1

REDEFINITION OF STANDARD EQUATION FOR DISCHARGE COEFFICIENT OF THROAT-

TAPPED FLOW NOZZLE

Noriyuki FURUICHI and Yoshiya TERAO

National Institute of Advanced Industrial Science and Technology (AIST)National Metrology Institute of Japan (NMIJ)

FLOMEKO 2019June 26-28, 2019, Lisbon, Portugal

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Throat-tapped flow nozzle

� Major applicationEvaluation of steam turbine (ASME PTC 6, IEC 60193 etc.)Feedwater flowrate measurement in nuclear power plant

� Discharge coefficient defined in ASME PTC 6

Flow nozzle

Flow conditioner

Upstream-taps (High) x 4

Throat-taps (Low) x 4

����� = �� −0.185

����.�

1 −361239

���

�.�

Determined by actual flow calibration, Nominal value = 1.0054

106 1070.99

1.00

1.01

Red

Cx,

CP

TC

6

: dT= 2mm : dT= 3.5mm : dT= 6mm

: CPTC6

: Reader-Harris et al. dT=3mm : Reader-Harris et al. dT= 4mm : Reader-Harris et al. dT= 6mm

3

Recent experiments for high Reynolds number

� Influence of the throat-tap diameter; dT� Reynolds number dependency

by Furuichi et al. and Dr. Reader-Harris et al.

4

Previous works by author’s

� Discharge coefficient behavior at high Reynolds number� Influence of the throat-tap diameter� Static pressure measurement error using wall tap� Theoretical analysis

� Propose new equations for the discharge coefficient

� Comparison with other facility (with PTB)

1) Comparison of high temperature and high Reynolds number water flows between PTB and NMIJ, Furuichi. N., Cordova L.,Lederer, T., Terao, Y., Flow Measurement and Instrumentation, 52 (2016), 157-162

2) Further investigation of discharge coefficient for PTC 6 flow nozzle in high Reynolds number, Furuichi, N., Terao, Y., Nakao,S., Fujita, K., Shibuya, K., Journal of Engineering for Gas Turbines and Power, 138 (2016), 041605-1-11

3) Static pressure measurement error at a wall tap of a flow nozzle for a wide range of Reynolds number, Noriyuki Furuichi,Yoshiya Terao, Flow Measurement and Instrumentation, 46 (2015), pp.103-111

4) New Discharge Coefficient of Throat Tap Nozzle Based on ASME Performance Test Code 6 for Reynolds Number From2.4 × 105 to 1.4 × 107, Furuichi, N, Cheong, KH, Terao Y., Nakao, S., Fujita, K., Shibuya, K., Journal of Fluid Engineering,136(1), 011105 (2013), doi:10.1115/1.4025513

5) Re-definition of discharge coefficient of throat-tapped flow nozzle and investigations on influence of geometric parameters,Furuichi, N., Terao, Y., Flow Measurement and Instrumentation, 65 (2019), pp.16-21.

Equation Reynolds number range

(i)

(ii)

(iii)

(iv)

(v)

Proposed equation for ideal nozzle

Tapf eCnC +=

Cf : Discharge coefficientCn : Ideal discharge coefficienteTap : Static pressure error ➡ Tap effectd : Diameter of throatdTap : Diameter of wall tapRed : Reynolds number

( )( )d

dRe

ReC

Tapd5.0

df 4344.2ln2053.0

41.80042.1 −+−=

d

d

ReC

Tap

5.0d

f 196.041.8

0042.1 +−=

d

d

ReReC Tap

8.0

d2.0

d

f 196.0400000

1255.0

0042.1 +

−−=

( )( )d

dRe

ReReC Tap

d

8.0

d2.0

d

f 9051.0ln0746.0400000

1255.0

0042.1 −+

−−=

Red<1.3×1055.0

df

41.80042.1

ReC −=

1.3×105<Red<4.0×105

4.0×105<Red<8.0×105

8.0×105<Red<3.0×106

3.0×106<Red

(i) (ii) (iii) (iv) (v)

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Proposed equation for ideal nozzle

105 106 1070.96

0.97

0.98

0.99

1.00

1.01

Red

Cx

: Tap1 : Tap2 : Tap3 : Tap4

Laminar Turbulent

No-effect Laminar Transition TurbulentCn

eTap

Dis

char

ge c

oeffi

cien

t

dTap2 mm3.5 mm5 mm6 mm

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Objective

To establish new equations as ISO standard,

� More detail examinations for dT/d

� Influence of upstream-tap diameter

� Roughness of nozzle surface

� Influence of upstream condition (flow conditioner)

� Individuality of manufacturing

Final equations for the throat-tapped flow nozzle are proposed.

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Examined parameters of throat-tapped flow nozzle

Pipe diameter D (mm) 100, 200, 350

Throat diameter d (mm) 50, 99, 165

Diameter ratio β app. 0.5

Throat-tap diameter dT (mm) 2, 3.5, 4, 5, 6, 7

dT/d 0.012－ 0.1

Upstream-tap diameter dU (mm) 2, 4, 5

Surfaceroughness

Ra (µm) 0.10, 0.80

Rt (µm) 0.60, 2.5

Ra

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High Reynolds number actual flow facility at NMIJ, AIST (Hi-Reff)

Experimental facility

Testing conditionWater temperature： T=20 °C ~ 75 °CFlowrate： q=30 m3/h ~ 2500m3/hReynolds number： Red=5.8x104 ~ 1.4x107

105 106 1070.97

0.98

0.99

1.00

1.01

Red

Cx,

CP

TC

6

CPTC6

10

Experimental result I

For variable dT/d

Cx = f (Red, dT/d)

� Discharge coefficient is given as

105 106 1070.97

0.98

0.99

1.00

1.01

Red

Cx,

CP

TC

6

CPTC6

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Experimental result II

105 1060.990

0.995

1.000

Red

Cx

dT =2 mm, dU =5 mm dT =2 mm, dU =2 mm

Upstream-tap effect� Influence of upstream-tap diameter is relatively

smaller than uncertainty of measurement.

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Experimental result III

Surface roughness

106 1070.995

1.000

1.005

1.010

Red

Cx

R1 R2 dT =3.5 mm dT =5 mm dT =6 mm

Ra

R1 : Ra = 0.1 µmR2 : Ra = 0.8 µm

� Influence of roughness is observer for Red>6x106.

� Discharge coefficient is decreasing with increasing roughness.

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Experimental result IV

Influence of upstream condition

106 1070.996

0.998

1.000

1.002

Cx

: with flow conditioner : without Flow conditioner : with half-moon plate

Red

DN600 DN400

Flow conditioner Flow nozzle

22D5D<30D

(a)

DN600 DN400

27D<30D

(b)

DN600 DN400

Half-moon plate

22D5D<30D

(c)

� With over 22D straight upstream pipe, the influence of upstream condition is less than 0.05%.

(a)(b)(c)

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Experimental result V

Individuality of nozzle manufacturing

105 106 1070.990

0.995

1.000

1.005

Red

Cx,

CP

TC

6

dTap = 4 mm. dTap/d=0.024 dTap = 5 mm, dTap/d=0.030 dTap = 6 mm, dTap/d=0.036 dTap = 7 mm, dTap/d=0.042

CPTC6

� Absolute discharge coefficient value is different.� Tap effect is not according to the physics.� However, the trend at high Reynolds number is similar.

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Summary of experiments

105 106 1070.96

0.97

0.98

0.99

1.00

1.01

Red

Cx,

CP

TC

6

CPTC6

Equation Reynolds number range

(i)

(ii)

(iii)

(iv)

(v)

Proposed equation for ideal nozzle

Tapf eCnC +=

( )( )d

dRe

ReC

Tapd5.0

df 4344.2ln2053.0

41.80042.1 −+−=

d

d

ReC

Tap

5.0d

f 196.041.8

0042.1 +−=

d

d

ReReC Tap

8.0

d2.0

d

f 196.0400000

1255.0

0042.1 +

−−=

( )( )d

dRe

ReReC Tap

d

8.0

d2.0

d

f 9051.0ln0746.0400000

1255.0

0042.1 −+

−−=

Red<1.3×1055.0

df

41.80042.1

ReC −=

1.3×105<Red<4.0×105

4.0×105<Red<8.0×105

8.0×105<Red<3.0×106

3.0×106<Red

dt/d = 0.024

105 106 1070.96

0.97

0.98

0.99

1.00

1.01

Red

Cx,

CP

TC

6

CPTC6

CP

0.5％

-0.5％

0.25%

-0.25%

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Summary of experiments

���� = 1.0042 −8.41

����.�

���� = 0.9558 −8.41

����.�

+ 0.00492 ln ���

���! = 1.0090 −8.41

����.�

���" = 1.0090 −0.255

����.�

1 −400000

���

�.�

���� = 0.9823 −0.255

����.�

1 −400000

���

�.�

+ 0.0018 ln ���

for Red<1.3×105

for 1.3×105<Red<4.0×105

for 4.0×105<Red<8.0×105

for 8.0×105<Red<3.0×106

for 3.0×106<Red

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� This paper presents experimental discharge coefficient for the several geometric parameters; throat-tap diameter, upstream-tap diameter, roughness of surface of nozzle and flow conditioner.

� The most influence parameter for the discharge coefficient is throat-tap diameter dT/d and the influence of the other parameters is generally negligible small.

� According to this result, new equations of the discharge coefficient for the throat-tapped flow nozzle is proposed. Although they are separated for five Reynolds number range, all experimental data in NMIJ is within ±0.5% of them.

Conclusion