Abstract

The flowrate in hydraulic turbines can be measured using the pressure-time method specified by the IEC 60041 standard. This method assumes a one-dimensional (1D) flow and is limited to straight pipes with a uniform cross section and specific restrictions on length (L > 10 m) and velocity (U × L > 50 m2 s−1). However, in low-head hydropower plants, the intake typically has a variable cross section and small length, making it challenging to use this method. This paper presents the development of a methodology that extends the applicability of the pressure-time method for variable cross section by using three-dimensional computational fluid dynamics (3D CFD). A combination of 3D CFD and 1D pressure-time methods is employed iteratively to estimate the kinetic energy correction factor. The obtained time-dependent values are then used in the 1D pressure-time method to calculate the flowrate. The new methodology is applied with experiments performed on a test rig with a reducer. The obtained results illustrate the significantly different kinetic energy correction factor obtained than those obtained using constant or quasi-steady assumptions. The proposed methodology changes the mean deviation compared to the reference flowmeter from −0.83% (underestimation of flowrate) to ±0.1%, increasing the method's accuracy.

References

1.
Saemi
,
S.
,
Raisee
,
M.
,
Cervantes
,
M. J.
, and
Nourbakhsh
,
A.
,
2018
, “
Numerical Investigation of the Pressure-Time Method Considering Pipe With Variable Cross Section
,”
ASME J. Fluids Eng.
,
140
(
10
), p. 101401.10.1115/1.4040718
2.
Baidar
,
B.
,
Nicolle
,
J.
,
Trivedi
,
C.
, and
Cervantes
,
M. J.
,
2016
, “
Winter-Kennedy Method in Hydraulic Discharge Measurement: Problems and Challenges
,” 11th International conference on hydraulic efficiency measurement (
IGHEM
), Linz, Austria, Aug. 24–26, pp.
11
21
.http://www.ighem.org/Papers_IGHEM/555.pdf
3.
IEC 60041,
1991 “
Field Acceptance Tests to Determine the Hydraulic Performance of Hydraulic Turbines, Storage Pumps and Pump-Turbines
,” International Standard, Reference number IEC 60041:1991(E).
4.
Gibson
,
N. R.
,
1959
, “
Experience in the Use of the Gibson Method of Water Measurement for Efficiency Tests of Hydraulic Turbines
,”
ASME J. Basic Eng.
,
81
(
4
), pp.
455
470
.10.1115/1.4008510
5.
Adamkowski
,
A.
, and
Janicki
,
W.
,
2010
, “
Selected Problems in Calculation Procedures for the Gibson Discharge Measurement Method
,”
GHEM
,
Roorkee, India
.
6.
Jonsson
,
P. P.
,
Ramdal
,
J.
,
Cervantes
,
M. J.
, and
Getz
,
A.
,
2009
, “
Experimental Investigation of the Gibson's Method Outside Standard
,”
24th Symposium on Hydraulic Machinery and Systems
,
IAHR
, Foz Do Iguassu, Brazil, Oct. 27–31, pp.
1
9
.http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A1000930&dswid=-9273
7.
Jonsson
,
P. P.
,
Cervantes
,
M. J.
, and
Finnström
,
M.
,
2007
, “
Numerical Investigation of the Gibson's Method: Effects of Connecting Tubing
,”
2nd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems
, Timisoara, Romania, Oct. 24–26, pp.
305
310
.
8.
Ramdal
,
J.
,
Jonsson
,
P.
, and
Nielsen
,
T.
,
2010
, “
Influence From Bends on a Pressure-Time Measurement
,”
IOP Conf. Ser. Earth Environ. Sci.
,
12
, p.
012078
.10.1088/1755-1315/12/1/012078
9.
Adamkowski
,
A.
,
Krzemianowski
,
Z.
, and
Janicki
,
W.
,
2009
, “
Improved Discharge Measurement Using the Pressure-Time Method in a Hydropower Plant Curved Penstock
,”
ASME J. Eng. Gas Turbine Power
,
131
(
5
), p.
053003
.10.1115/1.3078794
10.
Adamkowski
,
A.
,
Janicki
,
W.
, and
Lewandowski
,
M.
,
2020
, “
Measurements of Discharge Through a Pump-Turbine in Both Flow Directions Using Volumetric Gauging and Pressure-Time Methods
,”
Energies (Basel)
,
13
(
18
), p.
4706
.10.3390/en13184706
11.
Neyestanaki
,
M. K.
,
Dunca
,
G.
,
Jonsson
,
P.
, and
Cervantes
,
M. J.
,
2023
, “
Experimental Study of the Pressure-Time Method With Potential Application for Low-Head Hydropower
,”
ASME J. Fluids Eng.
,
145
(
7
), pp.
1
45
.10.1115/1.4062090
12.
Franzini
,
J. B.
,
Finnemore
,
E. J.
, and
Daugherty
,
R. L.
,
1997
, “
Fluid Mechanics With Engineering Applications
,” McGraw-Hill, New York, p.
807
.
13.
Teleszewski
,
T. J.
,
2018
, “
Experimental Investigation of the Kinetic Energy Correction Factor in Pipe Flow
,”
E3S
Web of Conferences, Bialystok, Poland, Apr. 16–18, pp.
1369
1374
.https://www.e3sconferences.org/articles/e3sconf/pdf/2018/19/e3sconf_eko-dok2018_00177.pdf
14.
Saemi
,
S.
,
Sundström
,
L. R. J.
,
Cervantes
,
M. J.
, and
Raisee
,
M.
,
2019
, “
Evaluation of Transient Effects in the Pressure-Time Method
,”
Flow Meas. Instrum.
,
68
, p.
101581
.10.1016/j.flowmeasinst.2019.101581
15.
Saemi
,
S.
,
Cervantes
,
M. J.
,
Raisee
,
M.
, and
Nourbakhsh
,
A.
,
2017
, “
Numerical Investigation of the Pressure-Time Method
,”
Flow Meas. Instrum.
,
55
, pp.
44
58
.10.1016/j.flowmeasinst.2017.05.003
16.
Fan
,
S.
,
Lakshminarayana
,
B.
, and
Barnett
,
M.
,
1993
, “
Low-Reynolds-Number k-ε Model for Unsteady Turbulent Boundary-Layer Flows
,”
AIAA J.
,
31
(
10
), pp.
1777
1784
.10.2514/3.11849
17.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.10.2514/3.12149
18.
Ahsan
,
M.
,
2014
, “
Numerical Analysis of Friction Factor for a Fully Developed Turbulent Flow Using k–ε Turbulence Model With Enhanced Wall Treatment
,”
Beni Suef Univ. J. Basic Appl. Sci.
,
3
(
4
), pp.
269
277
.10.1016/j.bjbas.2014.12.001
19.
ANSYS, Inc.
,
2016
,
ANSYS Fluent User's Guide, Release 17.2
,
ANSYS, Inc.
,
Canonsburg, PA
.
20.
SaemI
,
S.
,
Raisee
,
M.
,
Cervantes
,
M. J.
, and
Nourbakhsh
,
A.
,
2019
, “
Computation of Two- and Three-Dimensional Water Hammer Flows
,”
J. Hydraulic Res.
,
57
(
3
), pp.
386
404
.10.1080/00221686.2018.1459892
21.
Neyestanaki
,
M. K.
,
Dunca
,
G.
,
Jonsson
,
P.
, and
Cervantes
,
M. J.
,
2023
, “
A Comparison of Different Methods for Modelling Water Hammer Valve Closure With CFD
,”
Water
15
(
8
), p.
1510
.10.3390/w15081510
22.
Kalantar
,
M.
,
Jonsson
,
P.
,
Dunca
,
G.
, and
Cervantes
,
M. J.
,
2022
, “
Numerical Investigation of the Pressure-Time Method
,”
IOP Conf. Ser. Earth Environ. Sci.
,
1079
(
1
), p.
012075
.10.1088/1755-1315/1079/1/012075
You do not currently have access to this content.