Final Report on the APMP Air Speed Key Comparison (APMP.M.FF-K3)

Transcription

1 Final Report on the APMP Air Speed Key Comparison (APMP.M.FF-K3) July, 00 (Revised) Yoshiya Terao, Yong Moon Choi, Mikhail Gutkin 3, Wu Jian 4, Iosif Shinder 5 and Cheng-Tsair Yang 6 NMIJ, AIST, Japan (Pilot) KRISS, Korea 3 VNIIM, Russia 4 NMC, A*STAR, Singapore 5 NIST, USA 6 CMS/ITRI, Chinese Taipei

2 . Introduction This key comparison, APMP.M.FF-K3 has been undertaken by APMP/TCFF, which is Technical Committee for Fluid Flow, and was piloted by National Metrology Institute of Japan (NMIJ, AIST). The objective of this key comparison is to demonstrate the degree of equivalence of the air speed standards held at the participating laboratories to the CCM.FF-K3 key comparison reference value (KCRV) and to provide supporting evidence for the calibration and measurement capabilities (CMCs) claimed by the participating laboratories in the Asia-Pacific regions. This Draft B report was prepared in accordance with the Guidelines for CIPM Key Comparisons () and The Guidelines on conducting comparisons (APMP-G) ().. Organization () Participants and test speeds The participants and their actual testing dates are listed in Table. The comparison was made at the air speeds of, 5, 0, 6 and 0 m/s. The test air speeds at each participant are also indicated in Table. Table. Participants and test air speed. Contact Person Test Air Speed Participant # Address and Phone Number (m/s) (Economy) Shipping Address Cheng-Tsair Yang 30, Da-Hsueh Rd.,Hsin-Chu city, 300 Taiwan Yong Moon Choi CMS/ITRI ctyang@itri.org.tw, (Chinese Center for Measurement Standards, Taipei) Industrial Technology Research Institute * * * * * Doryong-Dong, Yuseong-Gu, Daejeon , Rep.of Korea KRISS ymchoi@kriss.re.kr, (Korea) Korea Research Institute of Standards and Science Center for Fluid Flow and Acoustics * * * * 3 Iosif Shinder NIST Iosif.Shinder@nist.gov, Link (USA) National Institute of Standards and Technoloty Lab 00 Bureau Drive, Stop 836 Gaithersburg, MD , USA * * * * * Wu Jian 4 #0-7, Science Park Drive, Singapore 8 Abdul Rahamn Mohamed NMC A*STAR wu_jian@nmc.a-star.edu.sg, (Singapore) National Metrology Centre, A*STAR, * * * * * NML-SIRIM Abd.rahman_mohamed@sirim.my, (Malaysia) National Metrology Laboratory, SIRIM BERHAD LOT PT 4803, Bandar Baru Salak Tinggi, Sepang, Selangor, Malaysia Mikhail Gutkin Withdrawn 6 Moskovsky Prospect 9, St. Pertersburg 90005, Russia Yoshiya Terao VNIIM 95mb@rambler.ru, m.b.gutkin@vniim.ru, (Russia) D.I.Mendeleyev Institute for Metrology * * * * * NMIJ/AIST 7 FF-K3@m.aist.go.jp, National Metrology Institute of Japan, Pilot (Japan) National Institute of Advanced Industrial Science and Technology * * * * * AIST Central 3, -- Umezono, Tsukuba, Ibaraki , Japan Six NMIs from APMP planned to participate. Among these NMIJ was the only laboratory that had taken a part in the relevant global key comparison (CCM.FF-K3). NIST, USA, who

3 also participated in CCM.FF-K3, was invited to ensure the linkage to the global key comparison in accordance with the APMP-G. During the circulation of the transfer standard started, NML-SIRIM withdrew their participation. As a result, the final number of the participants was six. () Test schedule The actual testing dates at each participant are listed in Table. 3. Transfer Standard Table. Participants and test schedule. Participating Lab From To NMIJ (#) February 6, 009 March 0 CMS March 6 April 0 NMIJ (#) April 07 April 3 NIST May 04 May 7 KRISS June July 08 A*STAR July 7 August 0 NMIJ (#3) August 3 September 3 VNIIM October 9 November 0 NMIJ (#4) December 07 December, 009 The ultrasonic anemometer to be used in this KC is manufactured by KAIJO SONIC CORPORAITION. The probe has three pairs of ultrasonic transducers, and measures the three-dimensional velocity vector derived from the propagation time of the ultrasonic waves between each pair of transducers. The signal processing unit provides a scalar value of the air speed, V m, which is given by, V m x y z V V V () where V x, V y and V z denote the components of the three-dimensional velocity vector. This signal processor also gives the time averaged air speed, V. m Photo shows the probe set to be calibrated in the test section of the wind tunnel at NMIJ. 3

4 Photo Probe of the ultrasonic anemometer 4. Calibration results () Calibration result to be reported At each participant, the ratios of the laboratory's reference air speed (V ref ) to the time averaged air speed V m were obtained at each test speed and reported along with their uncertainty. The averaging time was 60 s. In this report the calibration result is represented by x V V () i, ref m where subscript i denotes the participant. () Reproducibility of the transfer standard observed at NMIJ Fig. shows the calibration results of the transfer standard at NMIJ during the circulation. This figure shows that the anemometer was very stable both at m/s and 0 m/s. 4

5 x NMI Test at CMS Test at NIST, KRISS and A*STAR m/s Test at VNIIM Feb-09 Apr-09 Aug-09 Nov-09 (a) m/s x NMI Test at CMS Test at NIST, KRISS and A*STAR 0 m/s Test at VNIIM.000 Feb-09 Apr-09 Aug-09 Nov-09 (b) 0 m/s Fig. Result of reproducibility test of the transfer standard (3) Calibration results of the participants NMI The calibration results reported by the participants are listed in Table 3. For NMIJ, the result obtained on April 6, 009 is presented here. Calibration Result x i Table 3 Calibration results reported by the participants. U(x i ) is an expanded uncertainty with coverage factor (k) of. Expanded Calibration Uncertainty Result U (x i ) x i Expanded Calibration Uncertainty Result U (x i ) x i Air Speed (m/s) Expanded Calibration Uncertainty Result U (x i ) x i Expanded Calibration Uncertainty Result U (x i ) x i Expanded Uncertainty U (x i ) NMIJ CMS NIST KRISS A*STAR VNIIM

6 5. Linkage to the global key comparison At the air speeds of m/s and 0 m/s, the two link laboratories have a result both from CCM.FF-K3 (CCM KC) (3) and APMP.M.FF-K3 (APMP KC). These results are plotted in Fig. with the key comparison reference value (KCRV), derived from CCM KC. These KCRV is used as the reference value after the results from APMP KC are corrected by the procedure described by Delahaye and Witt (4). A correction, which should be applied to the result from APMP KC, was obtained by equation (3): D wd (3) i i where D i is the difference between the results from CCM KC and APMP KC at a same link laboratory (NMIJ or NIST) as presented by equation (4), and w i is the weighing coefficient obtained from the uncertainty at each link lab as presented by equation (5). D x x (4) i i, CCM i, APMP w i ui u u NMIJ NIST With this procedure, the correction was calculated as: D at m/s, 0.00 at 0 m/s. (5) (6) Finally, corrected value i i, APMP x i for each participant of APMP KC was calculated as: x x D. (7) This correction provides an estimate of what would have been the result from the APMP KC participants, if they had actually participated in CCM KC. Thus those result from APMP KC participants can be compared with KCRV and the participants results at CCM KC. For m/s and 0 m/s, the corrected results are plotted in Fig. 3 and 7 along with KCRV and results from NMi-VSL and PTB, who participated only in CCM KC. The results at other air speed are plotted in Fig. 4 to x i APMP KC NMIJ NIST NMIJ CCM KC KCRV NIST x i APMP KC NMIJ NIST NMIJ CCM KC KCRV NIST (a) m/s (b) 0 m/s Fig. Results from the link laboratories at CCM KC and APMP KC 6

7 CCM KC x i' NMIJ CMS NIST KRISS A*STAR VNIIM KCRV NMi PTB Fig. 3 Corrected calibration results at m/s. Values of KCRV, NMi and PTB are taken from Final report of CCM KC x i.00 x i NMIJ CMS NIST KRISS A*STAR VNIIM NMIJ CMS NIST KRISS A*STAR VNIIM Fig. 4 Calibration results at 5 m/s. Fig. 5 Calibration results at 0 m/s. 7

8 x i x i' CCM KC NMIJ CMS NIST KRISS A*STAR VNIIM NMIJ CMS NIST A*STAR VNIIM KCRV NMi PTB Fig. 6 Calibration results at 6 m/s. Fig. 7 Corrected calibration results at 0 m/s. Values of KCRV, NMi and PTB are taken from Final report of CCM KC. 6. Degree of Equivalence () Degree of Equivalence to KCRV For each participating laboratory, the degree of equivalence (DoE) was calculated using d x x (8) i i ref where x ref denotes KCRV. The results are listed in Table 4. Among the eleven DoEs shown in Table 4, the ten DoEs, except that of VNIIM at 0 m/s, are within the expanded uncertainty of the KCRV (U(x ref )), which is at 0 m/s and at m/s with k =. Table 4. Degree of equivalence of each lab to KCRV m/s 0 m/s NMIJ CMS NIST KRISS A*STAR VNIIM () Degree of Equivalence between participants For each combination of two participating laboratories, the DoE was calculated using d x x at m/s and 0 m/s (9) i, j i j d x x at other air speeds (0) i, j i j The expanded uncertainty was obtained using 8

9 Udi, j udi, j and u di, j u xi u xj () () The results are listed in Table 5 to 9. Table 5 Degree of equivalence between participants and its expanded uncertainty (k = ) at m/s NMIJ CMS NIST KRISS A*STAR VNIIM d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) NMIJ CMS NIST KRISS A*STAR VNIIM Table 6 Degree of equivalence between participants and its expanded uncertainty (k = ) at 5 m/s NMIJ CMS NIST KRISS A*STAR VNIIM d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) NMIJ CMS NIST KRISS A*STAR VNIIM Table 7 Degree of equivalence between participants and its expanded uncertainty (k = ) at 0 m/s NMIJ CMS NIST KRISS A*STAR VNIIM d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) NMIJ CMS NIST KRISS A*STAR VNIIM Table 8 Degree of equivalence between participants and its expanded uncertainty (k = ) at 6 m/s NMIJ CMS NIST KRISS A*STAR VNIIM d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) NMIJ CMS NIST KRISS A*STAR VNIIM

10 Table 9 Degree of equivalence between participants and its expanded uncertainty (k = ) at 0 m/s NMIJ CMS NIST A*STAR VNIIM d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) d i,j U (d i,j ) NMIJ CMS NIST A*STAR VNIIM Summary and conclusion A selected transfer standard had been circulated among the six participants in eleven months starting February 009. The repeated calibration results at NMIJ demonstrated sufficient reproducibility of the transfer standards. At m/s and 0 m/s, a linkage to the global key comparison (CCM.FF-K3) was established by applying correction to the participants results based on the results from the link laboratories. 8. References () Guidelines for CIPM key comparisons, March 999 (Revised in October 003). () APMP-G: The Guidelines on conducting comparisons, 003 (3) Final Report on the CIPM Air Speed Key Comparison (CCM.FF-K3), October, 007 (4) Linking the Results of Key Comparison CCEM-K4 with the 0 pf Results of EUROMET Project 345, François Delahaye and Thomas J. Witt, Metrologia 39(00) Technical Supplement

11 Appendix - Uncertainty budget of participating laboratories In this appendix, the uncertainty budget of each participating laboratory is presented. Each part is taken from the document submitted by a participant and has not been edited by the pilot lab. Part CMS The uncertainty budget of the CMS air speed standards The real air speed at the anemometry position can be expressed as V tunnel V ldv = f (Vldv,δ, ε) () where Vldv : air speed measured by using LDV Vtunnel : real air speed at the position of anemometry δ : correction factor for flow characteristic ε : correction factor for wind-tunnel performance According to equation (), the uncertainty of air speed in the measurement zone can be expressed as u u c c ( V where c: sensitivity coefficient of the variable Vldv; c: sensitivity coefficient of the variable δ; c3: sensitivity coefficient of the variable ε; The relative uncertainty u ( V c V c u( V ) c u( ) c u( ) ( V ) tunnel tunnel tunnel tunnel f ) V ldv ) u( V (( V ldv ldv u( V ldv ) ) ldv ) f u( ) u( ) ( ) 3 u( ) ( ) / The uncertainty budget of the air speed measurement system is shown in Table f u( ) ) c c c 3 () f V ldv f V ldv f V ldv (3)

12 Table : Uncertainty summary item Sources u(x i )/x % i ν X u( V ldv ) ] V ldv LDV Facility Flow and particle influences of LDV Measurement u( ) particle lag [ ] Velocity bias Turbulence int Fring bias Flow velocity distribution in wind tunnel [ u( ) [ ] along vertical direction along horizonal direction u [ ( V c tunnel V tunnel ) ] 3 along flow direction Combined standard uncertainty U ( V [ k.07 3 tunnel V tunnel ) ]

13 Part KRISS Combined uncertainty and Expanded uncertainty of KRISS The model equation of an air speed measurement using pitot tube as follows; p v s ( ) tu v () The meaning of symbols in Eq.() as follows, ) Air speed measured by pitot tube: v s [m/s] ) Calibration factor of the pitot tube: [-] 3) Compressibility factor: [-] 4) Differential pressure measurements: p [Pa] -Differential pressure measured by gauge: pm [Pa] -Blocking effect of the pitot tube: ( p) [Pa] -Pressure loss due to pitot tube: [Pa] -Installation angle of pitot tube: p [Pa] 5) Density of air: [kg/m 3 ] 6) Turbulence intensity: tu [m/s] 7) Velocity difference caused by the location of measurement: v [m/s] The uncertainty of the v in Eq. () yields, s c u ( ) c u ( ) c u ( p) c u ( ) c u ( tu) c u ( ) uc ( vs ) p tu v v () The sensitivity coefficients can be obtained by differentiating Eq. (). p c ( ) [Pa / (kg/m 3 ) -/ ] p c [Pa / (kg/m 3 ) -/ ] c p ( ) [(Pa kg/m 3 ) -/ ] p p c ( ) [Pa 3 / (kg/m 3 ) -3/ ] c tu = c v For example, at 6.0 m/s, p is 5.9 Pa, air density is.88 kg/m 3, pitot coefficient is.005 from ISO3966, and the compressibility correction factor ( ) is Then, the sensitivity factors are as follows, in units given above: c.60, c. 6, c 0. 55, c , c c (3) p The combined standard uncertainty of the velocity measurement using Pitot tube and the degrees of freedom are calculated with the root-sum-square method from the following standard uncertainties in Table and the degrees of freedom. tu v Table Standard uncertainty of the parameters of KRISS air speed 3

14 Parameter u ( x i ) c i Type A Type B Type A Type B n/a.00e-03 n/a 55.60E+0 ( ) 4.5E-07.0E E+0 p (Pa).84E-0 4.8E E-0 (kg/m 3 ) 5.7E-05.7E E+00 tu (m/s) 4.5E-05 N/A 0000 N/A v (m/s).67e-0 N/A 9 N/A Therefore, the combined uncertainty of v s can be calculated, u c ( v s ) = m/s. The effective degrees of freedom is eff =5. The coverage factor is.0 with 95% confidence level. Final results for v s =6.0 m/s is v s = m/s. The same kind of uncertainty analysis is repeated from.0 to 6 m/s. Results are shown in Table and these are the calibration measurement capability of the pitot tube measurement in the wind tunnel. Table Expanded uncertainty of the pitot tube measurement v (m/s) s U pitot (m/s).5e-0 3.E E-0 8.9E-0 * U pitot (%) k eff

15 Part 3 NIST The uncertainty of the NIST air speed standards 0.~30 m/s, k= Source of uncertainty Type u [m/s] Misalignment of LDA with disk B Disk radius B Disk rotation rate B LDA resolution A LDA - Disk calibration factor A 0.% At m/s for k= Source of uncertainty Type u [m/s] Misalignment of LDA with disk B Disk radius B Disk rotation rate B LDA resolution A LDA - Disk calibration factor A Expanded Uncertainty, [m/s] Expanded Uncertainty, [%] At 0 m/s for k= Source of uncertainty Type u [m/s] Misalignment of LDA with disk B Disk radius B Disk rotation rate B LDA resolution A LDA - Disk calibration factor A Expanded Uncertainty, [m/s] Expanded Uncertainty, [%] (This part has been taken from the final report of CCM Key comparison (3). Detailed uncertainty analysis has been published as "NIST Special Publication 50-79". The original text can be found at ) 5

16 Part 4 NMC A*STAR ESTIMATION OF MEASUREMENT UNCERTAINTY OF A*STAR FOR APMP.M.FF-K3. CALIBRATION EQUIPMENT Features Examined Air velocity m/s; 5m/s; 0m/s; 6m/s; Equipment ) Precision Wind-tunnel System Expanded measurement uncertainty Measurement Range ). Laser Doppler Anemometer Expanded measurement uncertainty Measurement Range 0m/s. Fig. Precision Wind Tunnel Standard 6

17 Fig. Laser Doppler Anemometer. COMPARISON SETUP 3. Environmental Condition Fig 3. The setting up for APMP M.FF-K3 comparison The calibration should be carried out under the ambient condition of Temperature : 3 ± ºC Humidity : 55 ± 5 % rh 7

18 4. TRACEABILITIES Dimension (m) Time (s) Speed calibration (m/s) Beam angle ( o ) Laser Doppler Anemometer Temperature Deferential pressure Barometric pressure Wind Tunnel Unit Under Test 5. ESTIMATED MEASUREMENT UNCERTAINTY 5. Calculate applied air velocity. Air velocity at the measurement point is given by: V= Kwt Kd Kt Kwl Kb Vwt () Where: V: Velocity at measurement position Vwt: Velocity set by wind tunnel Kwt: Calibration factor of wind tunnel Kd: Correction due to wind distribution Kt: Correction due to wind turbulence Kwl: Correction due to wind tunnel long term stability Kb: Correction due to wind blockage 5. Air velocity generated by wind tunnel via pressure and air density measurement V P wt 4 () β: nozzle compression ratio ΔP: the pressure drop across nozzle ρ: density of air Kwt = VLDA/Vwtc (3) VLDA Measurement value of LDA (Laser Doppler anemometer) 8

19 5.3 Calculate velocity calibration of air velocity meter. 5.4 Estimate measurement uncertainty: VUUT=V-Error (4) (V) = ( Kwt, Kd, Kt, Kwl, Kb, Vwt, Vuut) 5.5 Combined measurement uncertainty: = (Kwt, Kd, Kt, Kwl, Kb, ΔP, ρ, VLDA, Vuut) (5) u c = (ckwt ukwt) + (ckd ukd) + (ckt ukt) + (ckwl ukwl) + (ckb ukb) + (cδp uδp) + (cρ uρ) + (cvlda uvlda) + (c Vuut u Vuut ) (6) 5.6 Expanded measurement uncertainty: U=k uc (7) 5.7 The estimated measurement uncertainty is listed at table ~3 in the following pages. 9

20 Table. Summary of Measurement Uncertainty (m/s and 5m/s) Ref no: Source of uncertainty Symbol Unit Uncertainty Absolute Relative Degree of freedom Sensitivity Std uncertainty (u i ) Coverage factor Calibration factor of wind tunnel K wt 0.400% 0.00% Correction due to wind distribution K d 0.00% 0.00% 3 Correction due to wind turbulence K t 0.050% 0.050% 4 Correction due to wind tunnel long term stability K wl 0.00% 0.00% 5 Correction due to wind blockage K b 0.050% 0.050% dp 6 Density of air ρ Kg/m % p 0.00% d 7 Pressure drop across nozzle ΔP Pa % 0.00% 8 Measurement value of LDA V LDA m/s 0.070% 0.035% 9 Unit under test V UUT 9. Repeatability u rep m/s % 0.000% 9. Resolution u res m/s % % Combined Uncertainty u c(density) 0.8% Expanded Uncertainty(at a level of confidence of 95% with k=) U 0.56% 0

21 Table. Summary of Measurement Uncertainty (0m/s) Ref no: Source of uncertainty Symbol Unit Uncertainty Absolute Relative Degree of freedom Sensitivity Std uncertainty (u i ) Coverage factor Calibration factor of wind tunnel K wt 0.400% 0.00% Correction due to wind distribution K d 0.00% 0.00% 3 Correction due to wind turbulence K t 0.050% 0.050% 4 Correction due to wind tunnel long term stability K wl 0.00% 0.00% 5 Correction due to wind blockage K b 0.050% 0.050% dp 6 Density of air ρ Kg/m 3 p 0.00% 0.00% d 7 Pressure drop across nozzle ΔP Pa % 0.00% 8 Measurement value of LDA V LDA m/s 0.070% 0.035% 9 Unit under test V UUT 9. Repeatability u rep m/s % 0.000% 9. Resolution u res m/s % % Combined Uncertainty u c(density) 0.4% Expanded Uncertainty(at a level of confidence of 95% with k=) U 0.48%

22 Table 3. Summary of Measurement Uncertainty (6m/s and 0m/s) Ref no: Source of uncertainty Symbol Unit Uncertainty Absolute Relative Degree of freedom Sensitivity Std uncertainty (u i ) Coverage factor Calibration factor of wind tunnel K wt 0.300% 0.50% Correction due to wind distribution K d 0.00% 0.00% 3 Correction due to wind turbulence K t 0.050% 0.050% 4 Correction due to wind tunnel long term stability K wl 0.00% 0.00% 5 Correction due to wind blockage K b 0.050% 0.050% dp 6 Density of air ρ Kg/m 3 p 0.00% 0.00% d 7 Pressure drop across nozzle ΔP Pa % 0.004% 8 Measurement value of LDA V LDA m/s 0.070% 0.035% 9 Unit under test V UUT 9. Repeatability u rep m/s % 9. Resolution u res m/s % Combined Uncertainty u c(density) 0.7% Expanded Uncertainty(at a level of confidence of 95% with k=) U 0.34%

23 Part 5 VNIIM Uncertainty budget of VNIIM Calibration of transfer standard ultrasonic anemometer has been performed by measuring the anemometer indicated speed and the VNIIM standard reading simultaneously. Measurements accomplished at aerodynamic facility: loop tube with open test section. Nozzle diameter is 700 mm, range 0, 00 m/s. Means of air speed measuring: mm. 0, 30 m/s LDA 5-00 m/s Pitot static tube with differential manometer Distance between nozzle exit plane and ultrasonic anemometer sensors was 70 While using LDA air speed determined as V=Kl *Kb*Kd* Vl Kl LDA calibration factor Kb correction factor due to duct blockage Kd correction factor due to velocity distribution across the duct Vl air speed indicated by LDA Expanded uncertainty sources and values 0,000. LDA calibration 0,0044. Duct blockage 3. Velocity distribution across the duct 0,0040 ( 0 m/s ) KC calibration result (VNIIM) V m/s Xi,00,007,005,004 0,9998 U(Xi) 0,006 0,006 0,006 0,006 0,006 Attached are photos of VNIIM standard facility. 3

24 Standard aerodynamic facility () 4

25 Standard aerodynamic facility () 5

26 LDA of aerodynamic tube 6

27 TC sensor at the test section 7

28 LDA, display panel 8

29 Part 6 NMIJ/AIST Uncertainty budget at NMIJ The anemometer calibration system at NMIJ consists of an LDV calibrator, an LDV transfer standard and a wind tunnel as shown in Fig. B-. The schematic of the LVD calibrator and the wind tunnel is illustrated in Figs. B- and B-3. The uncertainty budget is shown Table B- and B-. LDV calibrator (Primary standard) LDV (Transfer standard) Wind tunnel with ultrasonic anemometers (Working standard) Customers' anemometer Fig. A- Anemometer Calibration System Optical power meter head Screen Rotor assembly Electronic shutter LDV probe Optical length scale Fine adjustment carriage Traverse table A- LDV Calibrator 9

30 Settling section Contraction Honeycomb screens Test section 3300 Corner vanes Fan 7500 DC Motor A-3 Calibration Wind Tunnel 30

31 Table A- Uncertainty sources and their sensitivity coefficient Input quantity Symbol Uncertainty source Reference air speed ref Sensivity coefficient V USR S meter S WT Correction factor to output value of ultrasonic reference anemometer Frontal projected area of DUT Cross-sectional area of calibration wind tunnel * U Output of ultrasonic USR reference anemometer when DUT is installed at the test section * U Output of ultrasonic USR0 reference anemometer at zero air speed S WT WT Type B(A) Smeter S S S S U U U U meter * USR * corrctd * USR0 * corrctd meter meter A A A A Repeatability of DUT V m - Table A- Uncertainty budget (Symbols are defined in Table A-) Air speed range Unit Uncertainty sources m/s V % ref % USR S meter WT S * U USR x0-04 x0-04 x0-04 x0-04 x0-04 x m/s * U USR0 x0-04 x0-04 x0-04 x0-04 x0-04 x0-04 x0-04 x0-04 x0-04 x0-04 x0-04 x0-04 m/s V m % x u x u x x U x x % % % % 3