Transcript UNCERTAINTY ANALYSIS FOR THE WIND MEASUREMENT INSTRUMENT IN THE CALIBRATION DEVICE Sha Yizhuo, Chang Shicong, Zhu Xumin (Meteorological Observation Center of CMA, Beijing 100081,

UNCERTAINTY ANALYSIS FOR THE WIND MEASUREMENT
INSTRUMENT IN THE CALIBRATION DEVICE
Sha Yizhuo, Chang Shicong,
Zhu Xumin
(Meteorological Observation Center of CMA, Beijing 100081, China)
17 Oct, 2012
Calibration Ability of RIC-Beijing
Laboratory Calibration Ability
← Automatic Gas Piston Gauge
Accurate humidity Generator →
← Climate Chamber
0.8-meter wind tunnel with two test
sections & its control system →
Precipitation
Calibration System →
Absolute
← Cavity Radiometer
AWS In-situ Calibration System
气象探测中心
Meteorological Observation Center
Wind Speed Calibration Devices
30m/s Circle Wind Tunnel
10m/s Wind Tunnel
70m/s Circle Wind Tunnel
气象探测中心
Meteorological Observation Center
Uncertainty Sources
The Compose of Wind Speed Calibration Devices:
The Calibration Devices is mainly composed of
0.8 meters low speed wind tunnel (involving crosssection dimension of the working section),
first-class standard Pitot static tube,
first-class compensated micro-manometer, etc.
The Pitot tube and micro-manometer are both standard devices, and the low
speed wind tunnel is used for supporting the standard equipment. Wind tunnel
working section provides wind speed or flow field meeting the requirement for
the standard devices and anemometer to be detected.
气象探测中心
Meteorological Observation Center
Uncertainty Sources
The uncertainty of verification apparatus mainly
comes from the following aspects:
 Uncertainty component caused by calibration coefficient of firstclass standard Pitot static tube is treated as type B evaluation.
 Uncertainty component caused by first-class compensated micromanometer is treated as type B evaluation.
 Uncertainty component caused by air density correction is treated
as type B evaluation.
 Uncertainty component caused by performance of wind tunnel flow
field is treated as type B evaluation.
 Uncertainty component caused by operators is treated as type B
evaluation.
气象探测中心
Meteorological Observation Center
Mathematics Model Building
According to Bernoulli equation of ideal fluid in fluid
mechanics and taking the factors of design and production
diversity of the standard Pitot static tube into consideration,
when Pitot static tube is used to measure wind speed,
following simplified formula (1) is available
(1)
v  1.278 PV  k p
In this formula,
V stands for air velocity;
Pv stands for the difference value between total pressure and static
pressure of Pitot static tube, namely, the reading of micro-manometer; ξ
stands for calibration coefficient of Pitot static tube;
Kp stands for correction coefficient of air density.
气象探测中心
Meteorological Observation Center
Mathematics Model Building
In the test and verification process of anemometer, the performance of
wind tunnel flow field and readings from different operators have respective
influences on the uncertainty of verification apparatus, and the relationship
between the influence quantity caused by the standard devices and
instruments and these two influence quantities is algebraic sum. Define
and as the two influence quantities respectively, the transfer function of
standard apparatus can be written as
V  1.278 PV  k p  l  
(2)
气象探测中心
Meteorological Observation Center
Mathematics Model Building
Because the first item of formula (2) is a multiplication of power functions, we
choose to use relative uncertainty for assessment. If we write relative standard
uncertainty of the variable mentioned in formula (2) in terms of , and the three
relative standard uncertainty component items on the right side of the formula (2)
in terms of ur1 , ur 2 , ur 3 , then the combined relative standard uncertainty of the
verification apparatus is obtained
ur 
ur21  ur22  ur23
(3)
Where the combined relative standard uncertainty is
ur1  p12ur2 ( )  p22ur2 ( Pv )  p32ur2 (k p )
(4)
气象探测中心
Meteorological Observation Center
Mathematics Model Building
In formula (4),
ur ( ) ,
ur (PV ) and ur (k p ) respectively
represent the relative standard uncertainty components
caused by calibration coefficient of Pitot tube  , reading
of micro-manometer
density
kp
PV
and correction coefficient of air
.
According
to JJF1059 and formula (1), we know
.
that p1  1
2
, p2  1 ,
2
p3  1 .
气象探测中心
Meteorological Observation Center
Uncertainty Analyses
1 Uncertainty component caused by calibration coefficient of
the first-class standard Pitot static tube
  1.003  0.001
(5)
ur ( )  0.001/ 0.003  0.1%
(6)
1
1
 

8
2
2
2  0.25
  ur ( )  
2

 ur ( ) 
(7)
气象探测中心
Meteorological Observation Center
Pitot calibration factor / -
1.01
NPL/ISO 3966
146
144
145
142
143
1.008
1.006
1.004
1.002
1
0
5
10
15
20
25
Wind speed / m/s
气象探测中心
Meteorological Observation Center
2 Uncertainty component caused by first-class compensated
micro-manometer
0.4 / 3 0.133 13.3
ur ( PV ) 


%
R
R
R
P 
1
   ur ( PV )  
2

u
(
P
)
r
V


2

(8)
1
 50
2  0.12
(9)
气象探测中心
Meteorological Observation Center
3 Uncertainty component caused by air density correction
1013.25(273.15  t )
288.15( P  0.378uew )
kp 
ur1 
p12ur2 ( )  p22ur2 ( PV )  p32ur2 (k p )
 0.0025 
(10)
44.22
%
R2
(11)
2
 eff 1 
 p1ur ( )
4

ur41
 p u ( P )
 2 r V
4
P
44.22 

8
0.0025


10


R2 


6.67 4
(
) 108
4
8
0.05 10
 R
8
50
(12)
气象探测中心
Meteorological Observation Center
4 Uncertainty component caused by the performance of
wind tunnel flow field
(1) Uncertainty component caused by nonuniform flow field
n
qi / q
2
(

1)

i 1 qi / q

n 1
1
ur (  )   0.43%  0.215%
2
   n 1  145 1  144
(13)
(14)
(15)
气象探测中心
Meteorological Observation Center
(2) Uncertainty component caused by unsteady flow field

qi  q
ur (q ) 
max
q
qi  q
max
1
 0.22%
2.73
1
 0.22%  0.11%
2
  m  (n 1)  5  (3 1)  10
1
ur (V )   0.11%  0.06%
2
(17)
kq
ur (q )  0.6% 
ur (V ) 
(16)
(21)
(18)
(19)
(20)
气象探测中心
Meteorological Observation Center
(3) Uncertainty component caused by flow turbulence intensity
Air flow turbulence intensity has a direct influence on total pressure and static
pressure values measured with Pitot static tube, and the larger turbulence intensity
is, the greater influences will be posed. Reference data provided by relevant
information show that, with regard to 10% of turbulence intensity, velocity measured
with Pitot static tube will be reduced by 0.5%. In more than one flow field test, the
turbulence intensity indexes of 0.8 meters wind tunnel in our station are less than or
equal to 0.4%, which is far from the reference data provided by international
standard, so this uncertainty component should be neglected.
气象探测中心
Meteorological Observation Center
(4) Uncertainty component caused by air flow deflection angle
According to International Standard ISO3966, when air flow deflection angle is less
than 3°, there is no need to correct such angle. In several flow field tests, the air
flow deflection angle indexes of 0.8 meters wind tunnel in our station are less than or
equal to 1°, so we can also neglect the uncertainty component caused by air flow
deflection angle.
ur 2  ur2 (  )  ur2 (V )  0.2152  0.0062 %  0.223%
 eff 2 
 ur (  ) 
4

 0.223% 

4
4
 0.215%    0.06% 
(22)
4
ur42
ur (V ) 


4

144
 154
(23)
10
气象探测中心
Meteorological Observation Center
5 Uncertainty component caused by operators
According to empirical data (based on lots of experiments), uncertainty
component ur 3 caused by readings from different operators is 0.05%, and
relative uncertainty estimation value of ur 3 is 10%, degree of freedom  eff 3 of
such uncertainty component is
 eff 3 
1
   ur 3  
2

u
 r3 
2

1
 50
2
2  0.1
(24)
气象探测中心
Meteorological Observation Center
6 Synthesis of the total uncertainty caused by verification
apparatus
From above analyses, the combined relative standard uncertainty of verification
apparatus ur is
44.22
2
2
%
ur  ur21  ur22  ur23  0.0025  44.22

0.223

0.05
%  0.055 
2
2
R
R
The effective degree of freedom
(25)
 eff of ur is
2
 eff 
 ur1 
4
 eff 1
ur4
u 
 r2
4
 eff 2
u 
 r3
4
 eff 3
44.22 

0.055



R2 


4
0.054  6.67  1 0.2234 0.054


  
8
50
 R  50 154
(26)
气象探测中心
Meteorological Observation Center
Table 1 List of total relative standard uncertainties and effective degree of
freedoms of verification apparatus with typical wind velocities
Corresponding
wind velocity
(m/s)
Corresponding
wind pressure
(Pa)
Relative uncertainty
of verification
apparatus
Effective degree
of freedom
5
15.31
0.49
80
10
61.23
0.26
226
15
137.76
0.24
192
20
244.91
0.24
183
25
382.66
0.24
180
30
551.04
0.23
179
35
750.02
0.23
179
40
979.62
0.23
179
45
1239.83
0.23
178
气象探测中心
Meteorological Observation Center
Summaries
In this paper, the uncertainty caused by verification apparatus of firstclass standard Pitot static tube in process of testing anemometer is
analyzed and assessed. And in the uncertainty assessment of an
anemometer’s verification and test results, the uncertainty from
verification apparatus is treated as type B component of its combined
uncertainty. In regard to the uncertainty assessment of anemometer,
besides the type B uncertainty component mentioned above and type A
uncertainty component obtained from processing test data by statistical
methods, we should also take these uncertainty components, which are
posed by installation of the detected anemometer, methods and so on,
into account. Additionally, if the windward area of the detected
anemometer and mounting bracket is 5% greater than the effective
cross-section area of the wind tunnel working section, not only need to
calculate the blocking coefficient, the uncertainty component caused by
blocking also should be considered.
气象探测中心
Meteorological Observation Center
气象探测中心
Meteorological Observation Center