International Journal of Fluid Machinery and Systems
Vol. 12, No. 4, October-December 2019
DOI: http://dx.doi.org/10.5293/IJFMS.2019.12.4.261
ISSN (Online): 1882-9554
Original Paper
Turbine Efficiency Measurement by Thermodynamic Test Method
Zhou Ye1, Pan Luoping1 and Cao Dengfeng1
1
Department of Hydraulic Machinery, China Institute of Water Resources and Hydropower Research
Fuxing Road A-1, Beijing, 100038, China, zhouye@iwhr.com, panlp@iwhr.com, caodf1987@foxmail.com
Abstract
According to the requirement of IEC60041, the paper introduces various turbine efficiency measurement methods,
and analyzes their feature and difficulties, then gives a detailed introduction for the principle and requirement of
thermodynamic test method. With an example of turbine efficiency test implemented in Costa Rica, the paper gives a
complete test procedure and data calculation for thermodynamic method. Finally, a comparison and verification among
thermodynamic method, ultrasonic method and Winter-Kennedy method has been made, the result shows that it has
great advantage and effectivity for thermodynamic method when using in flow measurement of high water head turbine.
Keywords: Turbine efficiency, hydropower unit, thermodynamic method, flow discharge, ultrasonic method, WinterKennedy Method.
1. Introduction
As the result of the measurement of turbine efficiency determines the quality evaluation and heavy fine, it has been one of the most
important process and factor in the international hydropower project. However, as it is related to unit type, turbine structure, water head
requirement and etc., it is difficult to carry out the turbine absolute efficiency test on site. In particular, the thermodynamic test method,
which requires high pressure withstanding equipment and accuracy thermos instrument, is rarely implemented.
In view of measurement difficulties, the paper makes a brief introduction for common turbine efficiency measurement methods
mentioned in IEC60041, analyzes the feature and difference, and gives an explanation for the test principle and thermodynamic method,
especially for the test requirement of IEC regulation. Then with a test example implemented in Costa Rica, the paper gives a complete
test procedure and data calculation case for thermodynamic method. Finally, the paper presents summary and analysis after comparing
the result of thermodynamic method with the results of other two methods - Winter-Kennedy method and ultrasonic method.
2. Turbine Efficiency Measurement
2.1 Turbine Efficiency Calculation
Before the production and delivery of turbine, the turbine model test will be made in hydraulic machinery model test laboratory, then
the porotype efficiency can be deducted with the model test result, but in international hydropower project, instead of model test, it is
necessary to carry out the prototype efficiency test to evaluation the machine quality.
The turbine efficiency calculation is not complicated as the following formula [1]：
t =
Pt
Pt
=
Ph   Q  g  H
(1)
where, Pt is turbine output power, kW; Ph is turbine input power, kW;  is water density, kg/m3, which can be indexed with water
temperature and pressure by Appendix E of IEC60041[2]; Q is turbine flow discharge, m3/s; g is gravity acceleration, m/s2, which can
be calculated by local latitude and altitude; H is turbine water net head, m.
The output of turbine can be acquired by the generator output, which is recorded from power transmiter, and generator efficiency
value, which is from generator efficiency test result or indexed by generator efficiency design curve.
The turbine work net head consists of two parts, static head and dynamic head, the first one can be calculated with spiral case inlet
pressure, draft tube outlet pressure and elevation difference of measuremnt points; dynamic head can be accquired with flow velocities
of two measuremnent sections, which are calculated with section areas and turbine flow discharge.
Then the key parameter of turbine efficiency measuremnet is flow discharge Q, the difficulties of measuremnt lie in the selection of
test method, the field implementation of test, verification of test result and etc.
Received March 28 2019; accepted for publication October 31 2019: Review conducted Yoshinobu Tsujimoto. (Paper number O19050S)
Corresponding author: Zhou Ye, Ph.D., zhouye@foxmail.com
* Part of this paper was presented at the 29th IAHR Symposium on Hydraulic Machinery and Systems, held at Kyoto, Sept. 16-21st, 2018.
261
2.2 Turbine Flow Measurement
The flow discharge of prototype turbine is much larger than that in model test, so the volumetric gauging method usually used for
model measurement, which is limited strictly by the pond volume and type, is hard to be implemented on site, meanwhile, the flow
state of prototype turbine is complicated that the flow distribution pattern changes with the unit operation condition and variance of
guide vane opening. When test is carried out on site, for ensuring the safety operation of plant, the installation period of test instruments,
test runs and schedule are restricted by the operation plan of power plant and power grid.
According to IEC60041, for measuring the flow discharge of turbine, there are current flow meter method, pressure-time method
(also called water hammer method), volumetric gauging method, Winter-Kennedy method, thermodynamic method and ultrasonic
method.
The pressure-time method is brought out by Gipson in 1923[3], when the method implemented, unit runs in sudden load rejection
mode, the guide vane closes rapidly, and water hammer occurs during the period, so the turbine flow discharge before the guide vane is
closed can be acquired by measuring the water pressure variance in intake pipe. But in test practice, considering the strict requirement
of intake pipe length, and the probable damage and mechanical effect caused by the several times load rejections of unit, it is unlikely
used in site.
The ultrasonic instrument has been developed rapidly in recent years, but the accuracy of surface mounted type is not very good,
there is higher accuracy for multi-channel and inner inserted type, but it needs heavy installation work during the construction of
hydropower project[4]. Furthermore, the ultrasonic method is listed in appendix, not in body content of IEC60041, which brings a lot
of difficulties to be used in verification of contract guarantee.
For the turbine of high water head which is max than 100 meters, thermodynamic method is a more effective way to measure the
turbine flow discharge, but it has high requirement of 0.001K accuracy thermos meters, which limits the usage of method.
Table 1 gives the feature and advantage of common flow measurement methods.
Method
Table 1 Feature list of common turbine flow measurement methods [5][6]
Advantage
Shortcoming
Pressure-time method
Small installation work
Thermodynamic method
High accuracy
Ultrasonic method
Can be equipped permanently
Winter-Kennedy method
Easy measurement
Current-meter method
For all water head
Lack of practical experience, damage risk of rejection load, strict requirement
for intake pipe.
High water head required, high water pressure-resisted, high accuracy thermometer needed
Normal accuracy, partly used for contract, large installation work. Field ca
libration and verification needed
Low accuracy, cannot get absolute flow discharge, cannot be used for contract
guarantee evaluation.
Enormous instrument installation, strict test requirement, risk for measurement.
3. Thermodynamic Method
3.1 Test Formula
The thermodynamic method results from the application of the principle of conservation of energy (first law of thermodynamics) to
a transfer of energy between water and the runner through which it is flowing. In the actual operation, when the water passes through
the turbine flow channel, it will produce a series of losses caused by friction, vortex, and flow separation and so on. All the losses will
transfer to the thermal energy and make the water temperature difference between the turbine inlet and outlet section. The temperature
difference is determined by the structure characteristics and work head of unit. Based on the temperature difference and water pressure,
we can calculate the efficiency of turbine.
In the case of actual machine operation, the energy per unit mass Eh delivered to a turbine shaft may be determined by measurement
of the performance variables (pressure, temperature, velocity and level) and from the thermodynamic properties of water, and it can be
calculated by the following equation[2],[7],[8].
(
)
E = P
−P
/  + ( v12 − v22 ) / 2 + g（
 Z1 − Z 2 )
h
abs1 abs 2
(2)
where,  , average water density of high and low pressure sections, kg/m3; g , average gravity at high and low sections, m/ s2; Pabs1,
Pabs2 , water pressure in high and low pressure sections, kPa; v1, v1 , water velocity in high and low pressure section, m/s; Z1, Z2,, the
level of high and low pressure measuring section, m;
And the expression of the specific mechanical energy Em is:
Em = a ( Pabs1 − Pabs 2 ) + CP (1 − 2 ) + ( v12 − v22 ) / 2 + g（
 Z1 − Z 2 ) +  Em
(3)
Here, 1, 2, water temperature of high and low pressure section, K, C P , the average water specific heat capacity, J·kg-1·K-1, a ,
the average isothermal factor of water, m3·kg-1, δEm, the corrective energy term of turbine mechanical energy, kW.
Normally, for the convenient of measurement, the water of high and low pressure measuring sections can be led into the sample
vessel, so we can install a high pressure sample vessel on the inlet pipe of turbine, and measured the related parameters of it, such as the
water pressure Pabs11, the water temperature 11, the flow velocity v11, the horizontal level of vessel Z11, instead of measurement
values in high pressure section of inlet pipe. Then, the specific mechanical energy Em can be calculated by:
Em = a ( Pabs11 − Pabs 2 ) + CP (11 − 2 ) + ( v112 − v22 ) / 2 + g（
 Z11 − Z2 ) +  Em
262
(4)
3.2 Calculation Procedure
Firstly, we can get the input power P of generator, with its output PG and efficiency ƞG, and get the turbine mechanical power Pm,
then calculate the specific mechanical energy Em with the parameters of sample vessel and low pressure measuring section.
The flow discharge Q of turbine can be calculated with Pm and Em, then the flow velocities in the high and low pressure section.
Finally, we can get the specific hydraulic energy Eh and hydraulic efficiency ƞh, with turbine hydraulic efficiency ƞh and turbine
mechanical efficiency ƞm, we can get the turbine efficiency ƞt.
Fig. 1 Calculation procedure scheme for thermodynamic method
The calculation procedure scheme for thermodynamic method is shown in fig. 1, it can be seen that the key data are Pm and Em,
and Q can be calculated by the equation:
Pm = QEm
(5)
Then the parameters for calculating Pm and Em can be measured as eq. (3) and eq. (4) shown by test sensors and transducers.
4. Field Test Case
4.1 Instruments Installation
Here is a field test for a hydropower plant in Costa Rica, the test has been carried out in 242m and 250m water head, the sensors
arrangement and installation scheme see fig. 2. During the test, we adjust the unit power output step by step, then check the water
temperature variance in each run, it can be estimated that the thermal equilibrium is reached when the water temperature variation per
minute is less than 0.005K[9].
Fig. 2 Sensors arrangement scheme for thermodynamic method test
On the side of high pressure measuring section, the water of turbine inlet is led into the sample vessel through the probe, which
measured for the physics parameters of flow discharge, temperature, pressure and etc. The water temperature in sample vessle is
measured with Seabird SBE35 high precision thermometer, the water head and spiral case differential pressure are measured by two
differential pressure transducers.
The tailrace water average temperature is measured with installed measurement frame at low-pressure side. The water velocity ,
pressure and other parameters of low-pressure side are measured to calculate specific mechanical energy of water. The draft tube outlet
water temperature of low-pressure side is measured by another Seabird SBE35 thermometer, the water level of tailrace channel is
measured with a water level meter. The flow velocity of tailrace can be calculated with iteration algrithm.
The fig. 3 and fig. 4 show the instruments installation picture in field test.
263
Fig. 3 Sample vessel installation picture
Fig. 4 Measurement frame picture for tailrace channel
4.2 Data Calculation
During the test, with the increasing of power output, the water temperature in two measuring sections is listed in Table 2, the
temperature trend curve is shown in fig. 5.
Table 2 Water temperature variance during the test
Item
Unit
θ11
Active Power (MW)
14.76
17.74
22.87
27.48
31.77
35.94
39.91
44.43
℃
21.198111
21.188072
21.183790
21.179316
21.178194
21.177841
21.178851
21.181315
θ20
℃
21.260023
21.226117
21.193009
21.175574
21.161528
21.158716
21.157987
21.166631
Δθ
℃
0.061912
0.038045
0.009219
-0.003742
-0.016666
-0.019125
-0.020864
-0.014684
According to the expression of specific mechanical energy Em, we can get the result with the measuring parameters of high pressure
sampling vessel and low pressure measurement section. Also, the turbine mechanical power Pm can be calculated with the generator
power output and generator efficiency, which curve of 1.0 power factor is provided by the generator manufacturer. Then the flow
discharge Q can be calculated with Em and Pm, the test result is listed as Table 3.
Table 3 The generator output working points of turbine efficiency test
Item
Unit
40%Pr
50% Pr
60% Pr
70% Pr
80% Pr
90% Pr
100% Pr
110% Pr
PG
MW
14.76
17.74
22.87
27.48
31.77
35.94
39.91
44.43
Δθ
℃
0.061912
0.038045
0.009219
-0.003742
-0.016666
-0.019125
-0.020864
-0.014684
Em
J/kg
2052.40
2145.79
2258.53
2292.31
2334.13
2328.62
2312.79
2269.42
ηg
%
96.18%
96.76%
97.37%
97.76%
97.97%
98.14%
98.27%
98.33%
Pm
kW
15436.68
18420.83
23569.81
28199.23
32512.86
36705.92
40696.96
45269.35
H
m
256.43
255.96
255.78
254.31
253.83
253.15
252.28
251.15
Q
m3/s
7.53
8.60
10.45
12.32
13.95
15.79
17.62
19.98
The turbine efficiency test curve in 250m sees fig. 6
Fig. 5 Temperature change trend between two sections
Fig. 6 turbine efficiency test result curve in 250m head
264
According to the section 6.1.2.2 of IEC41, if 0.99  (n / E ) / (nsp / Esp )  1.01 , the turbine efficiency ƞ doesn’t need correction,
but the conversion of flow discharge Q and power output P should be made at 6.1.2.2 a) formula. If (n / E ) / (nsp / Esp ) is outside
the range, it is necessary to make a correction of ƞ, in addition to Q and P conversion. the test result converting to 250 meters’ water
head is shown in Table 4.
Table 4 The turbine efficiency value list corrected to 250m water head
QPercentage
H
Psp
Qsp
ηtsp
%
m
kW
m3/s
%
41.32%
47.20%
57.40%
14776.44
7.44
81.38%
17697.63
8.50
85.32%
22692.20
10.33
89.96%
67.86%
76.91%
250
27401.04
31695.10
12.21
13.84
91.89%
93.78%
87.15%
97.46%
110.73%
35937.36
15.69
93.84%
40061.47
17.54
93.54%
44871.77
19.93
92.22%
5. Result Comparison and Analysis
5.1 Calibration for Winter-Kennedy Method
According to the principle of Winter-Kennedy method, the turbine discharge can be represented by Q=K*Δhn, here Δh is differential
pressure between spiral case inlet and draft tube outlet, k and n are the coefficients. As the absolute flow discharge is calculated, one
differential pressure transducer of Rosemount 3051CD with 0.075% accuracy is installed for determining the Winter-Kennedy
coefficient and verifying the flow discharge measurement.
Figure 7 shows the relationship curve between spiral case differential pressure and absolute flow discharge calculated by
thermodynamic method, and the corresponding Winter-Kennedy coefficients as k=8.2314, n=0.5095 can be acquired with exponential
fitting algorithm, the result comparison between two methods is shown in fig. 8.
Fig. 7 Differential pressure versus turbine discharge
Fig. 8 Discharge comparison for two methods
5.2 Compare with Ultrasonic Method
The multi-channel ultrasonic flow meter has been installed in the unit, so three series of measuring values of ultrasonic flow meter
from DCS (Distributed Control System) are exported and compared with test values in 250m head. The results are shown in Table 5.
The Qua, Qub and Quc represent the values of three channels data from DCS.
Table 5 Turbine flow discharge and ultrasonic discharge value list
Item
Qtest
Qua
Qub
Quc
Qave
Difference
Unit
m3/s
m3/s
m3/s
m3/s
m3/s
%
47.76%
8.60
8.530
8.573
8.827
8.643
0.54%
Discharge Percentage (%)
68.44%
77.50%
12.32
13.95
12.243
13.970
12.374
14.497
12.565
14.088
12.394
14.185
0.60%
1.69%
58.06%
10.45
10.465
10.912
10.667
10.681
2.20%
87.70%
15.79
15.98
15.905
16.287
16.057
1.72%
97.90%
17.62
17.460
17.620
18.214
17.765
0.81%
In the period of test working points, the compare results between three series of ultrasonic flow meter values and test discharge value
are shown in the fig. 9.
265
Fig. 9 Multi-channel ultrasonic discharges versus test discharge
Fig. 10 Ultrasonic discharge mean value versus test discharge
From the fig. 9, it can be found that values of ultrasonic flow meter are close to the test measuring result. Among the three series of
values, the result of channel A is similar to the test value, the result of channel C is most far from, but still is close to the test value.
From the fig. 10, it can be seen that the average value of three series of ultrasonic flow meter is slightly larger than the test result, it may
be caused by the installation condition and calibration result of ultrasonic flow meter.
5.3 Result Analysis
When turbine mechanical power Pm and specific mechanical energy Em are obtained, the flow discharge and work net head can be
calculated, then the turbine efficiency can be determined directly by the eq. (1). If needed, according to the procedure scheme shown in
Fig. 1, the turbine hydraulic efficiency and mechanical efficiency can be calculated separately.
In the thermodynamic method, there are partial expansion operating procedure and direct operating procedure. In the test, the direct
operating procedure is adopted, in which both the pressure and temperature of water are measured. For partial expansion operating
procedure, an expansion valve is needed in the sampling circuit composed of the pipe at the high pressure side and the corresponding
measuring vessel, then the measurement is made by adjusting the expansion valve to achieve the temperature equality between the two
measuring sides. But as the high pressure of sampling vessel and connection part caused by high water head, the continual and frequent
adjustment for the valve is not recommended, furthermore, in some load test runs, it is hard to achieve the temperature equality, so
direct operating procedure is preferred in the test.
In order to meeting the requirement of temperature measurement accuracy up to 0.001K, in the past, the temperature measuring
bridge with thermal resistor has been used. However, since the distance between measuring locations of spiral case inlet and draft tube
outlet are usually far, the resistance of long wire will decrease the accuracy of measurement greatly, also it is hard to connect the two
side wires and draw wires out from the draft tube channel. Therefore, two high accuracy thermometers of Seabird SBE35 are used for
optimizing the test uncertainty. The result shows the uncertainty is less than 0.79%.
According to the requirement of IEC60041[2], if the difference between the efficiency values at any two locations for low pressure
measuring side is larger than 1.5%, then the thermodynamic method is not recommended. As the high accuracy thermometer is
expensive, the advanced draft tube outlet measuring frame is designed for meeting the IEC’s requirement with only one thermometer in
low pressure measuring side. The measuring depth is changed step by step when the frame is pulled by lifting rope, the data and
efficiency result at different location in one test run can be acquired and compared.
Comparing the test results of thermodynamic method, Winter-Kennedy method and ultrasonic method, the thermodynamic method
shows a good consistency, and the measurement equipment installed in the unit can be used as a long-term flow discharge
measurement equipment. Furthermore, for multi-channel ultrasonic flow meter, there is maximum error of 2.2%, and minimal error of
0.54% between the average flow discharge and test result by thermodynamic method, it basically meets the uncertainty requirement
within 1.0% to 2.0%[10].
6. Conclusion
The paper describes the calculation method of turbine efficiency in detail, compares and analyzes various measurement methods
mentioned in IEC60041 for absolute flow discharge, as the key parameter of efficiency test. Then the calculation and deduction
procedure of thermodynamic method is summarized, and a complete test example including instrument installation and data calculation
is given. The test data and results are compared and analyzed with which of Winter-Kennedy method and ultrasonic method, the result
shows that when the field test meets the requirement of IEC, thermodynamic method has good performance with high accuracy and
consistency, the test and calculation example in the paper can be reference for similar test projects to performed in other hydropower
plants.
Acknowledgments
The paper is supported by the IWHR Research & Development Support Program (HM0145B182017).
266
Nomenclature
Pt
P
PG

Q
H
Z
Eh
Cp
ƞG
ƞb
Turbine output power [kW]
Generator axial power [kW]
Generator power output [kW]
Water density [kg/m3]
Turbine flow discharge [m3/s]
turbine water net head [m]
Level of measuring section
Specific hydraulic energy [kW]
Specific heat capacity [J·kg-1·K-1]
Generator efficiency
Turbine hydraulic efficiency
Ph
Pm
g
P
v

Em
a
ƞm
ƞt
Turbine input power [kW]
Turbine mechanical power output [kW]
Gravity acceleration [m/s2]
Water pressure [kPa]
Water velocity [m/s]
Water temperature [℃]
Specific mechanical energy [kW]
Isothermal factor of water [m3·kg-1]
Turbine mechanical efficiency
Turbine efficiency
References
[1] Zhou Y., Pan L.,Cao D., Liu Y., 2018, “Research of key technology for turbine efficiency measurement based on
thermodynamics method,” 29th IAHR Symposium on Hydraulic Machinery and Systems, Kyoto, Japan.
[2] IEC Code 60041, 1991, Field acceptance tests to determine the hydraulic performance of hydraulic turbines, storage pumps
and pump-turbines, Geneva.
[3] Thi V., Marcel K., Maxime G., Claire D., 2011, “Flow simulation and efficiency hill chart prediction for a Propeller turbine,”
International Journal of Fluid Machinery and Systems, Vol.4, No.2, pp.243-254.
[4] Beaulieu S., Deschênes C., Iliescu M., Fraser R., 2009, “Flow Field Measurement Through the Runner of a Propeller Turbine
Using Stereoscopic PIV,” 8th International Symposium on Particle Image Velocimetry – PIV09, Melbourne, Australia.
[5] Duquesne P., Iliescu M., Fraser R., Deschênes C., Ciocan G. D., 2010, “Monitoring of velocity and pressure fields within an
axial turbine,” 25th IAHR Symposium on Hydraulic Machinery and Systems, Timisoara, Romania.
[6] Petr S., 2014, “Turbine efficiency measured by thermodynamic method against measurement using ultrasonic flowmeter,” Int.
Conf. on Hydro Turbo.
[7] Verma H., Kumar A., 2007, “Performance testing and evaluation of small hydropower plants,” Int. Conf. on Small
Hydropower, Sri Lanka, pp.22-24.
[8] You G., Zhou X., Yu H., 2005, “Field thermodynamic efficiency tests for pumps and water turbines of THP pumped storage
power station,” East China Electric Power, PP.33-41.
[9] Gao Z., Lv S., Wei Y., 2008, “Discussion and application of pump efficiency measure by thermodynamic method,” Applied
Energy Technology, Vol.14, No.7, pp.5-8.
[10] Li C., An L., Wang S., 2000, “The progresses in the thermodynamic analyzing method for the pump efficiency monitoring,”
Journal of North China Electric Power University, Vol.10, No.4, pp.88-92.
267