror thermal environment
• Modeling
• Example cases
• Step response trade study

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M1 Thermal Environment

• Time-dependent problem
• Backside cooling
• Controlled frontside temperature

time lag through substrate
knobs
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M1 Thermal Loading

• Time-dependent problem this is one snapshot

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Thermal Control System Concept
Desiccant chamber included in cell to dry air
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Alternate Cooling Concept
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Flow Loop
Concept A Closed cycle, liquid coolant (heats or
cools)
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M1 Thermal Modeling

• Modeling hierarchy
• 0D,t Lumped capacity
• 1D,t the workhorse
• 2D,t support pad effects
• 3D,t mirror edge effects
• Control models

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1D,t Thermal Model

• Solves Fourier equation in mirror substrate
• Subject to boundary conditions
• Sun side convection (time-varying Te)
• Sun side imposed heat flux (time-varying)
• Coolant side convection, conduction, and
  radiation (time-varying)
• Finite-difference method
• Explicit, implicit, or RC formulation
• Written in IDL
• Runs very quickly on PC

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Example 1 Ideal Inputs
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Example 1 Boundary Conditions
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Example 1 Result
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Example 1 Surface-Air DT
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Example 2 Better Tc Profile
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Example 2 Surface-Air DT
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Example 3 Flatline
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Example 3 Surface-Air DT
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Step Response Trade Study

• Explore the effects of
• Reduced substrate thickness
• Cooling scheme (contact plates or air jets)
• Conventional versus cold tension control
• Desired characteristics
• Fast response
• Simplicity
• Low subcooling
• Method examine step response

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Aside Cold Tension/Surface Heating

• Idea (originally from Gemini Project)
• Heat the mirror surface by passing current
  through the mirror coating
• Cool the back side as usual, except that now we
  remove both the solar loading and the surface
  heating
• Larger temperature gradient through mirrorkeeps
  a large portion of the substrate cooler than the
  conventional approach
• Directly control the front surface temperature by
  modulating the surface heating (brakes gas)
• Backside cooling remains constant

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Trade Space

• Two cooling strategies conventional versus cold
  tension
• Conventional coolant temperature stepped in four
  magnitudes -5, -10, -20, and -30 C
• Cold tension surface heating stepped in four
  magnitudes, corresponding to four equilibrium
  coolant temperatures 10, 5, 0, and -5 C
• Two cooling methods air jets (h 56 W/m2K)
  versus contact plates (h 1000 W/m2K)
• Three substrate thicknesses 100, 75, and 50 mm
• Te and qabs held constant at 20 C and 100 W/m2

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Experiment (Conventional)

• Metrics
• Time to change 5 C
• Time to change 2 C
• Exponential constant

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Experiment (Cold-Tension)

• Metrics
• Time to change 5 C
• Time to change 2 C
• Exponential constant

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Trade Study Results
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Trade Study Results (part 2)
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Trade Study Conclusions

• A 100 mm thick, air jet cooled, conventional
  mirror with a coolant subcooling of 20 C will
  change by 2 C in about 63 min (0.032 C/min).
• A 75 mm thick, air jet cooled, conventional
  mirror with a coolant subcooling of 20 C will
  change by 2 C in about 38 min (0.053 C/min).
• Thinner substrates dramatically reduce thermal
  lag
• Contact cooling reduces texp by 30 and reduces
  tm2 and tm5 dramatically
• Cold tension yields a faster time response at
  similar system subcoolings, at the expense of
  greater complexity

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Control Strategies

• Predictive
• Whiz-bang controller
• Can we predict the weather?
• Reactive
• Follow current ambient temperature
• No effort to predict
• Can we control with large time delay?

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Predictive Control

• Whiz-bang controller
• Uses method of weighted residuals to compute
  optimal coolant temperature profile, given a
  desired surface temperature profile
• Sets up a large number of trial functions
  (pulses) and tests the mirror response to each
• Solution is a linear combination of the trial
  functions (similar to the Finite Element Method)
• If desired profile is known accurately, then we
  can always control the mirror to be in the green
  zone
• Can we predict the weather?

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Predictive Control Example
(known)
Ts solution
Tc solution
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Reactive Control

• Follow current ambient temperature
• Difficulty of time-delaycan we control surface
  temperature with a large time delay?
• See afternoon talk for example caselooks
  promising.

42
Future Plans

• Incorporate the 1D,t model into a MATLAB/Simulink
  control system model
• Use the Simulink model to further refine mirror
  thickness, cooling strategy, and control strategy