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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
2
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)
6
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
7
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.
8
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
9
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
11
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.
12
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.
13
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)
14
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.
15
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%
17
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
18
� 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