- Email: [email protected]
s
Flow Measurement and Instrumentation 66 (2019) 132–140
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
New air speed calibration system at NMIJ for air speeds up to 90 m/s a,∗
a
a
a
Aya Iwai , Tatsuya Funaki , Noboru Kurihara , Yoshiya Terao , Yong Moon Choi
b
T
a
National Institute of Advanced Industrial Science and Technology (AIST), National Metrology Institute of Japan (NMIJ), Tsukuba Central 3, Umezono 1-1-1, Tsukuba, 305-8563, Japan Korea Research Institute of Standards and Science (KRISS), Division of Physical Metrology, 209 Gajeong-ro, Yuseong-gu, Daejeon, 305-340, Republic of Korea
b
ARTICLE INFO
ABSTRACT
Keywords: Air speed standard Wind tunnel Calibration Pitot static tube Hot-wire anemometer Volume flowrate
National Metrology Institute of Japan (NMIJ) has established a high air speed standard facility and has been providing a calibration service since 2015. The facility has an air speed range of 40 m/s to 90 m/s with a relative expanded uncertainty (k = 2) of 0.63%. The purpose of this primary standard is mainly to contribute to the improvement of meteorological observation research and to the evaluation of flow field inside a turbo machine and around a high speed vehicle. The reference air speed is derived from the national primary gas flowrate standard of Japan. A conversion device from flowrate to air speed is installed in the test line of the closed-loop calibration facility. The reference air speed at the nozzle exit of the conversion device is obtained by comparing the integral of the air speed profiles and the reference volume flowrate. The total pressure tube used as a transfer standard is then calibrated against the reference air speed at the center of the nozzle exit. The Eiffel-type wind tunnel, which is a working standard for the daily calibration service, is calibrated using this total pressure tube. The present paper describes the calibration system, the traceability chain, and an uncertainty analysis using a validation method.
1. Introduction NMIJ has been operating two air speed standard systems for several decades. One provides a low air speed standard, which covers the air speed range from 0.05 m/s to 1.5 m/s using a tow carriage [1–4]. The other system provides a medium air speed standard, which covers the air speed range from 1.3 m/s to 40 m/s using a rotating disk and an LDV [4,5]. In order to improve the meteorological observation and research and to meet the needs of industrial fields, NMIJ started a new calibration service for Pitot static tubes in 2015. The air speed range of the high air speed standard is from 40 m/s to 90 m/s. The reference air speed is determined by comparing the integral of the non-dimensional air speed profile with the reference volume flowrate. Van Swinden Laboratory (VSL), which is the National Metrology Institute of the Netherlands, also uses this procedure to establish an air speed standard [6]. At present, three NMIs offer air speed standards over 40 m/s using a rotating disk and an LDV as primary standard [7]. In Russia, D.I. Mendeleev Institute for Metrology (VNIIM) operates a calibration service for air speeds of up to 100 m/s [8,9]. In the United States, National Institute of Standards and Technology (NIST) offers a calibration service for air speeds of up to 75 m/s [10,11]. Finally, in Germany, Physikalisch-Technische Bundesanstalt (PTB) offers a calibration service for air speeds of up to 65 m/s [12]. ∗
An overview of the procedure for realizing the air speed standard is shown in Fig. 1 as a traceability chain. The procedure involves three processes. The first process is the evaluation of a reference air speed at the nozzle exit of the conversion device from a reference volume flowrate. The second process is the calibration of a total pressure tube against the reference air speed. The above two processes were performed at the closed-loop calibration facility at NMIJ [13]. The third process is the calibration of the high air speed calibration wind tunnel by using the total pressure tube. The calibration service of the devices under test (DUTs), i.e., Pitot static tubes from customers are conducted in the wind tunnel. The present paper describes in the detail the realization process and the validation of the calibration results and their uncertainty for the high air speed standard. 2. Calibration of total pressure tube 2.1. Determination of reference air speed The closed-loop calibration facility [13] is used in the first and second processes to determine the reference air speed. A schematic diagram of the facility is shown in Fig. 2. The facility is composed of a nozzle chamber, a blower, a
Corresponding author. E-mail address: [email protected] (A. Iwai).
https://doi.org/10.1016/j.flowmeasinst.2019.02.004 Received 29 March 2018; Received in revised form 26 December 2018; Accepted 17 February 2019 Available online 26 February 2019 0955-5986/ © 2019 Elsevier Ltd. All rights reserved.
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Nomenclature
CDUT
Cpit cpit Cpit i
Ct CWT
ni Qv
r re
R Se s 2 (Cpit i )
DUT Air speed at measurement point r (m/s) Non-dimensional air speed at measurement point r (m/s) Reference air speed at the center of the conversion nozzle exit (m/s) Air speed measured by the total pressure tube (m/s) Reference air speed of the high air speed calibration wind tunnel (m/s) Dynamic pressure calculated by subtracting the static pressure from the measured total pressure during total pressure tube calibration (Pa) Dynamic pressure calculated by subtracting the static pressure from the measured total pressure during calibration of the high air speed calibration wind tunnel (Pa) Dynamic pressure measured by the DUT (Pa) Differential pressure between the nozzle inlet and outlet during calibration of the high air speed calibration wind tunnel (Pa) Differential pressure between the nozzle inlet and outlet during DUT calibration (Pa) Angular position of the measurement lines along the radii at the conversion nozzle exit (º) Fluid density at the test line of the closed-loop calibration facility (kg/m3)
v (r ) v (r ) vc
Corrective coefficient of a Pitot static tube as the DUT, which was measured repeatedly and calculated as the arithmetic mean (−) Corrective coefficient of a Pitot static tube as the DUT from single measurement (−) Mean measured corrective coefficient of the DUT Corrective coefficient of the DUT obtained for the ith measurement Corrective coefficient of the total pressure tube (−) Corrective coefficient of the high air speed calibration wind tunnel (−) Number of repeated measurements Reference volume flowrate at the test line of the closedloop calibration facility (m3/h) Measurement point in the cross-sectional area of the conversion nozzle exit (m) Measurement point at the edge of the jet of the conversion nozzle exit (m) Radius of the conversion nozzle exit (m) Effective cross-sectional area at the conversion nozzle exit (m2) Experimental variance of the corrective coefficient of the
vp v WT PCd
PNd
Ppit PWT1
PWT2
temperature controller, and test lines. The nozzle chamber contains 12 critical flow Venturi nozzles calibrated by the medium gas flowrate standard of the NMIJ. Through various combinations of the nozzles, a volume flowrate of up to 1000 m3/h with dry air and up to 500 kPa can be produced in the test lines with a relative expanded uncertainty (k = 2) of 0.28%. In order to determine the reference air speed, a conversion device was placed in the upstream side of an open area made in the nominal 100 mm-diameter test line. The conversion device was composed of a diffuser, a settling chamber, a conversion nozzle, and a traverse device, as shown in Fig. 3. The diffuser translates the diameter of the test line from 100 mm to 200 mm. The settling chamber was composed of three screens and a honeycomb structure. The diameter of the conversion nozzle exit is 60 mm, and the nozzle ratio is 1:11.11. The shape of the contraction nozzle is indicated by a third-
order polynomial curve [14]. Since the turbulence intensity at the center of the jet was approximately 0.3% during the measurement, steady and uniform flow was produced at the nozzle exit. A pressure port was placed on the inner wall surface 20 mm upstream from the nozzle exit. The wall static pressure at the pressure port was used as the base pressure of the total and static pressure measurement. The traverse device for the measurement of the air speed profiles and the calibration of the total pressure tube has radius and rotation direction degrees of freedom. The temperature in the test room was maintained at 24.5 ± 1 °C by controlled air conditioning and the temperature in the jet at the conversion nozzle exit was maintained at 24.5 ± 0.3 °C by a temperature controller installed at the facility. The reference air speed at the center of the jet from the conversion nozzle exit, vc , is determined based on the reference volume flowrate and the non-dimensional air speed profiles, which are measured along the radii at the conversion nozzle exit. Fig. 4 shows an overview of the procedure. This method for calculation from velocity to flowrate is called tangential method [15]. The non-dimensional air speed profiles were defined as follows: (1)
v (r ) = v (r )/ vc
Assuming both Q v and v (r ) are known, the volume flowrate can be expressed in terms of the integral of the non-dimensional air speed profile from the flowrate definition, as follows: re
Qv = 2
v (r ) r dr
(2)
0
Next, Se is defined as the area integration of v (r ) from the center to the edge of the jet, as follows: re
Se =
v (r ) dA = 2
v (r ) r dr 0
(3)
Therefore, vc is given as:
vc = Q v /Se Fig. 1. Traceability chain of the high air speed standard.
The uncertainty of Q v and Se are described in Appendix A2. 133
(4)
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Fig. 2. Closed-loop calibration facility with a conversion device at the test line.
measured 1 mm downstream of the nozzle exit. The sampling rate of the output voltage was 1 kHz. The measured voltages were averaged at 1 s intervals and were recorded on a personal computer. At each volume flowrate, the profiles were measured along eight radii at 45° intervals from 0° to 315°. Each radius had 30 measurement points at intervals of 5 mm in the potential core area of the jet and intervals of 0.05 mm at the edge of the jet. The profiles were normalized by the output voltage of the center of the jet. The normalized output voltage profiles are identical to the non-dimensional air speed profiles. Fig. 6 shows the non-dimensional air speed profiles at 400 m3/h and, Fig. 7 shows the same profiles expanded near the edge of the jet. All of the profiles agree very well, and this trend is the same at the other volume flowrates, which indicates that the jet is axisymmetric. Fig. 8 shows non-dimensional average air speed profiles near the edge for various volume flowrates. The difference in the profiles at each volume flowrate is noticeable near the edge of the jet. The larger the volume flowrate, the thinner the shear layer. Finally, vc was calculated based on these profiles. To evaluate the assumption for calibration of the hot-wire anemometer, a recursive calculation of the air speed profile v (r ) at 1000 m3/ h was conducted. Correction factors for v (r ) were calculated at the four setting volume flowrates as ratio of each effective cross-sectional area Se to the value at 1000 m3/h. The obtained correction factor is shown in Fig. 9. Then the air speed profile v (r ) at 1000 m3/h was corrected by multiplying each correction factor. As the result of the recursive calculation of v (r ) at 1000 m3/h on the first try, the air speed at the center vc was changed only 0.01%. Thus it is considered to be appropriate to assume the air speed at the center of the nozzle exit was proportional to the reference flowrate.
Fig. 3. Conversion device installed at the test line of the closed-loop calibration facility.
Fig. 4. Overview of the procedure for determining air speed.
2.2. Measurement of the air speed profiles using a hot-wire anemometer A hot-wire anemometer is generally calibrated against a reference air speed before each measurement in order to obtain linearity between the output voltage and the actual air speed. In the present study, the hot-wire anemometer was calibrated using the air speed calculated from the reference flowrate based on an assumption that the air speed at the center of the nozzle exit was proportional to the reference flowrate. The uncertainty due to the linearity of the output voltage was evaluated based on the standard deviation of the output voltage around the fitting line. An I-type 55P11 probe (Dantec Dynamics A/S) of the hot-wire anemometer was placed at the traverse device and was aligned in the flow direction. The axis of the wire was aligned in the tangential direction of the conversion nozzle exit in order to improve the spatial resolution. Fig. 5 shows an overview of the measurement procedure. The volume flowrates were set to be 400 m3/h, 600 m3/h, 800 m3/ h, and 1000 m3/h. Therefore, the air speeds at the center of the jet at the conversion nozzle exit corresponding to the volume flowrates were approximately 40 m/s, 60 m/s, 80 m/s, and 100 m/s, respectively. Next, the output voltage profiles along the radii of the jet were
Fig. 5. Overview of the air speed profile measurement procedure by hot-wire anemometer. 134
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Fig. 6. Non-dimensional air speed profiles at 400 m3/h.
Fig. 9. Correction factors for correction of v (r ) at 1000 m3/h.
each volume flowrate, the differential pressure between the total pressure and the base pressure at the pressure port in Fig. 3 was measured. The static pressure was also measured with the static pressure tube shown in Fig. 10 by replacing the total pressure tube. Because the static pressure holes were set in the same location of the total pressure hole, the error of the static pressure is negligible small. In the present study, vp was calculated in terms of PCd and using Bernoulli's theory. Here, PCd was calculated by subtracting the static pressure from the total pressure. Moreover, Ct was calculated as follows:
Ct = vc/ vp
(5)
The results for Ct are shown in Fig. 11, in which the error bars indicate the standard uncertainties calculated in Appendix A2. Based on these results, Ct is approximately constant. In the next section, the values of Ct between the measured points were determined by linear interpolation.
Fig. 7. Non-dimensional air speed profiles near the edge of the jet at 400 m3/h.
3. Calibration of high air speed calibration wind tunnel The high air speed calibration wind tunnel is an Eiffel-type wind tunnel composed of a blower, a diffuser, a settling chamber, and a contraction nozzle, as shown in Fig. 12. The length of the diffuser is 2703 mm, and it transforms the cross-sectional area from a square to a circle and increases the cross-sectional area. The settling chamber, which has a diameter of 400 mm, contains three screens and a honeycomb structure. The contraction nozzle diameter is 100 mm, and the nozzle ratio is 1:16. At the inlet and outlet of the contraction nozzle, four pressure ports are located equiangularly. The pressure at the outlet ports was used as the base pressure for the total and static pressure measurements. The temperature of the test room air, which serves as working fluid, was 18 ± 3 °C during measurement. The temperature of the jet when the air speed was set at 90 m/s was approximately 25 °C
Fig. 8. Non-dimensional average air speed profiles at various volume flowrates.
2.3. Calibration of the total pressure tube The total pressure tube was calibrated against the reference air speed obtained in the previous section. A schematic diagram of the total pressure tube is shown in Fig. 10. The external diameters of the supporting part and the nose part are 3 mm and 1 mm, respectively. The total pressure tube provides better spatial resolution and smaller blockage effect due to its smaller diameter than a Pitot tube. The total pressure tube was placed at the traverse device and was aligned in the flow direction. The total pressure hole was located at the center of the jet 1 mm downstream of the conversion nozzle exit. At
Fig. 10. Schematic diagrams of the total and static pressure tubes. Top: Overall view. Lower left: Tip of the total pressure tube. Lower right: Tip of the static pressure tube. 135
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Fig. 11. Corrective coefficients of the total pressure tube. Error bars indicate standard uncertainties.
Fig. 14. Example of the calibration results.
Fig. 12. Schematic diagram of the high air speed calibration wind tunnel. A detailed diagram of the nozzle is shown in the dashed-line square.
Fig. 15. Example of the results of internal comparison to the medium air speed standard (MASS) at 40 m/s. The error bars indicate expanded uncertainties (k = 2). The specifications of the tubes are shown in Table 1.
CWT = Ct
PNd/ PWT1
(6)
Since PNd and PWT1 were measured simultaneously, was assumed to be equal. Therefore, the fluid density term was reduced from Eq. (6). The value of CWT calculated by Eq. (6) is shown in Fig. 13. The error bars in Fig. 13 represent the standard uncertainty calculated in Appendix A3, and the figure indicates that CWT is approximately constant in the measured range.
Fig. 13. Corrective coefficients of the high air speed calibration wind tunnel. Error bars indicate standard uncertainties.
4. Calibration of Pitot static tube
due to the heat generated by the blower. The total pressure tube calibrated in Section 2 was placed at the traverse device and was aligned in the flow direction. The total pressure hole was located at the center of the nozzle exit. The air speed at the contraction nozzle exit was varied as 40 m/s, 50 m/s, 60 m/s, 70 m/s, 80 m/s, and 90 m/s. At each air speed, the differential pressure between the total pressure and the base pressure was measured. During the measurement of the total pressure, PWT1 was measured at the same time. The static pressure at the same location at which the total pressure was measured was measured using the same procedure with the static pressure tube used in Section 2. In the same manner as in Section 2, PNd was calculated based on the total and static pressures. Using Bernoulli's theory, CWT was calculated as follows:
The Pitot static tube being calibrated, i.e., the DUT, was placed at the Pitot tube holder and was aligned in the flow direction at the nozzle exit. The air speed at the contraction nozzle exit was varied as 40 m/s, 50 m/s, 60 m/s, 70 m/s, 80 m/s, and 90 m/s. Both Ppit and PWT2 were measured at each air speed. Next, Cpit was calculated as follows using Bernoulli's theory:
Cpit = CWT
PWT2/ Ppit
(7)
where was reduced from Eq. (7) as the same reason of Eq. (6). Moreover, Cpit includes the compressibility effect in this paper. An example of the calibration results for eight Pitot static tubes is shown in Fig. 14 and Table 1 including their specification. The error bar in Fig. 14 indicates the expanded uncertainty calculated in Appendix 136
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Table 1 Specifications of the Pitot static tubes. The length of the each tube is normalized by the tube's diameter. Name
Type
Diameter of the tube (mm)
Length of the head (d)
Length from the total pressure hole to the static pressure hole (d)
Length from the static pressure hole to the stem (d)
AMCA-1 AMCA-2 AMCA-3 JIS NPL-1 NPL-2 NPL-3 NPL-4
AMCA AMCA AMCA JIS NPL NPL NPL NPL
2.4 4.7 6.4 4.0 2.3 3.0 6.0 8.0
14.0 17.7 17.0 – 16.4 16.4 16.4 15.6
4.0 6.6 6.3 6.0 7.8 8.0 8.0 7.6
10.0 11.1 10.7 – 8.6 8.5 8.4 7.9
A4. The values of Cpit are approximately unity and increase slightly with air speed.
Comment
Stemless type With Gloss
the medium air speed standard were used. The difference between the medium and high air speed standards is very small compared to the relative expanded uncertainty. Moreover, the En values were 0.59 at maximum. Therefore, the validity of the high air speed standard was confirmed at 40 m/s.
5. Internal comparison The calibration results for the DUTs obtained the proposed procedure were validated experimentally. The eight DUTs described in Section 4 were calibrated at 40 m/s at the medium air speed standard facility of the NMIJ. The relative expanded uncertainty (k = 2) of the medium air speed standard is 0.35% at 40 m/s, and the validity of the medium air speed standard was confirmed by international comparisons with overseas NMIs [4,6,8]. The internal comparison results for the eight DUTs and the En values are shown in Fig. 15 [16]. The En values were calculated based on the comparison results and the expanded uncertainties and indicate the validity of the standard. When ∣En∣ ≦ 1, the comparison results confirmed that the standard was valid. In the present study, the results of
6. Conclusion NMIJ has established a new primary standard of high air speed, for which the air speed ranges from 40 m/s to 90 m/s with a relative expanded uncertainty (k = 2) of 0.63%. Based on internal comparisons with the medium air speed standard at the NMIJ, the validity of the high air speed standard was confirmed. However, the validation results as the air speed exceeds 50 m/s have not yet been evaluated. International comparison for high air speeds will be necessary in the near future. The evaluation of compressibility in the corrective coefficient of the Pitot pressure tube is a subject for future investigation.
Appendix. Uncertainty analysis The uncertainties of the measurement are estimated in accordance with the “Guide to the expression of uncertainty in measurement (GUM)” [17]. A1. Uncertainty analysis for the high air speed standard The corrective coefficient of a Pitot static tube without repeatability Cpit is calculated as follows: (5)
Ct = vc/ vp CWT = Ct Cpit = CWT
(6)
PNd/ PWT1 PWT2/ Ppit
(7)
The sources of uncertainty of the calibration result given as Cpit , which is calculated using Eqs. (5)–(7), correspond to all the parameters contained on the right side of the three equations. Therefore, the relative standard uncertainties of these parameters are first calculated, and uc (Cpit )/Cpit is then estimated using the law of propagation of uncertainty, as follows:
[uc (Cpit )/ Cpit ]2 = [u (vc)/ vc]2 + [ u (vp )/vp]2 (a)
(b)
+ ( 1/2)2 [u ( PWT1)/ PWT1]2 (c )
+ (1/2)2 [u ( PNd)/ PNd]2 (d )
+ (1/2)2 [u ( PWT2)/ PWT2]2 (e )
+ ( 1/2)2 [u ( Ppit )/ Ppit ]2 (A.1)
(f )
The correlation among the sources of the uncertainty is considered to be sufficiently small, as compared to the major sources of the uncertainty, and can thus be ignored.
137
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
A2. Uncertainty derived from Ct The reference air speed is obtained from the volume flowrate produced by the closed-loop calibration facility and the effective cross-sectional area obtained by integrating the air speed profile. The first term of Eq. (5) can therefore be broken down as follows:
[u (vc )/ vc]2 = [u (Q v )/ Q v ]2 + [u (Se )/ Se]2 (a )
(a1)
(A.2)
(a2)
[u (vp )/vp]2 = (1/2)2 [u ( PCd)/ PCd]2 + ( 1/2) 2 [u ( )/ ]2 (b1)
(b )
(A.3)
(b2)
where vc is obtained in terms of Q v and Se , and vp is obtained in terms of Next, Ct can be expressed as follows:
PCd and
[u (Ct )/ Ct ]2 = [u (Q v )/ Q v ]2 + [u (Se)/Se]2 + (1/2)2 [u ( PCd )/ PCd]2 + ( 1/2)2 [u ( )/ ]2 (a1)
(a2)
(b1)
(b2)
during the total pressure tube calibration.
(A.4)
where u (Q v )/ Q v is estimated by assuming that the standard uncertainty at each volume flowrate is 0.14% of the total volume flowrate using the data of the medium gas flowrate standard at the NMIJ. Moreover, the volume flowrate is varied as 400 m3/h, 600 m3/h, 800 m3/h, and 1000 m3/h. In order to estimate the uncertainty derived from the entrainment effect, the entrained volume flowrate of a round free jet 1 mm downstream from the conversion nozzle outlet is assumed to be 0.173% of the total volume flowrate [18]. Reproducibility is evaluated based on the variation of standard volume flowrates observed during the measurement of eight non-dimensional air speed profiles. As a result, at all of the volume flowrate set points, the uncertainty of the reference volume flowrate is estimated as:
u (Q v )/ Q v = 0.223 × 10
(A.5)
2
The sources of u (Se)/ Se include the experimental standard deviation of non-dimensional air speed profiles, the reproducibility of measurements, and the position error of the measurement line. The experimental standard deviation includes the fluctuation at an output voltage of 0 V, the linearity of the hot-wire anemometer, and the variation of positioning derived from the traverse device, in addition to the experimental standard deviation at each measurement point. The experimental standard deviation at each measurement point, the fluctuation at an output voltage of 0 V, and the traverse device are taken into account in the non-dimensional air speed profile. The linearity of the hot-wire anemometer is taken into account only at the outer edge of the jet. The uncertainty derived from the position error of the measurement line is estimated using the difference between the center of the non-dimensional air speed profile and the center of the conversion nozzle exit at each volume flowrate. Because of two reasons, the uncertainty due to flow stream direction was estimated negligible small. First, it is expected that there was no secondary flow at the measuring point, because the flow from the conversion nozzle exit are stable and uniform due to axisymmetric configuration of each nozzles. It means that the flow direction is coincident with the nozzle axis. Second, the angular difference between the tubes installed on the traverse and the flow direction is small. Besides, the angular difference between the tubes installed on the traverse and the nozzle center axis is small by visual confirmation. The uncertainties of the traverse device take into account the uncertainty derived from the positioning procedure and the uncertainty derived from the dial gauge used to evaluate the accuracy of the probe measurement. By combining the above uncertainties, u (Se)/ Se at a volume flowrate of 400 m3/h is the largest:
u (Se)/ Se = 0.220 × 10
(A.6)
2
The sources of u (vp)/ vp are u ( PCd)/ PCd and u ( )/ during measurement and the reproducibility of the measurements. Here, u ( PCd)/ PCd is calculated by combining the experimental standard deviation in the measurements of total and static pressures and the uncertainty of the differential pressure gauge used in the measurement. Moreover, u ( )/ during measurement is estimated to be 0.034% based on the data of the medium gas flowrate standard at the NMIJ. The uncertainty derived from the reproducibility is calculated based on the variation of the measured air speed. By combining the above uncertainties, u (vp)/ vp at the volume flowrate of 400 m3/h is the largest:
u (vp)/ vp = 3.3 × 10
(A.7)
4
In the following analyses, u (Ct ), which is dependent on the air speed, is calculated at the air speed in each measurement [19]. The recalculated uncertainty at 40 m/s of u (Se)/ Se is 0.218% and u (vp)/ vp is 0.032%. These values are shown in Table A1. A3. Uncertainty derived from CWT The uncertainty u (CWT ) can be expressed as:
[u (CWT)/ CWT]2 = [u (Ct )/Ct ]2 + ( 1/2)2 [u ( PWT1)/ PWT1]2 + (1/2) 2 [u ( PNd )/ PNd]2 (c )
(d )
(A.8)
The air speed was varied as 40 m/s, 50 m/s, 60 m/s, 70 m/s, 80 m/s, and 90 m/s. The sources of u (CWT ) are u (Ct ) , u ( PWT1) (term c in Eq. (A.1)) and u ( PNd ) (term d in Eq. (A.1)). Then, u ( PWT1)/ PWT1 is obtained by combining the experimental standard deviation in the measurement and the standard uncertainty of the differential pressure gauge. By combining the above uncertainties, u ( PWT1)/ PWT1 at an air speed of 40 m/s is the largest:
u ( PWT1)/ PWT1 = 3.7 × 10
(A.9)
4
Moreover, u ( PNd )/ PNd is obtained by combining the experimental standard deviation in the measurement and the standard uncertainty of the differential pressure gauge. By combining the above uncertainties, u ( PNd )/ PNd at an air speed of 40 m/s is the largest:
138
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
(A.10)
4
u ( PNd )/ PNd = 5.0 × 10
Then, u (CWT ) can be calculated by adding the uncertainty derived from u (Ct ) to the sources of uncertainty expressed by Eqs. (A.9) and (A.10). A4. Uncertainty derived from Cpit The uncertainty u (Cpit ) is expressed as follows:
[u (Cpit )/Cpit]2 = [u (CWT )/ CWT]2 + (1/2)2 [u ( PWT2)/ PWT2]2 + ( 1/2)2 [u ( Ppit )/ Ppit ]2 (e )
(A.11)
(f )
The air speed was varied as 40 m/s, 50 m/s, 60 m/s, 70 m/s, 80 m/s, and 90 m/s. The sources of u (Cpit ) are u (CWT ) , u ( PWT2) (term e in Eq. (A.1)), and u ( Ppit ) (term f in Eq. (A.1)). Moreover, u ( PWT2 )/ PWT2 is obtained by combining the experimental standard deviation in the measurement and the standard uncertainty of the differential pressure gauge. By combining the above uncertainties, u ( PWT2 )/ PWT2 at an air speed of 40 m/s is the largest:
u ( PWT2)/ PWT2 = 3.6 × 10
(A.12)
4
Moreover, u ( Ppit )/ Ppit is obtained by combining the experimental standard deviation in the measurement and the standard uncertainty of the differential pressure gauge. By combining the above uncertainties, u ( Ppit )/ Ppit at an air speed of 40 m/s is the largest:
u ( Ppit )/ Ppit = 3.9 × 10
(A.13)
4
Then, u (Cpit ) can be calculated by adding the uncertainty derived from u (CWT ) to the sources of uncertainty expressed by Eqs. (A.12) and (A.13). A5. Relative combined standard uncertainty derived from the calibration equipment in the calculation of Cpit When each standard uncertainty is substituted into Eq. (A.1), the combined standard uncertainty at an air speed of 40 m/s is the largest:
uc (Cpit )/Cpit = 0.316 × 10
(A.14)
2
When the coverage factor is 2 (k = 2),
U (Cpit )/Cpit = k × uc (Cpit )/ Cpit
= 2 × 0.316 × 10
2
0.63 × 10
(A.15)
2
Table A1 shows the uncertainty budget for Cpit . A6. Uncertainty of uc (CDUT) In order to obtain uc (CDUT) , measurements were taken repeatedly, and their arithmetic mean was calculated. The uncertainty of the measurement result, which is the mean of multiple measurements, is attributed to random effects. In accordance with Eq. (4) in GUM 4.2.2 and Eq. (5) in GUM 4.2.3 [17], uc (CDUT) is estimated as follows:
Cpit =
1 n
ni
Cpit i
(A.16)
i=1
s 2 (Cpit i ) =
ni i=1
Cpit )2
(Cpit i ni
1
u (Cpit )/ Cpit =
s 2 (Cpit i )/ Cpit 2 ni
=
3.696 × 10 8/0.994 = 2.726 × 10 5
5
= 0.003 %
(A.17)
In this calibration, the measurement is repeated five times. The experimental standard deviation of CDUT is approximately 0.006%. After incorporating the relative combined standard uncertainty of the wind tunnel, uc (CDUT) is expressed as:
uc (CDUT)/ CDUT =
[u (Cpit )/Cpit]2 + [u (Cpit )/Cpit ]2 =
(0.316 × 10 2)2 + (0.003 × 10 2)2 = 0.316 %
(A.18)
Table A.1
Uncertainty of the measurement of Cpit Source of uncertainty
Relative standard uncertainty
Sensitivity coefficient
Effective degree of freedom
Reference volume flowrate Effective cross-sectional area Air speed indicated by the total pressure tube Dynamic pressure of the total and static pressure tubes Differential pressure between the nozzle inlet and outlet ports Differential pressure between the nozzle inlet and outlet ports Dynamic pressure measured by the DUT
0.223% 0.218% 0.032% 0.050% 0.037% 0.036% 0.039%
1 1 1 0.5 −0.5 0.5 −0.5
∞
Relative combined standard uncertainty
0.316%
139
18 18
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Essentially, in this calibration, a coverage factor of k = 2 is used for the relative expanded uncertainty. In the case of the normal distribution, the confidence interval for which the level of confidence of approximately 95% is estimated as follows:
U (CDUT)/ CDUT = k [uc (CDUT)/ CDUT] = 2[u c (CDUT)/ CDUT] = 0.632 %
0.63 %
(A.19)
845–847. [10] T.T. Yeh, J.M. Hall, Airspeed Calibration Service vols. 250–79, NIST Special Publication, 2007, pp. 1–26. [11] I.I. Shinder, C.J. Crowley, B.J. Filla, M.R. Moldover, Improvement to NIST's Air Speed Calibration Service, FLOMEKO, 2013. [12] Reconstruction of PTB Wind Tunnel with 320 mm Nozzle Completed, PTB news, 2011, pp. 1–2. [13] M. Ishibashi, T. Morioka, The renewed airflow standard system in Japan for 5-1000 m3/h, Flow Meas. Instrum. 17 (Issue 3) (2006) 153–161. [14] H. Rouse, M.M. Hassan, Cavitation-free inlets and contractions, Mech. Eng. 71 (1949) 213–216. [15] S. Wada, N. Furuichi, Influence of obstacle plates on flowrate measurement uncertainty based on ultrasonic Doppler velocity profile method, Flow Meas. Instrum. 48 (2016) 81–89. [16] Japanese Industrial Standard, Conformity assessment-General requirements for proficiency testing, JIS Q (2011) 17043 (in Japanese). [17] ISO, Guide to the Expression of Uncertainty in Measurement, (2008) ISO Guide 98-3. [18] L. Boguslawski, Cz O. Popiel, Flow structure of the free round turbulent jet in the initial region, J. Fluid Mech. 90 (1979) 531–539 part 3. [19] Japanese Industrial Standard, Procedures for calibration and testing for liquid flowmeter, JIS B (2011) 7552 (in Japanese).
References [1] Y. Terao, M. Takamoto, Low velocity standard for air flow using a towing carriage, Trans. Soc. Instrum. Control Eng. 26 (1) (1990) 1–8 (in Japanese). [2] Y. Terao, M. Takamoto, G.E. Mattingly, Preliminary intercomparison of anemometer calibration systems at very low speeds between the national standard laboratories in Japan and the USA, JSME Int. J. Series B 40 (No.3) (1997) 509–515. [3] Y. Terao, Study on measurement standard of very low air speed, Bull. NRLM 47 (196) (1998) 217–256 (in Japanese). [4] H. Müller, et al., CIPM Key Comparison of Air Speed, 0.5 m/s to 40 m/s (CCM-FFK3.2011), Metrologia vol. 54, (2017) Technical Supplement 07013. [5] N. Kurihara, Y. Terao, S. Nakao, M. Takamoto, An uncertainty of laser Doppler velocimeter calibration for air speed standard, Transactions of the Japan Society of Mechanical Engineers, Series B 71 (No.708) (2005) 2100–2107 (in Japanese). [6] Y. Terao, M. van der Beek, T.T. Yeh, H. Müller, Final report on the CIPM air speed key comparison (CCM.FF-K3), Metrologia 44 (2007) Technical Supplement 07009. [7] Bureau International des Poids et Mesures (BIPM), Key comparison database, Appendix C, CMCs (online), available from < http://kcdb.bipm.org/AppendixC/ country_list.asp?Iservice=M/FF.9.7.1 > , (accessed on 24 Jan, 2018). [8] Y. Terao, et al., Final report on the APMP air speed key comparison (APMP.M.FFK3), Metrologia 47 (2010) Technical Supplement 07012. [9] K.V. Popov, et al., State Standards, Measurement Techniques 57 (No.8) (2014)
140
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
New air speed calibration system at NMIJ for air speeds up to 90 m/s a,∗
a
a
a
Aya Iwai , Tatsuya Funaki , Noboru Kurihara , Yoshiya Terao , Yong Moon Choi
b
T
a
National Institute of Advanced Industrial Science and Technology (AIST), National Metrology Institute of Japan (NMIJ), Tsukuba Central 3, Umezono 1-1-1, Tsukuba, 305-8563, Japan Korea Research Institute of Standards and Science (KRISS), Division of Physical Metrology, 209 Gajeong-ro, Yuseong-gu, Daejeon, 305-340, Republic of Korea
b
ARTICLE INFO
ABSTRACT
Keywords: Air speed standard Wind tunnel Calibration Pitot static tube Hot-wire anemometer Volume flowrate
National Metrology Institute of Japan (NMIJ) has established a high air speed standard facility and has been providing a calibration service since 2015. The facility has an air speed range of 40 m/s to 90 m/s with a relative expanded uncertainty (k = 2) of 0.63%. The purpose of this primary standard is mainly to contribute to the improvement of meteorological observation research and to the evaluation of flow field inside a turbo machine and around a high speed vehicle. The reference air speed is derived from the national primary gas flowrate standard of Japan. A conversion device from flowrate to air speed is installed in the test line of the closed-loop calibration facility. The reference air speed at the nozzle exit of the conversion device is obtained by comparing the integral of the air speed profiles and the reference volume flowrate. The total pressure tube used as a transfer standard is then calibrated against the reference air speed at the center of the nozzle exit. The Eiffel-type wind tunnel, which is a working standard for the daily calibration service, is calibrated using this total pressure tube. The present paper describes the calibration system, the traceability chain, and an uncertainty analysis using a validation method.
1. Introduction NMIJ has been operating two air speed standard systems for several decades. One provides a low air speed standard, which covers the air speed range from 0.05 m/s to 1.5 m/s using a tow carriage [1–4]. The other system provides a medium air speed standard, which covers the air speed range from 1.3 m/s to 40 m/s using a rotating disk and an LDV [4,5]. In order to improve the meteorological observation and research and to meet the needs of industrial fields, NMIJ started a new calibration service for Pitot static tubes in 2015. The air speed range of the high air speed standard is from 40 m/s to 90 m/s. The reference air speed is determined by comparing the integral of the non-dimensional air speed profile with the reference volume flowrate. Van Swinden Laboratory (VSL), which is the National Metrology Institute of the Netherlands, also uses this procedure to establish an air speed standard [6]. At present, three NMIs offer air speed standards over 40 m/s using a rotating disk and an LDV as primary standard [7]. In Russia, D.I. Mendeleev Institute for Metrology (VNIIM) operates a calibration service for air speeds of up to 100 m/s [8,9]. In the United States, National Institute of Standards and Technology (NIST) offers a calibration service for air speeds of up to 75 m/s [10,11]. Finally, in Germany, Physikalisch-Technische Bundesanstalt (PTB) offers a calibration service for air speeds of up to 65 m/s [12]. ∗
An overview of the procedure for realizing the air speed standard is shown in Fig. 1 as a traceability chain. The procedure involves three processes. The first process is the evaluation of a reference air speed at the nozzle exit of the conversion device from a reference volume flowrate. The second process is the calibration of a total pressure tube against the reference air speed. The above two processes were performed at the closed-loop calibration facility at NMIJ [13]. The third process is the calibration of the high air speed calibration wind tunnel by using the total pressure tube. The calibration service of the devices under test (DUTs), i.e., Pitot static tubes from customers are conducted in the wind tunnel. The present paper describes in the detail the realization process and the validation of the calibration results and their uncertainty for the high air speed standard. 2. Calibration of total pressure tube 2.1. Determination of reference air speed The closed-loop calibration facility [13] is used in the first and second processes to determine the reference air speed. A schematic diagram of the facility is shown in Fig. 2. The facility is composed of a nozzle chamber, a blower, a
Corresponding author. E-mail address: [email protected] (A. Iwai).
https://doi.org/10.1016/j.flowmeasinst.2019.02.004 Received 29 March 2018; Received in revised form 26 December 2018; Accepted 17 February 2019 Available online 26 February 2019 0955-5986/ © 2019 Elsevier Ltd. All rights reserved.
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Nomenclature
CDUT
Cpit cpit Cpit i
Ct CWT
ni Qv
r re
R Se s 2 (Cpit i )
DUT Air speed at measurement point r (m/s) Non-dimensional air speed at measurement point r (m/s) Reference air speed at the center of the conversion nozzle exit (m/s) Air speed measured by the total pressure tube (m/s) Reference air speed of the high air speed calibration wind tunnel (m/s) Dynamic pressure calculated by subtracting the static pressure from the measured total pressure during total pressure tube calibration (Pa) Dynamic pressure calculated by subtracting the static pressure from the measured total pressure during calibration of the high air speed calibration wind tunnel (Pa) Dynamic pressure measured by the DUT (Pa) Differential pressure between the nozzle inlet and outlet during calibration of the high air speed calibration wind tunnel (Pa) Differential pressure between the nozzle inlet and outlet during DUT calibration (Pa) Angular position of the measurement lines along the radii at the conversion nozzle exit (º) Fluid density at the test line of the closed-loop calibration facility (kg/m3)
v (r ) v (r ) vc
Corrective coefficient of a Pitot static tube as the DUT, which was measured repeatedly and calculated as the arithmetic mean (−) Corrective coefficient of a Pitot static tube as the DUT from single measurement (−) Mean measured corrective coefficient of the DUT Corrective coefficient of the DUT obtained for the ith measurement Corrective coefficient of the total pressure tube (−) Corrective coefficient of the high air speed calibration wind tunnel (−) Number of repeated measurements Reference volume flowrate at the test line of the closedloop calibration facility (m3/h) Measurement point in the cross-sectional area of the conversion nozzle exit (m) Measurement point at the edge of the jet of the conversion nozzle exit (m) Radius of the conversion nozzle exit (m) Effective cross-sectional area at the conversion nozzle exit (m2) Experimental variance of the corrective coefficient of the
vp v WT PCd
PNd
Ppit PWT1
PWT2
temperature controller, and test lines. The nozzle chamber contains 12 critical flow Venturi nozzles calibrated by the medium gas flowrate standard of the NMIJ. Through various combinations of the nozzles, a volume flowrate of up to 1000 m3/h with dry air and up to 500 kPa can be produced in the test lines with a relative expanded uncertainty (k = 2) of 0.28%. In order to determine the reference air speed, a conversion device was placed in the upstream side of an open area made in the nominal 100 mm-diameter test line. The conversion device was composed of a diffuser, a settling chamber, a conversion nozzle, and a traverse device, as shown in Fig. 3. The diffuser translates the diameter of the test line from 100 mm to 200 mm. The settling chamber was composed of three screens and a honeycomb structure. The diameter of the conversion nozzle exit is 60 mm, and the nozzle ratio is 1:11.11. The shape of the contraction nozzle is indicated by a third-
order polynomial curve [14]. Since the turbulence intensity at the center of the jet was approximately 0.3% during the measurement, steady and uniform flow was produced at the nozzle exit. A pressure port was placed on the inner wall surface 20 mm upstream from the nozzle exit. The wall static pressure at the pressure port was used as the base pressure of the total and static pressure measurement. The traverse device for the measurement of the air speed profiles and the calibration of the total pressure tube has radius and rotation direction degrees of freedom. The temperature in the test room was maintained at 24.5 ± 1 °C by controlled air conditioning and the temperature in the jet at the conversion nozzle exit was maintained at 24.5 ± 0.3 °C by a temperature controller installed at the facility. The reference air speed at the center of the jet from the conversion nozzle exit, vc , is determined based on the reference volume flowrate and the non-dimensional air speed profiles, which are measured along the radii at the conversion nozzle exit. Fig. 4 shows an overview of the procedure. This method for calculation from velocity to flowrate is called tangential method [15]. The non-dimensional air speed profiles were defined as follows: (1)
v (r ) = v (r )/ vc
Assuming both Q v and v (r ) are known, the volume flowrate can be expressed in terms of the integral of the non-dimensional air speed profile from the flowrate definition, as follows: re
Qv = 2
v (r ) r dr
(2)
0
Next, Se is defined as the area integration of v (r ) from the center to the edge of the jet, as follows: re
Se =
v (r ) dA = 2
v (r ) r dr 0
(3)
Therefore, vc is given as:
vc = Q v /Se Fig. 1. Traceability chain of the high air speed standard.
The uncertainty of Q v and Se are described in Appendix A2. 133
(4)
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Fig. 2. Closed-loop calibration facility with a conversion device at the test line.
measured 1 mm downstream of the nozzle exit. The sampling rate of the output voltage was 1 kHz. The measured voltages were averaged at 1 s intervals and were recorded on a personal computer. At each volume flowrate, the profiles were measured along eight radii at 45° intervals from 0° to 315°. Each radius had 30 measurement points at intervals of 5 mm in the potential core area of the jet and intervals of 0.05 mm at the edge of the jet. The profiles were normalized by the output voltage of the center of the jet. The normalized output voltage profiles are identical to the non-dimensional air speed profiles. Fig. 6 shows the non-dimensional air speed profiles at 400 m3/h and, Fig. 7 shows the same profiles expanded near the edge of the jet. All of the profiles agree very well, and this trend is the same at the other volume flowrates, which indicates that the jet is axisymmetric. Fig. 8 shows non-dimensional average air speed profiles near the edge for various volume flowrates. The difference in the profiles at each volume flowrate is noticeable near the edge of the jet. The larger the volume flowrate, the thinner the shear layer. Finally, vc was calculated based on these profiles. To evaluate the assumption for calibration of the hot-wire anemometer, a recursive calculation of the air speed profile v (r ) at 1000 m3/ h was conducted. Correction factors for v (r ) were calculated at the four setting volume flowrates as ratio of each effective cross-sectional area Se to the value at 1000 m3/h. The obtained correction factor is shown in Fig. 9. Then the air speed profile v (r ) at 1000 m3/h was corrected by multiplying each correction factor. As the result of the recursive calculation of v (r ) at 1000 m3/h on the first try, the air speed at the center vc was changed only 0.01%. Thus it is considered to be appropriate to assume the air speed at the center of the nozzle exit was proportional to the reference flowrate.
Fig. 3. Conversion device installed at the test line of the closed-loop calibration facility.
Fig. 4. Overview of the procedure for determining air speed.
2.2. Measurement of the air speed profiles using a hot-wire anemometer A hot-wire anemometer is generally calibrated against a reference air speed before each measurement in order to obtain linearity between the output voltage and the actual air speed. In the present study, the hot-wire anemometer was calibrated using the air speed calculated from the reference flowrate based on an assumption that the air speed at the center of the nozzle exit was proportional to the reference flowrate. The uncertainty due to the linearity of the output voltage was evaluated based on the standard deviation of the output voltage around the fitting line. An I-type 55P11 probe (Dantec Dynamics A/S) of the hot-wire anemometer was placed at the traverse device and was aligned in the flow direction. The axis of the wire was aligned in the tangential direction of the conversion nozzle exit in order to improve the spatial resolution. Fig. 5 shows an overview of the measurement procedure. The volume flowrates were set to be 400 m3/h, 600 m3/h, 800 m3/ h, and 1000 m3/h. Therefore, the air speeds at the center of the jet at the conversion nozzle exit corresponding to the volume flowrates were approximately 40 m/s, 60 m/s, 80 m/s, and 100 m/s, respectively. Next, the output voltage profiles along the radii of the jet were
Fig. 5. Overview of the air speed profile measurement procedure by hot-wire anemometer. 134
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Fig. 6. Non-dimensional air speed profiles at 400 m3/h.
Fig. 9. Correction factors for correction of v (r ) at 1000 m3/h.
each volume flowrate, the differential pressure between the total pressure and the base pressure at the pressure port in Fig. 3 was measured. The static pressure was also measured with the static pressure tube shown in Fig. 10 by replacing the total pressure tube. Because the static pressure holes were set in the same location of the total pressure hole, the error of the static pressure is negligible small. In the present study, vp was calculated in terms of PCd and using Bernoulli's theory. Here, PCd was calculated by subtracting the static pressure from the total pressure. Moreover, Ct was calculated as follows:
Ct = vc/ vp
(5)
The results for Ct are shown in Fig. 11, in which the error bars indicate the standard uncertainties calculated in Appendix A2. Based on these results, Ct is approximately constant. In the next section, the values of Ct between the measured points were determined by linear interpolation.
Fig. 7. Non-dimensional air speed profiles near the edge of the jet at 400 m3/h.
3. Calibration of high air speed calibration wind tunnel The high air speed calibration wind tunnel is an Eiffel-type wind tunnel composed of a blower, a diffuser, a settling chamber, and a contraction nozzle, as shown in Fig. 12. The length of the diffuser is 2703 mm, and it transforms the cross-sectional area from a square to a circle and increases the cross-sectional area. The settling chamber, which has a diameter of 400 mm, contains three screens and a honeycomb structure. The contraction nozzle diameter is 100 mm, and the nozzle ratio is 1:16. At the inlet and outlet of the contraction nozzle, four pressure ports are located equiangularly. The pressure at the outlet ports was used as the base pressure for the total and static pressure measurements. The temperature of the test room air, which serves as working fluid, was 18 ± 3 °C during measurement. The temperature of the jet when the air speed was set at 90 m/s was approximately 25 °C
Fig. 8. Non-dimensional average air speed profiles at various volume flowrates.
2.3. Calibration of the total pressure tube The total pressure tube was calibrated against the reference air speed obtained in the previous section. A schematic diagram of the total pressure tube is shown in Fig. 10. The external diameters of the supporting part and the nose part are 3 mm and 1 mm, respectively. The total pressure tube provides better spatial resolution and smaller blockage effect due to its smaller diameter than a Pitot tube. The total pressure tube was placed at the traverse device and was aligned in the flow direction. The total pressure hole was located at the center of the jet 1 mm downstream of the conversion nozzle exit. At
Fig. 10. Schematic diagrams of the total and static pressure tubes. Top: Overall view. Lower left: Tip of the total pressure tube. Lower right: Tip of the static pressure tube. 135
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Fig. 11. Corrective coefficients of the total pressure tube. Error bars indicate standard uncertainties.
Fig. 14. Example of the calibration results.
Fig. 12. Schematic diagram of the high air speed calibration wind tunnel. A detailed diagram of the nozzle is shown in the dashed-line square.
Fig. 15. Example of the results of internal comparison to the medium air speed standard (MASS) at 40 m/s. The error bars indicate expanded uncertainties (k = 2). The specifications of the tubes are shown in Table 1.
CWT = Ct
PNd/ PWT1
(6)
Since PNd and PWT1 were measured simultaneously, was assumed to be equal. Therefore, the fluid density term was reduced from Eq. (6). The value of CWT calculated by Eq. (6) is shown in Fig. 13. The error bars in Fig. 13 represent the standard uncertainty calculated in Appendix A3, and the figure indicates that CWT is approximately constant in the measured range.
Fig. 13. Corrective coefficients of the high air speed calibration wind tunnel. Error bars indicate standard uncertainties.
4. Calibration of Pitot static tube
due to the heat generated by the blower. The total pressure tube calibrated in Section 2 was placed at the traverse device and was aligned in the flow direction. The total pressure hole was located at the center of the nozzle exit. The air speed at the contraction nozzle exit was varied as 40 m/s, 50 m/s, 60 m/s, 70 m/s, 80 m/s, and 90 m/s. At each air speed, the differential pressure between the total pressure and the base pressure was measured. During the measurement of the total pressure, PWT1 was measured at the same time. The static pressure at the same location at which the total pressure was measured was measured using the same procedure with the static pressure tube used in Section 2. In the same manner as in Section 2, PNd was calculated based on the total and static pressures. Using Bernoulli's theory, CWT was calculated as follows:
The Pitot static tube being calibrated, i.e., the DUT, was placed at the Pitot tube holder and was aligned in the flow direction at the nozzle exit. The air speed at the contraction nozzle exit was varied as 40 m/s, 50 m/s, 60 m/s, 70 m/s, 80 m/s, and 90 m/s. Both Ppit and PWT2 were measured at each air speed. Next, Cpit was calculated as follows using Bernoulli's theory:
Cpit = CWT
PWT2/ Ppit
(7)
where was reduced from Eq. (7) as the same reason of Eq. (6). Moreover, Cpit includes the compressibility effect in this paper. An example of the calibration results for eight Pitot static tubes is shown in Fig. 14 and Table 1 including their specification. The error bar in Fig. 14 indicates the expanded uncertainty calculated in Appendix 136
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Table 1 Specifications of the Pitot static tubes. The length of the each tube is normalized by the tube's diameter. Name
Type
Diameter of the tube (mm)
Length of the head (d)
Length from the total pressure hole to the static pressure hole (d)
Length from the static pressure hole to the stem (d)
AMCA-1 AMCA-2 AMCA-3 JIS NPL-1 NPL-2 NPL-3 NPL-4
AMCA AMCA AMCA JIS NPL NPL NPL NPL
2.4 4.7 6.4 4.0 2.3 3.0 6.0 8.0
14.0 17.7 17.0 – 16.4 16.4 16.4 15.6
4.0 6.6 6.3 6.0 7.8 8.0 8.0 7.6
10.0 11.1 10.7 – 8.6 8.5 8.4 7.9
A4. The values of Cpit are approximately unity and increase slightly with air speed.
Comment
Stemless type With Gloss
the medium air speed standard were used. The difference between the medium and high air speed standards is very small compared to the relative expanded uncertainty. Moreover, the En values were 0.59 at maximum. Therefore, the validity of the high air speed standard was confirmed at 40 m/s.
5. Internal comparison The calibration results for the DUTs obtained the proposed procedure were validated experimentally. The eight DUTs described in Section 4 were calibrated at 40 m/s at the medium air speed standard facility of the NMIJ. The relative expanded uncertainty (k = 2) of the medium air speed standard is 0.35% at 40 m/s, and the validity of the medium air speed standard was confirmed by international comparisons with overseas NMIs [4,6,8]. The internal comparison results for the eight DUTs and the En values are shown in Fig. 15 [16]. The En values were calculated based on the comparison results and the expanded uncertainties and indicate the validity of the standard. When ∣En∣ ≦ 1, the comparison results confirmed that the standard was valid. In the present study, the results of
6. Conclusion NMIJ has established a new primary standard of high air speed, for which the air speed ranges from 40 m/s to 90 m/s with a relative expanded uncertainty (k = 2) of 0.63%. Based on internal comparisons with the medium air speed standard at the NMIJ, the validity of the high air speed standard was confirmed. However, the validation results as the air speed exceeds 50 m/s have not yet been evaluated. International comparison for high air speeds will be necessary in the near future. The evaluation of compressibility in the corrective coefficient of the Pitot pressure tube is a subject for future investigation.
Appendix. Uncertainty analysis The uncertainties of the measurement are estimated in accordance with the “Guide to the expression of uncertainty in measurement (GUM)” [17]. A1. Uncertainty analysis for the high air speed standard The corrective coefficient of a Pitot static tube without repeatability Cpit is calculated as follows: (5)
Ct = vc/ vp CWT = Ct Cpit = CWT
(6)
PNd/ PWT1 PWT2/ Ppit
(7)
The sources of uncertainty of the calibration result given as Cpit , which is calculated using Eqs. (5)–(7), correspond to all the parameters contained on the right side of the three equations. Therefore, the relative standard uncertainties of these parameters are first calculated, and uc (Cpit )/Cpit is then estimated using the law of propagation of uncertainty, as follows:
[uc (Cpit )/ Cpit ]2 = [u (vc)/ vc]2 + [ u (vp )/vp]2 (a)
(b)
+ ( 1/2)2 [u ( PWT1)/ PWT1]2 (c )
+ (1/2)2 [u ( PNd)/ PNd]2 (d )
+ (1/2)2 [u ( PWT2)/ PWT2]2 (e )
+ ( 1/2)2 [u ( Ppit )/ Ppit ]2 (A.1)
(f )
The correlation among the sources of the uncertainty is considered to be sufficiently small, as compared to the major sources of the uncertainty, and can thus be ignored.
137
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
A2. Uncertainty derived from Ct The reference air speed is obtained from the volume flowrate produced by the closed-loop calibration facility and the effective cross-sectional area obtained by integrating the air speed profile. The first term of Eq. (5) can therefore be broken down as follows:
[u (vc )/ vc]2 = [u (Q v )/ Q v ]2 + [u (Se )/ Se]2 (a )
(a1)
(A.2)
(a2)
[u (vp )/vp]2 = (1/2)2 [u ( PCd)/ PCd]2 + ( 1/2) 2 [u ( )/ ]2 (b1)
(b )
(A.3)
(b2)
where vc is obtained in terms of Q v and Se , and vp is obtained in terms of Next, Ct can be expressed as follows:
PCd and
[u (Ct )/ Ct ]2 = [u (Q v )/ Q v ]2 + [u (Se)/Se]2 + (1/2)2 [u ( PCd )/ PCd]2 + ( 1/2)2 [u ( )/ ]2 (a1)
(a2)
(b1)
(b2)
during the total pressure tube calibration.
(A.4)
where u (Q v )/ Q v is estimated by assuming that the standard uncertainty at each volume flowrate is 0.14% of the total volume flowrate using the data of the medium gas flowrate standard at the NMIJ. Moreover, the volume flowrate is varied as 400 m3/h, 600 m3/h, 800 m3/h, and 1000 m3/h. In order to estimate the uncertainty derived from the entrainment effect, the entrained volume flowrate of a round free jet 1 mm downstream from the conversion nozzle outlet is assumed to be 0.173% of the total volume flowrate [18]. Reproducibility is evaluated based on the variation of standard volume flowrates observed during the measurement of eight non-dimensional air speed profiles. As a result, at all of the volume flowrate set points, the uncertainty of the reference volume flowrate is estimated as:
u (Q v )/ Q v = 0.223 × 10
(A.5)
2
The sources of u (Se)/ Se include the experimental standard deviation of non-dimensional air speed profiles, the reproducibility of measurements, and the position error of the measurement line. The experimental standard deviation includes the fluctuation at an output voltage of 0 V, the linearity of the hot-wire anemometer, and the variation of positioning derived from the traverse device, in addition to the experimental standard deviation at each measurement point. The experimental standard deviation at each measurement point, the fluctuation at an output voltage of 0 V, and the traverse device are taken into account in the non-dimensional air speed profile. The linearity of the hot-wire anemometer is taken into account only at the outer edge of the jet. The uncertainty derived from the position error of the measurement line is estimated using the difference between the center of the non-dimensional air speed profile and the center of the conversion nozzle exit at each volume flowrate. Because of two reasons, the uncertainty due to flow stream direction was estimated negligible small. First, it is expected that there was no secondary flow at the measuring point, because the flow from the conversion nozzle exit are stable and uniform due to axisymmetric configuration of each nozzles. It means that the flow direction is coincident with the nozzle axis. Second, the angular difference between the tubes installed on the traverse and the flow direction is small. Besides, the angular difference between the tubes installed on the traverse and the nozzle center axis is small by visual confirmation. The uncertainties of the traverse device take into account the uncertainty derived from the positioning procedure and the uncertainty derived from the dial gauge used to evaluate the accuracy of the probe measurement. By combining the above uncertainties, u (Se)/ Se at a volume flowrate of 400 m3/h is the largest:
u (Se)/ Se = 0.220 × 10
(A.6)
2
The sources of u (vp)/ vp are u ( PCd)/ PCd and u ( )/ during measurement and the reproducibility of the measurements. Here, u ( PCd)/ PCd is calculated by combining the experimental standard deviation in the measurements of total and static pressures and the uncertainty of the differential pressure gauge used in the measurement. Moreover, u ( )/ during measurement is estimated to be 0.034% based on the data of the medium gas flowrate standard at the NMIJ. The uncertainty derived from the reproducibility is calculated based on the variation of the measured air speed. By combining the above uncertainties, u (vp)/ vp at the volume flowrate of 400 m3/h is the largest:
u (vp)/ vp = 3.3 × 10
(A.7)
4
In the following analyses, u (Ct ), which is dependent on the air speed, is calculated at the air speed in each measurement [19]. The recalculated uncertainty at 40 m/s of u (Se)/ Se is 0.218% and u (vp)/ vp is 0.032%. These values are shown in Table A1. A3. Uncertainty derived from CWT The uncertainty u (CWT ) can be expressed as:
[u (CWT)/ CWT]2 = [u (Ct )/Ct ]2 + ( 1/2)2 [u ( PWT1)/ PWT1]2 + (1/2) 2 [u ( PNd )/ PNd]2 (c )
(d )
(A.8)
The air speed was varied as 40 m/s, 50 m/s, 60 m/s, 70 m/s, 80 m/s, and 90 m/s. The sources of u (CWT ) are u (Ct ) , u ( PWT1) (term c in Eq. (A.1)) and u ( PNd ) (term d in Eq. (A.1)). Then, u ( PWT1)/ PWT1 is obtained by combining the experimental standard deviation in the measurement and the standard uncertainty of the differential pressure gauge. By combining the above uncertainties, u ( PWT1)/ PWT1 at an air speed of 40 m/s is the largest:
u ( PWT1)/ PWT1 = 3.7 × 10
(A.9)
4
Moreover, u ( PNd )/ PNd is obtained by combining the experimental standard deviation in the measurement and the standard uncertainty of the differential pressure gauge. By combining the above uncertainties, u ( PNd )/ PNd at an air speed of 40 m/s is the largest:
138
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
(A.10)
4
u ( PNd )/ PNd = 5.0 × 10
Then, u (CWT ) can be calculated by adding the uncertainty derived from u (Ct ) to the sources of uncertainty expressed by Eqs. (A.9) and (A.10). A4. Uncertainty derived from Cpit The uncertainty u (Cpit ) is expressed as follows:
[u (Cpit )/Cpit]2 = [u (CWT )/ CWT]2 + (1/2)2 [u ( PWT2)/ PWT2]2 + ( 1/2)2 [u ( Ppit )/ Ppit ]2 (e )
(A.11)
(f )
The air speed was varied as 40 m/s, 50 m/s, 60 m/s, 70 m/s, 80 m/s, and 90 m/s. The sources of u (Cpit ) are u (CWT ) , u ( PWT2) (term e in Eq. (A.1)), and u ( Ppit ) (term f in Eq. (A.1)). Moreover, u ( PWT2 )/ PWT2 is obtained by combining the experimental standard deviation in the measurement and the standard uncertainty of the differential pressure gauge. By combining the above uncertainties, u ( PWT2 )/ PWT2 at an air speed of 40 m/s is the largest:
u ( PWT2)/ PWT2 = 3.6 × 10
(A.12)
4
Moreover, u ( Ppit )/ Ppit is obtained by combining the experimental standard deviation in the measurement and the standard uncertainty of the differential pressure gauge. By combining the above uncertainties, u ( Ppit )/ Ppit at an air speed of 40 m/s is the largest:
u ( Ppit )/ Ppit = 3.9 × 10
(A.13)
4
Then, u (Cpit ) can be calculated by adding the uncertainty derived from u (CWT ) to the sources of uncertainty expressed by Eqs. (A.12) and (A.13). A5. Relative combined standard uncertainty derived from the calibration equipment in the calculation of Cpit When each standard uncertainty is substituted into Eq. (A.1), the combined standard uncertainty at an air speed of 40 m/s is the largest:
uc (Cpit )/Cpit = 0.316 × 10
(A.14)
2
When the coverage factor is 2 (k = 2),
U (Cpit )/Cpit = k × uc (Cpit )/ Cpit
= 2 × 0.316 × 10
2
0.63 × 10
(A.15)
2
Table A1 shows the uncertainty budget for Cpit . A6. Uncertainty of uc (CDUT) In order to obtain uc (CDUT) , measurements were taken repeatedly, and their arithmetic mean was calculated. The uncertainty of the measurement result, which is the mean of multiple measurements, is attributed to random effects. In accordance with Eq. (4) in GUM 4.2.2 and Eq. (5) in GUM 4.2.3 [17], uc (CDUT) is estimated as follows:
Cpit =
1 n
ni
Cpit i
(A.16)
i=1
s 2 (Cpit i ) =
ni i=1
Cpit )2
(Cpit i ni
1
u (Cpit )/ Cpit =
s 2 (Cpit i )/ Cpit 2 ni
=
3.696 × 10 8/0.994 = 2.726 × 10 5
5
= 0.003 %
(A.17)
In this calibration, the measurement is repeated five times. The experimental standard deviation of CDUT is approximately 0.006%. After incorporating the relative combined standard uncertainty of the wind tunnel, uc (CDUT) is expressed as:
uc (CDUT)/ CDUT =
[u (Cpit )/Cpit]2 + [u (Cpit )/Cpit ]2 =
(0.316 × 10 2)2 + (0.003 × 10 2)2 = 0.316 %
(A.18)
Table A.1
Uncertainty of the measurement of Cpit Source of uncertainty
Relative standard uncertainty
Sensitivity coefficient
Effective degree of freedom
Reference volume flowrate Effective cross-sectional area Air speed indicated by the total pressure tube Dynamic pressure of the total and static pressure tubes Differential pressure between the nozzle inlet and outlet ports Differential pressure between the nozzle inlet and outlet ports Dynamic pressure measured by the DUT
0.223% 0.218% 0.032% 0.050% 0.037% 0.036% 0.039%
1 1 1 0.5 −0.5 0.5 −0.5
∞
Relative combined standard uncertainty
0.316%
139
18 18
Flow Measurement and Instrumentation 66 (2019) 132–140
A. Iwai, et al.
Essentially, in this calibration, a coverage factor of k = 2 is used for the relative expanded uncertainty. In the case of the normal distribution, the confidence interval for which the level of confidence of approximately 95% is estimated as follows:
U (CDUT)/ CDUT = k [uc (CDUT)/ CDUT] = 2[u c (CDUT)/ CDUT] = 0.632 %
0.63 %
(A.19)
845–847. [10] T.T. Yeh, J.M. Hall, Airspeed Calibration Service vols. 250–79, NIST Special Publication, 2007, pp. 1–26. [11] I.I. Shinder, C.J. Crowley, B.J. Filla, M.R. Moldover, Improvement to NIST's Air Speed Calibration Service, FLOMEKO, 2013. [12] Reconstruction of PTB Wind Tunnel with 320 mm Nozzle Completed, PTB news, 2011, pp. 1–2. [13] M. Ishibashi, T. Morioka, The renewed airflow standard system in Japan for 5-1000 m3/h, Flow Meas. Instrum. 17 (Issue 3) (2006) 153–161. [14] H. Rouse, M.M. Hassan, Cavitation-free inlets and contractions, Mech. Eng. 71 (1949) 213–216. [15] S. Wada, N. Furuichi, Influence of obstacle plates on flowrate measurement uncertainty based on ultrasonic Doppler velocity profile method, Flow Meas. Instrum. 48 (2016) 81–89. [16] Japanese Industrial Standard, Conformity assessment-General requirements for proficiency testing, JIS Q (2011) 17043 (in Japanese). [17] ISO, Guide to the Expression of Uncertainty in Measurement, (2008) ISO Guide 98-3. [18] L. Boguslawski, Cz O. Popiel, Flow structure of the free round turbulent jet in the initial region, J. Fluid Mech. 90 (1979) 531–539 part 3. [19] Japanese Industrial Standard, Procedures for calibration and testing for liquid flowmeter, JIS B (2011) 7552 (in Japanese).
References [1] Y. Terao, M. Takamoto, Low velocity standard for air flow using a towing carriage, Trans. Soc. Instrum. Control Eng. 26 (1) (1990) 1–8 (in Japanese). [2] Y. Terao, M. Takamoto, G.E. Mattingly, Preliminary intercomparison of anemometer calibration systems at very low speeds between the national standard laboratories in Japan and the USA, JSME Int. J. Series B 40 (No.3) (1997) 509–515. [3] Y. Terao, Study on measurement standard of very low air speed, Bull. NRLM 47 (196) (1998) 217–256 (in Japanese). [4] H. Müller, et al., CIPM Key Comparison of Air Speed, 0.5 m/s to 40 m/s (CCM-FFK3.2011), Metrologia vol. 54, (2017) Technical Supplement 07013. [5] N. Kurihara, Y. Terao, S. Nakao, M. Takamoto, An uncertainty of laser Doppler velocimeter calibration for air speed standard, Transactions of the Japan Society of Mechanical Engineers, Series B 71 (No.708) (2005) 2100–2107 (in Japanese). [6] Y. Terao, M. van der Beek, T.T. Yeh, H. Müller, Final report on the CIPM air speed key comparison (CCM.FF-K3), Metrologia 44 (2007) Technical Supplement 07009. [7] Bureau International des Poids et Mesures (BIPM), Key comparison database, Appendix C, CMCs (online), available from < http://kcdb.bipm.org/AppendixC/ country_list.asp?Iservice=M/FF.9.7.1 > , (accessed on 24 Jan, 2018). [8] Y. Terao, et al., Final report on the APMP air speed key comparison (APMP.M.FFK3), Metrologia 47 (2010) Technical Supplement 07012. [9] K.V. Popov, et al., State Standards, Measurement Techniques 57 (No.8) (2014)
140