experimental results of flow nozzle based on ptc 6 for

EXPERIMENTAL RESULTS OF FLOW NOZZLE BASED ON PTC 6 FOR HIGH REYNOLDS NUMBER

Noriyuki Furuichi AIST, NMIJ

Tsukuba, Ibaraki, Japan

Kar-Hooi Cheong AIST, NMIJ


Yoshiya Terao AIST, NMIJ


Shinichi Nakao Flow Col

Yokohama, Kanagawa, Japan

Keiji Fujita Flow Engineering


Kazuo Shibuya Flow Engineering


Leopoldo Cordova PTB

Berlin, Germany

Thomas Lederer PTB

Berlin, Germany

ABSTRACT Discharge coefficients for three flow nozzles based on

ASME PTC 6 are measured under many flow conditions at AIST, NMIJ and PTB. The uncertainty of the measurements is from 0.04% to 0.1% and the Reynolds number range is from 1.3105 to 1.4107. The discharge coefficients obtained by these experiments is not exactly consistent to one given by PTC 6 for all examined Reynolds number range. The discharge coefficient is influenced by the size of tap diameter even if at the lower Reynolds number region. Experimental results for the tap of 5 mm and 6 mm diameter do not satisfy the requirements based on the validation procedures and the criteria given by PTC 6. The limit of the size of tap diameter determined in PTC 6 is inconsistent with the validation check procedures of the calibration result. An enhanced methodology including the term of the tap diameter is recommended. Otherwise, it is recommended that the calibration test should be performed at as high Reynolds number as possible and the size of tap diameter is desirable to be as small as possible to obtain the discharge coefficient with high accuracy.

INTRODUCTION

The throat tap flow nozzle based on PTC 6 [1] is widely used in power plants not only to evaluate efficiency of steam turbines but also as a flow meter to measure a feed-water in nuclear power plants. This type of flow nozzle is one of the significant management equipment in power plants. Because the PTC 6 defines detail manufacturing requirements and strict

checking procedures of the performance of the flow nozzle to ensure a good overall performance.

PTC 6 defines the next equation to give the discharge coefficient CPTC6 of the flow nozzle.

8.0

d2.0

d

TPTC6

3612391

185.0

ReRekC (1)

where, Red is Reynolds number based on the throat diameter of flow nozzle and the velocity at the throat. The nominal value of kT is 1.0054, but is practically determined using the data of calibration. This equation is derived in theoretical by Murdock et al [2]. PTC 6 defines the Reynolds number range as 1.0106<Red<5.0107 that Eq.(1) can be applied. The discharge coefficient is estimated by Eq.(1) for the Reynolds number in the field, even if the Reynolds number at the calibration is lower than that.

However, recent experiments show a different behavior of the discharge coefficient from Eq.(1) at higher Reynolds numbers. Reader-Harris et al. [3][4] performed experiments for the flow nozzle using gas flow up to Reynolds number in the order of 107. The Authors also performed experiments for the flow nozzle using the high Reynolds water flow calibration facility in AIST, NMIJ up to 107 order of Reynolds number [5]. Both results show that the discharge coefficient of the flow nozzle depends on the size of tap diameter, and also largely deviates from Eq.(1). Especially, the behavior of the discharge coefficients with Reynolds number is different from Eq.(1). The deviation of discharge coefficient between these experiments

Proceedings of the ASME 2014 Power Conference POWER2014

July 28-31, 2014, Baltimore, Maryland, USA

POWER2014-32116

1 Copyright © 2014 by ASME

and Eq.(1) increases with Reynolds number and reaches up to 0.75% at Red=1.4107.

To investigate precisely measurement results for the discharge coefficient of the flow nozzle based on PTC 6, additional experiments are performed in this paper. The purpose of this paper is to present various examinations with high quality results at different conditions. These examinations were performed at high accurate and high repeatable flow test facilities in order to provide a robust and reliable basis for the analysis. The measurements of the discharge coefficients of the flow nozzle are carried out at AIST, NMIJ (Advanced Industrial Science and Technology, National Metrology Institute of Japan) in Japan and at PTB Berlin (Pyhsikalisch-Technische Bundesanstalt) in Germany. Experimental parameters are temperature and pressure of the working fluid, the diameter of the throat, the diameter of the tap, the flowrate and the Reynolds number. The experiments are performed at a wide Reynolds number range Red=1.3105 ~ 1.4107.

NOMENCLATURE a Intercept of Cr b Slope of Cr C Discharge coefficient obtained experimentally CPTC6 Discharge coefficient given by standard equation in

PTC 6 Cr Discharge coefficient given by fitting curve Cx Coefficient for validation check D Diameter of upstream pipe (m) DS Scattering of test data d Nozzle throat diameter (m) dTap Tap diameter (m) I Number of pulse output from reference flowmeter (-) K K-factor of reference flowmeter (Pulse number/m3) kT Coefficient for CPTC6 P Gauge pressure at test section (Pa) p Differential pressure (Pa) q Flowrate (m3/h) Red Reynolds number based on nozzle diameter T Temperature at test section (C) td Duration time (s)

ts Student t value with 95% confidential level V Standard volume of Prover (m3) P Correction coefficient of pressure for Prover system T Correction coefficient of temperature for Prover

system Diameter ratio (=d/D) T Density of water in weighing tank (kg/m3) DUT Density of water at upstream of nozzle (kg/m3) air Density of air surrounding weighing tank (kg/m3) FLOW NOZZLES

In this experiment, three flow nozzles are examined as shown in Table.1. The nominal diameter of the flow nozzle types A and B is 350 mm the diameter for C is 200mm. Hereafter, each type flow nozzle is called as Nozzle A, Nozzle B and Nozzle C respectively. Except to Nozzle B, the flow nozzles are manufactured completely according to PTC 6. The detail figure of Nozzle B is shown in Fig.1. Nozzle B has four taps with different diameter which is 2 mm (Tap1), 3.5mm (Tap2), 5 mm (Tap3) and 6 mm (Tap4). PTC 6 defines the tap diameter as from 3.175 mm to 6.35 mm so that Tap1 does not satisfy the standard.

The shapes of each flow nozzle were measured by the coordinate measuring machine (Mitutoyo Inc., CRT-A710) whose expanded uncertainty is less than 0.0023 mm. The geometry of Nozzle A is similar to the geometry of Nozzle C including the taps.

Table 1. Specifications of flow nozzles

Nozzle A Nozzle B Nozzle C

Nominal Diameter (mm) 350 350 200

Eclipse diameter (mm) 165.2103.3 165.2 103.3 99.962.5

Throat diameter d (mm) 165.187 165.220 99.894

Upstream pipe diameter D (mm) 338.96 338.96 199.90

Diameter ratio 0.4873 0.4874 0.4997

Throat tap diameter dTap (mm) 6 2, 3.5, 5, 6 3.5

Upstream tap diameter dU (mm) 6 6 4

165.2

165.

22

206.

5

247.

8

103.

3

123.910°

dTap

TAP4 TAP2

TAP3

TAP1

2

5

6

3.5

φ

φ φ

φ

φ φ φ

Fig.1 Flow nozzle (Nozzle B)


EXPERIMENTAL FACILITIES High Reynolds number facility in AIST, NMIJ

The high Reynolds number facility in AIST, NMIJ is shown in Fig.2 [6]. The feed water line is shown by the red arrows as “Circulation line” in Fig.2. Water is supplied to test section by four circulation pumps of which maximum flowrate is 3000 m3/h. The four lines are combined upstream of the test section. The length of the test section is 35 m and the straight pipe length is over 50D for DN600 pipe. The specifications of the high Reynolds number facility are as follows: the flowrate range is from 750 m3/h to 12,000 m3/h; the temperature range is from 20 C to 80 C ; the pressure range is from 0.3 MPa to 0.7 MPa, and the possible maximum Reynolds number is 2.0107. The pipe diameter of a device under test is available for from 200 mm to 800 mm. In this experiment, the reference flowrate at the test section is given by the reference flowmeters installed in each line at downstream of pumps. This reference flowmeters are calibrated using the 50t weighing tank system and Prover system described in the following. See the reference [6] for detail calibration method of the reference flowmeters. The expanded uncertainty (k=2) of the facility is 0.10%.

Weighing tank system in AIST, NMIJ AIST, NMIJ has several weighing tank systems. For the detail of these weighing tank systems, see the reference [7]. In this paper, 50t and 5t weighing tank systems are used. When 50t weighing tank system is used, the test section is same with the high Reynolds number facility. The feed water line is shown by the blue dotted arrows as “50t weighing tank feed line” in Fig.2. Feed water to the test section is carried out by the circulation pumps. Water from the over flow head tank is supplied to the test section through the header, the circulation pumps and the reference flowmeters of high Reynolds number facility and it is feed to 50t weighing tank. The expanded uncertainty (k=2) of the facility is 0.060%.

Overflow Head Tank

Pressure Tank

Header

ReservoirTank

50t Weighing Tank

Test Section

ElectromagneticFlowmeters

UltrasonicFlowmeters

CirculationPumps

Feed Pumps

Feedback Line

Reference Flowmeters (WS)

Prover

Circulation line

50t weighing tank feed line

Fig.2 High Reynolds number facility in AIST, NMIJ

Fig.3 Test facility with 5 t weighing tank system in AIST, NMIJ

Fig.4 Test facility with Prover system in AIST, NMIJ

Measuring sections- length = 25 m (stainless steel)- corrugation < 1 mm / 25 m- roughness < 5 µm (smoothed)- flange mismatch < 50 µm

20t Weighing ScaleCalibration standards:

36 x 550 kg (U<2.8g)

Diverters

Air conditioned weighting tank

Collection tank

Acceleration pumps

Air-liquid separator

Main Pumps

Basement

Operation area

65 m³ Constant pressure Storage tank

Constant head tank at 12 m height

Fig.5 Heat Meter calibration Facility of the PTB


The test facility with 5t weighing tank system is shown in Fig.3. In this case, water is supplied to the test section from the over flow head tank. Maximum flowrate to use 5t weighing tank is 300 m3/h and water temperature is ambient. This test line is used to the test for Nozzle B and C. The expanded uncertainty (k=2) of the facility is 0.042%.

Prover system in AIST, NMIJ The experimental facility with Prover system in AIST, NMIJ is shown in Fig.4. This facility is capable for flowrate 200 m3/h~800 m3/h and temperature 20 C~80 C. The maximum Reynolds number in the test section is approximately 3.7106. The reference flowrate is given by Prover system which is one of a calibration system as a volumetric method. Inside of the pipe, sphere ball is installed and it touches to the detection sensors moving to one side to another side. The flowrate is given as the volume between two sensors divided by the time between two sensors. The volume between two sensors is obtained using 50t weighing tank. See the reference [7] for the detail method to obtain the volume. The expanded uncertainty (k=2) of the facility is 0.070%. Heat Meter calibration facility of the PTB

A schematic of the heat meter calibration facility of the PTB is shown in Fig.5. It is divided basically into two levels: The basement level with the flowrate generation systems, and the upper level with the test lines and the measurement systems. The flowrate is generated with two sets of pump cascades, with an overflow constant pressure tank in between to ensure highest flow rate stability. Since the measurements are performed on a flying start stop basis, two diverter systems are used.

Evaporation at higher water temperatures is controlled by reducing the water concentration gradient on the air near all

free water surfaces. This is accomplished by encapsulating the diverting system and by introducing saturated tempered humid air into the empty tank before the measurements. Evaporation cannot be completely avoided; therefore, by performing a water vapor mass balance based on humidity measurements on the air evacuated by the water, the amount of water lost can be estimated.

A weighing scale calibrated on a daily basis is the reference system. The heat meter testing facility of the PTB reaches a worst case expanded uncertainty of 0.04% and a very high repeatability for temperatures between 4 °C and 90 °C and flowrates up to 1000 m³/h at 0.1 MPa up to 0.5 MPa. The length of the test lines is 25 m. For more details refer to [8].

EXPERIMENTAL CONDITION AND METHOD Experimental condition

The experimental conditions are listed in Table 2. In this experiment, flowrate range is from 30 m3/h to 2550 m3/h and temperature range is from 14 C to 75 C. The Reynolds number range based on the throat diameter and the velocity at the throat is from 1.3106 to 1.4107. The temperature fluctuation during one measurement which is from 15 second to 15 minutes is less than 0.2 C and the pressure fluctuation is less than 0.01 MPa. Experimental method

Discharge coefficient C of the throat tap nozzle is given by the following equation.

pπd

qC

)1(8 4

2 (2)

Schematic diagrams of the measurement of the discharge

Table 2. Experimental condition

Nozzle Exp. No.

Lab. Reference of flowrate Flowrate q

(m3/h) Temperature T

(C) Pressure P

(MPa, Gage) Re number range

A

Exp.1 AIST, NMIJ Weighing tank (50 t) 100 – 800 20 2 0.2 0.03 2.4105 – 1.8106

Exp.2 AIST, NMIJ Ref. flowmeter 770 – 2270 20 4

40,60,70 2 0.7 0.10 1.8106 – 1.4107

B



Exp.5 AIST, NMIJ Ref. flowmeter 770 – 2270 20 4

70, 75 2 0.3, 0.7 0.10

1.8106 – 1.4107

C


Exp.7 AIST, NMIJ Prover 250 – 600 20, 30, 40, 53,

65, 80 2 0.3 0.10 9.0105 – 5.8106

Exp.8 PTB Weighing tank (20 t) 395 – 745 20, 30, 40, 53,

65, 80 1 0.36 – 0.56 1.5106 – 7.2106


coefficient are shown in Fig.6. Fig.6(a) is using the reference flowmeters in the high Reynolds number facility, Fig.6(b) is for the weighing tank system and Fig.6(c) is for Prover system.

Differential pressure p measurement is performed by the digital manometer (DP meter) of Yokogawa Co. Ltd. (MT210). In the experiments, two types of the digital manometer are used, which were calibrated before the measurements. The resolution of them is a : 1 Pa and b : 10 Pa. In generally, type a is used for p<130 kPa and type b is used for p>130 kPa. The start and the stop of the differential pressure measurement are completely synchronized with the duration time of the reference flowrate. The sampling rate of the digitized differential pressure is 1 sec for nozzle A and B and 0.5 sec for the nozzle C and.

The volumetric flowrate measured by the reference

flowmeters in the high Reynolds number facility is given by the following equation.

D

DD

C

CC

B

BB

A

AA

dDUT

1

K

I

K

I

K

I

K

I

tq

(3)

Here, the subscripts "A" to "D" mean the values of the reference flowmeters used. The duration time td is set to 300 sec. Here, K-factors (pulse number/m3) of the reference flow meters are determined by the weighing tank method and other calibration devices before the measurements [5]. The reference flow meters are calibrated at 750, 1500, 2250, 3000 m3/h at 20 C and 70 C. The K-factor for measurement condition in this paper is given by an interpolation of the function of Reynolds number based on the calibration results. The measurement in this method is repeated 3 times. The volumetric flowrate measured by the weighing tank system of 50t, 5t system in AIST, NMIJ and PTB is given by the next equation.

DUTTaird )/1(

t

Mq (4)

where, 1-air/T means a buoyancy correction. The mass flowrate obtained by the accumulated water in the weighing tank and the duration time is converted to the volumetric flowrate using the density of water. The measurement in this method is repeated 3 or 5 times.

The volumetric flowrate using Prover system is given by the next equation.

P

DUT

d

PT

t

Vq (5)

The standard volume is corrected for the expansion caused by the temperature and pressure. The duration time is controlled by the detector sensor switch. This sensor switch works when the sphere ball which is installed in Prover passes under it. The measurement in this method is repeated 10 times. EXPERIMENTAL RESULTS Experimental result of each nozzle

Experimental results of Nozzle A are shown in Fig.7. The solid line is Eq.(1) with nominal kT, 1.0054, for Red>1.0106. The small dotted line for Red<1.0106 is referred PTC 6-1976 [9]. Figure 7(a) shows the result of Tap1 at different temperatures. The discharge coefficients are on a certain line and no influence of flow temperature is observed. Figure 7(b) shows the results of Exp.1, Exp.2 at 20 C and 70 C for each tap. The discharge coefficients of all taps show the same behavior. This means that the flow nozzle and the taps are manufactured correctly based on PTC 6 and the flow condition in the flow nozzle is completely axisymmetric.

Experimental results of Nozzle B are shown in Fig.8. Figure 8(a) shows the result of Tap4, which is the 6 mm diameter tap. The results are also on the same curve, being

(a)

Reference Flowmeter

IA

Counter Pulse

Gate

External Trigger

A Line

B Line

C Line

D Line

IBICID

K-factor : KA

K-factor : KB

K-factor : KC

K-factor : KD

Flow nozzle

DP meter : pPressuremeter : P

Timer : td

PC

Flow Direction Thermometer : T

(b)

DP meter : pTimer : td

GateScale : M

WeighingTankDiverterFlow

Direction

Thermometer : T

PCPressuremeter : P

Flow nozzle

(c)

Gate

Temperature : T

Temperature : TPPressure : PP

Prover (Standard Volume : V)

Detector sensor

DP meter: p

Flow Direction

Pressuremeter : P

Flow nozzle

Fig.6 Schematic diagram of measurement (a) Reference flowmeter, (b) Weighing tank and (c) Prover system


independent on flow conditions. Figure 8(b) shows the results for all taps. As shown in Table.2, Nozzle B has four taps with different tap diameters. The discharge coefficients of Nozzle B have different behaviors for the size of tap diameter. The behavior of each tap does not agree with one of PTC 6-1976 for Red<1.0106 and Eq.(1) in PTC 6-2004 for Red>1.0106. On the other hand, the discharge coefficients of Tap1 for Red<5.0105 agrees well with the previous experiment by Buckland et al. [10] as shown by the large dotted line in Fig.8(b). The discharge coefficients of other taps also approach to their result with decreasing of Reynolds number.

It should be noted that Fig.8(b) indicates the important issue, tap effect. The larger the size of tap diameter is, the larger the discharge coefficient is. Moreover, the increasing rate of the discharge coefficient with Reynolds number also depends on the size of tap diameter. In the ranges of Red<5.0105 and Red>3.0106, the larger the size of tap diameter is, the larger the increasing rate is. This result clearly shows that the discharge coefficient of the flow nozzle is influenced by the size of tap

diameter. The influences of tap diameter will be discussed again in the following sections in details.

Experimental results of Nozzle C are shown in Fig.9. The discharge coefficients of this flow nozzle are measured at two laboratories. The results of AIST, NMIJ are shown in Figure 9(a) and (c) and the results of the PTB are shown in Fig.9(b). Figure 9(a) and (b) show the experimental results of Tap1 for variable temperatures. Each result is clearly on a certain line and no influences of temperature difference are observed. Moreover, each discharge coefficients behaves almost the same trend as shown in the following section. Figure 9(c) is the results for each tap. The discharge coefficients of each tap are completely coincident, except that of Tap3. The difference of Tap3 might be caused by the manufacturing error.

Validation check of experimental results

The results of Nozzle A and Nozzle B are shown in Fig.10. The discharge coefficients of each flow nozzle show almost similar behavior. The difference between them is

105 106 1070.980

0.990

1.000

1.010

Red

C

:Exp.1:Exp.2, T=20°C:Exp.2, T=40°C:Exp.2, T=60°C:Exp.2, T=70°C

: PTC 6-2004 [1]

: PTC 6-1976 [9]

Nozzle A, Tap1

(a)

105 106 1070.980

0.990

1.000

1.010

Red

C

:Tap1:Tap2:Tap3:Tap4

: PTC 6-2004 [1]

: PTC 6-1976 [9]

Nozzle A

(b)

Fig.7 Test result of Nozzle A

105 106 1070.980

0.990

1.000

1.010

Red

C

:Exp.3:Exp.4:Exp.5(T=20 °C, P=0.7 MPa):Exp.5(T=70 °C, P=0.7 MPa):Exp.5(T=70 °C, P=0.3 MPa):Exp.5(T=75 °C, P=0.7 MPa)

:PTC 6-2004 [1]

:PTC 6-1976 [9]

Nozzle B, Tap4 (dTap=6mm)

(a)

105 106 1070.980

0.990

1.000

1.010

Red

C


: PTC 6-2004 [1]

: PTC 6-1976 [9]

: Buckland et al. [10]

Nozzle B

(b)

Fig.8 Test result of Nozzle B


approximately 0.08%. The results of these flow nozzles with the same characteristics prove the validity of the manufacturing

of the flow nozzles and the taps. The comparison result AIST, NMIJ and PTB is shown in

Fig.11. The comparison is performed using the result of Tap1 and Tap3 of Nozzle C. The discharge coefficient in AIST, NMIJ is coincident with PTB although small difference is observed only at the highest Reynolds number. The averaged difference between them for whole examined Reynolds number range is less than 0.01%. Tap effect

As showing in Fig.8(b), the discharge coefficient of the flow nozzle based on PTC 6 is strongly influenced by the size of tap diameter. PTC 6 defines that the size of tap diameter is from 3 mm to 6 mm. and Eq.(1) does not have the term including the size of tap diameter. However, the experimental results show that the difference between Tap2 and Tap4 of Nozzle B is over 0.5% at high Reynolds number region. This

105 106 1070.980

0.990

1.000

1.010

Red

C:Nozzle A, Tap4:Nozzle B, Tap4

: PTC 6-2004 [1]

: PTC 6-1976 [9]

Fig.10 Comparison between Nozzle A and B

105 106 1070.980

0.990

1.000

1.010

Red

C

:Exp.6:Exp.7(T=20°C):Exp.7(T=30°C):Exp.7(T=40°C):Exp.7(T=53°C):Exp.7(T=67°C):Exp.7(T=80°C)

Nozzle C, Tap 1

:PTC 6-2004 [1]

:PTC 6-1976 [9]

(a)

105 106 1070.980

0.990

1.000

1.010

Red

C

:Exp.8(T=20°C):Exp.8(T=30°C):Exp.8(T=40°C):Exp.8(T=53°C):Exp.8(T=67°C):Exp.8(T=80°C)

Nozzle C, Tap 1

:PTC 6-2004 [1]

:PTC 6-1976 [9]

(b)

105 106 1070.980

0.990

1.000

1.010

Red

C


:PTC 6-2004 [1]

:PTC 6-1976 [9]

:Buckland et al. [10]

Nozzle C

(c)

Fig.9 Test result for Nozzle C

106 1070.990

0.995

1.000

1.005

1.010

Red

C

:Tap1 (NMIJ):Tap1 (PTB):Tap3 (NMIJ):Tap3 (PTB)

:PTC 6-2004 [1]

:PTC 6-1976 [9]

Nozzle C ( dTap=3.5 mm)

Fig.11 Comparison between NMIJ and PTB


suggests that the equation to give the discharge coefficient should be have the term of the size of tap diameter.

The results of Tap4 of Nozzle B and Tap1 of Nozzle C are compared in Fig.12. As mentioned, the geometries of these two nozzles and the taps are similar and the result shows good agreements each other. This indicates that the relation between the discharge coefficient and Reynolds number is a function of the tap diameter normalized by the throat diameter d. According to this result, the authors have presented the modified equations including the tap effect above mentioned although they are not described in this paper. For detail, see the references [5][11]. VALIDATION CHECK BASED ON PTC 6

PTC 6 requires the calibration of the flow nozzle, and kT of Eq.(1) is determined by the next equations.

N

i

iCxN

k1

T

1 (6)

8.0

d2.0

d

3612391

185.0

ReReCCx ii (7)

where, i=1~N and N is a number of measurement Reynolds number points. Ci is the discharge coefficient measured at each Reynolds number point. PTC 6 defines that N is a minimum of 20. PTC 6 gives several checking procedures of the test data. To check a dependency of Cxi for Reynolds number, the following linear relation between Cxi and Red is given.

dbReaCr (8)

where, a and b is determined by the least square method. Moreover, the next equation is defined in PTC 6 to check the scatter of Cxi.

N

StD kts

S (9)

where, Skt is given by the next equation.

21

2

kt

N

CrCx

S

N

i

ii

(10)

where, Cri is given by substituting Red corresponding to Cxi to Eq.(8).

According to PTC 6, kt, b and DS must be satisfied the following criteria.

1) 1.0029 kT 1.0079 (0.25% tolerance) 2) b 2.710-10 3) DS 3.010-4

Here, PTC 6 defines the range of Reynolds number as 1.0106<Red<5.0107 to which Eq.(1) can be applied and the calibration must be carried out in this range, however it does not define to which these criteria can be applied. This lack of definition induces that kT, b and DS depend on the examined Reynolds number range. In the following paragraph, kt, b and DS are calculated using the experimental data in the Reynolds number range Red-min<Red<Red-max to evaluate these checking procedures.

Figure 13 shows the behavior of kT given by Eq.(6) and the acceptable range defined in PTC 6. The minimum examined Reynolds number is fixed at Red-min=1.0106. The horizontal axis Red-max is the maximum examined Reynolds number. Therefore, kT is calculated using the experimental data in 1.0106<Red<Red-max. kt clearly depends on the maximum examined Reynolds number. kt for Tap3 is in the acceptable range defined in PTC 6 for Red-max<5.0106, but it goes out of the acceptable range in Red-max>5.0106. This result indicates

105 106 1070.980

0.990

1.000

1.010

Red

C

:Nozzle B, Tap4:Nozzle C, Tap1

: PTC 6-2004 [1]

: PTC 6-1976 [9]

Fig.12 Comparison between Nozzle B, Tap4 and Nozzle C

106 1071.000

1.005

1.010

1.015

Red-max

k T


Nozzle B

Acceptable rangeof PTC6

Fig.13 Behavior of kT for 1.0106 <Red< Red-max


that the maximum examined Reynolds number should be limited to accept the criteria defined in PTC 6.

On the other hand, it is needless to say that the estimated error decreases with increasing Red-max. Figure 14 shows a deviation between the discharge coefficient given by the experiments and one given by Eq.(1) for each tap. The vertical axis is the deviation normalized by CPTC6 at the highest examined Reynolds number. This figure indicates the significant issue that the deviation is over 0.25% in Red-

max<5.0106 for Tap2, 3 and 4. To obtain high accuracy of flow measurement, it is strongly recommended that the calibration should be carried out at as higher Reynolds number as possible, even if kT is not within the acceptable range. Otherwise, the size of tap diameter should be as small as possible. Because kT of Tap1 is within acceptable range of PTC 6 and the deviation from Eq.(1) is less than 0.2%, although the tap diameter of the Tap1 is not acceptable for PTC 6.

PTC6 describes that Cx given by Eq.(7) must show no or less dependence on Reynolds number. The background of this description might be that the coefficient b for the discharge coefficient given by Eq.(1) with nominal kT is approximately 2.010-10 in 3.0106<Red<8.0106. However, the increasing rate of discharge coefficient in the experiments is obviously larger than one given by Eq.(1), as shown in Fig.8(b). The behavior of the coefficient b obtained by the experiments is shown in Fig.15, where Red-min is also fixed at 1.0106. The coefficient b is over the acceptable range of PTC 6 in higher Reynolds number region. The inconsistency between the experimental results and Eq.(1) causes that the validation procedure and the criterion in PTC 6 consider only limited Reynolds number range.

DS means that the scattering of the experimental data from Eq.(8). The behavior of DS in the experiment is shown in Fig.16. DS is smaller than the acceptable value except the

lowest Red-max, and decreases with increasing Red-max. On the other hand, the relations between Reynolds number and the discharge coefficient are not proportional, being not only in Eq.(1), but also the experimental results in this paper. The validation checking procedure for DS is also not enough for measurement of discharge coefficients, although the criterion is almost satisfied.

The validation checking procedures and the criteria defined in PTC 6 are applicable to only the limited Reynolds number as discussed. For example, when the calibration is performed at 3.0106<Red<5.0106, most experimental results satisfy the criteria and they are conformity. However, if the calibration is carried out for wide range Reynolds number up to order of 107, most results cannot satisfy the criteria in PTC 6. On the other hand, when the calibration is carried out at higher Reynolds number, the estimated error can be decreased, even if

106 1070.0

0.1

0.2

0.3

0.4

0.5

Red-max

(C-C

PT

C6)/

CP

TC

6


Nozzle B

[%]

Fig.14 Deviation between the experimental discharge coefficient and one given by the standard equation in PTC 6 at the highest examined Reynolds number

106 107-10

0

10

Red-max

b


Nozzle B

Acceptable rangeof PTC6

[x10-10]

Fig.15 Behavior of coefficient b for 1.0106 <Red< Red-max

106 1070.0

2.0

4.0

6.0

8.0

Red-max

DS


Nozzle B

[x10-4]

Upper limit of PTC6

Fig.16 Behavior of DS for 1.0106 <Red< Red-max


the standard equation described in PTC 6 is used. For high accurate flow measurements, the calibration should be carried out at as high Reynolds number as possible. CONCLUSION

The discharge coefficients of three flow nozzles based on ASME PTC 6 are measured under several flow conditions at the AIST, NMIJ in Japan and at the PTB in Germany. The experiments are performed with the uncertainty from 0.04% to 0.10% and the examined Reynolds number range Red is from 1.3105 to 1.4107.

The discharge coefficients obtained by these experiments is not exactly consistent to one given by PTC 6 [1][9] for all examined Reynolds number range. The discharge coefficient is influenced by the size of tap diameter even if at the lower Reynolds number region. The larger the tap diameter is, the larger the discharge coefficient is. The present results clearly indicate that the size of tap diameter is one of a parameter in the equation which gives the discharge coefficient of throat tap nozzle as shown in the previous papers [5][11]. On the other hand, the results for dTap=5 mm and 6 mm do not satisfy the requirements based on the validation procedures and the criteria given by PTC 6.

The experimental results in this paper indicate that the limit of the size of tap diameter determined in PTC 6 is inconsistent with the validation check procedures of the calibration result. An enhanced methodology including the term of the tap diameter is recommended. Otherwise, it is recommended that the calibration test should be performed at the as high Reynolds number as possible and the size of tap diameter is desirable to be as small as possible to obtain the discharge coefficient with high accuracy.

REFERENCES [1] Steam Turbines, Performance Test Codes, ASME PTC 6-2004 [2] Murdock, J.W. and Keyster, D.R., Theoretical basis for extrapolation of calibration data of PTC 6 throat tap nozzles, Transactions of the ASME, Journal of Engineering for Gas Turbines and Power, 113 (1991), 228-232 [3] Reader-Harris, M., Gibson, j., Hodges, D., Nicholson, I.G., Rushworth, R., The performance of flow nozzles at high Reynolds number, Proceedings of FLOMEKO 14 (Johannesburg, South Africa), 2007 [4] Reader-Harris, M., Flow measurement and energy, Proceedings of FLOEMEKO 15 (Taipei, Taiwan), Keynote Lecture, 2009 [5] Furuichi, N, Cheong, KH, Terao Y., Nakao, S., Fujita, K., Shibuya, K., New Discharge Coefficient of Throat Tap Nozzle Based on ASME Performance Test Code 6 for Reynolds Number From 2.4 × 105 to 1.4 × 107, Journal of Fluid Engineering, 136-1 (2013), 011105, doi:10.1115/1.4025513 [6] Furuichi, N., Terao, Y., Takamoto, M., A new calibration facility of flowrate for high Reynolds number, Flow Measurement and Instrumentation, 20-1 (2009), 38-47

[7] Furuichi, N., Terao, Y., Takamoto, M., Calibration Facilities for Water Flowrate in NMIJ, Proceeding of 7th ISFFM, (Anchorage, USA), (2009) [8] Mathies, N. “Messunsicherheit einer gravimetrischen Kalt- und Warmwasser-Normalmessanlage für große Volumenströme“ Dissertation, Technische Universität Berlin (2005), Mensch & Buch Verlag Berlin [9] Steam Turbines, Performance Test Codes, ANSI/ASME PTC 6 - 1976 [10] Buckland, B.O., Schenectday, N.Y., Fluid‐meter nozzles, Trans. ASME 56 (1934), pp.827-832 [11] Furuichi, N, Cheong, KH, Terao Y., Nakao, S., Fujita, K., Shibuya, K., Experimental investigation of discharge coefficient and tapping error of PTC 6 flow nozzle using high Reynolds number calibration rig, Proceedings of FLOMEKO 2013 (Paris), 2013


experimental results of flow nozzle based on ptc 6 for

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