The comparative analysis of the current-meter method and the pressure-time method used for discharge measurements in the Kaplan turbine penstocks

Transcription

1 IOP Conference Series: Earth and Environmental Science The comparative analysis of the current-meter method and the pressure-time method used for discharge measurements in the Kaplan turbine penstocks To cite this article: A Adamkowski and Z Krzemianowski 2012 IOP Conf. Ser.: Earth Environ. Sci Related content - Some experiences with flow measurement in bulb turbines using the differential pressure method A Adamkowski and M Lewandowski - Experimental and numerical results of the influence of dynamic Poisson effect on transient pipe flow parameters A Adamkowski, S Henclik and M Lewandowski - Treatise on water hammer in hydropower standards and guidelines A Bergant, B Karney, S Pejovi et al. View the article online for updates and enhancements. This content was downloaded from IP address on 05/09/2018 at 23:28

2 The comparative analysis of the current-meter method and the pressure-time method used for discharge measurements in the Kaplan turbine penstocks A Adamkowski and Z Krzemianowski The Szewalski Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Fiszera Str. 14, Gdansk, Poland aadam@imp.gda.pl Abstract. The paper presents experiences gathered during many years of utilizing the currentmeter and pressure-time methods for flow rate measurements in many hydropower plants. The integration techniques used in these both methods are different from the recommendations contained in the relevant international standards, mainly from the graphical and arithmetical ones. The results of the comparative analysis of both methods applied at the same time during the hydraulic performance tests of two Kaplan turbines in one of the Polish hydropower plant are presented in the final part of the paper. In the case of the pressure-time method application, the concrete penstocks of the tested turbines required installing a special measuring instrumentation inside the penstock. The comparison has shown a satisfactory agreement between the results of discharge measurements executed using the both considered methods. Maximum differences between the discharge values have not exceeded 1.0 % and the average differences have not been greater than 0.5 %. 1. Introduction Water discharge (volumetric water flow rate) belongs to the group of a few basic quantities needed to determine the hydraulic performance characteristics of hydraulic turbines and pumps. Discharge always represents the most difficult quantity to measure and accuracy of its measurement is worse and very difficult to estimate in comparison with the specific hydraulic energy (head) and active power. Despite immense progress in discharge measurement techniques, this part of the hydraulic machine performance tests is often a major challenge, even for experienced test teams. Either the method of the local velocity distribution determined by means of the current-meters or pressure-time method (the so-called Gibson method) belong to primary methods for discharge measurement in hydropower systems [1], [2]. Conducting the measurements using these methods requires not only an appropriate application of measuring devices, but correctly carrying out process of analyzing the data, including the use of integration techniques. The paper presents authors own experiences gathered during many years of utilizing the mentioned methods for flow rate measurement in many hydropower plants. The special integration techniques (concerning both methods) in the form of their own coded programs using the progressive numerical algorithms have been developed. The techniques differ from the recommendations contained in the relevant international standards [1], [3], mainly from the graphical and arithmetical ones. Published under licence by Ltd 1

3 The results of the comparative analysis of both methods used simultaneously during the hydraulic performance tests of two Kaplan turbines in one of the Polish hydropower plant are presented in the final part of the paper. 2. Current meter method Propeller water current meters are very often used in the velocity-area method for absolute discharge measurements in low-head hydropower systems. The volumetric flow rate is determined by integrating the distribution of local flow velocities over the entire area of the measuring (hydrometric) crosssection. The local flow velocity component is measured based on the current meter rotor revolutions counted in a given time period, and the experimentally determined relationship between the current meter rotation speed and local flow velocity. Uncertainty of measurement by the means of the current meters depends on a lot of factors, mainly on: (1) measurement of local velocity using current meters; (2) measurement of a cross-section geometry of flow channel; (3) determining of streamlines (current meters orientation); (4) determining of parameters for velocity function in a boundary layer; (5) the applied method of calculations. From the authors experience it can be concluded that the last two factors may have very important influence on uncertainty of discharge measurement. The differences can exceed significantly more than 0.5 % for different approaches of calculations. Particularly it concerns the flows with highly irregular velocity distribution, especially in case of short intakes. The velocity field integration methods are based on graphical and arithmetic techniques according to the very outdated literature [3], [5]. However, due to big progress in computer technology, graphical and arithmetic techniques have been practically replaced by various numerical schemes. Nowadays, the most popular ones are based on spline techniques [6], [7]. The expected advantages of the spline approach are, inter alia, the following: (1) increasing the accuracy of calculation in comparison to graphical and arithmetical techniques; (2) easy and fast carrying out the flow rate calculations; (3) easy possibility of applicability to cases with irregular velocity distributions; (4) easy possibility of an immediate visualization of velocity distributions etc. The most often applied technique calculates the discharge using Classic Cubic Splines. It should be highlighted that this approach may lead sometimes to inconsistent with reality (inaccurate) flow velocity distributions, especially in highly irregular regions of velocity. It is related to the difficulties to obtain smoothed velocity function that interpolates the areas of strong bending curve as it happens in a boundary layer region. This problem illustrates figure 1. Figure 1. Comparison of the curves based on the classic cubic splines and the B-spline functions (NURBS). Example from authors own measurement. Because of that the authors of this paper decided a few years ago to adapt another more sophisticated spline technique to interpolate velocities obtained by the means of the current meters. This technique involves the advanced spline functions, the so-called Non-Uniform Rational B-Splines (NURBS) [8]. Nowadays, this kind of splines is commonly used in modeling of the complicated geometrical shapes because of their smoothness. It has been assessed that it represents much better kind of interpolation than the classic spline functions. Figure 1 presents an example of the comparison between the interpolation functions based on both mentioned techniques. 2

4 The authors own software, called FLOWMAX, is used to calculate volumetric flow rate Q by the means of current meters in a cross-section A represented in rectangular (x, y) or circular (r, ) coordinate system, which may be written, respectively, as follows: Q Vz x, y) dxdy A ( Q rvz ( r,) drd A where: x, y coordinates in Cartesian system; r, radial and angular coordinates in cylindrical system; V z normal velocity distribution obtained using current-meters in cross-section A and von Karman law in a boundary layer zone. Program gives possibility to calculate the volumetric flow rate from local velocities measured in the hydrometric sections of different shapes for rectangular closed conduits or open channels (with optional chamfers and roundings) or circular. Generally, the essential principal of the NURBS approach can be very shortly characterized as follows. At each interpolated point, the NURBS function value results from the linear sum of four 3 rd degree polynomials, properly calculated from the given points. The mutual influence of each polynomial at an interpolated point allows avoiding exaggerated deformation and makes the interpolated curve be more smoothed than the classic cubic spline in which only one 3 rd degree polynomial is considered at each interpolated point. According to the program FLOWMAX, the velocity distribution in the boundary layer is interpolated by the von Karman formula that can be written in the following form: VzBL x 1 m x Vz0 BL where: x distance from wall, V z0 velocity of the nearest current meter to boundary layer, BL boundary layer thickness, m boundary layer exponent dependent on a Reynolds number. According to the ISO 3354 [3], the boundary layer thickness is calculated as follows: W Z (1) (2) BL 0.2 (3) Rez where: Z distance from water intake to cross-section of current meters, W empirical coefficient recommended by international standards to be equal: W = 0.37, Re z Reynolds number dependent on a distance Z calculated as follows: Re z Vz av Z where: V z-av arithmetical mean velocity from the current meters, water kinematic viscosity. The boundary layer parameter m may be determined according to the procedure described in the ISO For this purpose the linear loss coefficient in a conduit can be calculated, for instance, using the formula [9]: lg Re 0.4 Re (5) D h where: wall roughness, D h hydraulic conduit diameter of a hydrometric cross-section, Re Reynolds number in a cross-section calculated as follows: V z av Dh Re (6) The m value is obtained on a basis of a table placed in the ISO 3354 that contains m values for ones (it may be introduced by user of the program as well). The software has been successfully used in the hydraulic turbine performance tests in Poland for several years. It can be especially recommended (4) 3

5 for highly irregular flows with high Reynolds numbers. Such conditions exist often in hydropower systems. In authors opinion, in cases of machines with a short intake and irregular inflow, using the classic cubic spline approach in the current meter flow measurement may lead to overestimation of efficiency of tested hydraulic turbines (underestimation of discharge). The technique of interpolation, presented and recommended in this paper, may significantly improve the accuracy of discharge measurement results. An example of the use of this technique, comparing to the pressure-time method use, is presented in the further part of the paper. 3. Pressure - time method The method is based on the second law of dynamics as applied to the decelerated mass of liquid stream flowing through a pipeline. The inertia force of the stopped liquid mass is manifested by the pressure difference between two measurement sections in the pipeline see figure 2. Figure 2. Segment of a pipeline with marks needed to explain the theoretical basis of the pressure-time method. The discharge is calculated by integrating the recorded pressure difference curve within properly determined time interval according to the formula [10]: t 1 Q0 C t f p( t) p d( t) Pf ( t) dt q l 0 (7) where: liquid density, C geometrical factor of the pipeline segment between cross-sections 2-2 and 1-1 (L length and A cross-section area), p = p 2 +gz 2 -p 1 -gz 1 the pressure difference measured between sections 2-2 and 1-1 related to a reference level, p d the dynamic pressure difference between sections 2-2 and 1-1, P f is the pressure drop due to friction losses between 1-1 and 2-2 cross sections, q l discharge under terminal conditions (usually the leakage rate through the cut-off device in the closed position that has to be measured or assessed using a separate method), t time, and (t 0, t f ) means time interval in which the flow conditions change from initial to final stage. The value of C factor has to be determined basing on geometry measurement of L distance between section 1-1 and 2-2 and A internal pipe cross-section area, from the formula: L dx C A( x) 0 The pressure drop P f due to hydraulic loss in the pipeline segment between sections 1-1 and 2-2 and the dynamic pressure difference p d in these cross-sections have to be extracted from the measured static pressure difference p. In the discussed method the friction pressure drop is determined using the square discharge function: (8) P K QQ (9) f in which the constant K f is calculated basing on the measured values of the initial flow conditions: f K f P f 0 K f 0 (10) Q0 Q0 4

6 The value of p d is independent of flow direction and can be calculated from the discharge function: Q( ) 2 p ( t) K t d d where: K d 2 2A 2 2 A (11) where: 1, 2 the Coriolis coefficients for 1-1 and 2-2 sections, respectively [11]. The need for calculating P f and p d quantities, using their simplified dependence on the square of the flow rate (equations (9), (10), (11)), unfavorably affects the uncertainty of measurement results of the method. Therefore, it is of great importance for achieving good accuracy of the flow measurement performed using the pressure-time method, that the contribution of the pressure difference attributed to friction loss and difference of dynamic pressures would be possibly the smallest and would not exceed a certain limit. This requirement can be written in the form of the following inequality: Pf 0 pd0 p m (12) where: p m the average value of the static pressure difference measured between the sections during liquid stream stop, but index 0 refers the initial flow conditions. According to the IEC standard, the value of is equal to 0.2 (20 %). The theoretical basis of the pressure-time method presented above is valid for both turbine and pump modes of operation. However, the IEC standard recommends using the method only in cases of turbine operation mode. The own experiences indicate on the possibility to utilize the method also in cases of pumping operation mode [12]. One of the necessary requirements in such cases is correct calculating the pressure drop caused by the friction loss between the hydrometric cross sections of a pipeline. Typical calculation procedures, including the presented in [1] and [2], assume the pressure drop to be dependent only on the square of the discharge value, as in the following equation: 2 P K Q (13) f f The hydraulic losses calculated in accordance with equation (13) do not depend on flow direction (both are always of the same sign) as contrary to the equation (9). Therefore, following this way of calculation may lead to additional error while determining the discharge in the pressure-time method. Calculation of the initial value of discharge Q 0 using the equation (7) requires to specify the time integration limits t 0 and t f. These values should determine the time interval in which the flow is cut-off. Contrary to t 0 time (lower limit of integration), the determination of t f time (upper limit of integration) presents difficulties. Even precise synchronization of recording of the flow cut-off device run with measurement of the pressure rise does not ensure the exact determination of t f time value. The reason for this is often the lack of the strict relation between the time moment at which the closing device movement is stopped and the time moment of flow cut-off finish in some cases despite the termination of flow cut-off run, the closing device is still in motion, e.g. in result of elastic strain. Therefore, the upper integration limit t f is determined from the character of free pressure oscillations [1]. These oscillations, as residual ones, remain in the penstock directly after the termination of flow cut-off. One of the procedures relating to the upper integration limit calculation in the pressure-time method is given in the IEC standard. However, the procedure includes mathematical inaccuracy it does not ensure to set a zero-value integral of free pressure oscillations that intent to eliminate their influence on the discharge measurement what has been proved in paper [12]. On the basis of theoretical consideration above presented, the original program, called GIB-ADAM has been developed in the Institute of Fluid-Flow Machinery PAS (IFFM PAS) in Gdansk, Poland. The program is one of the most important tools enabling the use of the pressure-time method in practice. The first practical application of this method with using the developed GIB-ADAM program was undertaken in Poland in the second half of 90 s. Since 1998, IFFM PAS has used different version of the pressure-time method in numerous plants in Poland and in Mexico [13]. 5

7 4. Simultaneous use of the pressure-time and current meter methods During the hydraulic performance tests of two similar Kaplan turbines in one of the Polish hydropower plant, the water current meter and pressure-time methods were used simultaneously to measure the discharge. The hydrometric section 0-0 for using the current meter method and the cross sections 1-1 and 2-2 for the pressure-time method were located in a concrete cylindrical penstock segment of 4 m inner diameter (D) figure 3. It is worth highlighting that both methods, in a similar way, were applied to two turbines. A cross-section 0-0 was established in distance of about 8 m (2 D) from the inlet of cylindrical penstock (distance from the intake grating threshold was about 16 m). In this cross-section 25 current meters were mounted on the stationary supporting frame figure 4. The trailing edges of current meters were located in front of supporting frame in distance of 10 diameters of the supporting frame arm from its axis. Hence, systematic uncertainty of velocity measurement taking into account supporting frame presence did not exceed 0.2 %. All applied current meters were calibrated (tarred). The blockage effect was taken into consideration according the ISO 3354 standard. Figure 3. Layout of the turbine penstock with marked hydrometric sections used for discharge measurement using the current meter method (0-0) and Gibson method (1-1) and (2-2). Figure 4. The current meters and the stationary supporting frame used to mount the current meters. Figure 5 presents the samples of the measured local velocity distributions obtained by the means of the FLOWMAX program. The impulse current meters data acquisition was made by the means of a digital card connected to computational system of data acquisition. Figure 5. Example of profiles of velocity distributions to calculate flow discharge obtained by the means of FLOWMAX. According to the estimation, the total systematic uncertainty of discharge measurement results using the current meters in the considered cases was not greater then +/ 1.5 %. In the considered tests, the classic version of the pressure-time method was used as the second method of discharge measurement. This version is based on direct measurement of pressure difference 6

8 between two hydrometric sections of the straight conduit of the same diameter using a pressure differential transducer. Both hydrometric sections 1-1 and 2-2 for using the pressure-time method were located in a concrete cylindrical penstock segment of 4 m diameter figure 6. Section 1-1 was located about 10 m (2.5 D) downstream the beginning of cylindrical segment penstock inlet and section 2-2 was located about 10 m upstream the turbine spiral case inlet. The length of segment between sections 1-1 and 2-2 was about 17 m for both tested turbines. In each of these sections four pressure taps were uniformly located on the circumference figure 6. Due to lack of access to the penstock from outside the special measuring equipment was installed inside the penstock [13]. In each measuring section (1-1 and 2-2) four flat bars with pressure receiving holes (taps) were mounted to the internal side of the penstock concrete wall, parallel to the water flow direction and connected to the manifold by means of the impulse cooper tubes figure 6. The manifolds of both hydrometric sections were connected by means of impulse tubes to the sealed housing with the differential pressure transducer installed inside. The static pressure difference measured by the precise differential pressure transducer between sections (1-1) and (2-2) was recorded by the computer data acquisition system with frequency sampling of 200 Hz. Then the GIB-ADAM software was used to calculate the values of the discharge. Figure 6. Distribution of the pressure receiving holes in the penstock hydrometric sections 1-1 and 2-2 (left) and measurement elements installed inside penstock in hydrometric section 1-1 (right). Example of the pressure difference recorded between the measuring cross-sections and flow rate calculated from this difference is presented in figure 7. Figure 7. Example of measurement of discharge through a turbine using the pressure-time method. The water discharge in the final conditions, as the rate of leakage flow through the closed guide vanes of the tested turbines, was determined basing on the measurement of rate of water level decrease in the cylindrical segment of the penstock. The total systematic uncertainty of discharge results by means of the pressure-time method used in the considered cases was estimated on not greater than +/ 1.5 %. Comparison between discharge measurement results received by means of the pressure-time and current-meter methods used in the tests of two similar water turbines are presented in figure 8. 7

9 Figure 8. Relative differences between discharge measurement results by means of Gibson and current-meter methods used for two similar turbines. It shows a satisfactory agreement between the results of discharge measurements using the both methods. Maximum relative differences between the discharge values have not exceeded 1.0% and the average differences are not greater than 0.5 %. The greater differences can be observed for lower value of measured flow rate. Such effect is associated with increased inaccuracy of measurement with the decrease of the measured discharge values. The results of comparison confirm the reliability of the techniques and computational software developed and used by the authors of this paper in the measurement of flow rate through hydraulic machines. 5. Conclusions Flow rate measurements using the local velocity distribution determined by the current-meters and pressure-time methods, the most important primary methods in hydropower systems, require in addition to proper use of measuring devices, correctly conducting analyses of the measuring data, including the integration techniques. The experiences of the authors of this paper show that the techniques of integration can affect the measurement results more than 0.5%. The NURBS functions have been adopted for calculating the discharge from the local velocities measured using the current meters. It is assessed that the NURBS represent much better kind of interpolation than the classic cubic spline functions, particularly in area of connections of the very strong velocity gradients in von Karman law boundary layers with velocity mainstream (core) regions at measuring cross-sections, and in cases with very irregular highly turbulent flows. On this basis the NURBS technique may be recommended for practical use of the current meter method, particularly in cases of highly irregular flows in open channels and closed conduits with high Reynolds numbers. The pressure-time method has been developed by introducing some modifications to the integration procedure in comparison to the IEC and ASME PTC 18 standards. The modifications concern generally the calculating the hydraulic losses and determining the upper limits of integration of recorded pressure variations in time. The results of the comparative analysis of both methods, with introduced modifications, used simultaneously during the hydraulic performance tests of two Kaplan turbines in one of the Polish hydropower plant have shown a satisfactory agreement between the results of discharge measurements executed using the both compared methods. Maximum differences between the discharge values have not exceeded 1.0 % and the average differences have not been greater than 0.5 %. These results and the results of many authors experiences from the use of the analyzed methods in different types of hydropower plants, assessed as very satisfactory, can confirm the validity of applicability of introduced modifications in both the methods. References [1] IEC Field acceptance tests to determine the hydraulic performance of hydraulic turbines, storage pumps and pump turbines [2] ASME PTC American National Standard: Hydraulic Turbines and Pump Turbine, Performance Test Codes (Consolidation of ASME PTC and ASME PTC ) [3] ISO Measurement of clean water flow in closed conduits - Velocity-area method using current-meters in full conduits and under regular flow conditions [4] ISO Measurement of fluid flow in closed conduits - Velocity-area methods of flow measurement in swirling or asymmetric flow conditions in circular ducts by means of current-meters or Pitot static tubes 8

10 [5] Troskolanski A T 1960 Hydrometry (Pergamon Press Ltd.: Oxford London New York Paris, PWN: Warsaw) [6] Berny R and Slota R 2000 Integrated system for hydrometric data processing and discharge evaluation in open channels and closed conduits Int. Conf. HYDROFORUM 2000, (Gdansk, Czorsztyn Poland, September 2000) (IMP PAN Publishers) pp [7] Leutloff S, Geromiller W, Fischer G 1983 Numerische Auswertung von Flügelmessungen in Kreisquerschnitten (Elektrizitätswirtschaft, Jg.82, H.5) pp [8] Yamaguchi F 1988 Curves and surfaces in computer aided geometric design (Berlin: Springer Verlag) [9] Nackab J 1988 Calcul direct, sans iteration, de la parte de charge en conduite par la formule de Colebrook (La Houille Blanche) No. 1 [10] Adamkowski A 2012 Discharge Measurement Techniques in Hydropower Systems with Emphasis on the Pressure-Time Method (Chapter no. 5 of the book Hydropower - Practice and Application) ISBN pp [11] Cengel Y A and Cimbala J M 2006 Fluid Mechanics. Fundamentals and Applications (New York: McGraw-Hill International Edition) [12] Adamkowski A and Janicki W 2010 Selected problems in calculation procedures for the Gibson discharge measurement method Proc. of 8th Int. Conf. on Hydraulic Efficiency Measurement IGHEM 2010 (Roorkie India) pp [13] Adamkowski A, Kubiak J, Sierra E F, Urquiza B G, Janicki W and Fernandez D J M 2008 Hydraulic Review Worldwide 16(6)