Analysis of the Gemini data
By
Oleg Likhatchev
Aerospace and Mechanical
Engineering Department
University of Arizona
Contents in Brief
• Introduction:
What can we learn from the Gemini data?
• Pressure and velocity data analysis for
the primary mirror:
* Autocorrelation functions
* Power Spectral Densities
• Buffeting forces on the secondary mirror:
* Semi-empirical theory
* Spectral analysis of unsteady forces
on the secondary mirror
The Gemini Telescope
Pressure Sensors Layout
+Y
-X
+X
-Y
Velocity Real Time Records c00030oo
+X
Second Mirror
-X
10
10
12
8
8
10
6
6
4
4
2
2
0
0
-2
-2
-2
-4
-4
-4
-6
-6
-8
-8
8
6
4
2
0
-6
-8
-10
-10
-10
0
50
100
150
200
250
300
0
50
100
150
200
250
0
300
50
100
150
200
250
300
250
300
time (sec)
-Y
+Y
8
10
6
8
Dome
10
6
4
5
4
2
2
0
0
-2
-2
-4
-4
0
-5
-6
-6
-8
-8
-10
0
50
100
150
200
250
300
-10
0
50
100
150
200
Ux
Uy
Uz
250
300
0
50
100
150
200
Pressure Real Time Records c00030oo
#12
10
#7
10
#23
10
8
6
4
2
8
8
6
6
4
4
2
2
0
0
0
-2
-2
-2
-4
-4
-4
-6
-6
-6
-8
-8
-8
-10
-10
-10
0
50
100
150
200
250
0
300
50
#18
10
100
150
200
250
0
300
50
100
150
200
250
300
X axis title
time (sec)
#13
10
#24
10
8
8
8
6
6
4
6
4
2
4
2
0
2
0
-2
0
-2
-4
-2
-4
-6
-4
-6
-8
-6
-8
-10
0
50
100
150
+X
200
250
300
-8
-10
0
50
100
150
-X
200
250
300
-10
0
50
100
150
200
-Y
250
300
c00030oo Velocity
Autocorrelations at +X
1.0
0.8
0.6
uu
0.4
0.2
0.0
-0.2
0
50
100
150
200
250
300
0
50
100
150
200
250
300
1.0
0.8
0.6
vv
0.4
0.2
0.0
-0.2
1.0
0.8
0.6
ww
0.4
0.2
0.0
-0.2
0
50
100
150
Lag  (sec)
200
250
300
c00030oo Velocity
Autocorrelations at -X
1.0
0.8
0.6
uu
0.4
0.2
0.0
-0.2
0
50
100
150
200
250
300
0
50
100
150
200
250
300
0
50
100
150
200
250
300
1.0
0.8
0.6
vv
0.4
0.2
0.0
-0.2
1.0
0.8
0.6
ww
0.4
0.2
0.0
-0.2
Lag  (sec)
c00030oo Pressure
Autocorrelations
0.2
Sensor #7
0.1
<U>=5.81 m/s
t=4.4 sec
St=0.2
L=5.1 m
-X
0.0
-0.1
-0.2
0
50
100
150
0.2
<U>=1.78 m/s
t=14 sec
St=0.2
L=4.98 m
200
250
300
#12
0.1
+X
0.0
-0.1
-0.2
0
50
100
150
200
250
300
0.2
#23
0.1
-Y
0.0
-0.1
-0.2
0
50
100
150
200
Lag  (sec)
250
300
Wind Buffeting
Quasi-Steady Assumption
The basic Bernoulli relation along a hypothetical streamline
(quasi-steady assumption!)
1
1
p   U 2  p  V 2
2
2
(*)
where



U   U   u t 
  
V  V  v t 
p  p  p t 
A pressure coefficient C p is defined by
p  p 
1
U 2 C p
2
If it is assumed that this may be extended to fluctuating cases
p  p t   p  
1
2
 U   u t  C p
2
which yields the quasi-steady result for the local pressure
p t   U  u t C p
the term u t  being assumed negligible with respect toU
2
2
t 
Comparison of PSD’s for Static and
Dynamic Pressures
From the basic equation (*)
 p  p     1  Vi  vi 2  U 2i 
i  1,2,3
2
or
 x, y , z 
(**)

p
where  and U  are the pressure and the velocity far
upstream

p
U
It is assumed that we can replace  and 

by the local static pressure and the mean velocityV
?!
(since we don't have anything more at this moment)
Finally, we can compare the PSD for
both sides of Equation (**)
Pressure Sensor #7
Velocity at –X
c00030oo
PSD(q)*f*10
4
3.0
Dynamic Pressure
2.5
2.0
1.5
1.0
0.5
0.0
0.01
0.1
1
10
1
10
PSD(p)*f*10
6
7
6
Static Pressure
5
4
3
2
1
0
0.01
0.1
f (Hz)
<U>=5.81 m/s; f=0.8 Hz; St=0.2; L=1.45 m
<U>=5.81 m/s; f=1.0 Hz; St=0.2; L=1.14 m
Pressure Sensor #12
Velocity at +X
c00030oo
0.5
Dynamic Pressure
PSD(q)*f*10
4
0.4
0.3
0.2
0.1
0.0
0.01
0.1
1
10
2.5
Static Pressure
PSD(p)*f*10
6
2.0
1.5
1.0
0.5
0.0
0.01
0.1
1
10
f (Hz)
<U>=1.78 m/s; f=0.26 Hz; St=0.2; L=1.4 m
Pressure Sensor #23
Velocity at -Y
c00030oo
PSD(q)*f*10
5
1.00
Dynamic pressure
0.75
0.50
0.25
0.00
0.01
0.1
1
2.0
10
PSD(p)*f*10
6
Static Pressure
1.5
1.0
0.5
0.0
0.01
0.1
1
10
f (Hz)
<U>=0.74 m/s; f=0.67 Hz; St=0.2; L=0.22 m
Pressure PSD’s for Sensor #12(+X)
Upwind Side of the Mirror 1
Cases c04530oo and c04530co
1.00
<U>=7.94 m/s
L=1.2 m
St=0.2
PSD(p)*f*10
5
c04530oo
0.75
0.50
0.25
0.00
0.01
0.1
1
0.1
1
1.00
0.75
<U>=7.3 m/s
L=1.2 m
St=0.2
c04530co
0.50
0.25
0.00
0.01
f*L/U
Pressure PSD’s for Sensor #12(+X)
Upwind Side of the Mirror 1
Cases c04530oo and t04530oo
1.0
c04530oo
<U>=7.94 m/s
L=1.2 m
St=0.2
PSD(p)*f*10
5
0.8
0.6
0.4
0.2
0.0
0.01
0.1
1
0.1
1
1.0
0.8
<U>=7.3 m/s
L=1.2 m
St=0.2
t04530oo
0.6
0.4
0.2
0.0
0.01
f*L/U
Buffeting Forces on the
Secondary Mirror
Buffeting Forces on a Rigid
Circular Cylinder in Cross Flows
(Water Tunnel Experiment, So & Savkar 1981 )
Lift
Drag
Strouhal
Lift & Drag
Re=1E+5
Buffeting
Lift & Drag
Re=2E+5
Re=3E+5
Experimental Drag and Lift
Coefficients
Semi-empirical Theory of
Buffeting Forces
U X  cos  U Y  sin 
V
W  U X  sin   U Y  cos
tg 
UY
UX
V  U X2  U Y2 
12
W 0
Buffeting Drag and Lift
FD
V2
 CD  2 ;
lRq
V
FL
W V2
V2
 C D   2  C L  2  sin t ;
lRq
V V
V
q
V 2
2
;
  2  St  V 2 R 
the linear approach
~2
~
V 2  V  V   V 2  2V 
Buffeting Drag on the Second Mirror
c04530oo
PSD(FD)*f/(LRq)
2
0.0000020
Ux=-0.69 m/s
Uy=-0.86
Uz=-0.26
R=1 m
L=2 m
U=1.1 m/s
St=0.5
5
Re=1.5*10
FD=2.4 N
0.0000015
f=0.90
First
harmonic
f=0.44
0.0000010
0.0000005
0.0000000
0.01
0.1
f Hz
1
10
1
10
0.0000020
St=0.78
0.0000015
0.0000010
0.0000005
0.0000000
0.01
0.1
f*2R/U
Unsteady Lift Due to Fluctuating Drag
c04530oo
PSD(FL)*f/(LRq)
2
0.000004
0.000003
0.000002
0.000001
0.000000
0.01
R=1 m
L=2 m
U=1.1 m/s
St=0.5
Re=1.5*10
f=0.62 Hz
f*2R/U=0.28
0.1
0.00006
f Hz
1
10
Plus Strouhal Lift
0.00004
5
0.00002
0.00000
0.01
0.1
1
f Hz
10
Buffeting Forces
Case c00030oo
Buffeting Forces
Case c09030oo