![Page 1: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/1.jpg)
BLOCK
SHELL
SHIELDS
A lumped thermal model of the STAR enclosure
Model: • thermal input is applied to the shell • thermal couplings include radiation and conduction • radiation approximated as linear in del-T • thermal couplings all equal (for now) • shields have equal heat capacities - Al • block has heat capacity of 1000 cc glass • temperatures referenced to T=0 starting condition • no gradients except between stages • shields numbered from the outside in
![Page 2: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/2.jpg)
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
TEM
PER
ATU
RE
OFF
SET,
deg
rees
10008006004002000TIME, arb. units
shell temp first shield second shield x100 third shield x100fourth shield x100 fifth shield x100 block x1000
Generic lumped thermal model analysis: Thermal response of all layers (note scale factors in box) Excitation: sine wave on outer shell starting at t = 0
![Page 3: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/3.jpg)
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0500040003000200010000
Behavior on a longer time scale:
![Page 4: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/4.jpg)
1.0605
1.0600
1.0595
1.0590
1.0585
135013001250
~ 50 nanodegrees
block x 1000, scale at left is: 500 nano-deg/division
Magnifying the behavior of the block near the maximum offset:
![Page 5: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/5.jpg)
1.0606405
1.0606400
1.0606395
1.0606390
1.0606385
1.0606380
1301.01300.51300.01299.51299.0
~ 0.05 nanodegrees
block x 1000, scale at left is: 0.5 nano-deg/division
Discretization of the computation:
![Page 6: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/6.jpg)
1.0
0.5
0.0
-0.5
-1.010008006004002000
Let’s add a servo to the first shield: just a proportional servo, gain not optimized
![Page 7: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/7.jpg)
30
20
10
0
-10
-20
x10-3
1000950900850
Looking more closely at the ‘final’ state with the servo:
![Page 8: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/8.jpg)
25.96
25.94
25.92
25.90
25.88
25.86
25.84
25.82
x10-3
980960940920900880860840
~ 50 nanodegrees
The behavior of the block near the maximum: (remember it is x1000)
![Page 9: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/9.jpg)
25.96
25.94
25.92
25.90
25.88
25.86
25.84
25.82
x10-3
980960940920900880860840
Block behavior with 10 micro-degree sigma random noise added to the servo input: - program updates once per second
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Conclusions from generic case:
• lumped model provides insight to overall behavior • sub-nanokelvin resolution is easy to achieve • startup transients are associated with phase lags • lumped results can be obtained quickly • servo implementation just requires the control law • outer stage servo is effective in suppressing transients • effects of servo noise can easily be evaluated • need to get quantitative parameters for quantitative results • useful for predicting behavior of hardware experiment • computation speed/memory not issues for lumped model • detailed gradient issues are more easily addressed in Comsol
![Page 11: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/11.jpg)
Response of all stages to a 1-degree temperature step on the shell:
![Page 12: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/12.jpg)
First look at model with ‘real’ parameter values from Joey, Using sine wave excitation at orbital period: - estimated attenuation: 3x108
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Magnified behavior of the block near the maximum:
![Page 14: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/14.jpg)
Replacing the sine wave excitation with Joey’s data for the shell temperature variation in an equatorial orbit:
![Page 15: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/15.jpg)
Detailed view of first few cycles:
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![Page 17: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/17.jpg)
Conclusions for baseline design:
• very good passive filtering of orbital period: - see << 1 nanodegree pp @ orbital - 2007 design gave ~ 5 microdegrees pp @ orbital - passive design now exceeds KT requirements even for equatorial orbit • improved design and analysis realism over 2007 proposal has improved passive lumped performance significantly • block-to-shell relaxation time is multi-days • need to refine parameter values to match hardware better • need to quantify thermal gradient issues further
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More realistic servos: Add a servo to outer shield: - simple proportional controller -starts when shield is at 0.1 K offset, moves to 0.4 K offset
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Move the servo to the inner shield, same gain and trigger:
![Page 20: A lumped thermal model of the STAR enclosure · A lumped thermal model of the STAR enclosure Model: • thermal input is applied to the shell • thermal couplings include radiation](https://reader031.vdocuments.mx/reader031/viewer/2022040405/5e98447dfcb7211c445def8b/html5/thumbnails/20.jpg)
Reducing the servo gain by a factor of 50:
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Teamwork: the art of working together
Joey: thanks for your help!