About determining discharge of low head turbine using themodynamic method.

Baya, Alexandru ; Anton, Liviu ; Stuparu, Adrian 等

1. INTRODUCTION

Discharge determination of hydraulic turbine operating in hydro power plant is one of the most difficult problems. (IEC 9041, 1991) suggests two methods of discharge measurement: one method for gross discharge and another concerning flow patterns. Anyway it is recommended an absolute method (IEC 9041, 1991) like velocity-area of current meters, Winter-Kennedy method, and others. The thermodynamic method of efficiency measurement allows obtaining discharge as a derived quantity from efficiency, specific energy and power measurements, (IEC 9041, 1991), (Stuparu et al., 2005).

In last 20 years was settled "International group for hydraulic efficiency measurements". Researchers, members of IGHEM, recommend attention in experimental determining of the discharge of hydraulic turbines by using thermodynamic method (Karlicek, 1996).

Accuracy of experimental data of discharge measurements by thermodynamic methods, in the case of a low head turbine is near to accuracy of other methods, as will be seen further in the paper.

The paper presents the principle of thermodynamic method and the test facility. Discharge measurements were performed in a hydropower plant equipped with Kaplan turbines. Experimental results are presented as function of wicket gates opening a0. Comparisons with results of other methods for the same cases are given.

2. THERMODYNAMIC METHOD

Hydraulic efficiency of a turbine is given by:

[[eta].sub.h] = [E.sub.m]/[E.sub.h] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [E.sub.h] is specific hydraulic energy and [E.sub.m] is specific mechanical energy of the turbine's runner:

In equation (3) [p.sub.absi], [P.sub.abs2] are absolute pressure in reference sections of turbine, [T.sub.1], [T.sub.2] are water temperature in reference sections, [v.sub.1], [v.sub.2] are average velocity in reference sections, [z.sub.1], [z.sub.2] are elevation of the reference sections, a is the mean isothermal coefficient and cp is the specific heat capacity at constant pressure of the water.

Specific mechanical energy is possible to be determinate by thermodynamic method, measuring the difference between absolute pressures in reference sections and temperature difference in the same sections.

3. METHOD OF DISCHARGE DETERMINATION

Knowing that the hydraulic efficiency is given also by next equation:

[[eta].sub.h] = [P.sub.m]/[P.sub.h] (4)

where [P.sub.m] is the mechanical power and [P.sub.h] is the hydraulic power given by equations:

[P.sub.m] = [[eta].sub.eg][P.sub.eg] (5)

[P.sub.h] = [[rho].sub.g]QH (6)

Then obviously:

Q = [[eta].sub.eg][P.sub.eg]/[rho]gH[[eta].sub.h] (7)

where [[eta].sub.eg] is the electric generator's efficiency, given by its manufacturer and Pe is the electric generator power measurable. In fact, turbine's discharge is obtained knowing turbine efficiency.

4. MEASUREMENT EQUIPMENT

Sensors of pressure and temperature for reference section upstream and downstream turbine are connected to a computer by a distribution box, see Figure 1.

[FIGURE 1 OMITTED]

Script "1" means upstream position at the inlet of the turbine and script "2" means downstream position for pressure p and temperature T. For measurements in power plant it was used a P22F Robertson equipment.

Some preliminary conditions must be satisfied (Kercan et. al. 1996), such as: establishing of sensors placement, knowing generator efficiency for all range of power, the reservoir must be full, secondary leaks must be redirection, the turbine must not be started after a long period of switching off.

In according with many recommendations (Hans & Doering, 1996), (Grego, 1996), sensors displacement must be in water current: for upstream sensors before spiral casing and for downstream sensors five runner diameters far from the runner exit, see Figure 2.

[FIGURE 2 OMITTED]

5. DISCHARGE MEASSUREMENTS

Discharge measurements were performed at constant head H = 23.8 m. Values of constants from equation (3) characteristic to real measurement conditions are:

* a = 1.0046 x [10.sup.-3] [m.sup.3] x [kg.sup.-1]

* [c.su= 4204 J-kg"1-K"1

* g = 9.8054 m/[s.sup.2]

Table 1 contains 7 sets of measured values of turbine discharge, considering opening of wicket gates a0 as parameter.

For each value of flow rate were performed about 80 to 100 measurements, so in table 1 are offered average values.

Dependence Q = f (a0) is represented in Figure 3.

[FIGURE 3 OMITTED]

In order to validate measured values, comparisons with other methods of discharge determining were made. For the same turbine, there are presented discharge versus opening wicket gates Q = f ([a.sub.0]), determined by thermodynamic method, Winter-Kennedy method and numeric simulation, see Figure 4.

[FIGURE 4 OMITTED]

6. CONCLUSIONS

Determining of a low head turbine discharge by thermodynamic method is technically possible. Experimental values of flow rate are in good agreement with the values determined with other methods. The right displacement of the sensors, upstream and downstream, eliminates the influences of the possible measuring errors due to pollutant heat sources.

Thermodynamic method is efficient, measurements can be done in short time, and the accuracy of the equipment is comparable with other methods accuracy.

7. REFERENCES

Grego G., (1996). Comparative Flow rate Measurements at Caneva Generating Plant Unit 2, Proceedings of the 1st International Group for Hydraulic Efficiency Measurement, Montreal, Canada, 1996, Montreal

Hans P., D. & Doering J.; C., (1996). A Comparison of Discharge Calculation Method, Proceedings of the 1st International Group for Hydraulic Efficiency Measurement, Montreal, Canada, 1996, Montreal

IEC 9041, (1991). International code for field acceptance tests to determine the hydraulic performance of hydraulic turbines, storage pumps and pump-turbines. Publication 41, 3rd edition

Karlicek R., F., (1996). Test Equipment and Results from 25 Hydraulic Turbine Tests using Thermodynamic Method, Proceedings of the 1st International Group for Hydraulic Efficiency Measurement, Montreal, Canada, 1996, Montreal

Kercan V., Djelic V., Rus T. & Vujanic V, (1996). Experience with Kaplan turbine efficiency measurements-current-meter and/or index test flow measurements, Proceedings of the 1st International Group for Hydraulic Efficiency Measurement, Montreal, Canada, 1996, Montreal

Stuparu A., Baya A. & Anton L., (2005). The Determination of the Flow Rate of a Kaplan Turbine Using the Thermodynamic Method, Proceedings of the Sustainability for Humanity & Environment in the Extended Connection Field Science-Economy-Policy, vol. 2, pp. 187-190, ISBN 973.625-204-3, Timisoara, Romania, 2005, Timisoara

Tab. 1. Measured values of turbine discharge

 [a.sub.0] [a.sub.0] [T.sub.1]- Q
No. [mm] [%] [T.sub.2] [K] [[m.sup.3]/s] H [m]

1 277.935 75.9 0.007 96.167 23.8
2 321.645 85.3 0.0065 119.086
3 229.575 65.5 0.008 76.861
4 234.225 66.5 0.008 80.353
5 351.87 91.8 0.0072 146.816
6 342.57 89.8 0.0076 126.093
7 389.535 100 0.005 159.919