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George Angeli 26 November, 2001
What Do We Need to Know about Wind for GSMT?
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Introduction
Wind information needed
Known (perceived) inconsistencies between models and experiments
GSMT modeling environment
What to expect from wind simulations?
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Design process
Concurrent engineering (structural, optical and control)
Design verification through simulation
Feedback to reiterate and improve the design
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Our approach
Structuraldesign
FEA
Realization
Opticaldesign
Ray tracing
Realization
HW/SWdesign
Controldesign
Realization
Designverification(Simulation)
MATLABSIMULINK
IDEAS
ZEMAX
Modal DE
Lin.trans.
FB DE
Lin.trans.
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Our approach
Advantages Highly improved simulation speed
Significantly reduced computer requirements
Potential for more complex model
Affordable price
Each discipline (mechanical, optical, control) keeps its preferred “native” tools and environment (unlike IMOS but like IODA)
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Our approach
Potential drawbacks Difficult to handle nonlinear effects in structure or
optics
Limits of the linear optical approach should be explored and established
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Structural model
mΦqq
uBΦMΩqqZΩq 0T12 mmm
uBΦM
0x
ZΩΩ
I0x
q
qx
0
T12 2
m
m
Modal description:
State-Space description:
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Optical model
Modal description:
Pqp OPD P - optical sensitivity
Zernike expansion:
pwrrr j
aperture
nj
aperture
jj npnZpZa d
mqWPΦWpa
Small deformations!
Ray tracing
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Integrated model
K(s)
A
C1
Br1(s)
y1(s)xu(s)
G(s)
C2
r2(s)
y2(s)
Edge detector feedback
Wavefront sensor feedback
Structural dynamics
Sky motion,atmosphere
Wind, gravity,heatNoise Noise
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What to expect?
Optimizing the shape and surface of structural elements to minimize the wind-to-force efficiency
Optimizing the geometry of structure to minimize the coupling of wind power into higher order modes
Recognize the need and location of additional damping and stiffening
Improve the design of the structure to make it less sensitive to wind load by
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What to expect?
Optimizing the shape and surface of the dome
Aid the enclosure design to optimize its effect on the wind by
Optimizing the vents and opening on the dome to achieve the required filtering effect
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What to expect?
Estimating the amplitude and bandwidth for wind induced deformation of telescope structure and primary mirror
Determining the necessary range and speed of actuators and sensors
Recognizing the need and location of actuators and sensors
Verify the control architecture by
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What to expect?
Providing well defined disturbance signals to reject
Aid the design of the various feedback loops by
Help to estimate the optical performance of the telescope
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Need to know…
Time evolution of wind forces on structural nodes
Velocity distribution in the vicinity of the structure with spatial sampling rate of node distances
Pressure distribution on the primary mirror with at least 3 samples per segments (to resolve torque)
Wind characteristics
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Need to know… Wind-to-force conversion
Drag and lift:
Validity of first order approximation
Vortex shedding (buffeting with Strouhal frequency at low Reynolds number)
Aerodynamic attenuation of large structures
Effect of enclosure generated turbulence
U
tuUACtD D 21
2
1 2ρ
U
twUAC
U
tuUBCtL DL
22
2
121
2
1ρρ
23
4
1
if
f
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Experimental wind data
0 50 100 150 200 250 300-4
-2
0
2
4
6
8
10Wind velocity at the Secondary Mirror in Series c00030oo
Time (seconds)
Win
d v
elo
city
(m
/s)
; Win
d A
zim
uth
(ra
d)
; Win
d E
leva
tion
(ra
d)
velocityazimuthelevation
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Use of experimental wind data
Problems
Using Gemini South wind measurements
Limited feedback to design (no understanding of process)
Current approach
Real amplitude and direction time functions, no “assumptions”
Limited relevance (different place, different size) No simulation flexibility (given sampling rate,
sample length, amplitude, etc.) Limited environment control (vent gates, direction,
elevation, etc.)
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Use of simulated wind data
CFD output
Amplitude and direction time functions
Flexible environmental and simulation parameters
Problems
Limited understanding of the process
Time and resource consuming
Off-line calculations and data transfer
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Use of calculated wind data Wind generated in Matlab
Problems
Process understanding applicable to design optimization
Calculation based on mathematical wind model (mean velocity and direction, velocity, pressure and direction PSDs, cross-correlations) – filtered random variable
On-line data generation
Significant research effort
Flexible environmental and simulation parameters
Probably: simplifying assumptions
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Atmospheric model
Kolmogorov’s isotropic turbulence theory
Energy cascade: large eddies ⇒ small eddies
Outer scale L0: turbulence not isotropic
Inner scale l0: turbulence disappears, energy dissipated through viscosity
Inertial subrange00
22
lL
πκ
π
3
5
,
κκ κ zFzvΦ Spatial PSD
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Atmospheric model
Taylor’s frozen flow hypothesis Atmospheric “dispersion”
zU
f
TzU
πκ
λ
2
3
5
,
fzFfz fvΦ
Temporal PSD
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Atmospheric model Problem
Infinite energy @ κ=0 (outside of outer scale)
Von Karman spectrum
3
42
10
2
10
1
1,
U
fc
U
fc
fzFz
m
m
DD κΦ Davenport spectrum
Solution 6
52
0
1
1,
ff
zFz vKvK κΦ
HOWEVER, inside the enclosure and around the structure the turbulence is NOT isotropic and homogenous
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Basic questions How are the statistics of the random
process of wind changing due to:
How is the interaction between the wind and telescope structure changing due to:
the mountain top environment; the enclosure; the telescope itself
the enclosure; the telescope itself
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Basic questions
How to scale our existing measurements to the GSMT?
What kind of additional measurements we need (if any)?
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Pressure/Force PSD on primary mirror
10-2
10-1
100
101
10-2
10-1
100
101
102
103
Modified PSD of Pressure on Primary Mirror
Frequency [Hz]
PS
D o
f pre
ssu
re [P
a/H
z]
fit 0.6/f5/3
data