description, analysis & testing of the pye laboratory … · 2007-07-18 · wind speed...

Description, Analysis & Testing

of the

Pye Laboratory

Anemometer Calibration System

Dale. E. Hughes

CSIRO Marine and Atmospheric Research

Version 1.5 July 2007

Authorised by: Mark Hibberd

Document revision details

Date Revision Details Authorised 30/10/2006 1.0 Initial version Dale Hughes 13/11/2006 1.1 First review amendments Dale Hughes 12/12/2006 1.2 Second review amendments Mark Hibberd 10/1/2007 1.3 Minor corrections Dale Hughes 6/3/2007 1.4 Change pressure uncertainty to ±0.3 Pa

& updated relevant calculations Dale Hughes

11/7/2007 1.5 Changes after NATA audit & blockage investigation.

Mark Hibberd

Calibration_system_manual_V1_5_final.doc of 58

Table of contents 1. Introduction..............................................................................................................4 2. Calibration Theory ..................................................................................................5

2.1 Pitot-static pressure - Pk .......................................................................................5 2.2 Air density - ρ ......................................................................................................6 2.3 Wind-tunnel calibration factor – kc ......................................................................9 2.4 Pitot-static tube coefficient - kh..........................................................................10 2.5 Flow correction factor – kf .................................................................................10

2.5.1 Blockage measurements..............................................................................11 2.5.2 Blockage theory ..........................................................................................14

2.6 Results................................................................................................................17 3. The Pitot-static tube...............................................................................................18

3.1 Mechanical requirements for Pitot-static tubes..................................................19 3.2 Reynolds number effects....................................................................................20 3.3 Compressibility of air ........................................................................................20 3.4 Suitability of the selected tube...........................................................................21

4. System Implementation.........................................................................................22 4.1 Pitot-static tube and anemometer.......................................................................22 4.1 Pressure measurement........................................................................................24 4.2 Calculation of air density ...................................................................................25 4.3 Measuring anemometer output ..........................................................................26 4.4 Wind-tunnel control ...........................................................................................27

5. Software ..................................................................................................................29 6. Uncertainty calculations and sensitivity analysis................................................32

6.1 The model ..........................................................................................................32 6.2 Sources of uncertainty........................................................................................33 6.3 Calculating standard uncertainties for each source of uncertainty ....................34 6.4 Calculating sensitivity coefficients ....................................................................38 6.5 Calculating the combined uncertainty ...............................................................41 6.6 Calculate the expanded uncertainty ...................................................................42

7. Testing and validation ...........................................................................................43 7.1 Testing with known inputs.................................................................................43

7.1.1 Functional testing of the Datataker DT50...................................................43 7.1.2 Functional testing of the Vaisala PTU 200 and calculation of air density..44 7.1.3 Testing of the Druck pressure transducer, associated plumbing and data acquisition hardware and software.......................................................................44 7.1.4 Reproducibility of measurements ...............................................................45

7.2 Functional testing of the overall system ............................................................46 7.3 Third party review..............................................................................................47

8. Summary of important points...............................................................................48 Appendix A: DT50 frequency and time-base check. ..............................................49 Appendix B: Test of air density calculations...........................................................50 Appendix C: Transducer and water column comparison......................................51 Appendix D: Reproducibility....................................................................................52 Appendix E: Sample calibration report and raw data file.....................................53 References...................................................................................................................57 Attachments................................................................................................................58


1. Introduction This document describes the theory, components and operation of the CSIRO Marine & Atmospheric Research Pye laboratory anemometer calibration system. The system is designed to perform ‘primary’ calibrations of cup and propeller anemometers. A ‘primary’ calibration, in this context, means a calibration which uses a Pitot-static tube to measure a pressure which is directly related to wind speed. Bernoulli’s theoremA is then used to calculate the local wind speed (U) from the measured Pitot-static pressure (Pk) and the calculated air density (ρ):

ρkPU 2 (1.1)

=

The following topics are covered in this document:

• the basic theory behind anemometer calibration • how the theory is implemented • a description of the software and how it functions • uncertainty of the final calibration result • evidence of due care in system design, testing and validation.

It is also intended that this document will provide a useful resource when the system is audited, upgraded or changed, or when other types of anemometers are to be calibrated. Where required, reference is made to NATAB, MEASNET C and ISOD documents which provide much technical detail about anemometer calibration. These documents provided significant input into the design and implementation of the calibration system. As the system has been designed to comply with the Measnet requirements, comparison is made between the Pye laboratory system and the Measnet specifications. It has been said (Duncan, Thom and Young 1962, p. 226) that accurate calibration of anemometers requires considerable care and is an art as much as a science:

‘Experience shows that it is extremely difficult to measure the velocity of a fluid with an accuracy substantially better than 1 percent’

This is as true today as it was in 1962 when the text was written…

A This is the basic version of this equation; we later include various factors to correct for ‘real world’ measurement uncertainty. B National Association of Testing Authorities; the body that oversees Australia’s national laboratory accreditation system. C MEASNET: A consortium of European Measuring Institutes that offer calibration services. D International Standards Organisation.


2. Calibration Theory Anemometers can be calibrated in a wind-tunnel by comparing their output with the ‘true’ wind speed. The true wind speed in the wind-tunnel is determined using the relationship between the differential pressure measured using a Pitot-static tube and wind speed (Bernoulli’s theorem): (2.1) where:

U calculated mean, free-stream, wind speed (m.s-1) Pk measured Pitot-static pressure (Pa) ρ air density (kg.m-3) calculated from air temperature, barometric

pressure and relative humidity kc wind-tunnel calibration factor that compensates for any pressure

difference between the positions of the Pitot-static tube and anemometer.

kh Pitot-static tube coefficient kf flow correction factor which may take into account:

• wind-tunnel blockage due to the presence of the anemometer • global corrections obtained by cross checking against another

calibration wind-tunnel. Each of the above independent variables will now be discussed.

2.1 Pitot-static pressure - Pk

The pressure difference (Pk) between the total head and static pressure ports of the Pitot-static tube is measured using a differential pressure transducer. The resultant pressure is quite low, typically between ~ 10 and 140 Pa for a velocity range of 4 to 16 m.s-1. The low pressure, particularly at the low speed end of the range places stringent demands on the sensitivity and stability of the pressure measuring device.

ρkh

kcf

kkU =P2


2.2 Air density - ρ Air density (ρ) can be calculated from the sum of partial pressures of the atmospheric components (dry air and water vapour):

(2.2) TR

PTR

P

w

w

o

a +=ρ where:

Pa partial pressure of dry air (Pa) Pw partial pressure of water vapour (Pa) T air temperature (K) Ro gas constant for dry air (287.05 J.kg-1.K-1) Rw gas constant for water vapour (461.5 J.kg-1.K-1).

The significant chemical species that make up dry air are given in the 57th Handbook of Chemistry and Physics, (1977), Page F210 as:

Species Concentration (%) Nitrogen 78.084 Oxygen 20.946 Argon 0.934

Carbon Dioxide 0.033 We measure the barometric pressure (B) and this is the sum of the partial pressures of the gases that make up the atmosphere:

(2.3) wa PPB += The partial pressure of the water vapour component of the atmosphere can be calculated from the relative humidity (θ) of the air. Relative humidity is here expressed as a fraction rather than a percentage:

(2.4)

s

w

PP

=θ The saturation vapour pressure of water (Ps) in Pascals can be calculated to an accuracy of 0.1 % using the following equation (Bolton 1980):

( )⎥⎦⎤

⎢⎣⎡

−−

=65.29

15.27367.17exp2.611T

TPs

(2.5)

Equations 2.4 and 2.5 link the relative humidity of the air to the vapour pressure of water at the measured temperature and this gives us the partial pressure of the water


vapour. Thus we can now rearrange equation (2.2) through the following steps to give equation (2.7):

(2.6) TR

PTRPB

w

w

o

−=ρ +w

The first term on the right hand side is the partial pressure of dry air and the second term is the partial pressure of water vapour. Therefore:

(2.7)


⎥⎦

⎤⎢⎣

⎡ ⎛⎟⎟⎠

⎞⎜⎜⎝

−+=∴ow

so RR

PRT

θρ B 111 Note (1): Air density decreases with increasing humidity as water vapour is less dense than air. Note (2): Strictly speaking, equation 2.5 (and other similar equations) for saturation vapour pressure of water applies to pure water vapour over liquid water, not to a gas of mixed components as the air causes a dilution of water vapour and the saturation vapour pressure needs to be corrected for the dilution. The dilution has the effect of increasing the saturation vapour pressure and an enhancement factor (fw) that depends on barometric pressure is suggested in Gibbins (1990):

www

w

fPP

Pf

×=

×+= −

'

6

&1046.30007.1

(2.8)

Where:

fw Enhancement factor P Barometric pressure (hPa) Pw Uncorrected saturation vapour pressure (Pa) Pw’ Corrected saturation vapour pressure (Pa)

The effect can be neglected in our calculation of air density as the effect is very small: fw ~ 1.004 at 960 hPa, leading to a reduction in air density by 0.002 % at 20 C and 50 % relative humidity.

TRP

TRP

TRB

TRP

TRPB

w

s

o

s

o

w

s

o

s

θθρ

θθρ

+−=

−∴ = +

∴

Note (3): The composition of ‘dry’ air given above also assumes that the concentration of CO2 is 330 PPM; the present value is approximately 370 PPM, and density calculation does not take into account that CO2 levels inside buildings are likely to be much higher than these values. As the concentration of CO2 is unlikely to exceed 0.1 %, the variable nature of CO2 is neglected in this case.


2.3 Wind-tunnel calibration factor – kc

The wind-tunnel calibration factor (kc) compensates for any pressure differences between the position of the anemometer under test and the Pitot-static tube when the tunnel is empty. A pressure survey of the wind-tunnel working section was undertaken using a Pitot-static tube mounted on the wind-tunnel traverse mechanism in conjunction with a 2 dimensional Laser Doppler Velocimeter probe mounted in undisturbed air windward (i.e upwind) of the working section. The LDV probe provided a reference velocity by which pressures measured using the mobile Pitot-static tube could be scaled. This configuration allowed accurate pressure and velocity measurements to be undertaken as all measurements could then be adjusted for changes in the wind-tunnel conditions.

Fixed Pitot-static tube

Laser Doppler probe

Movable Pitot-static tube

Figure 2.1: General setup for measuring pressure and velocity using a Pitot-static tube mounted on the wind-tunnel traverse mechanism. The fixed Pitot-static tube and anemometer were removed for ‘empty tunnel’ measurements.

The results (figure 2.2) show that there is a small variation in pressure across the tunnel between the position of the Pitot-static tube and cup anemometer. This difference is of order 0.2 Pa; however the measurement uncertainty (just considering the recorded data) is of the same order, so it seems reasonable to make the calibration coefficient, kc = 1 with a standard uncertainty of 0.2 Pascals, or 0.2% . Note that these measurements are at the limit of our existing pressure measurement capability.


Cross-stream pressure readings at X=0 & X=-800Empty wind-tunnel (Uref via LDV)

y = -0.0005x + 81.938R2 = 0.3168

y = 0.0005x + 81.617R2 = 0.2688

81

81.2

81.4

81.6

81.8

82

82.2

82.4

-500 -400 -300 -200 -100 0 100 200 300 400 500

Y (mm)

P (P

a)

11.8

11.85

11.9

11.95

12

12.05

12.1

12.15

12.2

Uref

(ms-1

)

P(X=0)P(X=-800)uncertainty(2sig)

PS tube

Anemo

LDV

Figure 2.2: Measured Pitot-static tube pressure across the wind-tunnel at the axis of the fixed Pitot-static tube (X = -800 mm) and the axis of the anemometer calibration position (X = 0 mm). The measurement height was the same as the cup centre-line (Z = 420 mm). The lines at the centre of the chart are the windward LDV reference velocity and they show that the wind-tunnel conditions were stable during the pressure measurements; the RHS scale is for the windward LDV measurements. The uncertainty displayed is ± 2 standard deviations and is approximately ± 0.4 Pa. (Hughes 2007, p. 98). Figure 4.4 shows the positions of the anemometer and Pitot-static tube.

2.4 Pitot-static tube coefficient - kh

For the Pitot-static tube we are using; a Dwyer Instrument 160E unit, which is a NPL type with ellipsoidal nose; ISO 3966-1977 section 7.2 and annex A give the give the tube coefficient as 0.997*. Thus we will use a value of 0.997 for kh.

2.5 Flow correction factor – kf

Factor kf is a flow correction factor which may take into account: • corrections obtained by calibration against another calibration wind-tunnel • differences in wind speed across the tunnel working section at the location of the

Pitot-static tube or anemometer under test • wind-tunnel flow distortion due to the presence of the anemometer. * ISO3966-1977 uses α (sect 7.2) as a calibration coefficient = 1.0015 (annex A) for the tube type we have (n=8). Doing the appropriate arithmetic: 1/α2 = kh = 0.997


Measurements indicate that the wind speed at the position of the Pitot-static tube and anemometer is relatively uniform, any variations being at the level of the measurement uncertainty. (See Figure 2.2) To date, no attempt has been made to calibrate the Pye laboratory wind-tunnel against another equivalent wind-tunnel (although this may happen in the future). Thus, the only component that concerns us at present is the component due to flow distortion and this distortion is commonly called ‘blockage’.

2.5.1 Blockage measurements As a wind-tunnel is a ‘closed conduit’ the response of an anemometer under test in such a tunnel will differ to its response in free air as the streamlines are confined by the tunnel walls. Application of a blockage correction factor ensures that the response of the anemometer in the wind-tunnel is the same as its response in free air. The blockage factor, kb, compensates for the change in wind speed due to the reduced cross sectional area through which the air flows when an anemometer is placed in the tunnel working section and for the restrictions of the wind ‘streamlines’ which further affect the anemometers response. The combined effect is to cause the anemometer wind speed to be slightly greater than the wind speed indicated by the Pitot-static tube and manometer. In the following description the blockage correction factor is kb and it is equal to the flow correction factor, kf, until a comparative wind-tunnel calibration is undertaken. Figures 2.3 & 2.4 show how the air speeds up around the anemometer in the wind-tunnel:

U(Pitot-static tube), X=0

11

11.5

12

12.5

13

13.5

14

-400 -300 -200 -100 0 100 200 300 400 500

Pitot-static tube position (mm) across tunnel

U(m

/s)

Ups(anemo in)x=0

Ups(anemo out)x=0

Figure 2.3: Measurements of wind speed at the anemometer test position, with and without an anemometer in position. In this case the X axis origin is taken to be the centre-line of the anemometer cups, and the nose of the Pitot-static tube was aligned with the centre of the cups.


U(Pitot-static tube), X=-145

11

11.5

12

12.5

13

13.5

14

-400 -300 -200 -100 0 100 200 300 400 500


U(m

/s)

Ups(anemo in)x=-145

Ups(anemo out)x=-145

Figure 2.4: Measurement of the -145 mm wind field windward of the anemometer position. This corresponds to a transect across the front of the anemometer approximately 45 mm in front of the rotating cups. Both of the above charts show that the flow around the anemometer is complex and that small movements in the measurement position can make large differences in the measured velocity. Note however, that in both the above cases, the velocity outside of the distorted flow around the anemometer shows an increase over the velocity when the tunnel is empty. Figures 2.5 and 2.6 show this more clearly:

U(Pitot-static tube), X=0

11.8

11.85

11.9

11.95

12

12.05

12.1

12.15

12.2

-400 -300 -200 -100 0 100 200 300 400 500


U(m

/s)

Ups(anemo in)x=0

Ups(anemo out)x=0error bars = +/-2sig

Figure 2.5: Vertically expanded version of figure 2.3


U(Pitot-static tube), X=-145

11.8

11.85

11.9

11.95

12

12.05

12.1

12.15

12.2

-400 -300 -200 -100 0 100 200 300 400 500


U(m

/s)

Ups(anemo in)x=-145

Ups(anemo out)x=-145error bars = +/-2sig

Figure 2.6: Vertically expanded version of figure 2.4 showing the speedup occurs even though the wind-speed at the front of the anemometer slows down.

The velocity increase, over the empty tunnel conditions, is approximately 0.05 (for 12 m.s-1 tunnel speed) for regions outside the immediate vicinity of the anemometer, showing that the anemometer is working in air that is flowing slightly faster than measured by the Pitot-static tube in the windward position. Figure 2.7 shows the speedup ratios calculated from the measured data. This speedup is due to the reduction in the effective cross-sectional area of the tunnel by the presence of the anemometer. It is accounted for by kf, which increases the wind speed (equation 2.1) so that the calibration of the anemometer corresponds to its performance in the ‘real world’.


Normalised streamwise windspeed ratio for anemometer

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

-850

-800

-750

-700

-650

-600

-550

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0 50 100

X (mm)

E

E(Y=-400)E(Y=400)

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

outin UpsUldvxUps

UpsUldvxUpsE

)0(/)(

)0(/)(1

error bars = 95% uncertainty = 0.002

Anemo

P.S tube

Figure 2.7: Speedup ratio (E) calculated from measured wind-tunnel data measured with Pitot-static tubes along two lines offset from the centreline (Y = ±400 mm). Uldv is an upwind speed reference, Ups(0) is the wind speed at X = -800, which is the position of the fixed Pitot-static tube in normal operation.

2.5.2 Blockage theory The theory on which blockage correction calculations are based is well developed for aerofoils and other shapes of aerodynamic interest. However an anemometer does not present a very ‘aerodynamic’ shape to wind flow in a wind-tunnel. By making some reasonable approximations the theory can be applied and a correction factor calculated. General practice has been to ignore this term if the blockage ratio is small, certainly when it is less than 2 % (where this is the ratio of the anemometer frontal area to the wind-tunnel cross section area, name S/C, as defined below) but anemometer calibrations require the blockage to be taken into account. Pankhurst and Holder (1952, p. 334) gives the following relationships:

(2.9)

mfc

mc

UkUUU=∴

+= )1( ε where:

Uc corrected velocity at the anemometer Um measured velocity at the Pitot-static tube ε blockage factor kb flow correction factor i.e. kb = 1+ε


Following Pankhurst and Holder, the blockage factorε is made up of two components representing the solid (ε s) and wake (ε w) blockages respectively:

(2.10) ws εεε +=

The solid blockage can be calculated for a body of revolution in a three dimensional flow using:

(2.11) 5.1

5.0

4.014 C

Vct

s ⎟⎠⎞

⎜⎝⎛ +⎟

⎠⎞

⎜⎝⎛= τπε

where:

τ a geometric factor ≈ 1 (see Pankhurst, p. 341) t thickness c chord V volume of body C cross sectional area of wind-tunnel at the blockage

In the case of an anemometer, we can divide it up into four cylindrical volumes that approximate the shape of the instrument under test:

1. a volume that covers the cups 2. a volume that represents the support shaft between the cups and body 3. a volume that represents the body of the anemometer 4. a volume for the instrument support shaft that extends to the floor of the wind-

tunnel. Parameter t is taken to be the height of each cylinder and c is the diameter of each cylinder. Solid blockage is calculated for each cylindrical section and the total wake blockage is the sum of the individual solid blockages. The wake blockage can be calculated using:

(2.12) Dw C

CS25.0=ε

where:

S frontal area of the object causing the blockage C cross sectional area of wind-tunnel at the position of above object CD the drag coefficient of the body with frontal area S.

The drag coefficient was estimated to be ≈ 1 (Hoerner 1965, pp. 3-9). The Reynolds number, which determines the drag, for the assumed cylinder was calculated from:

(2.13) ν

UDRD =


where:

RD Reynolds number U wind speed ( ) D cylinder diameter (D = 0.046 m) υ kinematic viscosity of air (1.51 x 10-5 m2.s-1 at 20 C)

From this, the Reynolds number was estimated to be ≈ 1.2 x 104 at a wind speed of 4 m.s-1 and using the maximum anemometer body diameter for the length, rising to 4.8 x 104 at a wind speed of 16 m.s-1, comfortably in the region where CD = 1. Pope & Harper (1966, p.325) gives a simplified method for blockage calculation and states: ‘When all is lost as far as finding blocking corrections for some unusual shape that needs to be tested in a tunnel, the authors suggest…’

CS

41

=ε (2.14)

where S and C have been previously defined. Equation 2.14 leads to a correction factor that is very close to the method based on the work of Pankhurst & Holder. The blockage ratio, CS , for two common anemometers and their mounts is given in Table 2.2:

Table 2.2: Blockage ratio for Vaisala and Riso anemometers.

Riso P2546A Vaisala WAA151 Blockage ratio 0.015 0.016

Taking all the above into account, gives the following table of blockage factors: Table 2.1: Blockage correction factors calculated for the CSIRO Pye Laboratory wind-tunnel. εa is the blockage factor calculated using the method outlined by Pankhurst and Holder, εb is calculated using Pope’s method.

Blockage Term Riso P2546A* Vaisala WAA151 εs 0.0008 0.0009 εw 0.0037 0.0040

εa = εs + εw 0.0045 0.0049 εb 0.0037 0.0040

* The Riso & Vaisala instruments are regularly calibrated in the wind-tunnel and are recognised as high quality instruments .


The similarity between the values of εa and εb indicate an uncertainty in ε of less than 0.001 for these two instruments, which contributes about 0.1% to the final uncertainty in velocity. The coefficient kf is composed of a number of possible components and kb is the only factor that is included at present, thus kf = kb = 1 + ε = 1.004 Note that the Pope method would usually be used because it is much simpler and gives correction factors that are within the uncertainty estimate.

2.6 Results Once all the preceding terms are known, the actual air speed can be calculated. Anemometer calibration consists of running the wind-tunnel at a range of wind speeds and measuring the anemometer output frequency and Pitot-static pressure at each wind speed. The relationship between wind speed and anemometer output is commonly expressed as a linear function:

(2.15) 01 aFaU += where:

U wind speed (m.s-1) F anemometer output frequency (Hz) a1 calibration coefficient a1 of the anemometer (slope) (m.s-1.Hz-1) a0 calibration coefficient a0 of the anemometer (intercept) (m.s-1)

Coefficients a1 a0 are also subject to uncertainty and a standard error is calculated for these coefficients at the end of each calibration run. The standard error for the slope and intercept are calculated at the end of each calibration and are shown on the instrument calibration certificate. A linear function is generally appropriate for wind speeds in the range of 4 to 16 although it should be noted that significant non-linearity is common the region between the start speed and 2 to 4 m.s-1.


3. The Pitot-static tube The fundamental instrument for measuring the velocity of air is the Pitot-static tube (Duncan, Thom and Young 1962, p. 224). The open end of the head faces into the air-stream and is connected by tubing to the high pressure side of the differential pressure transducer. Since, in steady conditions there is no flow into the transducer, the air just inside the open end (the ‘stagnation point’) is at rest and the pressure at that point is the total pressure, i.e. the sum of the ‘static pressure’ and the ‘dynamic pressure’ (or ‘stagnation pressure’). Sufficiently far downstream from the stagnation point, small holes in the side of the probe head allow the pressure in the outer tube to become equal to the pressure in the free stream, i.e. the ‘static pressure’, and this pressure is transmitted by tubing to the low pressure side of the differential pressure transducer. Applying Bernoulli’s equation to the measured differential pressure allows us to calculate the wind speed.

Figure 3.1: Schematic diagram of a Pitot-static tube and its connections. (Adapted from Goldstein 1983, p. 62)

As the Pitot-static tube is crucial to the measurement of wind speed it is important to understand the possible sources of measurement error that may arise when using the instrument. Measurement errors can be caused by:

• incorrect tube construction and installation • measuring below a critical Reynolds number • the compressibility of air.

These errors are described in international standard ISO 3966-1997 which discusses the measurement of fluid flow in a closed conduit, e.g. a wind-tunnel. The discussion which follows applies the requirements of the standard to the Pitot-static tubes used in the Pye laboratory calibration system: Dwyer Instruments type 160E.


3.1 Mechanical requirements for Pitot-static tubes ISO 3966-1997 Clause 4.2 specifies the basic mechanical details for the Pitot-static tube and its installation. If the tubes meet these requirements and is one of the types shown in annex A of the standard, it will be suitable for our purpose. The following points address each requirement from ISO 3966-1997 clause 4.2 and footnote 1: a) The response of the differential pressure to tube inclination, caused either by misalignment or swirl in the flow such that the pressure will be within ± 1.5 % up to a 14o yaw in uniform flow:

1: Accurate alignment of the tube is possible and there is no evidence of swirl in the tunnel. 2: The mounting system for the Pitot-static tube ensures that the tube stays accurately aligned to the wind-tunnel axis. Sighting along the tunnel to a fixed reference point allows alignment of the tube to better than ± 2o of yaw.

b) Calibration factors for different tubes of the same type shall be identical to within ± 0.25 %. To the best of our knowledge, the tubes are identical, so individual calibration is not required. c) Cavitations from the nose is not applicable as the tube is being used in air. d) The static-pressure holes shall be:

1: Static pressure holes are 1.02 mm diameter (must be no larger than 1.6 mm) 2: Eight static holes are provided on the 160E Pitot-static tubes (must be at least six static holes) 3: The static holes must be at least six head diameters from the tip of the nose. The tube diameter is 7.94 mm and the holes are 63.5 mm from the tip, thus the tube

complies as the static holes are 699.794.75.63

>= head diameters from nose.

4: Static holes are greater than eight head diameters from the stem axis.

e) Not applicable as the stem is of constant diameter. f) The junction between the head and the stem has a bend radius 23 mm, therefore

5.039.294.7

23±≈==

diameterheadradiusBend the tube meets the requirements of clause 4.2.f

g) An alignment arm is provided to ensure accurate alignment with the mean flow. The tube is a modified ellipsoidal type which conforms to annex A of the standard.


3.2 Reynolds number effects The first part of section 7.1 of ISO 3966-1997, Verification of conditions of measurements, concerns the Reynolds number based on the diameter of the total head pressure hole of the Pitot-static tube which should be greater than 200. For the 160E tube, the total head pressure hole diameter is 3.175 mm, thus

2008531051.10032.04

5min >=

××

=×

= −υDURe

where:

Umin the minimum wind speed D the diameter of the total pressure head hole υ kinematic viscosity of air (1.51 x 10-5 m2.s-1 at 20 C)

Hence the 160E tube meets this requirement.

3.3 Compressibility of air ISO 3966-1977 places a limit on the ratio of measured pressure to the static pressure, beyond which corrections must be made: Table 3.1: Limiting value of the ratio of measured pressure to the static pressure. (ISO 3966-1977, Clause 7.1, Table 1, p. 8) γ 1.1 1.2 1.3 1.4 1.5 1.6 1.7

PPΔ 0.035 0.038 0.042 0.046 0.048 0.052 0.054

Where:

ΔP the differential pressure measured by the Pitot-static tube (200 Pa maximum, limited by the pressure transducer)

P the local static pressure (typical barometric pressure in Canberra is 950 hPa)

γ ratio of specific heat at constant pressure and specific heat at constant volume. γ = 1.402 for air at standard pressure and temperature

In the case of measurements made during the course of anemometer calibrations this ratio will be:

002.095000

200≈=

ΔPP

This means that the pressure measurements do not require correction for compressibility effects.


3.4 Suitability of the selected tube From the foregoing analysis, the Dwyer Instruments 160E Pitot-static tube meets all of the requirements of ISO 3966-1997 and is suitable for use in the wind-tunnel for measurements of wind speed over the range of 4 to 16 m.s-1.


4. System Implementation The system consists of a number of instruments and devices that measure and record parameters needed to calibrate the anemometer under test. These instruments are:

• A Pitot-static tube to measure the dynamic head and static pressure. • Druck pressure transducers to convert the measured head to an electrical

signal. • An IOtech DaqLab data acquisition system to digitize the analog output

from the transducers. • A Datataker DT50 data-logger to count the output pulses from the test

anemometer. • A Vaisala PTU 200 to measure the environmental conditions. • An interface to the Variable Speed Drive that powers the wind-tunnel fan. • A host computer to control the instruments and record results.

The following sections provide detail on most of these devices.

Figure 4.1: Block diagram of the calibration system.

4.1 Pitot-static tube and anemometer The anemometer under test is placed in the centre of tunnel working section, 800 mm downwind from a single Pitot-static tube. These areas are known to have a highly uniform air flow. The Pitot-static tube conforms to the requirements of ISO 3966-1977 as shown in section 3 of this document. Any pressure differences between the position of the Pitot-static tube and anemometer are compensated for by the


calibration coefficient kc, which here is equal to 1.000 (section 2.3). Note that the Pitot tube is 400 mm off the centreline but at the same height as the anemometer under test. Pressure lines from the Pitot-static tube are connected by copper tubing to the pressure transducers in the wind-tunnel control room. To ensure the integrity of the pressure measurement the pressure lines have been tested to ensure that there are no leaks. Accurate alignment of the Pitot-static tube is ensured by sighting along the Pitot-static tube to a fixed reference point that is in line with the tunnel axis.

Figure 4.2: Anemometer and Pitot-static tube in the wind-tunnel. Figure 4.4 gives the dimensions of the instrument setup.

Figure 4.3: Aligning the Pitot-static tube with the wind-tunnel axis by means of an upwind reference. The square is located at the same distance from the wall as the tube and 4.8 m windward of the Pitot-static tube. With care, alignment accuracies of better than 1 degree can be achieved.


Figure 4.4: Positions of Pitot-static tube and anemometer shown in figure 4.2.

4.1 Pressure measurement The pressure transducers used in the calibration process are Druck LP9000 units with a pressure range of ± 200 Pa. Traceability is ensured by means of a NATA endorsed calibration performed by the Australian Pressure Laboratory Pty Ltd or by the National Measurement Institute. Measurement of the pressure transducer output voltage is by means of an Iotech DaqLab 2005 data acquisition unit. This device digitises the ± 5 V transducer output and transfers the 16 bit binary values to the host PC via a direct network connection. Traceability of this device is ensured by a NATA endorsed calibration performed by the suppliers, Scientific Devices Australia Pty Ltd.

Figure 4.5: Pressure transducer and associated pressure manifold. A third pressure outlet is available for connection to an external gauge*. * The transducer power supply has been subsequently removed from the transducer enclosure to reduce any possibility of temperature drift in the pressure transducers due to heat generated by the power supply.


Figure 4.6: The DacLab data acquisition unit.

Pressure is calculated from the measured output voltage of the transducer:

(4.1) )( ofspp VVaP −×=

where: P Pressure in Pascals ap Slope of transducer calibration Vp Measured voltage Vofs Measured voltage at P = 0

Before each calibration starts, the offset voltage of the transducer and associated acquisition system is measured by making a series of measurements with wind speed at zero. This is done instead of applying the offset of the transducer and acquisition system as the offset is more prone to drift over time and temperature than the slope, ap, of the devices. The measured offset value is applied to all pressure measurements during the calibration run that follows. The offset voltage is recorded in the ‘raw’ data file along with all other system measurements so that a calibration record could be reconstructed from the raw data alone. The DaqLab unit records 45000 samples for each calibration speed. An average and variance is calculated from these samples and the calculated values are used in the regression and uncertainty calculations.

4.2 Calculation of air density Air density is calculated from three measurements: Barometric pressure, air temperature and relative humidity. These three quantities are measured using a


Vaisala PTU 200 unit. Data from the PTU 200 is transmitted to the host PC via and RS232 connection. The LabVIEW code collects the information from the PTU 200 and calculates air density. The barometric pressure is measured inside the wind-tunnel to account for any variations in pressure (and hence air density) due to the open-return blower method of operation of the tunnel. Air temperature and relative humidity are measured inside the wind-tunnel laboratory. Traceability is ensured by means of an endorsed calibration certificate from The National Measurement Institute (Australia).

4.3 Measuring anemometer output Output pulses are counted using the pulse counting channels of a Datataker DT50 data-logger. The pulses are counted for 190 seconds and a frequency is then calculated. In operation, two DT50 counter channels are connected in parallel. Counter 1 operates on a 10 second scan and counter two operates on a 190 second scan. At the end of the 190 second scan, the value in counter 1 is subtracted from the value in counter 2 to give a 180 second measurement period. This is done because the start period of the DT50 data-logger is not synchronised to the host PC so the length of the first scan period is indeterminate. Traceability of the time-base period is ensured by counting pulses from a calibrated oscillator which is linked to the national standard of time. (See procedure: CAR-NATA-WI-WT-32h Calibration of the Datataker DT50 time-base and test oscillator for a description of how the test oscillator is calibrated.) Figure 4.7: Datataker for counting anemometer pulses and PTU 200 for measuring air temperature, barometric pressure and relative humidity.


Figure 4.8: Screen from the LabVIEW source code showing the DT50 macros and logging commands. 4.4 Wind-tunnel control The tunnel wind speed is controlled by the angular velocity of the fan. The wind-tunnel fan is driven by a belt coupled motor that is powered by a Zener Electric MCS3 80 kW Variable Speed Drive. Instructions that control the motor speed are sent from the host computer to the VSD via an RS485 circuit. The voltage levels are converted from RS232 to RS485 by means of an optical-isolator interface. MODBUS protocol is used to control the variable speed drive. In addition to the automatic control, a manual controller is available to control the fan speed and vane settings.

Figure 4.9: Variable Speed Drive manual control dial and enable switch.

! Note: The enable switch on the manual control box must be ON before the fan will run. This switch can also be used as an emergency stop switch.


The control room is air conditioned to maintain a constant temperature for the measuring instruments. This is done to minimise instrument drift due to temperature change.

Figure 4.10: Wind-tunnel control room.


5. Software The software that runs the calibration process is written in LabVIEW which is a graphical programming language. A LabVIEW program is known as a ‘Virtual Instrument’. This VI is made up of software modules called subVIs which are equivalent to subroutines in text based languages. Each subVI is connected by means of ‘wires’ which transfer data from one subVI to another. Overall program timing and execution sequence is controlled by the actual flow of data into, and out of, subVIs. LabVIEW is a ‘multi-threaded’ language, so it is possible to have various parts of the program operating simultaneously and this is shown in the following flow chart (Figure 5.1). The system can perform two types of tests:

• 6 point calibration for testing prior to servicing an anemometer • 13 point test to fully characterise an anemometer.

The operator can select the test type before starting the program. All required information is entered on various ‘tabs’. The setup and system parameter ‘tabs’ (i.e. instrument calibration coefficients) are protected by a password so that inadvertent changes cannot be made. Progress of the calibration process is shown by means of ‘pop-up’ windows which show the status of the system at various times. The access to the system settings, such as calibration coefficients and speed settings is restricted by means of a password. Access to the system source code is similarly restricted. To allow the wind-tunnel to settle between speed changes, a waiting time is provided so that the wind speed is stable before the measurements commence. The length of time is variable depending on the change in velocity, with larger changes needing a longer wait time. A number of checks have been performed to ensure that adequate time has been allowed for the air speed to settle after each speed change.


Start

Initialise hardware

OK?

Set fan speed = 0 & get pressure

transducer offset

Wait for bearing warm-up

Set wind speed & wait to settle

Read P.S Pressure via

DaqLab

Read PTU200 &

calc ρ

Log count via DT50

All speeds done?

no

Calc’ U from P.S pressure

Calc’ fit & uncertainty

Create report & Display

Exit

no Fault exit

yes

(5min)

Figure 5.1: Calibration flow chart.


The end result of each calibration is a calibration report and a raw data file. The report is a HTML document which lists all the information required by ISO 17025. Each page of the report is linked to pages before and after for ease of display and checking. Each report name is based on the report number which links the report to an individual instrument and ‘hard copy’ entry in a laboratory notebook. The raw data file contains all the measured values and enough information for a report to be generated, so that if the HTML report is lost another report can be manually created. The report number is derived in the following way:

P123_05_06_A12345

123 = page 123 of notebook 5

P = Pye laboratory report Year in which calibration performed

Anemometer serial number

Typical file names produced would be:

Final report: P123_05_06_A12345.html Raw data: P123_05_06_A12345.prn

These files are stored on a server PC maintained and backed up by CSIRO IT*. Pre-calibration (6 point) tests have the suffix _pre appended to the report name. The ‘hard copy’ records contained in the laboratory notebook contains a printed copy of the raw data acquired during the calibration along with other relevant information recorded by the operator at the time of the calibration. So that the stability of the system can be checked over a period of time and an audit trail created, a log file is created which appends time, date, report number, test conditions, transducer offset, anemometer regression coefficients and tunnel settings every time a test is run. The name of the log file is cal_log.txt and this is stored on the server PC in a log file directory. When the calibration program starts it initialises the measurement hardware, if any errors are detected in the initialisation process a message is given to the operator and the test aborts. * File paths have not been given as they may change from time to time. Actual file paths and server details are contained in the relevant work instructions for the wind-tunnel calibration system.


6. Uncertainty calculations and sensitivity analysis This section explains the calculations used to assess the measurement uncertainty of the anemometer calibration system at CMAR Pye laboratory. The method broadly follows that described in the MEASNET document which is based on the ISOGUM method. The actual calculations are performed in a separate Excel spreadsheet which should be read in conjunction with this document. (See attachment 1) Cook (2002) describes six steps in the process of determining the measurement uncertainty:

1. make a model of the measurement system

2. list all the sources of uncertainties

3. calculate the standard uncertainties for each component

4. calculate sensitivity coefficients

5. calculate the combined uncertainty, and, if appropriate its effective degrees of freedom

6. calculate the expanded uncertainty. Use a nominal or a calculated coverage

factor. Round the measured value and the uncertainty to obtain the reported values.

The following pages work through each of these steps.

6.1 The model From first principles, wind speed can be computed by measuring the differential Pitot-static tube pressure and air density and then applying Bernoulli’s equation:

ρh

kcf k

PkkU 2= (6.1)

where:

U wind speed (m.s-1) kf flow correction factor kc wind-tunnel calibration factor Pk Pitot-static tube pressure (Pa) kh head coefficient of Pitot-static tube ρ air density (kg.m-3)


Air density is calculated using:

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

ows

o RRP

RB

T111 θρ (6.2)

where:

B barometric pressure in Pascal’s (not hPa) θ relative humidity expressed as a fraction (i.e. 50 % = 0.5) Ps saturation vapour pressure of water (Pa) T air temperature (K) Ro gas constant of dry air (287.05 J.kg-1.K-1) Rw gas constant of water vapour (461.5 J.kg-1.K-1)

The anemometer to be tested is operated in the air stream and its output is recorded at various wind speeds. A straight line can then be fitted to the data and an equation which describes the anemometer’s transfer function can be obtained:

(6.3) 01 aFaU +=

where U, F, a0 and a1 have been previously defined.

6.2 Sources of uncertainty Two types of uncertainties are addressed in this section: Type A: Uncertainty which can be deduced from the measurements themselves. In our case the turbulent intensity of the air flow inside the wind-tunnel is the only component to consider. Cook (2002) states it as ‘when a measurement is repeated several times, the mean value and standard deviation can be calculated’. Type B: Assesses each component of the system and determines its limits, range and nature of its dispersion and how these factors affect the overall measurement uncertainty. Equations 6.1, 6.2 and 6.3 include many sources of uncertainty:

1. Uncertainty in the wind-tunnel correction factor (kf). This factor takes into account flow corrections caused by blockage or horizontal wind shear. It also takes into account corrections generated by cross checks against other standard anemometers.

2. Uncertainty in the wind-tunnel calibration factor (kc). This factor takes into

account pressure differences between pressures measured at the Pitot-static tube position and the anemometer under test position.


3. Uncertainty in the pressure measured by the pressure transducer and associated signal processing and digitization.

4. Uncertainty in the Pitot-static tube coefficient (kh) and its sensitivity to

orientation to the mean air flow.

5. Uncertainty in the calculation of air density due to measurement uncertainty of air temperature, barometric pressure and humidity. (We assume the gas constants Ro and Rw are known to a high level of accuracy so that the uncertainty in their values is negligible.)

6. Uncertainty in the counting of pulses output from the anemometer under test.

7. Uncertainty in the data-logger time-base.

8. Statistical uncertainty in the pressure measurement due to the turbulent

intensity of the air stream in the wind-tunnel. Items 1 through 7 rely upon ‘type B’ assessment and item 8 uses a ‘type A’ assessment.

6.3 Calculating standard uncertainties for each source of uncertainty For each of the above items, a standard uncertainty can be calculated. This process follows the MEASNET example and uses values that are relevant to the Pye laboratory wind-tunnel and instrumentation. In these calculations, ui is the standard uncertainty for the measurement; it is not necessarily a velocity. Note however the product of the standard uncertainty, ui, and the sensitivity factor, ci, i.e. ui ci must be a velocity.

1. Wind-tunnel correction factor (kf). Theory and measurements indicate that a value of kf = 1.004 with a standard uncertainty of 0.002 should be used (section 2.5.2). These values lead to a standard uncertainty in velocity = 1.15 x 10-2 m.s-1 @ 10 m.s-1. A rectangular distribution has been assumed.

2. Wind-tunnel calibration factor (kc). Measurements indicate (section 2.3) that a

value of kc = 1.000 with a standard uncertainty of 0.002 should be used which leads to a standard uncertainty in velocity = 5.774 x 10-3 m.s-1 @ 10 m.s-1. A rectangular distribution has been assumed.

3. Uncertainty in pressure transducer measurement is quoted by Australian

Pressure Laboratory to be ±0.3 Pa. This leads to an uncertainty in velocity: uptcpt = 1.335 x 10-2 m.s-1 @ 10 m.s-1. In addition to the transducer uncertainty, is the uncertainty in the signal processing which consists of three parts:

1. gain uncertainty quoted to be 0.04 % 2. noise quoted to be 2 least significant bits 3. non-linearity quoted to be 1 least significant bit.


As the analog to digital converter has a resolution of 15 bits plus sign (16 bits in total), the quantisation level is 0.0001526 volts/bit and the overall uncertainty in pressure due to signal processing is: ups = 1.18 x 10-2 Pa @ 10 m.s-1 which leads to an uncertainty in velocity, upscps = 1.048 x 10-3 m.s-1 @ 10 m.s-1. This assumes a rectangular distribution and takes the half-width of the limits of .018 volts.

4. Uncertainty in the Pitot-tube coefficient and its orientation to the mean wind is

based upon a chart given in ISO 3966-1977, p. 28, which shows that the total uncertainty for a Pitot-static tube is less that 0.1 % for a 2° deviation. This amounts to an uncertainty of uh = 5.0 x 10-3 m.s-1 @ 10 m.s-1, based on a nominal coefficient of kh = 0.997

5. Air density is calculated from air temperature, barometric pressure and relative

humidity. The stated uncertainty for these measurements are:

• Temperature: ± 0.15 C • Barometric pressure: ± 0.09 hPa • Humidity: ± 1.0 %

The instrument used in this system produces a digital output and we can use the stated uncertainty above to calculate a standard uncertainty for each measurement by assuming a normal distribution. The end result is an uncertainty in density of uρ = 1.157 x 10-3 kg.m-3. This leads to an uncertainty in velocity of 2.569 x 10-3 m.s-1 @ 10 m.s-1.

6. Pulses output from the anemometer are counted by a Datataker DT50 data-

logger. The counter has a resolution of ± 1 count, but there is a maximum uncertainty of ± 2 counts which can occur due to just missing or just capturing counts at the start and end of the measurement period. A rectangular distribution is assumed.

7. The time-base accuracy has been tested using a calibrated crystal oscillator

and the time-base uncertainty was found to be better than 0.008 %. A normal distribution is assumed.

8. Uncertainty due to turbulent variations of wind speed is treated using a

statistical method. Measurements made in the Pye Laboratory tunnel using a TSI Laser Doppler Anemometer indicated that the turbulent intensity is approximately 1 % as shown in Figure 6.1.


U & Turbulent Intensity across tunnel at test position

10.1

10.15

10.2

10.25

10.3

10.35

10.4

10.45

10.5

10.55

10.6

-200 -100 0 100 200 300 400 500 600

Y (mm)

U (m

/s)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

I (%

)

U meanI%

Figure 6.1: Mean stream-wise velocity and turbulent intensity at anemometer test position. (Hughes, 2007, p. 70)

The turbulent intensity shown above was measured for 30 seconds at each location; and the data rate for each measurement point was approximately 500 Hz; a rate very much faster than either a cup anemometer or pressure transducer can respond. The standard deviation of the wind speed at a given mean can be calculated from:

(6.4) U

I Uσ= where:

I measured turbulent intensity σU standard deviation of mean wind U

The data acquisition system makes 45000 measurements at each calibration speed and the contributions to the uncertainty due to the turbulent intensity can be calculated from:

nu u

sσ

=(6.5)

where: us standard uncertainty of the mean wind speed n is the number of independent measurements taken


However, due to the low-pass filter effects of the:

• tubing connecting the Pitot-static tube, • pressure transducer, • and anemometer under test,

the contribution to the overall uncertainty of the turbulent intensity is likely to be under-estimated as each measurement is unlikely to be completely independent. A more reasonable estimate would be to assume that the frequency response of the anemometer, tubing and pressure transducer is approximately 1 Hz. This would mean that there would be 180 independent measurements during each calibration speed step. Thus the standard uncertainty component of the turbulent intensity becomes:

11 [email protected]

1001. −−≈×

= smsmus (6.6)

For the purposes of calculating the theoretical uncertainty, a turbulent intensity of 1% is used. However, during the actual calibration process in the wind-tunnel the uncertainty calculated for each calibration point includes a component of turbulent intensity calculated from the measured variations in the pressure sensed by the Pitot-static tube. The measured value may be greater or less than 1%.


6.4 Calculating sensitivity coefficients The sensitivity factors for each of the above components can be computed using partial differentiation. As we are interested in the maximum possible change, the absolute value of the sensitivity factors will be used, i.e. the sign will be ignored. The equation for wind speed is:

ρh

kcf k

PkkU 2= (6.7)

Performing partial differentiation for each variable we get: For the flow correction factor (kf) the sensitivity coefficient is cf:

ff

h

kc

ff

kUc

kPk

kUc

=∴

⎟⎟⎠

⎞⎜⎜⎝

⎛=

∂∂

=21

2ρ

(6.8)

For the wind-tunnel calibration factor (kc) the sensitivity coefficient is cc:

cc

f

f

c

f

h

kc

h

kc

c

f

h

kc

h

kf

cc

kUc

kU

kU

kk

kPk

kPk

kk

kPk

kPk

kUc

2

2

222

2212

22

21

21

=∴

=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛××=

∂∂

=

−

−

ρρ

ρρ

(6.9) Similarly for the Pitot-static tube pressure, the sensitivity coefficient is cp:

kkp P

UPUc

2=

∂∂

= (6.10)


For the Pitot-static tube coefficient the sensitivity coefficient is ch:

hh

f

f

h

f

h

kcf

h

kc

hh

kUc

kU

kU

kk

kPkk

kPk

kUc

2

2

22

2

22

21

2

=∴

×−

=

⎟⎟⎠

⎞⎜⎜⎝

⎛××⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

∂∂

=

−

ρρ

(6.11) and for air density, the sensitivity coefficient is cρ:

ρρρρ 22UUUc =

−=

∂∂

= (6.12) Air density is calculated using:

[ ]

⎥⎦

⎤⎢⎣

⎡−==

+=

+=∴

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+=ρ

owo

s

s

ows

o

RRkand

Rk

whereT

PkTBk

PkBkT

RRP

RB

T

111

1

111

21

21

21

θ

θρ

θ

(6.13) where B, θ, Ps , T, Ro and Rw have been previously defined. The uncertainty (again ignoring sign and assuming the uncertainty in R0 and Rw is negligible) of ρ to its various inputs is: (The partial derivatives are equivalent to the sensitivity coefficients above.)

( )

sPBT

s

s

s

Puu

Bu

Tuu

Tk

P

TPk

Tk

B

TPKBk

T

s ∂∂

+∂∂

+∂∂

+∂∂

=∴

=∂∂

=∂∂

=∂∂

+=

∂∂

ρθρρρ

θρθρ

ρ

θρ

θρ

2

2

1

221

(6.14)


However the saturation vapour pressure (Ps) also depends upon T:

TPuu s

TPs ∂∂

=∴ (6.15) Taking the last term of equation (9) and combining with equation (10) we get:

Tu

PTPu

Pu

T

s

sT

sPs

∂∂

=

∂∂

∂∂

=∂∂

ρ

ρρ

(6.16) Including (10) in (8), the uncertainty of air density due to changes in temperature, pressure and humidity becomes:

θρρρ

ρθρρ

(6.17)

Combining (14) & (17) we get:

(6.18) For the anemometer, the relationship between its output and the wind speed is:

(6.19) where:

U wind speed (m.s-1) F anemometer output frequency (Hz) C pulses counted during period t ao calibration equation intercept a1 calibration equation slope

ρ

θ

θρ

∂∂

+∂∂

+∂∂

=

∂∂

+∂∂

+∂∂

+∂∂

=

uB

uT

u

Tuu

Bu

Tuu

BT

TBT

2

( )TPku

Tku

TPkBkuu s

Bs

T21

2212 θρθ

+++

=

01

01

atCa

aFaU

+=

+=


The sensitivity coefficients for the counter (cdc) and time base (cdt) are:

(6.20)

tFa

tCa

tCa

tUc

andac =∂

=tC

U

dt

dc

12

12

1

1

==−=∂∂

=

∂

6.5 Calculating the combined uncertainty The combined uncertainty is then calculated using a quadrature sum of the individual components. The weighting factors due to the various distributions are included in the spreadsheet calculations and are not explicitly shown in the following equation:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )222222222

2

21

212

222222

222

222222

22222

dtdtdcdcshhpspsptptccff

dtdcsh

hk

psk

ptc

cf

f

dtdcsh

hk

psk

ptc

cf

fx

cucuucucucucucucu

tCa

uta

uucUuUu

PUu

PUu

kUu

kUu

tUu

CUuu

cUuUu

PUu

PUu

kUu

kUuu

++++++++=

⎟⎠

⎞⎜⎝

⎛+⎟

⎠

⎞⎜⎝

⎛++⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎠⎞

⎜⎝⎛

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

++⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

=

ρρ

ρ

ρ

ρ

ρ

(6.21)

Table 6.1: Tabulated standard uncertainties @ U = 10 m.s-1: Source of uncertainty Symbol Magnitude (m.s-1) Pressure transducer uptcpt 1.335 x 10-2

Wind-tunnel flow correction factor ufcf 1.150 x 10-2

Statistical uncertainty of mean wind speed us 7.45 x 10-3

Wind-tunnel calibration factor uccc 5.774 x 10-3

Pitot-static tube uncertainty uhch 5.000 x 10-3

Air density uncertainty* uρcρ 2.569 x 10-3

Analog to Digital Converter (DaqLab) upscps 1.048 x 10-3

DT50 pulse counting uncertainty udccdc 6.415 x 10-4

DT50 time-base uncertainty udtcdt 7.407 x 10-7

Adding the above components in quadrature gives a combined standard uncertainty, uc, of 2.08 x 10-2 at 10 m.s-1. From the above it can be seen that the major sources of uncertainty are:

1. Pressure transducer calibration = 1.335 x 10-2 m.s-1 2. wind-tunnel flow correction (blockage etc) = 1.150 x 10-2 m.s-1

*Best practice uncertainty is 2 parts in 104 (NPL Good Practice Guidance Note, 2002)


and that these components contributing approximately 93 % of the combined standard uncertainty, with the other components contributing approximately 7 %.

6.6 Calculate the expanded uncertainty Thus, the expanded uncertainty for )22.6(295 cc ukuu ==95 % confidence limit (k = 2) is: A spreadsheet has been developed (Hughes, 2006) which calculates and displays the measurement uncertainty for wind speeds over the range 4 to 16 m.s-1 using the foregoing analysis. From this spreadsheet the following figure shows the combined expanded measurement uncertainty:

Measurement Uncertainty - u 95

'Master' Calibration System

0

0.02

0.04

0.06

0.08

0.1

0.12

4 6 8 10 12 14 16

Mean Wind speed (ms-1)

du (m

s-1)

0.000.200.400.600.801.001.201.401.601.802.002.20

du (%

)

m/s%

Figure 6.2: Calculated expanded uncertainty over the range of wind speeds. Note: The MEASNET document specifies that a maximum combined uncertainty of 0.1 m.s-1 or 1 % @10 m.s-1 must be achieved (See Measnet 1997, p. 7). This has been interpreted here to be the expanded uncertainty, u95 (k = 2), rather than the combined standard uncertainty. The Pye laboratory calibration system meets this requirement. If the combined uncertainty as expressed in the Measnet document is simply the standard uncertainty (k = 1), then the Pye laboratory calibration system meets the Measnet requirement by an even greater margin. The limits we place on the calibrations result, (based on safety margin over the uncertainty measurements) which if exceeded the calibration fails, will be 0.07 m.s-1 or 1 %, which ever is larger.


7. Testing and validation Testing and validation of the system has been undertaken in the following ways:

• testing the system and its components with known inputs • functional testing with ‘known’ anemometers • by third party review.

Each part is described in the following sections.

7.1 Testing with known inputs All of the system hardware can be tested by applying known inputs and comparing the known input to the instrument or system output. Instruments with NATA, or other recognised calibration certificates are, by virtue of that certificate, considered as tested. This covers the following instruments:

1. the Datataker DT50 data-logger 2. the Vaisala PTU 200 which is used to measure barometric pressure, air

temperature and relative humidity 3. the Iotech DaqLab 2005 which is used to measure the pressure transducer

output 4. the Druck pressure transducer and associated plumbing.

All the system hardware can be tested using Virtual Instruments that display and process the known inputs. The test VI’s use the same software modules that the complete calibration system uses so that the user can have confidence in the overall system. Items 3 & 4 above can be tested simultaneously by comparing the pressure reading of the system to that of an independent pressure indicator.

7.1.1 Functional testing of the Datataker DT50 The Datataker hardware and software is tested using a calibrated oscillator and running the data acquisition program that is used in the calibration system. The test VI is called validate_DT50_freq_meas.vi, and it uses the same subVI that is used in the main calibration VI. The test VI allows the user to measure a known input frequency so that the DT50 time-base accuracy may be checked. Accurate measurement of the test oscillator frequency is possible by counting the output pulses over an extended period of time. Knowing the times at which the pulse counting started and stopped it is possible to measure the input frequency to a high level of accuracy. By using an appropriate source of time information, the measurement can be shown to be traceable to the National Standard of time. The accuracy of the DT50 frequency measurement can then be compared to the calibrated measurement:


Table 7.1.1: Comparison of measured frequencies.

Actual frequency 99.997 ± 0.001 Hz System measured frequency 100.00 ± 0.02 Hz

The results show that the DT50 measures the input frequency to be 0.003 ± 0.008 %. This result indicates that the DT50 is sufficiently accurate for anemometer calibration. Appendix A shows the measured results and calculations.

7.1.2 Functional testing of the Vaisala PTU 200 and calculation of air density Accurate determination of air density is an important factor in the overall anemometer calibration process. As air density depends on barometric pressure, air temperature and relative humidity it is important that there is confidence in the measurement of these variables. The PTU 200 device contains:

• Two independent silicon capacitive absolute barometric pressure transducers. The mean value from both transducers is the reported barometric pressure.

• A platinum resistance temperature sensor • A capacitive thin film humidity sensor.

The output of the unit can be displayed using the test VI validate_ptu_meas.vi which reads the device output every second, displays the measured value and calculates the air density based on the method shown earlier in this document. Another method is to use the values of air temperature, barometric pressure and relative humidity that are recorded in the raw data file for each calibration. These measurements can be used to independently calculate the air density. Appendix B shows the result of the calculations, the results show that the air density calculated by the calibration system is identical to values calculated using an Excel spreadsheet.

7.1.3 Testing of the Druck pressure transducer, associated plumbing and data acquisition hardware and software Leak testing of the pressure measurement system was done after installation of the four Pitot-static tubes. The wind-tunnel was run at about 15 m.s-1 and the Pitot-static pressure was measured (~100 Pa) When the pressure had stabilised, the valves on the Pitot-static manifold were closed. Any leaks would be shown by a decrease in measured pressure. No decrease in pressure was observed over a 30 minute period. The pressure reading of the Druck pressure transducer was compared to the laboratory water manometer for a general check of the transducer and data acquisition system performance. Two calibration runs, which generated reports P55_Y23207 and P56_Y23207, were performed with the water manometer connected to the pressure distribution manifold inside the transducer enclosure. The pressure shown on the manometer was manually recorded at each test speed and the pressure readings from


the saved raw data files (P55_Y23207.txt & P56Y23207.txt) were combined to compare the readings of the water manometer and pressure transducer.

Water Column Manometer vs Transducer #0

y = 1.0065x + 0.0345R2 = 1

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160

Water Column Pressure (Pa)

Tran

sduc

er T

0 Pr

essu

re (P

a)

Figure 7.1.3.1: Comparison between Druck pressure transducer s/n 2274469 and a Betz water column manometer showing a very good match between instruments.

Note that the Betz water column is not a traceable instrument; it is however a laboratory quality instrument and the agreement in pressure readings give a high degree of confidence in the pressure transducer and associated data acquisition and software systems. Appendix C shows the Excel spreadsheet for the above test.

7.1.4 Reproducibility of measurements To assess the reproducibility of the system, calibrations of the same anemometer at different times were compared. Regression coefficients from six reports were compared at an anemometer output of 100 Hz, the maximum difference, i.e.

min

minmax100U

UU −× (7.1)

was found to be 0.17 %. The individual results of these repeated calibrations are shown in Appendix D


7.2 Functional testing of the overall system Functional testing has been performed by calibrating several anemometers that have been calibrated by similar test facilities. Two Vaisala WAA151 anemometers (s/n Y23202 & Y22348) and two Riso P2546A anemometers (s/n 2175 & 2179). The following test certificates and regression coefficients are compared:

Table 7.2.1: Comparison of inter-laboratory Calibration coefficients

Laboratory Report Type s/n Date a1 a0

CMAR Pye P065/07/07_Y23202 Vaisala Y23202 4/7/2007 0.0987 0.3452 CMAR Aspendale 119/68/05 Vaisala Y23202 3/5/2005 0.0996 0.3184 CMAR Pye P053/07/07_Y22348 Vaisala Y22348 26/6/2007 0.0992 0.2988 CMAR Aspendale 076/74/07 Vaisala Y22348 6/7/2007 0.0993 0.32 CMAR Pye P63a/07/07_2175 Riso 2175 3/7/2007 0.6228 0.2436 Svend Ole Hansen Aps 06.02.2899 Riso 2175 1/12/2006 0.62418 0.25303 CMAR Pye P064/070/7_2179 Riso 2179 3/7/2007 0.6233 0.2504 Svend Ole Hansen Aps 06.02.2901 Riso 2179 1/10/2006 0.62694 0.22148

The results show that the Pye coefficients indicate a slightly lower wind speed than if the coefficients from the other institutes are used, with the overall difference less than 0.5% at 10 m.s-1.

Comparison of Calibrations Between Pye and othersfor 13 calibration points. (dU = Uother-Upye)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Upye (m/s)

dU (m

/s) 2175

2179Y23202Y22348

Figure 7.2.1: Comparison of laboratory calibrations. Solid lines indicate the acceptance limits of 0.07 m.s-1 or 1%, whichever is greater.


International Standard ISO17025:2005 application document specifies a method of proficiency testing that can be applied to compare calibration results. Results can be evaluated using En ratios, where En stands for Error normalised which is defined as:

REFLab UUREFLabEn

22 +

−= (7.2)

Where: Lab Participating laboratory’s result (Pye result) REF Reference laboratory’s result (Other labs’) ULab Participating laboratory reported uncertainty (1% @ 10 m.s-1) UREF Reference laboratory reported uncertainty

For Svend Ole Hansen Aps: 0.05 m.s-1 @ 10 m.s-1

For CMAR Aspendale*: 1% @ 10 m.s-1

For a result to be acceptable, the absolute value of the En ratio should be less than one, and the closer to zero the better, i.e.

1⟨nE (7.3)

For the above calibration coefficients at a wind speed close to 10 m.s-1 with a stated uncertainty of 1 % for the Pye and Aspendale results and 0.05 m.s-1 for Svend Ole Hansen results, we get: Table 7.2.2: Results of proficiency testing using normalised error number, En

Anemometer Reference laboratory EnVaisala Y23202 CMAR Aspendale -0.091 Vaisala Y22348 CMAR Aspendale -0.216

Riso 2175 Svend Ole Hansen Aps -0.277 Riso 2179 Svend Ole Hansen Aps -0.258

Note: These results, while very good, will not reveal systematic measurement bias that may be common to the measurement techniques of the reference and participating laboratories.

7.3 Third party review Third party review was achieved by cross checking of the annotated computer source code and independent operation of the system. * CSIRO Marine and Atmospheric Research operates two NATA accredited wind-tunnels; one in Canberra at the Pye laboratory (CMAR Pye), and the other at the CSIRO Aspendale laboratories (CMAR Aspendale).


8. Summary of important points The following table show lists the specifications for the Pye Laboratory wind-tunnel calibration system: Table 8.1: Important system details Item Symbol Value Limit Wind-tunnel flow correction coefficient kf 1.004 Wind-tunnel blockage ratio* 0.015 0.05 Wind-tunnel calibration coefficient kc 1.000 Pitot-static tube coefficient kh 0.997 Turbulent intensity @ 10 m.s-1 1 % 2 % Flow uniformity across wind-tunnel at calibration position

± 0.1 % ± 0.2 %

Combined standard uncertainty @ 10 m.s-1 0.021 m.s-1 Expanded uncertainty (k=2) @ 10m.s-1 u95 0.042 m.s-1 0.1 m.s-1

Range of calibration wind speeds 4 to 16 m.s-1 4 to 16 m.s-1

Number of measurement speeds (full calibration)

13 13

Reproducibility of measurements (Difference between 5 sets @ 10 m.s-1 )

0.17 % 0.5 %

Difference between inter-laboratory comparison @ 10 m.s-1

~0.3 % 1%

The values shown in the Limit column are Measnet limits and were adopted as design and operational limits for this anemometer calibration system. * The blockage ratio is dependent on the particular anemometer under test; the value shown is for a Vaisala WAA151 instrument.


Appendix A: DT50 frequency and time-base check. Test of DT50 timebase accuracy. DT s/n 19980

31/3/2006 counter s/n 1832A00588By Dale HughesReferenced to speaking clock File: dt_test_20060330.xls

Actual count TimeDT50 DT50 Start Stop Start Stop

100 Avg 100.004 Hz 0 5735805 counts 30/3/2006 31/3/2006100 difference 15:56

100.0083 Stdev 0.007 Hz Hours 15100.0083 Frequency 99.997 Hz Minutes 56100.0083 seconds 57360

100100100

100.0083 Uncertainty in reference counts100.0083 +/- 22 counts

100100 Fhi 99.99698 Hz

100.0083 Flo 99.99622 Hz100

100.0167 S.E 0.000443 Hz100.0083100.0083100.0083

100 Uncertainty = 0.00755 %100.0083100.008399.9917

100.0167100

100.0083100

100.0083100

99.9917100.0083100.0167100.0167100.0083100.0083

100

To allow for reaction time (2 by 100ms) and counter uncertainty (+/- 2 counts)

Converted to standard error assumingrectangular distribution: (Fhi-Flo)/sqrt(3)

(Fmeas-Ftrue)/Ftrue

DT50 reads high by 0.0076%

This column is 250 measurements of frequency from calibrated source.

Freq = count/seconds

Extract from calibration file. Note that uncertainty is rounded to 0.008 %


Appendix B: Test of air density calculations. Comparison of air density calculations between LabVIEW and Excelfile:air_dens_comp.xls

Data from calibration raw data file Convert to Pascals, Kelvin &fractional humidity

P71_2178 hPa T(C) RH% Rho B (Pa) T kelvins Theta949.8 20.5 28 1.124 94980 293.65 0.28949.8 20.5 28 1.124 94980 293.65 0.28949.8 20.5 27 1.124 94980 293.65 0.27949.7 20.6 27 1.123 94970 293.75 0.27949.7 20.7 27 1.123 94970 293.85 0.27949.6 20.8 27 1.122 94960 293.95 0.27949.6 20.9 27 1.122 94960 294.05 0.27949.6 20.9 27 1.122 94960 294.05 0.27949.6 20.9 27 1.122 94960 294.05 0.27949.6 20.8 27 1.122 94960 293.95 0.27

Calculations

1/Ro 1/Rw 1/Rw - 1/Ro Ps Rho0.00348371 0.00216685 -0.00131687 2410.348 1.1240.00348371 0.00216685 -0.00131687 2410.348 1.1240.00348371 0.00216685 -0.00131687 2410.348 1.1240.00348371 0.00216685 -0.00131687 2425.269 1.1230.00348371 0.00216685 -0.00131687 2440.27 1.1230.00348371 0.00216685 -0.00131687 2455.353 1.1220.00348371 0.00216685 -0.00131687 2470.518 1.1220.00348371 0.00216685 -0.00131687 2470.518 1.1220.00348371 0.00216685 -0.00131687 2470.518 1.1220.00348371 0.00216685 -0.00131687 2455.353 1.122

( )⎥⎦⎤

⎢⎣⎡

−−

=65.29

15.27367.17exp2.611T

TPs

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

ows

o RRP

RB

T111 θρ

This value is used bythe system to calibratean anemometer

These values are measuredby the PTU100 and arerecorded for each calibrationspeed

These are the same algorithms used by the calibration system.


Appendix C: Transducer and water column comparison. Comparision of water column & Druck pressure transducer.File: WC_vs_T0.xlsUsing water column manometer Offset corrected Using Transducer #T0

VSD% Raw P55 Raw P56 P55(Pa) P56(Pa) P55(Pa) P56(Pa)0 4 420 14.5 14.2 10.5 10.2 10.423 10.31825 21.8 21.5 17.8 17.5 17.804 17.51330 31 30.5 27 26.5 26.966 26.61535 41.5 41 37.5 37 38.129 37.60540 54.8 54 50.8 50 51.026 50.33145 69 68.2 65 64.2 65.888 64.98950 86 84.8 82 80.8 82.312 81.23455 104 102.7 100 98.7 100.859 99.50860 124.2 123 120.2 119 120.895 119.51165 146 144 142 140 142.894 141.021

Water Column Manometer vs Transducer #0

y = 1.0065x + 0.0345R2 = 1

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160

Water Column Pressure (Pa)

Tran

sduc

er T

0 Pr

essu

re (P

a)


Appendix D: Reproducibility. Comparison of anemometer calibration coefficients for Vaisala anemometer Y22348file: cal_comp_2.xls

Tunnel settings kf kc ch1.004 1 0.997

Report date B(hPa) T© RH% a0 a1 U@100Hz(ms-1) dU wrt AVG(%)P053/7/7 26/6/2007 947.21 18.3 39.8 0.2988 0.0992 10.219 0.065P130 19/6/2007 938.69 17.8 36.6 0.3052 0.0991 10.215 0.030P129 18/6/2007 942.60 18.5 42.3 0.3122 0.099 10.212 0.000P128 18/6/2007 943.98 18.3 43.2 0.3078 0.0991 10.218 0.055P127 18/6/2007 945.73 17.9 43.8 0.3075 0.099 10.208 -0.046P120 1/6/2007 953.72 18.7 41.0 0.3015 0.099 10.202 -0.104

Average 10.212 ms-1

max' diff' 0.170 %

min

minmax100U

UU −×


Appendix E: Sample calibration report and raw data file. For each calibration a ‘raw’ data file is created and this file contains sufficient information (in addition to the laboratory notebook) to recreate any given calibration report. The intention is that this document is printed out for calibration and the page is then glued into the laboratory notebook so that a ‘hard copy’ of each calibration is retained.

P064_07_07_2179.prn Dale Hughes 3/07/2007 Riso P2546A 2179 Vofs Vadc Pa hPa T(C) RH% Rho U(m/s) Hz u(m/s) Residual -0.0037 0.3702 14.8268 943.6264 19.2405 37.2004 1.1206 5.1726 7.9056 0.0553 -0.0054 -0.0037 0.6812 27.2829 943.6264 19.2405 37.2004 1.1206 7.0166 10.8444 0.0447 0.0068 -0.0037 1.1524 46.1542 943.5265 19.1406 38.2474 1.1207 9.1254 14.2389 0.0408 -0.0002 -0.0037 1.7426 69.7961 943.5265 19.2405 37.2004 1.1204 11.2234 17.6111 0.0412 -0.0043 -0.0037 2.3577 94.4311 943.5265 19.2405 37.2004 1.1204 13.0546 20.5500 0.0435 -0.0048 -0.0037 3.1654 126.7816 943.4266 19.3405 37.2004 1.1199 15.1299 23.8944 0.0473 -0.0142 -0.0037 3.6090 144.5482 943.4266 19.4405 37.2004 1.1195 16.1582 25.5278 0.0495 -0.0040 -0.0037 2.7448 109.9352 943.5265 19.5404 37.2004 1.1192 14.0933 22.1722 0.0453 0.0226 -0.0037 1.9933 79.8364 943.5265 19.5404 37.2004 1.1192 12.0100 18.8722 0.0420 -0.0037 -0.0037 1.4313 57.3273 943.4266 19.5404 37.2004 1.1191 10.1776 15.9111 0.0406 0.0096 -0.0037 0.8998 36.0407 943.5265 19.4405 37.2004 1.1196 8.0679 12.5389 0.0420 0.0019 -0.0037 0.4914 19.6808 943.4266 19.4405 37.2004 1.1195 5.9622 9.1611 0.0496 0.0016 -0.0037 0.2319 9.2880 943.4266 19.3405 37.2004 1.1199 4.0952 6.1778 0.0678 -0.0059 kf kc ch 1.004 1.000 0.997 a0 a1 Rsqrd 0.2504 0.6233 1.0000

The above is the contents of file P064_07_07_2179.prn, the corresponding calibration report is shown on the following pages. Each calibration report is a HTML document and each page is linked so that a standard web browser may be used. This method of presentation also is secure as it is very difficult to modify the contents of the HTML document. It is believed that this approach represents a significant improvement over the earlier system that used Excel spreadsheets.


Report Number: P064_07_07_2179 Operator: Dale Hughes

Test Date: 3/07/2007 Test Procedure: CAR_NATA_WI_ WT_32e

Test Temperature: 19.4 +/- 0.2 C Barometric Pressure: 943.5 +/- 0.1 hPa Instrument Manufacturer: Riso Instrument Model: P2546A Instrument S/N: 2179 Cup S/N: n/a Client: Inter Laboratory Calibration CSIRO Marine & Atmospheric Research Pye Laboratory Clunies-Ross St Canberra ACT 2601 Approved by: Dale Hughes (Authorised signatory) This document is issued in accordance with NATA's accreditation requirements. Accredited for compliance with ISO/IEC 17025. The calibration is traceable to Australian National Standards of measurement. This document shall not be reproduced, except in full. Page 1 of 3 Previous page <- -> Next page

R:\user_level\PS_anemo_cal_LV16.vi


Table of calibration data for Instrument S/N: 2179 Report Number: P064_07_07_2179 Test Date: 3/07/2007

U(m/s) Hz 5.2 7.91 7.0 10.84 9.1 14.24 11.2 17.61 13.1 20.55 15.1 23.89 16.2 25.53 14.1 22.17 12.0 18.87 10.2 15.91 8.1 12.54 6.0 9.16 4.1 6.18 Table of calibration data for instruments used:

Instrument Serial Number Calibration Certificate Date

Pressure Transducer: 2274469 APL073225 28/2/2007

PTU: A3640006 RN070533 31/5/2007 DataTaker: 19980 CMAR 2 8/5/2007 DaqLab: 803226 8248 19/3/2007 Anemometer calibration statistics: A1(slope) = 0.6233 A0(intercept) = 0.25 Rsquared = 0.99999 Standard error A1 = 0.0004 Standard error A0 = 0.01 Covariance A1A0 = -0.000003 Page 2 of 3 Previous page <- -> Next page



Calibration & uncertainty charts for Instrument S/N: 2179 Report Number: P064_07_07_2179 Test Date: 3/07/2007

Page 3 of 3 Previous page <- -> Next page



References Bolton, D., 1980, The Computation of Equivalent Potential Temperature, Monthly Weather Review, Volume 108. American Meteorological Society. Cook, R.R., 2002, Assessment of uncertainties of measurement for calibration & testing laboratories, 2nd Edition, NATA, Melbourne. Duncan, W.J., Thom, A.S., Young, A.D., 1962, The Mechanics Of Fluids, Edward Arnold Ltd, London. Gibbins, C.J., 1990, A survey and comparison of relationships for the determination of the saturation vapour pressure over plane surfaces of pure water and of pure ice, Annales Geophysicae 8, (12), 859-886 Goldstein, R.F., 1983, Fluid Mechanics Measurements, 1983, Springer-Verlag, Berlin. Good Practice Guidance Note, 2002, Buoyancy Correction and Air Density Measurement, National Physical Laboratory, Teddington, Middlesex. Hoerner, S.F., 1965, Fluid-Dynamic Drag, Hoerner, New Jersey. Hughes, D.E., 2007, Laboratory notebook, CSIRO Marine & Atmospheric Research, Canberra. Hughes, D.E., 2006, uncertainty_calcs.xls ISO 3966-1977 (E), Measurement of fluid flow in closed conduits – Velocity area method using Pitot static tubes, 1st Edition, International Organisation for Standardization, Switzerland. ISO/IEC 17025:2005 (E), General requirements for the competence of testing and calibration laboratories, 2nd Edition, International Organisation for Standardization, Switzerland. ISO/IEC 17025 Application Document. Supplementary requirements for accreditation in the field of physical and dimensional metrology, 2004 Version 1. NATA, Melbourne. MEASNET, 1997, Cup Anemometer Calibration Procedure, Version 1. Pankhurst, R.C. & Holder D.W., 1952, Wind-Tunnel Technique, Sir Isaac Pitman & Sons Ltd, London. Pope, A. & Harper, J. J., 1966, Low-Speed Wind Tunnel Testing, John Wiley & Sons, Inc, New York.


Attachments

1. Uncertainty calculations spreadsheet.


Calculation of uncertainty based onMeasnet sample data U = 10 (m/s)example and specifications of our instruments. Assumes Vaisala WAA151 anemometer T 20 C

B 950 hPaDEH 7/11/2005, first version DEH 6/3/2007, REV 11 Rh (θθθθ) 0.5DEH 1/2/2006, Rev 2 DEH 10/5/2007, REV 12 c h 0.997DEH 21/3/2006, Rev 3 DEH 25/5/2007, REV 13DEH 6/4/2006, Rev 4 DEH 30/5/2007, REV 14 calculated from above constantsDEH 28/9/2006, Rev 5 DEH 18/6/2007, REV15 degrees K K 293.15 R o 287.05DEH 5/10/2006, Rev 6 Saturation vapour pressure P s 2336.947123 Pa R w 461.5DEH 10/10/2006, Rev 7 air density ρ 1.123704834 k1 0.003484DEH 11/10/2006, Rev 8 Pitot-static tube pressure P k 56.1852417 Pa k2 -0.00132DEH 24/10/2006, Rev 9DEH 7/12/2006, Rev 10 Standard Degrees

Uncertainty Sensitivity freedomItem Error Source Value, u i Value, c i u i c i (m/s) (u i c i ) 2 νννν

1 WT flow correction factor Use calculated correction factor = 1.004 and k f = 1.004 u f = 1.155E-03 9.960E+00 1.150E-02 1.323E-04 50 3.49923E-10use 0.002 as standard uncertainty (from measurement)Rectangular distribution.

2 WT calibration factor Use Kc = 1.000 with standard uncertainty of 0.002 k c = 1.000 u c = 1.155E-03 5.000E+00 5.774E-03 3.333E-05 50 2.22222E-11positions as this better describes our tunnelRectangular distribution.

3 Pressure transducer sensitivity Quoted 95% (k=2) uncertainty = 0.3 Pa k pt = 0.3 u pt = 1.500E-01 8.899E-02 1.335E-02 1.782E-04 60 5.29182E-10Standard uncertainty from Cal' cert'

4 & 5 ADC uncertainty 15 bit (Plus sign) input to ADCTransducer o/p = 0..5V for 0..200 Pa

Quantisation (V/bit) 0.000152588

Noise quoted as 2 Least Sig' Bits 0.000305176 VNon-linearity quoted as +/- 1 LSB 0.000152588 V

Gain error quoted as 0.04% max for X1 rangeat test U --> Volts 0.000561852 V

From calibration report = +/- 0.0006V Total ADC error in Volts = sum of these 0.001019616 V

(200 Pa = 5 v) Total ADC error in Pascals assuming k ps = 0.00102 u ps 1.177E-02 8.899E-02 1.048E-03 1.098E-06 60 2.00846E-14Rectangular distribution & half of range

6,7,8 Uncertainty due to air density caused Quoted 95% (k=2) uncertainties for:10,11,12 by uncertainty in measuring barometric T = +/- 0.13 C

14 pressure (B), air temperaure (T) and B = +/- 0.07 hParelative humidity (θ) θ = +/- 1.5 %

For PTU200 device: Expanded uncertainties from Cal' cert' c i u i c iT = +/- (celsius) 0.15 0.007666415 0.000574981B = +/- (hPa) 0.09 1.18837E-05 5.34768E-07θ = +/- (%/100) 0.01 0.010497858 5.24893E-05

Total standard uncertainty in air density 5.77372E-04 u ρρρρ 5.774E-04 4.450E+00 2.569E-03 6.600E-06 60 7.26011E-13

9 Uncertainty due to Pitot-static tube 2 degree deviation gives 0.1% change k h1 = 0.001 u h 9.970E-04 5.015E+00 5.000E-03 2.500E-05 50 1.25E-11see ISO 3966-1977 chart P 28 of nominal coefficient of 0.997 k h2 = 0.997

13 Statistical uncertainty in the mean of Measured turbulent intensity (LDV) % k s = 1 u s c s = 7.454E-03 5.556E-05 179 1.72426E-11the wind speed time series Number of samples k s = 180

Uncertainty due to pulse counting (Rectangular distribution) +/- counts = d count = 4 u dc 1.155E+00 5.556E-04 6.415E-04 4.115E-07 50 3.38702E-15and time base: (normal dist') Measured with calibrated oscillator (fraction) d time = 0.00008 u dt 1.333E-05 5.556E-02 7.407E-07 5.487E-13 50 6.02136E-27(assume use of Vaisala anemometer: a1 ~ 0.1)

Time base (s) = 180Typical (for Vialsala) a1 = 0.1

Combined standard uncertainty = u c 2.080E-02 9.31819E-10

Expanded, 95% uncertainty,u 95 = ku c 0.0410 m/s @ test U 0.41 % 200.7051226

Rounded results 0.05 m/s k = 1.972558 ννννeff = 200

fff k

UkUc =∂∂=

ccc k

UkUc 2=∂∂=

kktp P

UPUc 2=∂∂

=

( )221

, 2 TPkBk

Tc sT

θρρ

+=∂

∂=

Tk

Bc B1

, =∂∂= ρ

ρ

ρρρ 2UUc =∂

∂=

hhh k

UkUc 2=∂∂=

[ ]s

ows

o

PkBkT

RRPRB

T

θ

θρ

211

111

+=

−+=

ρhkc

f kPkkU 2

=

( )

−−= 65.29

15.27367.17exp2.611 TTPs

TPkc s

Ps2

, =∂∂= θρ

ρ

2

195

= ∑

=

n

iii cuku

ta

CUcdc 1=∂∂=

tFa

tUcdt 1=∂∂=

∑ =

=Ni

i

ii

ceff cu

u

1

4

4

νν

∑ =

Ni

i

ii cu1

4

ν

i

ii cuν

4

Type A assessmentso ν = n-1

Calibration certificategives k = 2 so ν = 60

'good' measurementsor estimate, so ν = 8.

νeff = effectivedegrees of freedom

'good' measurements,so ν = 50. Also for frequency& timebase measurement.

I think we have a 'good'chance of keeping alignmentwithin +/- 2 degrees at alltimes.

kksp P

UPUc 2=∂∂=

uncertainty_calcs_2.xls

description, analysis & testing of the pye laboratory … · 2007-07-18 · wind speed...

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