UNCERTAINTY ANALYSIS FOR THE WIND MEASUREMENT INSTRUMENT IN THE CALIBRATION DEVICE

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

气象探测中心Meteorological Observation Center

Calibration Ability of RIC-Beijing

Laboratory Calibration Ability

AWS In-situ Calibration System

0.8-meter wind tunnel with two test sections & its control system →

Accurate humidity Generator →

← Climate Chamber

← Automatic Gas Piston Gauge

Absolute← Cavity Radiometer

PrecipitationCalibration System →


Wind Speed Calibration Devices

70m/s Circle Wind Tunnel

30m/s Circle Wind Tunnel

10m/s Wind Tunnel


Uncertainty Sources

The Compose of Wind Speed Calibration Devices:

The Calibration Devices is mainly composed of

0.8 meters low speed wind tunnel (involving cross-section 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.


Uncertainty Sources

The uncertainty of verification apparatus mainly comes from the following aspects:

Uncertainty component caused by calibration coefficient of first-class standard Pitot static tube is treated as type B evaluation.

Uncertainty component caused by first-class compensated micro-manometer 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.


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)

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.

1.278 V pv P k



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

1.278 V pV P k l (2)



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 , , , then the combined relative standard uncertainty of the verification apparatus is obtained

2 2 21 2 3r r r ru u u u

Where the combined relative standard uncertainty is

2 2 2 2 2 21 1 2 3( ) ( ) ( )r r r v r pu p u p u P p u k

(3)

(4)

1ru 2ru 3ru



( )ru ( )r Vu P ( )r pu k

VP

pk

112

p 212

p 3 1p

.

In formula (4), , and respectively

represent the relative standard uncertainty components

caused by calibration coefficient of Pitot tube , reading

of micro-manometer and correction coefficient of air

density .

According to JJF1059 and formula (1), we know that

, , .


Uncertainty Analyses

1 Uncertainty component caused by calibration coefficient of the first-class standard Pitot static tube

1.003 0.001

( ) 0.001/ 0.003 0.1%ru

2 2

1 1 82 0.25( )

2( )r

r

uu

(5)

(6)

(7)


1

1.002

1.004

1.006

1.008

1.01

0 5 10 15 20 25Wind speed / m/s

Pito

t calib

ratio

n fa

ctor

/ -

NPL/ISO 3966146144145142143


2 Uncertainty component caused by first-class compensated micro-manometer

0.4 / 3 0.133 13.3( ) %r Vu PR R R

2 2

1 1 502 0.1( )

2( )

P

r V

r V

u Pu P

(8)

(9)


3 Uncertainty component caused by air density correction

1013.25(273.15 )288.15( 0.378 )p

w

tkP ue

(10)

2 2 2 2 2 21 1 2 3( ) ( ) ( )r r r V r pu p u p u P p u k

2

44.220.0025 %R

(11)

41

1 4 41 2( ) ( )

reff

r r V

P

up u p u P

28

2

4 84 8

44.220.0025 10

6.67( ) 100.05 108 50

R

R

(12)


4 Uncertainty component caused by the performance of wind tunnel flow field(1) Uncertainty component caused by nonuniform flow field

2

1

/( 1)/

1

ni

i i

q qq qn

(13)

1( ) 0.43% 0.215%2ru (14)

1 145 1 144n (15)


(2) Uncertainty component caused by unsteady flow field

maxiq q

q

(16)

max( )i

r q

q qu

kq

(17)

1( ) 0.6% 0.22%2.73r qu (18)

1( ) 0.22% 0.11%2r Vu (19)

( 1) 5 (3 1) 10m n (20)

1( ) 0.11% 0.06%2r Vu (21)


(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.


(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.

2 22 ( ) ( )r r r Vu u u 2 20.215 0.006 % 0.223% (22

)

42

2 4 4( ) ( )r

effr r V

uu u

4

4 4

0.223%154

0.215% 0.06%144 10

(23

)


5 Uncertainty component caused by operators

According to empirical data (based on lots of experiments), uncertainty component caused by readings from different operators is 0.05%, and relative uncertainty estimation value of is 10%, degree of freedom of such uncertainty component is

3ru3ru 3eff

3 2 23

3

1 1 502 0.1

2eff

r

r

uu

(24)


6 Synthesis of the total uncertainty caused by verification apparatus From above analyses, the combined relative standard uncertainty of verification apparatus is ru

2 2 21 2 3r r r ru u u u 2 2

2

44.220.0025 0.223 0.05 %R

2

44.220.055 %R

(25)

The effective degree of freedom of is eff ru

4

4 4 41 2 3

1 2 3

reff

r r r

eff eff eff

uu u u

2

2

44 4 4

44.220.055

0.05 6.67 1 0.223 0.058 50 154 50

R

R

(26)


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

Table 1 List of total relative standard uncertainties and effective degree of freedoms of verification apparatus with typical wind velocities


Summaries

In this paper, the uncertainty caused by verification apparatus of first-class 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.

UNCERTAINTY ANALYSIS FOR THE WIND MEASUREMENT INSTRUMENT IN THE CALIBRATION DEVICE

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