What Do We Need to Know
about Wind for GSMT?
George Angeli
26 November, 2001
Introduction

GSMT modeling environment

Wind information needed

Known (perceived) inconsistencies between
models and experiments

What to expect from wind simulations?
Design process

Concurrent engineering (structural,
optical and control)

Design verification through simulation

Feedback to reiterate and improve the
design
Our approach
IDEAS
Structural
design
Modal DE
FEA
Lin.trans.
Realization
ZEMAX
Optical
design
Realization
HW/SW
design
Realization
Lin.trans.
Ray tracing
MATLAB
SIMULINK
Control
design
FB DE
Design
verification
(Simulation)
Our approach

Advantages
 Highly improved simulation speed
 Significantly reduced computer requirements
 Potential for more complex model
 Each discipline (mechanical, optical, control)
keeps its preferred “native” tools and environment
(unlike IMOS but like IODA)
 Affordable price
Our approach

Potential drawbacks
 Difficult to handle nonlinear effects in structure or
optics
 Limits of the linear optical approach should be
explored and established
Structural model
Modal description:
q  Φqm
 m  2ZΩq
 m  Ωqm  M1ΦTB0u
q
State-Space description:
q m 
x 
q m 
 0
x  
2

Ω

0
I 


 x  M 1ΦT B  u
 2ZΩ
0

Optical model
Modal description:
pOPD  Pq
Small deformations!
P - optical sensitivity
Zernike expansion:
aj 
aperture
Z j r pr dr   Z j n pn   w j p

n
aperture
a  Wp  WPΦ qm
Ray tracing
Integrated model
Wind, gravity,
heat
Noise Noise
Sky motion,
atmosphere
G(s)
A
B
r1(s)
r2(s)
K(s)
u(s)

x
C1
Structural dynamics
C2
Edge detector feedback
Wavefront sensor feedback
y1(s)
y2(s)
What to expect?

Improve the design of the structure to
make it less sensitive to wind load by
 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
What to expect?

Aid the enclosure design to optimize its
effect on the wind by
 Optimizing the shape and surface of the dome
 Optimizing the vents and opening on the dome to
achieve the required filtering effect
What to expect?

Verify the control architecture by
 Estimating the amplitude and bandwidth for wind
induced deformation of telescope structure and
primary mirror
 Recognizing the need and location of actuators and
sensors
 Determining the necessary range and speed of
actuators and sensors
What to expect?

Aid the design of the various feedback
loops by
 Providing well defined disturbance signals to reject

Help to estimate the optical performance
of the telescope
Need to know…

Time evolution of wind forces on structural
nodes

Wind characteristics
 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)
Need to know…

Wind-to-force conversion
 Drag and lift:
u t  
1

Dt   CD  ρA U 2  1  2
U 
2

u t  
1

1
2  w t 
 Lt   CL  ρB U 2  1  2

C
ρ
A
U


D

U 
2

2
 U
 Vortex shedding (buffeting with Strouhal frequency at
low Reynolds number)
 Aerodynamic attenuation of large structures
 
1   f
  fi




4
3




2
 Effect of enclosure generated turbulence
 Validity of first order approximation
Wind velocity (m/s) ; Wind Azimuth (rad) ; Wind Elevation (rad)
Experimental wind data
Wind velocity at the Secondary Mirror in Series c00030oo
10
velocity
azimuth
elevation
8
6
4
2
0
-2
-4
0
50
100
150
200
Time (seconds)
250
300
Use of experimental wind data

Current approach
 Using Gemini South wind measurements
 Real amplitude and direction time functions, no
“assumptions”

Problems
 Limited relevance (different place, different size)
 No simulation flexibility (given sampling rate,
sample length, amplitude, etc.)
 Limited environment control (vent gates, direction,
elevation, etc.)
 Limited feedback to design (no understanding of
process)
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
Use of calculated wind data

Wind generated in Matlab
 Calculation based on mathematical wind model
(mean velocity and direction, velocity, pressure and
direction PSDs, cross-correlations) – filtered
random variable
 Process understanding applicable to design
optimization
 Flexible environmental and simulation parameters
 On-line data generation

Problems
 Significant research effort
 Probably: simplifying assumptions
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 subrange
 Spatial PSD
2π
2π
κ 
L0
l0
Φv z, κ   Fκ z κ

5
3
Atmospheric model

Taylor’s frozen flow hypothesis
 Atmospheric “dispersion”
U z T  λ
κ
2πf
U z 
 Temporal PSD
Φv z, f   Ff z f

5
3
Atmospheric model

Problem
 Infinite energy @ κ=0 (outside of outer scale)

Solution
ΦvK z, κ   FvK z 
 Von Karman spectrum
 Davenport spectrum

ΦD z, κ   FD z 
1
f
1
 f 
1   
  f0 
2
 cmf

 U10
2
 c f
1   m
  U10









2
5
6



4
3
HOWEVER, inside the enclosure and
around the structure the turbulence is
NOT isotropic and homogenous
Basic questions

How are the statistics of the random
process of wind changing due to:
 the mountain top environment;
 the enclosure;
 the telescope itself

How is the interaction between the wind
and telescope structure changing due
to:
 the enclosure;
 the telescope itself
Basic questions

How to scale our existing
measurements to the GSMT?

What kind of additional measurements
we need (if any)?
Pressure/Force PSD on
primary mirror
10
3
Modified PSD of Pressure on Primary Mirror
fit 0.6/f 5/3
data
PSD of pressure [Pa/Hz]
10
10
10
10
2
1
0
-1
-2
10 -2
10
10
-1
10
Frequency [Hz]
0
10
1