1

EXPERIMENTS WITH THE THERMODYNAMIC METHOD Emmanuel Côté, Eng. and Gilles Proulx, Eng.

Test Engineers, Hydro-Québec, 5565, rue De Marseille, Montréal, Qc, Canada, H1N 1J4

SUMMARY The thermodynamic method was recently used for efficiency testing in a high-head plant in northern Québec, and the results were compared with results obtained with the acoustic transit-time method. Uncertainty caused by energy distribution was evaluated, and experiments were performed to find answers to unresolved questions and to verify hypotheses so that application of the thermodynamic method at Hydro-Québec could be improved.

Four total-head probes were used to extract sample discharges upstream of the spiral casing. Water temperature was measured directly in the probe, while pressure was measured at the probe ports. One of the probes was longer than the others, to check the impact of wall proximity on the measurements obtained. Possible environmental heating of the water and friction heating of the thermometer sensor (friction with the sampling discharge) were also tested by varying the sampling discharge for a given turbine operating point. An adiabatic measuring chamber was also installed downstream of one of the sampling probes to validate that specific mechanical energy measured would be the same in quasi-stagnant conditions.

Eight thermometers (with current meters for weighting purposes) were placed on a frame to scan flow vertically at the end of the draft tube. All but one of these thermometers were equipped with an aluminum cylinder that completely surrounded the temperature sensor and reduced water velocity around it. The remaining thermometer was equipped with a protector that allowed flow to circulate freely around the temperature sensor. A measuring vessel was also installed on the frame to measure total temperature and pressure in reduced-velocity conditions.

The results obtained with the thermodynamic method corresponded very well with those obtained with the acoustic method, and the additional testing and analyses answered many ongoing questions about the thermodynamic method. Environmental heating of the sampling probes was greater than anticipated, while no friction heating of the temperature sensors was detected. Downstream measurements in the main flow were confirmed in quasi-stagnant conditions, but higher temperatures were measured in the absence of a flow-reducing protector around the temperature sensor. This paper describes and analyzes the testing methods, results and additional experiments conducted in this case study.

2

SITE AND OBJECTIVES The thermodynamic method uses the principle of conservation of energy to determine the efficiency of a hydraulic turbine from measurements of performance variables (such as pressure, temperature, velocity and level) and the thermodynamic properties of water. The accuracy of the method increases with the amount of specific hydraulic energy measured, and the method is thus preferably used to assess high-head turbines (head ≥ 100 m), as stated in the IEC 41 standard.

For this case study, thermodynamic tests were carried out on a Francis turbine with a specified net head of 330 m in an underground two-unit power plant in northern Québec, Canada. As shown in Figure 1, spiral cases are supplied with water by an 8.5-km headrace tunnel that leads to a surge tank and then a manifold, a converging section and a ball valve. Specified unit output is 440 MW at a flow of about 150 m³/s.

Figure 1: Cross section of site and unit

Following the commissioning of the units, efficiency tests were performed for contractual and operating purposes. To increase the level of confidence of the results, two methods were used: thermodynamic and acoustic transit-time. To reduce the uncertainty of the thermodynamic method and answer several questions, about temperature measurement in particular, additional measures were taken. Details and results of these measures are discussed in the additional experimentation section.

Manifold Penstock

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3

THERMODYNAMIC METHOD With the thermodynamic method, efficiency is defined as the ratio of specific mechanical energy to specific hydraulic energy. Both these specific energies are measured differences between a high-pressure section upstream and a low-pressure section downstream of the turbine. Figure 2 shows the locations of these sections.

Figure 2: Positioning of the measuring sections

Specific hydraulic energy is commonly measured for efficiency testing, and good precision is relatively easy to achieve. However, computing specific mechanical energy with accuracy requires measuring water temperature differences of only a few mK. To do this, sampling discharges were extracted by four probes installed in the high-pressure section while the low-pressure section was scanned with thermometers and current meters on a frame in motion.

High-Pressure Section Figure 3 shows the installation of one of the four sampling probes. The cylindrical total-head probe facing the flow inside the conduit is shown on the left, and the piping and insulation are shown in the center and on the right respectively.

Figure 3: Installation of sampling probe

When a sampling discharge is extracted, temperature is immediately measured in the probe. A pressure sensor is positioned just outside the conduit at the outside end of the probe. After passing by the temperature and pressure sensors, water circulates around the thermometer, to insulate it from ambient temperature, and finally crosses a small propeller flow meter before discharge to the drain. All piping is insulated to minimize heat exchanges with ambient air.

High-pressure measuring section Low-pressure

measuring section

4

Low-Pressure Section

Figure 4 shows the measuring frame: CAD representation on the left, picture in the centre and zoom on one of the eight thermometers with its current meter on the right.

Figure 4: Low-pressure measuring frame

For each operating point, the frame scans the flow vertically in the stoplog gates at the end of the draft tube. The frame is equipped with eight thermometers equally spaced along the lower horizontal profiled rod. A current meter beside each thermometer measures water velocity. Gathering data over the entire measuring section allows computation of temperature and velocity profiles. Temperature is then integrated and weighted with the velocity profile to obtain average temperature for the low-pressure section. Pressure is read on the two static pressure taps located on the side walls.

Specific Mechanical Energy Corrections

The corrective term for specific mechanical energy was calculated taking three factors into account, in accordance with IEC 41:

1. Water temperature variation during travel between the two measuring sections. 2. Heat exchanges with the sampling probes 3. Heat exchanges with ambient air introduced by aeration

TRANSIT-TIME ACOUSTIC METHOD

The transit-time acoustic method of discharge measurement uses the difference in time of travel of acoustic pulses transmitted downstream versus upstream on a given path crossing the conduit to determine the average velocity of water along that path. Discharge is computed by integrating the velocity of multiple paths, assuming a fully-developed velocity profile.

To increase the accuracy of the results, the velocity profile at the measuring section should be stable, axisymmetric and fully developed. Therefore, the section should be as far as possible from any disturbance. IEC 41 recommends ten conduit diameters of straight length upstream and three downstream. The location of the measuring section is shown in Figure 5. As the figure shows, it was not possible to follow the recommendation, but the disturbance of a slightly converging section is usually small.

Figure 5: Acoustic measurement section

Like most systems meeting IEC 41 requirements, the layout of the transducers consists of two four-path planes at 65°, for a total of 16 transducers. With four-path planes, quadrature integration methods can be used, and use of two planes eliminates the effect of traverse velocity components.

Acoustic velocity measurement section

L ≈ 6D D = 4.250 m

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COMPARISON OF RESULTS

Figure 6 shows the efficiency curves resulting from thermodynamic testing of units 2 and 1 and acoustic method testing of unit 2.

Figure 6: Comparison of thermodynamic on both units and acoustic testing

The two thermodynamic curves are of quite similar shape, with peak efficiency located at about the same output. Unfortunately, no data are available at higher discharges for unit 1, since the thermodynamic testing was stopped once peak efficiency was reached. However, results indicate that unit 1 is about 0.3% more efficient than unit 2 over most of the operating range. These measured differences are what justifies testing every unit. Mean weighted efficiency was very close to guaranteed efficiency in both units.

Figure 6 also shows that the thermodynamic method yields a lower efficiency than the acoustic method in unit 2 when discharge is low, but a higher efficiency after optimal discharge is reached. Comparison with the index curve of static pressure difference in the converging section suggests the efficiency value obtained via the acoustic method is slightly overvalued before the peak. However, the efficiency value yielded by the thermodynamic method seems to be overvalued for the three runs at highest output, with the discrepancy starting at a discharge of about 120 m³/s, or 80% wicket gate opening.

A 120-m³/s discharge gives an average velocity of about 15 m/s at the upstream sampling section. At such velocities, friction can heat the probe slightly, causing the temperature of the sampling water to rise by a few mK. Though difficult to validate, this seems the most plausible explanation of what appears to be a slight overvaluation of efficiency by the thermodynamic method at high velocity. In future testing, this will be checked using a sampling probe shaped more like a Pitot tube.

Nonetheless, all efficiency deviations remained small and within the expected uncertainty margin for these methods of efficiency testing.

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ENERGY DISTRIBUTION AND NUMBER OF SAMPLINGS IEC 41 suggests that uncertainty due to the absence of exploration of energy distribution can amount to ±0.2% and ±0.6% for the high- and the low-pressure sides respectively. Energy distribution is shown for both sides and uncertainty estimated by plotting standard deviation as a function of the number of samplings.

High-Pressure Section

Figure 7 presents the energy distribution of the samplings on the high-pressure side. Left and right are referenced looking downstream.

Figure 7: High-pressure energy distribution

Deviations were about +0.20% and -0.15% respectively for the lower-left and upper-right samplings. Figure 8 shows standard deviation of specific mechanical energy versus number of samplings.

Figure 8: Uncertainty for high-pressure exploration

Based on Student’s “t” distribution, the estimated 0.037% standard deviation for four samplings gives an uncertainty of 0.059% on average with a 95% level of confidence. The 0.2% uncertainty estimate for sampling without exploration seems accurate in the present case.

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Low-Pressure Section

Figure 9 shows temperature distribution of the eight thermometers on the low-pressure side.

Figure 9: High-pressure energy distribution

Temperature distribution fluctuates greatly with flow. The average standard deviation of temperature distribution is 3 mK. Figure 10 shows standard deviation of specific mechanical energy versus the number of thermometers taken into account.

Figure 10: Uncertainty for high-pressure exploration

Based on Student’s “t” distribution, the estimated 0.14% standard deviation gives an uncertainty of 0.12% on average with a 95% level of confidence. The 0.6% uncertainty estimate for sampling without exploration is close, but slightly higher than these results.

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ADDITIONAL EXPERIMENTATION WITH THE THERMODYNAMIC METHOD

To validate different theories and increase the confidence level of the results obtained with the thermodynamic method, additional verifications were performed.

Upstream Expansion Chamber To test the influence of water velocity on temperature measurement, a measuring chamber was installed downstream of one of the sampling probes. This second measurement of specific mechanical energy was made at much lower velocity (16 times slower, since the pipe diameter is four times larger). Figure 11 shows the measuring vessel, supplied by sampling water downstream of the installation shown in Figure 3.

Figure 11: Upstream measuring vessel

If there is no heat exchange with the ambient air, the specific mechanical energy measured at both locations should be the same. Therefore, mineral wool was installed to insulate the tubes carrying the sampling discharge.

Efficiencies computed using the data collected in the measuring vessel were all at least 1.75% too high. The variation in specific mechanical energy as a function of sampling flow suggests the insulation was not sufficient to prevent heat exchanges with the ambient environment.

Sampling Probe Length To test the impact of the distance between the wall and the location where the sampling is done, one of the four probes was slightly longer. IEC 41 specifies only that sampling must be done more than 5 cm from the wall. Figure 12 shows the two types of probes.

Figure 12: Sampling probes (two lengths)

No significant difference was found between the results obtained with the longer probe and those obtained with the other probes. The differences between the results obtained with probes of different length were small and not greater than those obtained with probes of the same length.

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Sampling Discharge

IEC 41 recommends a sampling discharge between 6 and 30 L/min. A lower discharge reduces the risk of heating the thermometer probe by friction, while a higher discharge reduces the risk of influence from an external source of energy. Since water temperature is measured directly in the sampling probe, the risk of external sources of energy influencing the measure seemed virtually nonexistent and a discharge of 6 L/min was targeted.

To test its influence on results, sampling discharge was altered from 2 to 16 L/min and four runs of data were taken at the same point of operation of the turbine. Figure 13 shows the specific mechanical energy measured (before correction for external heat exchange) as a function of the inverse value of the sampling discharge.

Figure 13: Influence of sampling discharge on specific mechanical energy

Since environmental heating is inversely proportional to sampling discharge, the intercept point of the linear regression gives the specific mechanical energy that would have been measured if the sampling discharge were infinite, meaning the measure is not influenced by external heating. Even though water temperature is measured immediately in the sampling probe and all conduits are insulated, specific mechanical energy is still influenced by environmental heating in the range of 0.3 % depending on the sampling discharge.

On the other hand, no additional heating that could have come from water friction on the temperature sensor was demonstrated at the maximum sampling discharge measured. A discharge of 16.4 L/min gives a velocity of 1.7 m/s at the sensor, within the recommendations of IEC 41 (<2.0 m/s). A greater increase in sampling discharge would have been necessary to start observing heating by friction.

In short, the correction for heat exchange gives accurate results. However, the correction could have been smaller without introducing friction heating of the temperature sensor if the sampling discharge had been increased so velocity approached 2.0 m/s at the thermometer.

y = 42.0185x + 3 052.9015R² = 0.9685

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Downstream Thermometer Protectors Seven of the eight thermometers installed on the downstream measuring frame had a cylindrical protector covering the temperature sensor in its entirety. In addition to protecting the sensor, this cylinder also controls the flow of water circulating around it; two small holes drilled near the downstream end of the cylinder allowed circulation of water while reducing the velocity of the flow on the sensor. The protector on the remaining thermometer protected the sensor from being hit by objects while allowing free circulation around it. Figure 14 shows the two types of protectors.

Figure 14: Two types of protectors

To test the flow-reducing cylinders, the second thermometer (T2) was installed with the simple protector allowing free flow around the sensor. Table 1 shows temperature measurements of thermometer T2 in comparison with those of its neighbors (T1 and T3).

Table 1: Temperature comparisons

Temperature measured by thermometer T2 is always a little higher than the average of the temperatures measured by its two neighbors. Results do not show correlation between the deviation and water velocity. Other thermometers also showed similar trends.

Water Velocity Deviation (mK)Run Mean(T1,T3) T2 V2 (m/s) T2 - Mean(T1,T3)57 6.8492 6.8505 1.72 1.343 6.9040 6.9070 1.07 3.056 6.8219 6.8245 1.19 2.644 6.7886 6.7917 2.15 3.139 6.9031 6.9056 2.17 2.555 6.8051 6.8098 2.23 4.759 6.8302 6.8316 2.04 1.549 6.7847 6.7860 1.79 1.345 6.7037 6.7049 1.85 1.348 6.7937 6.7953 2.31 1.647 6.7607 6.7656 2.63 4.946 6.7194 6.7214 2.98 1.9

Mean Deviation: 2.5

Downstream Temperature (°C)

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Downstream Measuring Chamber To verify the downstream measure of specific mechanical energy directly in the flow, a measuring vessel (Figure 15) was installed on the frame with the thermometers and current meters. Water from the main flow enters the vessel through a Pitot tube-type total head input and exits through a small hole on the opposite side that controls circulation. Total temperature and pressure are thus measured in the vessel in quasi-stagnant conditions. Static pressure is also measured at the same elevation outside the vessel.

Figure 15: Downstream measuring vessel

Since pressure sensor signals become saturated when the sensor is too deeply submerged, only data from the higher part of the draft tube could be analyzed. It was still possible, nonetheless, to compare temperatures and energies measured by both methods. Table 2 shows the results of these comparisons.

Table 2: Comparison between measurements in the flow and in the vessel

Even though specific mechanical energy is slightly lower when measured using the vessel, the mean deviation of 0.05% is minimal and confirms the validity of temperature measurement in the flow.

Run T7 (°C) Tv (°C) Deviation (mk) Em,T7 (J/kg) Em, Vessel (J/kg) Deviation (%)57 6.8470 6.8481 1.0 2980.84 2977.21 -0.12%43 6.9029 6.9036 0.8 3052.24 3049.25 -0.10%56 6.8175 6.8180 0.5 3071.08 3069.38 -0.06%44 6.7737 6.7749 1.2 3083.97 3083.07 -0.03%39 6.8967 6.8979 1.2 3093.43 3092.02 -0.05%55 6.8026 6.8038 1.2 3064.29 3062.79 -0.05%59 6.8349 6.8363 1.3 3057.79 3055.05 -0.09%49 6.7875 6.7878 0.4 3058.32 3057.97 -0.01%45 6.7068 6.7069 0.1 3054.83 3055.26 0.01%48 6.7931 6.7941 1.0 3051.37 3049.92 -0.05%47 6.7506 6.7514 0.8 3039.94 3039.73 -0.01%46 6.7156 6.7171 1.5 3031.65 3030.44 -0.04%

Downstream Temperature (°C) Specific Mechanical Energy (J/kg)

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CONCLUSIONS Efficiency measured by the thermodynamic method averages 0.07% higher than efficiency measured with the acoustic transit-time method. Though the shapes of the curves of these measured efficiencies are somewhat different, the deviation never exceeds 0.5% at any given operating point. There seems to be a slight overvaluation of thermodynamic efficiency at higher discharges, where friction heating of the sampling probes is possible. There is a 0.33% difference in efficiency between the two units of the plant and efficiency uncertainty on unit 2 is evaluated at 0.35%.

With four sampling probes in the high-pressure section and eight thermometers in the low-pressure section, uncertainties for energy distribution exploration are evaluated at 0.037% and 0.12% for the high- and low- pressure sections respectively.

External heating of the sampling probes was greater than anticipated. An approximate 0.3% correction of the specific mechanical energy value obtained was necessary due to heating of the sampled water by the external environment before temperature measurement in the sampling probes.

On the other hand, no friction heating of the temperature sensors was detected. Maximum sampling discharge gave a velocity of only 1.7 m/s at the temperature sensor, which is probably too slow to generate significant friction heating.

Downstream measurements with a frame in motion in the main flow were confirmed in quasi-stagnant conditions. Mean deviation between specific energy measured directly in the flow and specific energy measured by a total-head expansion chamber was only 0.05%.

However, higher temperatures were measured when there was no flow-reducing protector around the thermometer sensor; mean deviation was 2.5 mK and did not correlate with water velocity.

REFERENCE 1. IEC 60041, “International Standard: Field acceptance tests to determine the hydraulic performance of

hydraulic turbines, storage pumps and pump-turbines,” third edition, 1991-11.

BIOGRAPHIES

Emmanuel Côté, Eng., graduated in Mechanical Engineering from the University of Sherbrooke in 2007. He has worked for Hydro-Québec Production’s testing department since 2008 and has conducted many tests of hydraulic turbine performance using the department’s main test methods—including the current-meter, acoustic transit-time, pressure-time and thermodynamic methods as well as different index tests.

Gilles Proulx, Eng., graduated in Mechanical Engineering from the École Polytechnique de Montréal in 1989 and has worked for Hydro-Québec’s test department since then. He has worked on the commissioning of major Hydro-Québec power plants and has performed many performance tests using different methods. He is responsible for the R&D team of the testing department and is the convenor of Maintenance Team 28 of the TC4 of IEC and a member of the ASME PTC 18 revision committee.

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A PROPSAL FOR IMPROVING THE THERMO DYNAMIC METHOD.

BY: Professor Emeritus Consultant Hermod Brekke, Norway

Introduction. The paper presents the Thermodynamic Efficiency Measurement at 2 power plants in Norway where both temperature and velocity have been measured proving that it is possible to weigh the energy in a correct way by this method. In addition the measurement of a vertical Small Hydro Pelton turbine is presented where the measuring condition made a systematic error when using perforated pipes for collection the water at the turbine outlet. A discussion on the possible reason for the error is given. Examples are given of measurement by using weighted energy from the measuring points by measurement of both velocity and temperature in each point. Measurement at Bratsberg Power plant. The technical data for the turbine at Bratsberg yields: P = 60 MW, Hn=130 m, n = 300 RPM. In general it will not be correct to measure the temperature in 3*3 = 9 positions and use the average temperature for the energy calculation of the energy at the outlet from the turbine. At Bratsberg a measurement was made by using a collector as illustrated in fig.1 for a test to include the influence from the stagnation pressure of the water to obtain the right amount of water from each point in 6 locations across the draft tube outlet.

Fig.1 The flow collector used for the temperature measurement at Bratsberg. /Ref. 1/ However, even if the stagnation pressure into each inlet was representative for each point a certain overpressure occurred in the collector where the pipes were jointed and thus this measurement did not get an inflow proportional to the speed of the water at each point./Ref.1/

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A new measurement was made at Bratsberg in 1995 with separate measurement of both velocity and temperature in 6 points on a traversing frame covering 6x6 measuring points. The result is shown in fig. 2 and fig 3.

Fig. 2 Measuing result from BratsbergPower plant at 68% load with measurement of both flow velocity and temperature proving that the point of highest velocity had an efficiency 0.4% below the mean velocity. /Ref. 2/.

Fig. 3 Measured velocities and deviations from mean efficiency at different locations in the draft tube outlet gate at 95% load at Bratsberg /Ref. 2/ Highest velocity was found near the point of average efficiency in this case.

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Measurement at Driva power plant Another measurement was made at Driva Power Plant on a high head Francis turbine where both velocity and temperature where measured at the draft tube gate. The technical data for the turbine which were measured are: P=71.5 MW, Hn=540 m, n=600 Rpm. This measurement was made by M.Sc. Erik Nielsen in his Ph.D work in 1992. By measuring both velocity and temperature it was proven that we would have no inflowing water from the lowest points in the draft tube if a collecting system of any kind had been used. By using flowmeters and measuring temperature and velocity separately the outlet energy could be calculated correctly. The measuring frame which was traversed from bottom to top on 3 levels according to IEC rules is shown in fig 4. The results of the measurement at 45 MW illustrated in fig. 5 is taken from this measurement.

Fig. 4 Measuring arrangement for the high head turbine for Driva Power plant. Left. The measuring frame moved up and down in the draft tube gate frame. Right the flowmeters.

Fig 5 Measuring result from Driva at 45 MW. /Ref. 3/

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Meassurement at Sværen power plant Sværen power plant is a small hydro power plant where one Pelton turbine is installed with following technical data: P = 2 946 kW, Hn=220 m and n = 600 RPM. It is well known that it is difficult to get god measuring condition when measuring efficiency by the Thermodynamic method in a Pelton turbine. The reason is that some water is sucked back up to the runner in the centre and then this water will hit the back of the buckets when streaming outwards driven by the centripetal force. When hitting the buckets foam is created by a mixture of water and air. This water have a much higher temperature than the average water and is floating in top in the outlet channel close to the turbine until it is mixed with the main flow of water some distance downstream of the turbine. This phenomena is well known and then the measuring point of temperature by the thermodynamic must take place a certain distance from the turbine where the foam has disappeared from the surface. Using perforated pipes will give a false temperature because water from the high velocity field i.e. at the surface will dominate the inflow. At Sværen power plant this problem was extremely difficult because the measuring point was planned to be located upstream of a weir. This weir was located approximately one turbine casing diameter downstream of the turbine outlet i.e. very close to the turbine. In fig. 6 left the arrangement of the perforated pipes is shown and to the right is shown the foam on top of the high velocity water streaming towards the weir, bypassing the perforated pipes.

Fig.6 Left. Arrangement of the perforated pipes upstream of wear the weir. Right. The foam bypassing the perforated pipes. In the case of Sværen a measurement with a combination of flowmeters and temperature probes, would have proven a strong variation in both flow velocity and temperature between bottom and top. However, by knowing both temperatures and velocities the total energy could be calculated like the example shown for Driva power plant. Still the measurement should have been further downstream from the turbine to avoid the low density foam which might give uncertainty in the velocity measurement. Especially in front of a weir both velocity and temperature must be measured separately to get a correct result because of the strong variation in velocity. Perforated pipes should never be used because water from the high velocity field will be dominating the temperature in the water inside the pipe and thus a false result will be the case. As illustrated in fig 7 the velocity field upstream of a weir will have a very low velocity at the bottom and the temperature in a perforated pipe will be dominated by surface water.

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Fig. 7 Schematic illustration of the flow crossing a weir. The result from the efficiency measurement at Sværen gives a clear indication of the dominating inflow of the water closest to surface especially because the efficiency dropped when the surface became lower at lower load both at reduced needle opening and at reduced number of jets in operation. In fig 8 is shown the result from the efficiency test.

Fig. 8 Result from efficiency test with 2 jets 4 jets and 6 jets at Sværen. Note the drop in efficiency at decreased flow and height of the surface in front of the weir. For a comparison the measured efficiency from a small hydro turbine and model turbines adjusted to the efficiency at full load at power plant Sværen, is shown in fig. 9.

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It should be remarked that the efficiency at 6 jets and 4 jets and often 2 jets normally have the same maximum efficiency as for 6 jets. Then we obviously have a systematic error in the measurement at SVÆREN caused by using perforated pipes. This error could be prevented by measuring both velocity and temperature and move the measuring point further downstream from the turbine. (For Sværen this would be difficult because the weir was built as a part of the cooling water system for the generator.)

Fig. 9 Index test based on similar efficiency measurements in a similar 6 jet small turbine and various model tests. CONCLUDING REMARKS At present time it should be no problem to arrange for measuring both velocity and temperature across the outlet of a turbine. Then a weighted efficiency from different measuring point should be used. It should however be emphasized on the fact that it is very difficult to make a reliable measurement too close to the Pelton turbines because of the “hot water” in the foam. Finally, perforated pipes may give false results and should be substituted by measurement of both velocity and temperature separately. This is in order to be able to weigh the energy as a function of both the velocity and temperature. In modern time it should be easy to get such equipment. The time collecting data and calculate the efficiency should be short with computerized equipment. REFERERENCES: Ref. 1: H.Brekke Measuring Uncertainties of Specific Energy in Draft Tube Outlet. GPMT 16.th Meeting in Salzbourg Oct. 05-08. 1992 Ref. 2: O.B.Dahlhaug A Study of Swirl Flow in Draft Tubes. PhD Work Norwegian University of Science and Technology 1997.

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IGHEM 2012

The 9th International conference on hydraulic efficiency measurements

Trondheim, Norway

June 27th - 30th, 2012

XXXXXX

Comparison of discharge measurements Comparison of discharge measurements Comparison of discharge measurements Comparison of discharge measurements ---- Thermodynamic to US ClampThermodynamic to US ClampThermodynamic to US ClampThermodynamic to US Clamp----

On, stationary US and Needle OpeningOn, stationary US and Needle OpeningOn, stationary US and Needle OpeningOn, stationary US and Needle Opening CurveCurveCurveCurve

Tobias Rau, Marco Eissner

Voith Hydro Holding GmbH & Co. KG

Alexanderstr. 11, 89522 Heidenheim, GERMANY

AbstractAbstractAbstractAbstract

For high head hydro turbines the thermodynamic method is the most common way to

measure the efficiency. This method uses the conversion of energy and enables to derive the

discharge from its results. Other methods measure the discharge directly to verify the turbine

efficiency at a hydroelectric unit.

According to the IEC code 60041 the thermodynamic method is a primary method and

therefore it will be taken as a reference in this paper for the comparison with three other

methods of discharge measurement: a stationary ultrasonic device installed in front of the

spherical valve and an ultrasonic clamp-on system between spherical valve and distributor inlet. In addition the needle opening of the six nozzles are used for the determination of the

discharge.

All the measurement methods are performed at a six nozzle vertical Pelton turbine with a head

of approximately 500m. Thus every measurement method has the same boundary conditions

and can be compared with each other.

All the described methods, compared with the thermodynamic method, are according to IEC

code 60041 secondary methods and can be used only for relative efficiency tests. The results

of this test show besides the accuracy of these methods also their limitations.

Partly the results correlate very well with those of the thermodynamic method. The ultrasonic

clamp-on system had higher deviations mainly in the lower load part, maybe caused by a not

optimal measuring position. The data of the stationary ultrasonic and the needle opening are

very similar in comparison to the primary method.

1111 IntroductionIntroductionIntroductionIntroduction

Finding solutions of doing more cost effective relative efficiency tests it becomes essential to

acquire more experience with different kind of discharge measurements. Especially compared

to absolute methods accepted by IEC code 60041, e.g. the thermodynamic method.

Within the last years the technical progress comes up to a point, where it is possible to

measure discharges quickly with clamp on devices for temporarily installation.

This paper shall give a better understanding and shall spread the experience made with

different kind of discharge measurement techniques and shall also show their limitations of use

by comparing these results to the results of a thermodynamic efficiency test.

In this paper the results of the thermodynamic efficiency test shall be the reference to all other

methods which are described and applied.

2222 Theoretical backgroundTheoretical backgroundTheoretical backgroundTheoretical background

2.12.12.12.1 ThermodynamicThermodynamicThermodynamicThermodynamic

The thermodynamic method results from the application of the conversation of energy. It is a

transfer of energy between the machine and the water passing through it. The hydraulic

efficiency (equation 4) of a turbine is defined as the ratio between the specific mechanical

energy (equation 1) and the specific hydraulic energy (equation 2).

This method gives the possibility to determine directly the energy that the water transmits to

the turbine shaft. Beginning from the inlet reference section derived from the measured quantities and from the thermodynamic properties of water. This energy is called specific

mechanical energy. The specific mechanical energy´s unit is Joule per kg water.

To measure all necessary quantities in practice a small portion of water will be extracted out of

the main flow of the turbine into so called vessels.

For the application of the thermodynamic method three different procedures can be used:

� Full expanded fluid (pressure term disappear)

� Partial expanded fluid (temperature term disappear)

� Not expanded fluid (measured quantities similar to the values in the main flow)

These days the method of full expansion and partial expansion usually is not used any more.

]/)[(*2

*)(* 2111

221

211

2111 KgJzzgvv

TcppaE pm −+−+∆+−=

equation 1 General definition of specific mechanical energy

]/)[(*2 21

22

2121 KgJzzg

vvppE −+−+−=

ρ

equation 2 General definition of specific hydraulic energy

][/ mgEH =

equation 3 Net head

[%]E

Emh =η

equation 4 Hydraulic efficiency

where

a isothermal factor of water

p11 pressure in the vessel on the high pressure side

p21 pressure in the vessel on the low pressure side

cp the specific heat capacity of water

∆T the differential temperature between high and low pressure side

v11 the velocity in the vessel on the high pressure side v21 the velocity in the vessel on the low pressure side

g the acceleration due to gravity

z11 the level of the vessel on the high pressure side

z21 the level of the vessel on the low pressure side

p1 the pressure in the reference section on the high pressure side

p2 the pressure in the reference section on the low pressure side

ρ the density of water

v1 the velocity in the reference section on the high pressure side

v2 the velocity in the reference section on the low pressure side

z1 the level of the reference section on the high pressure side

z2 the level of the reference section on the low pressure side

Figure Figure Figure Figure 1111 Schematic Schematic Schematic Schematic arrangementarrangementarrangementarrangement of measuring poiof measuring poiof measuring poiof measuring points for the nts for the nts for the nts for the tttthermodynamic methodhermodynamic methodhermodynamic methodhermodynamic method

Figure 1 shows the schematic arrangement of the measuring points for the thermodynamic

method at a vertical Pelton machine which was applied for this comparison. On the high

pressure side the water was extracted with two sampling probes and taken into vessels. In

both vessels the pressure, the temperature and the amount of extracted water was measured

separately for the determination of the specific mechanical energy. In the penstock at high

pressure side the inlet pressure was measured as an average of four pressure taps.

On the low pressure side a measuring frame was installed with nine temperature sensors and two level probes. With this set up the energy distribution can be determined with a good

resolution and accuracy. The measuring frame was installed in a distance of app. 8 x D that

means the minimum distance recommended by IEC60041 was met.

By indirect determination of the mechanical power and the determination of specific mechanic

energy the discharge through the machine can be calculated.

2.22.22.22.2 Stationary UStationary UStationary UStationary Ultrasonic Systemltrasonic Systemltrasonic Systemltrasonic System

The acoustic method of discharge measurement (ultrasonic, time of flight or transit time) is

predicated on the propagation of velocity of an acoustic signal and the main flow velocity is

vectorial summed. An acoustic signal sent downstream travels at a faster absolute velocity

than an acoustic signal sent upstream. By measuring the travel times in both directions it is

possible to determine the average axial velocity of the acoustic path crossing a certain cross

section.

ϕsin***2 1

_

wi

n

iaxii Lvw

DQ ∑

==

equation 5 General equation for discharge according to transit time method [1]

where

D penstock diameter

Lwi the length of the acoustic path wi the weighting coefficients

vaxi the averaged axial flow velocity

n the number of acoustic paths in one plane φ the angle of the acoustic paths

The stationary ultrasonic system was installed to detect the leakage in the penstock (see figure

2), e.g. in case of penstock rupture. It measures continuously the flow rate in the 2 penstocks

and in the 4 inlet pipes to each turbine. Each penstock and the two corresponding inlet pipes

will be compared continuously. The flow rates are measured with an ultrasonic transit-time

measurement device on each line. For the comparison test the result of the section before the

main inlet valve was used to measure the discharge by acoustic transit time method. The

scope of this installation was not the measurement of efficiencies or performance guarantees.

Figure Figure Figure Figure 2222 Single Line Single Line Single Line Single Line Diagram of leakage monitorDiagram of leakage monitorDiagram of leakage monitorDiagram of leakage monitoringinginging [2][2][2][2]

Figure 3 shows the arrangement of the acoustic paths before main inlet valve. In general the

arrangement is dependent on the flow profile and the pipe diameter. For this project an

arrangement of four planes with four paths was installed.

FFFFigigigigure ure ure ure 3333 Arrangement of Arrangement of Arrangement of Arrangement of acoustic pathsacoustic pathsacoustic pathsacoustic paths (US stationary)(US stationary)(US stationary)(US stationary)

4 plane arrangement with single path

2.32.32.32.3 ClampClampClampClamp----On Ultrasonic SystemOn Ultrasonic SystemOn Ultrasonic SystemOn Ultrasonic System

The principle of the US Clamp-On system is the same like described in 2.2 Stationary U. An

acoustic pulse which is sent upstream travels at a lower absolute speed than an acoustic

pulse sent downstream. The average axial velocity of the fluid crossing the path of the pulses

is determined by measuring the travel times of the acoustic signal sent in the two directions.

Major different to the stationary system is that each path for the clamp-on device travels

through the center of the penstock cross section (refer to figure 4). That means the

determination of the velocity profile corresponding to the stationary US-device is not possible.

For the comparison test it was chosen a one plane arrangement with single path. The choice

of the measuring position was limited by accessibility to the penstock. Therefore the

measuring section was selected directly after the main inlet valve (MIV) near to the distributor

inlet. The conditions for this arrangement were not good because the measuring section was

in a conical part of the penstock and the outlet of the measuring sections was only in a

distance of app. 1xD to the distributor inlet.

FFFFigure igure igure igure 4444 Arrangement of acoustic path (US clamp on)Arrangement of acoustic path (US clamp on)Arrangement of acoustic path (US clamp on)Arrangement of acoustic path (US clamp on)

2.42.42.42.4 Needle OpeningNeedle OpeningNeedle OpeningNeedle Opening

The flow through the machine can be determined with the needle opening curve as well. The

net head and the cross section of the needle opening depend on the needle stroke. The net

head results from the determination of the specific hydraulic energy (refer to equation 2 and

equation 3) and the needle stroke can be measured directly with any kind of linkage sensor.

With the needle stroke the needle cross section can be determined.

To achieve an accurate needle opening curve a tested model is beneficial. The results and

experience can be adopted to the prototype and the standard flow function can be adjusted.

Of course the accuracy is also depending on the deviation between theoretical design of the

needle and the manufactured needle at the prototype. That means the more the analogy from

design to prototype is fulfilled the merrier is the accuracy of this kind of discharge

determination.

Hgw **2*98,0=

equation 6 Standard flow function with loss factor

wAQ *=

equation 7 Discharge

3333 ComparisonComparisonComparisonComparison of discharge valuesof discharge valuesof discharge valuesof discharge values

Results of all methods were compared to the results of the thermodynamic efficiency test.

Deviations between the different methods and the results of the thermodynamic efficiency test

were determined.

The results show clearly that the measurement with the clamp on system has significant

deviations to the reference measurement. There are several reasons why the deviations are

higher than expected compared to the reference. The clamp on system was installed in a

slightly conical part of the penstock. This matter did not account for a higher accuracy but

does not explain such high deviations. Additionally the system was installed very close to the

distributor inlet (because of accessibility to the penstock) were the flow distribution can change

keenly when at lower loads not all nozzles are opened. With just one path an adequate

determination of the flow velocities over the cross section is not possible especially if there is a

highly disturbed flow pattern. With the results achieved from the clamp on system it was not

possible to derive a reasonable index test curve because the deviations were not constant and even changed their prefix.

Relative deviation of US clamp on to Thermodynamic measurement

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

75,8 75,8 52,2 52,2 61,9 61,9 52,6 52,6 38,4

Needle Opening [%]

Rel

ativ

e d

evia

tion

[%]

FFFFigure igure igure igure 5555 Relative deviation of US cRelative deviation of US cRelative deviation of US cRelative deviation of US clamp on to reference measurementlamp on to reference measurementlamp on to reference measurementlamp on to reference measurement

The deviations of the stationary ultrasonic system to the reference measurement are in an

acceptable range if you consider that it is a four planes system with single paths arrangement.

The deviations of the stationary ultrasonic system are all below 1%. Except of one outlier all

deviations have the same prefix and are all in the same magnitude. With values achieved from

the stationary ultrasonic device it was possible to reproduce the shape of the efficiency curve

according to the results of the reference measurement. For index testing the device deliver acceptable results.

Relative deviation of stationary US to Thermodynamic measurement

-1,2

-1

-0,8

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

75,8 75,8 52,2 52,2 61,9 61,9 52,6 52,6 38,4

Needle Opening [%]

Rel

ativ

e d

evia

tio

n [

%]

FFFFigure igure igure igure 6666 Relative deviation of stationary US to reference measurementRelative deviation of stationary US to reference measurementRelative deviation of stationary US to reference measurementRelative deviation of stationary US to reference measurement

The deviations of the needle curve discharge are all below 0.9%. The deviations have all the

same prefix and are roughly in the same magnitude. The deviations getting higher to smaller

loads of the unit that means in the 2 and 3 nozzle operation of the machine the deviations are higher compared to the reference measurement. With values achieved from the needle curve it

was possible to reproduce the shape of the efficiency curve according to the results of the

reference measurement. For index testing this method deliver acceptable results.

Relative deviation of discharge to Thermodynamic measurement

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

75,8 75,8 52,2 52,2 61,9 61,9 52,6 52,6 38,4

Needle Opening [%]

Rel

ativ

e d

evia

tio

n [

%]

FFFFigure igure igure igure 7777 Relative deviation of discharge to reference measurementRelative deviation of discharge to reference measurementRelative deviation of discharge to reference measurementRelative deviation of discharge to reference measurement

4444 SummarySummarySummarySummary

The results of this comparison show explicit that the choice of the measuring method, the

measuring section and the measuring arrangement has to be carefully chosen according the

aim of the respective measurement. Furthermore a detailed validation of the test results and

the conducted test setup is essential.

Especially for the ultrasonic clamp-on discharge measurement special care has to be taken to

achieve reasonable results. The general statement that a clamp on device can be easily

installed without focus on the right position and setup cannot be confirmed based on the

results of this comparison. Contrariwise good measuring conditions are more important to

achieve reasonable values.

The four plane single path stationary ultrasonic device achieved reasonable results without any

correction. This experience confirms that for Index tests ultrasonic devices with a smaller

amount of paths can be used properly and without special focus on the borderlines of the

measuring setup. For the use at absolute efficiency tests it is strongly recommended to use at

least a 4 planes 8 paths system to achieve the necessary accuracy. Otherwise special care has to be taken to measuring set up and the flow distribution (e.g. by CFD).

The results of the needle opening curve give quiet good results. Especially if you consider that

the effort for this measurement is quiet small. At a Pelton machine just the measurement of the

inlet pressure, the electrical power and the needle opening is necessary to achieve an

efficiency curve. Even if you don’t achieve absolute efficiencies by this method it is a cost

effective measurement for Index testing. In this comparison the results agree quiet well to the

reference measurement.

5555 List of referencesList of referencesList of referencesList of references

[1] IEC, Bureau Central de la CEI (1991): International Code for the Field Acceptance Tests to determine the hydraulic performance of hydraulic turbines, storage pumps and pump turbines, Publication 41, third edition, Genève

[2] Systec Controls GmbH (2007): Operations and Maintenance Manual of Combined

Water loss Detection and Flow Measurement System, Puchheim