CASE STUDIES OUR EXPERIENCE IN HYDRAULIC TRANSIENTS AND VIBRATIONS

Transcription

1 CASE STUDIES OUR EXPERIENCE IN HYDRAULIC TRANSIENTS AND VIBRATIONS Bryan Karney: Professor, Department of Civil Engineering, University of Toronto, Canada Aleksandar Gajic, Prof, Department of Mechanical Engineering University of Belgrade, Serbia Stanislav Pejovic, Research Associate, Dept. of Civil Engineering, University of Toronto, Canada Key Words: Hydraulic Transients, Waterhammer, Hydraulic vibrations, pump, turbine, pump-turbine, resonance, stability, network. Abstract: Computerized transient-flow models have been used with great success in the analysis of water-hammer events in topologically simple pipeline systems, and the performance of these models is well documented. This paper addresses case studies the area of transients in complex pipe networks and illustrates a formulation permitting system demands to be represented as a distributed pipe flux is presented. This approach is compared with two conventional methods for modelling demands in pipe networks. The computer models are generally in good agreement with the field test data. Several cases of hydraulic transients, vibrations and resonance in hydroelectric and pump plants as well as simple and complex gravitational systems experienced by authors are presented to verify the theories by field tests. The phenomena were analysed both by the transfer matrix method and method of characteristics and compared with measurements. Waterhammer and Hydraulic vibrations have provoked strong pressure fluctuation in hydraulic systems making problems and accidents in exploitation. Introduction A trend towards larger and more powerful units and complex networks has been a characteristic for the recent designs of hydraulic systems. This fact, together with high construction, equipment and labour costs, stresses the need for a more rational design of new plants. The components of systems should be strained as close to the allowable limits as possible, without endangering the safety of the structures. This goal can be achieved only with a reliable knowledge of possible loads in the whole system. The most dangerous stresses are those provoked by pressure surges and vibrations, especially if the resonance appears, which is the worst case. Maximum pressures during transient operations, such as rapid closing down, opening-up, equipment breakdowns, earthquakes, etc., may destroy pipelines, valves or some other parts and cause considerable damage and sometimes even loss of human lives. The sound design of a new plant is impossible without a complete analysis of these transients. This knowledge also helps in preventing resonance in the existing systems, thus avoiding serious risks and damage to the plants. In such a way, the reliability of the project may be increased, and the operating and maintenance costs significantly reduced. The analysis of transients is rather a complex and time consuming task, each case introducing some original problems. Our experience, gathered on several plants, where safety of the plant was in danger of destruction or could have been endangered by hydraulic oscillations and waterhammer surges, are described. 1

2 Transients In Distribution Networks: Field Tests and Demand Models The results of a field test conducted, by the City of Calgary Waterworks staff on one of the city's major transmission and distribution subsystems is presented. (McInnis, et al., 1995)The observed pressures are compared with those predicted by a skeletal network transient model using three different representations of system consumptive demand; which arc: (1) Aggregated discrete, constant withdrawals; (2) aggregated withdrawals using an "equivalent" orifice technique; and (3) a distributed pipe flux model. The first two methods are widely accepted and utilized techniques in the hydraulic modelling of water distribution systems; the third method is less used. The complete pipe network is shown in Fig. 1. Excluding the mm residential service connections, of which there are approximately 6,800, the smallest pipes are 150 mm in diameter. The largest pipe diameter is 1,350 mm. The total length of transmission and distribution pipe in the subnetwork is about 90 km. The vast majority of pipes that are 300 mm, or greater, in diameter are of reinforced concrete. Figure 1. Bearspaw Northwest Feeder and Associated Network and Aggregated Water Consumption in Residential Areas (indicated by vertical bars). Bearspaw pumping station Although three pumping stations are shown in the figure, only one pump in the Bearspaw water-treatment plant is supplying potable water to the zone during the field test. Cutting power to the operating pump motor at the Bearspaw treatment plant simulated the pump failure scenario. Fig. 2 shows the time history of piezometric pressures recorded at both pressure transducer locations. On the same graphs, the output from the computer model is also plotted for comparison. Several key features are apparent: (1) The model tracks the initial downsurge very closely; (2) following the first low-pressure wave, more energy is dissipated in the actual system than is indicated by the model results; and (3) there is an apparent "phase shift" between the residual transient waves of the pipe system and those of the computer model. It is interesting that the very sharp wavefronts, typical of the method of characteristic solutions for hyperbolic differential equations, represent the observed results. 2

3 Figure 2. Field Test Data and Model Results with Discrete Nodal Demands Proceedings of the International Conference on CSHS03 The full capacity computer simulation was also carried out using the distributed demand representation. The residual pressures are damped here by the action of a surgeanticipating valve. Fig. 6 shows the pressure response at the pumping station meter vault for case simulated pump failure when running two pumps at the current installed capacity of 1.11 m 3 /s. For comparison, the recorded pressure trace and the simulated case 3 (distributed demand) results are also shown. Figure 3. Comparison of Field Test Data and Computer Model at Actual Test and Installed Capacity Flow Rates 3

4 The pipe network presented is not especially complex when compared to a full distribution system with multiple pressure zones, automatic control valves, multiple pumping stations, reservoirs, and a host of other appurtenant structures and hydraulic devices. Nevertheless, the system exhibits the topological complexity that distinguishes a network from a simple branched or series pipeline. Several conclusions are drawn from this field test, and some insight was gained from the computer analysis. Transients are important phenomena in complex pipe networks. Even a minor event can produce a distinct and predictable water-hammer response, in terms of expected maximum and minimum pressures. Therefore, transients should not be casually excluded from the design and operational aspects of pipe networks. Low Pressure Distribution Tunnel The pressure envelops for measured and calculated transients are shown in Fig. 5 for the drinking water distribution system presented in Fig. 4. (Pejovic et al., 1989 Pejovic et al., 1992) Both the experiments and simulations have stated that the vacuum can appear in the suction pipeline if two pumps fail simultaneously, but the model has permitted an insight into the parts of the system, which were inaccessible for measurements such as aeration pipes of the tunnel interior. The simulation revealed that absolute vacuum appears in the third section of the tunnel, causing water column separation and serious shock afterwards. Furthermore, air was sucked-in through both aeration pipes. Free air in the tunnel usually means operational troubles. Figure 4. Scheme of Drinking Water Distribution system 4

5 Figure 5. Pressure Envelopes Along the Tunnel for Different Measured and Calculated Cases Figure 6. Air Entering into the System This system has vertical intake structure located in the large reservoir of drinking water, the level of which changes as well as the discharge. Therefore, in some regimes of operation the submergence was not deep enough to prevent vortices of air to enter the system, as shown in the photograph in Fig. 6 made by submerged camera. As an example, pressure measured downstream of the valve 24 after load rejection of one pump is presented in Fig. 7. Pressure spikes are registered whenever air travels though the valve. These are pressure drops, but upstream in the suction tunnel pressure rises occur. As pressure waves they travel and reflect through the system Figure 7. Pressure Measured Downstream of the Valves 24 And 25. The Pumps 42 and 43 in Operation; Power Failure of the Pump 43. 5

6 In 1989 pumps in PSV1 were out of operation when pump power, failure occurred in the PSV2. Pressure drop and water column separation in the inlet piping system of the pumping station PSV1 was so severe that all pumps were damaged. Broken volutes of two centrifugal pumps are shown in Figs 8. Figure 8 Broken Volutes of Two Centrifugal Pumps Water Supply System A main pipeline several kilometres long, shown in the Fig. 9, transports water by gravity from a reservoir near the treatment plant to the small distribution reservoirs located along the pipeline, and the inflow is controlled (regulated) by valves; to prevent the overflow of clear water. When a reservoir is completely filled, this valve rapidly closes the inlet pipe provoking pressure waves, which travel along the main line, causing pressure surges. Unfortunately, a good pan of the main pipelines is made of asbestos-cement pipes, which are very sensitive to overstress. Several breakdowns did actually happen, and the whole system was investigated both experimentally and theoretically(pejovic et al., 1989; Pejovic S, 1989) Figure 9. A Regional Water Supply System Figure 10. Fluctuations of Pressure After a Large Reservoir (1) Shutdown from Discharge 100 1/s to 0. The pressure recorded at characteristic points along the pipelines and computer analyses are presented in Fig. 10. The theoretical values agree well with the observed ones. The experiments were limited to such changes, which cannot cause serious damage to the pipeline, but once the model was calibrated, the analysis of more dangerous cases was possible (Fig. 11). Several runs were made, revealing the points of the original design where pressure surges could have been followed by high-pressure peaks. 6

7 Figure 11. Pressure Fluctuations iin Three Points of The System after the Reservoir (3) Shutdown Collapse of the Thin-Walled Penstock The collapse of the thin walled pipeline of the public water supply system, shown in Fig. 12 (4. Storage of clear water, 6. Pipeline in the tunnel, 2. Pumping station, 7. Gravitational pipeline, 3. Discharge penstock, 8. Regulating valve, 4. Free level reservoir, 9. Distribution reserve. 5. Outlet valve of free level reservoir), was caused by vacuum. The photographs (Fig. 13) show the 1570 m of buckled pipeline in the tunnel 6 (Pejovic, et al., 1992). Figure 12. Regional Water Supply System Figure 13. Collapsed Thin Walled Steel Pipe 7

8 Air - Chambers (Gas - Accumulator) Proceedings of the International Conference on CSHS03 An air chamber connected to the discharge pipe of the pump reduces the intensity of the surge pressure, due to the expansion and contraction of the compressed air in the air vessel. The throttling, which occurs at the connection to the pipeline, is very significant for the optimal design of a system. A diameter, losses, and length of connecting pipe(s) could have a great influence on pressure surges as shown in Fig. 14, which presents the results of computer analysis for various local losses between 0 and 100. The selected best throttling calculated case and site measurement are compared in Fig. 14c showing that the modern transient analysis is of paramount importance (Gajic et al., 1980). Figure 14. Air Chamber with Optimal Throttling. (a) Scheme, (b) Selection of Throttling, (c) Optimal Throttling. Earthquake Effects The hydro power plant, (Fig. 15), is located in an area where some 30 years ago a serious earthquake happened. All buildings and structures constructed since then are able of withstand earthquakes up to 8 degrees of Mecali scale (acceleration up to 200 cm/s 2 ); the dam of this plant was designed to be even stronger (for maximum acceleration up to 300 cm/s 2. (Gajic et al., 1986; Obradovic et al.,, 1986; Pejovic S, 1989; Pejovic, et al., 1992) Figure 15. Bottom Outlet of the Existing Power Plant Several recorded earthquakes were studied, and the strongest one, shown in Fig. 16, had been selected for numerical analysis, Maximum-recorded velocity was 40.4 cm/s, maximum acceleration 440 cm/s 2 and maximum displacement of soil 11 cm. Both the transfer matrix method (frequency domain) and the method of characteristics (time domain) were applied. The solutions depend upon the proper choice of boundary conditions. The closed end of the pipe moves in the manner dictated by the earthquake, with the velocity Vg=f(t), taken from the earthquake time history (Fig-16). 8

9 Figure 16. Time History of the Earthquake The amplitudes of pressure fluctuations are the strongest at the closed gate (dead-end in Fig. 17) where they achieve maximum +5.3 bar and minimum -5.7 bar. The water column separation (caused by excessive vacuum) occurs at the closed valve. Water column separation was not simulated in these calculations. Figure 17. Earthquake: Pressure Envelopes in the Bottom Outlet for Minimum Water Level in The Storage Basin By varying the frequency over rather a wide range the pressure oscillations in the system was computed and it can be seen that several natural frequencies are within the range of earthquake excitations, and therefore the response of the system in the case of resonance could be violent (Fig. 18). Figure 18. Frequency Response of the Bottom Outlet Air Release Orifice A pump after started, compresses and vents the air, to the atmosphere through an outlet orifice and than the flow is instantaneously stopped when the air is completely pumped out. Water velocity through the orifice is neglected to the sonic velocity of air outflow of ~340 m/s when pressure in the pipe p is greater than critical pressure 9

10 Figure 19. Start-up. Air Outflow Orifice 32 mm The basic Joukowsky equation of waterhammer describes the pressure rise, but the wave reflected at the closed butterfly valve will double the pressure amplitude as sown in Fig. 19. This start up procedure and simultaneous air venting through an orifice should be avoided whenever it is possible because the waterhammer reflected waves could damage the pump and other equipment or, if the orifice is small to reduce the high pressure waves, the time of pump operation at very low flow in the zone of high vibrations is prolonged. Auto-Oscillation Resonance In the pump storage power plant, shown schematically In Fig. 20 (turbine operation: output 2x250 MW, speed of rotation 300 rpm. head 213 to 227 m, pump operation: input 2x217 MW, head 210 to 239 m) self-excited oscillations of the ball valve had occurred when both units were out of operation and the ball valves were closed. (Jemcov et all., 1980; Pejovic, 1980: Pejovic S, 1989; Pejovic S., et all., 1992) The construction of the ball valve is schematically given in Fig. 21 and the damaged aeration valve is shown in Fig. 22. Auto-oscillation resonance may be provoked by a seal ring of a closed valve of any type. A score of such cases has been reported from various plants and installations, such as power plants, pump stations, water supply systems, and any hydraulic system. These events caused some damage, sometimes with rather serious consequences. The reason was insufficient-sealing pressure (a spool valve has been damaged by cavitation). The case was thoroughly analysed by the transfer matrix method. First computations were done on a simplified model: one pipeline with a downstream-end valve. The results are given in the Fig. 23 (abscissa: frequency, f; ordinate: maximum amplitudes of pressure oscillations, H). It is clear that natural frequencies are equal to f = na/4l (n = 1, 3, 5,...). Figure 20. Pumped Storage Powerplant 10

11 Figure 22. Sealing System of the Ball Valve Figure 21. Damaged 600 mm Aeration Valve SEAT A more detailed model was then prepared and two cases distinguished: (a) one machine is operating, the second one with a damaged seal is closed down; (b) both machines are stopped; one has a damaged seal ring. Mode shapes for the first harmonic of the case "b" are shown in the Fig. 24. Note that maximum pressure amplitudes appear in both branches in spite of the fact that only one ball valve was excited. Figure 24. Amplitudes in the Simplified System Figure 23. Mode Shape of Aauto-Oscillations. Both Ball Valves Closed Figure 25. Variation of The Maximum Pressure in the Tunnel (H T ) and Penstocks (H C ) as the Function of the Relative Wave Speed (A/S 0 ). Frequency (F) Varies Too. 11

12 The wave speed cannot be computed very accurately, even for the existing plants, since the measurements "on the spot" are not very accurate either, due to errors introduced by the imperfections of instruments. Therefore in order to evaluate the influence of an inaccurate wave speed values on final results, the sensitivity analysis was done. Local wave speed (a) in the tunnel (some 8000 m long) was varied. And the results are summarized in the Fig. 25 (abscissa: relative wave speed, a/a 0, ordinates: amplitude of pressure oscillations in the tunnel, H T in the penstock, H C and frequency f). It can be seen that this influence is rather strong: a variation of wave speed from 98% to 106% only makes differences of pressure head fluctuation in a wide range. In the worst case the amplitudes in the tunnel reach 150 mwc (for a/a 102%) and in the best case (for a/a (98 to 101%) amplitudes are 10 mwc only. The pressure amplitudes in penstock also vary considerable, from 100 to 350 mwc The resonance of another system was also caused by an inoperative ball valve(pejovic et al., 1987; Pejovic S., et all., 1992). Serious damage was prevented by prompt intervention of the staff. When the oscillations took place, an oscillograph was installed on the spot and the amplitudes of pressure oscillations in the Surge tank chamber, shown in Fig 33 were, measured. Figure 26. Auto-Oscillation of the Ball Valve Time (s) Auto-Oscillations of the Wheel Gates and Ball Valve Auto-oscillations in a low-head hydroelectric plant (Fig. 27) with the closed inlet wheel gate happened during commissioning tests: a load rejection and emergency turbine quick closure, closuring simultaneously the intake wheel gate (Pejovic S., et al., 1992). During the test, all were normal, the wicket gates closed in 7 s and wheel gate in about 30 s but a few seconds later, in the 33rd second approximately, water in the penstock started to oscillate (Fig. 28). At the beginning the pressure in the penstock (at points 2 and 6, Fig 27) dropped a little and the pressure in front of the closed wheel gate (point 1, Fig. 27) jumped a bit. After a period of nearly constant pressure, oscillating with small amplitudes and high frequency of 12 Hz, the process was repeated. Few minutes later the pressure drop in the penstock reached 3,3 bar, with the frequency of 0,6 Hz. At the beginning and at the end of this phenomena the pressure drop was quite small and its frequency was about 0,3 Hz. Only a very low sound was heard; one had to put the ear against the penstock wall to hear this sound clearly. It was identified as the movement of the wheel gate in its slots. After the closure of seals, the leakage of water through the closed guide-vanes decreased accordingly and the pressure fluctuations increased. The measured leakage of water through the wicket gates was more than 370 1/s with fully opened seals and 4,3 l/s only if the seals were closed. The leakage through the wheel gate was from 14.2 to 27,3 l/s. 12

13 Figure 27. Low Head Powerplant Figure 28. Emergency Quick Closure and Auto-Oscillations, which Followed Emptying of the penstock has been carried out afterwards. Suddenly similar fluctuations of pressure appeared when the small ball valve (diameter 250 mm) connecting the penstock (diameter 5500 mm) and the draft tube was opened partially. The low frequency was equal to 0,63 Hz at all measuring points (Fig. 35), and high frequencies were about 5,5 Hz and 12 Hz. All high frequency amplitudes were stronger then in previous cases when the small ball valve was closed. The sound produced by the ball valve clearly has indicated that high frequency self-excited vibrations have caused the high frequency pressure oscillations. During the commissioning tests and additional vibration tests, performed a few months later on both units of the power plant the same unstable steady state resonance were measured. 13

14 Figure 29. Dewatering of the Penstock through the By-Pass Ball Valve Proceedings of the International Conference on CSHS03 From the measured data, it was concluded that the pressure fluctuations were excited by the inside leakage through the intake structure wheel gate into the penstock and outside leakage through the guide vanes and/or the ball valve outside of it. A stability analysis base on transfer matrix method showed that the system was unstable at some small leakages depending on the diameter of aeration pipe (Fig. 30). The elements of the mathematical model shown in Fig. 31, are: 1-2 intake structure, 2-3 wheel gate shaft, 4-5 aeration pipe, penstock, and draft tube, 8-9 and draft tube gates shafts, 6 closed turbine, 21-wheel gate (partially closed), 14-15, 16-17, and measuring pipes of snail diameter, drainage by-pass line, with the ball valve 22. The wave speeds are: in the steel pipe 710 m/s, steel-lined concrete pipe 1300 m/s, and in the draft tube 1250 M/S. In the case of two-phase flow in the draft tube, the wave speed was supposed to be 50 m/s (line 6-7) and 100 m/s (lines 7-10, 7-13). Figure 30. Coefficient of Attenuation Shows Instability at the Leakages between 0 and 1500 l/s and Ddiameters between 1.2 and 1.6 m Figure 31. Scheme of the Powerplant Numerical analysis of hydraulic oscillations was carried out for the two operating conditions: (1) one-phase flow in the entire system, (2) one-phase flow in the penstock and 14

15 two-phase flow - water and air bubbles mixture in the draft tube. The second case vas analysed since the very small quantity of air bubbles reduced the wave speed to the very small value of 30 to 100 m/s and turbines operates in the zone of incipient cavitation.. For the second case, natural frequency of 15.2 Hz is very critical in all operating regimes. The system response would be very high pressure oscillations since the coefficient of attenuation is positive even - instability of oscillations. Fig 30 shows that by changing diameters of penstocks and connecting pipes (or something else) it is possible to reduce amplitudes of oscillations. S shaped Characteristics of the Pumped Storage Power Plant "Bajina Basta," one of the highest head single stage hydraulic machine, shown in Fig. 32, has the tunnel about 8,000 m long, penstock over 1200 m, surge tank with both lower and upper chambers, and an asymmetric branching at the inlet. Two pump-turbines, generate 315 MW each at 600 m head, and power consumption 2x310 MW pumping 2x 50.8 m 3 /s flow. The maximum pumping head is 621 m. Figure 32. Pumped Storage Power Plant "Bajina Basta Load Rejection Field tests were carried out and compared with measurements (Fig, 33). Both units generate 2x298 MW, unit one load rejecting, and its wicket gates close down rapidly while another unit continue generating in spite of the violent pressure surges (Obradovic et al., 1988; Pejovic S, 1989; Pejovic S., et all., 1992). The wicket gates of unit one remain open for some sec, and then start to close down, first rapidly, and than slowly. The diagrams show the time history of pressures in the spiral casing H u and draft tube H D, angular speed ω, flow Q and guide vane opening a. The unit 2 generates connected to the system with the wicketgates blocked in the open position a. The agreement between the measured and computed values is good, although no calibration was done. The wave velocity used for the computation is slightly greater than the real one (compare peaks!), and the prototypes are different from the model; they are relatively better and more efficient, especially in the zone of medium and small openings. Further calibration could have brought computational results closer to the measured one, but even this degree of accuracy was satisfactory. 15

16 Figure 33. Pumped-Storage Plant "Bajina Basta" Unit 1 Load Rejection, Unit 2 Continue Generating The experiments cannot tell everything about the internal processes but the mathematical model is able to, because all variables are available. Studying results of calculations it was found that unit 1 did enter the fourth quadrant, marked RP (reverse pump Fig. 33) in the diagram where discharge Q is negative (pump direction) between 6.9 and 10.3 s after power failure. These results are also plotted in the characteristic diagram in Fig. 34. The unit 1 follows the S shaped curve rather far into the fourth quadrant, goes back under the curve of zero efficiency, and so forth. The unit 2 remains in a relatively narrow range around the initial operating point. Consequently, the machines enter this dangerous zone of reverse pump operation characterized by strong hydraulic vibrations and cavitation, even in the most regular cases as the one described. Figure 34. Consequences of One Unit Power Failure in Turbine Operation 16

17 Analyses of the time history of the measured and calculated simultaneous two units load rejections, which were generated at full load, show that the flow of 62.3 m 3 /s at full generating turned into the-30 m 3 /s, reverse pump discharge followed by asymmetric travel through S instability. The computer simulation of this S form instability was published in(pejovic at all.,1976)1976 (Fig 35 Two units load rejection) and explained in four quadrant torque characteristics, Fig 36. The transient speed of the unit runner is given by the equation Figure 35. Computer Simulation Published 6 Years before the Commissioning Tests dω J = M M h dt where J is the inertia of rotor, ω angular speed M shaft torque, M h hydraulic torque, and t time. Shaft electric machine torque, vanish at load rejection, M = 0. Substituting M h and ω = nπ/30 from unit characteristics n 11 = n o d M, M 11 = 3 H d o H reads the equation which explain instability π H dn J 30d dt 11 = d 3 HM 11 Figure 36. Four Quadrants S Shaped Low Specific Speed Pump-Turbine If the transient phenomenon begins at point A and the gate opening is not changing, the operating point goes to point B since m 1 > 0. At the Pont B, m 1 > 0, however, when n 1 < 17

18 n 1B the working point jumps from point B to point C. At this moment m 1 < 0, and n 1 will go up to point D. At point D m 1D < 0, and when n 1 > n 1D working point jumps from point D to point E, where m, 1 > 0. The process is further repeating, passing through the points EBCDE... end will never come to a stop. Due to the waterhammer in the penstock the head changes quickly, and this permits the operating regime to pass through points B and D, operating in the zone between points B and D, as well as in the zone n 1 < n 1C and a new passage to the zone n 1 > n 1E. Thus, all types of operations shown by four-quadrant characteristics are possible. This nature of pump-turbine curves brings about the sudden changes in pressure, discharge, revolving speed and torque, which; causes unfavourable superposition of pressure fluctuations, followed by resonance. These operating conditions are pointed out in the diagrams. Based on this transient analysis in the stage of design the control system was adopted to prevent accidents in the cases of load rejection and pump power failure. In this case manufacturer and client have understood the importance of transients, vibrations and stability on time and prevented a serious troubles that could have happened in operation. Pump power failure Fig. 37 shows the time history of the penstock valve emergency closure test when pumping 40 m 3 /s at 104 mm servomotor stroke and in the graphs Fig 47 are added the output from the computer model for comparison. The model tracks the initial downsurge very closely; following the first low-pressure wave, and there is an apparent "phase shift" between the residual transient waves of the pipe system and those of the computer model. Figure 37. Penstock Valve Emergency Closure at Partial Load Pump Operation 18

19 Figure 38. Measured and Calculated Penstock Valve Emergency Closures Proceedings of the International Conference on CSHS03 Key features Several key features are obvious: (1) the pump-turbines with S shaped characteristics enter the fourth quadrant (reverse pump operation) regularly after a load rejection from turbine operation (and pump power failure), even if the wicket gates are closed down rapidly, (2) the mathematical model tracks the initial upsurge very closely; (3) following the first lowpressure wave less accurately, (4) there is an apparent "phase shift" between the residual transient waves of the pipe system and those of the computer mode, (4) the similarity laws when applied to a high prototype/model ratio lead to underestimation of actual pressure surges; therefore a calibration procedure is helpful, (5) it is better each unit to have its penstock to reduce the frequency of surges in the S shaped runaway characteristic, (6) draft tube piping should be as short as possible to decrease amplitudes or pressure fluctuations, (7) penstock valve must automatically close to prevent S characteristic resonance. Bolney Water Supply System The Bolney-Husky water supply system collects water from a couple of different supply locations and feeds this water, through a fairly extensive pipeline system, to several Steam Assisted Gravity Drainage (SAGD) steam plants that are used for the recovery of oil from a subsurface reservoir. The pipeline system itself consists of 6 Husky water intake wells with associated well pumps, forcemain and discharge control valves. An inline booster pump station and by-pass line with control valve (V-notch ball valve) drawing from all Husky water intake wells and discharges into a forcemain that actually supplies the SAGD facilities. Three Mobil water intake wells with associated well pumps, forcemain and discharge control valves also supplies the SAGD facilities. An in-line flow control valve regulates the flow rate from the Mobil well field. Additional Husky river water intake pumps and a second booster pump will be installed to expand the system to supply the required flow rate. In general, the Bolney system is characterized by pipes with long length, carrying fluid with high velocity under high pressure. The system is topologically complicated by the fact that there are several converging pipe junctions as the water is progressively accumulated from two primarily locations, and then distributed to several delivery locations (see Fig. 39). The pipeline has an up-and-down or undulating profile as it generally follows the topography of the ground. The system is subject to relatively high degree of variability in flow states, with numerous combinations of different flows from 19

20 different sources and to different demand points being possible. Finally, the structural strength of the system as a whole is quite variable. Figure 39: Plan view of Bolney/Rex system with boundary device nodes shown In terms of the pressure and flow control system, the intention is to control the characteristics of the booster pumps based on the discharge header pressure. Both pumps are to be VFD driven, and so the lead pump is to change speed to maintain header pressure until a second pump is required. When two pumps are required, they will both operate at the same speed. The header pressure set-point is to be adjusted, either manually or automatically, based on the desired flow rate from the booster station. The pumps for the booster station are expected to be expanded or upgraded in the future to increase their capacity. Initially, the booster station will transfer approximately 7865 m 3 /day, but the station capacity is to be increased to 9700 m 3 /day at some later time (considered full development in this report). The operation of this steady state control system does interact directly with the transient analysis in a number of ways, particularly for the case of closing a downstream valve. From a high-pressure perspective, the worst-case scenario is that the control system does not register or react to a reduced flow signal in time to assist the transient event, and the surge protection equipment (particularly the junction by-pass) is designed to handle this eventuality. Both the Husky and Mobil forcemains combine (at Junction 4-21 or node 130) into one forcemain supplying the SAGDs (Mobil 1-17, Husky 8-29, Husky 8-32) modeled as either a fixed demand or orifice demand as appropriate as depicted in Figure 1 (actual plan view from TransAM Data File). Currently all pumps are modeled as constant speed types even if they are VFDs since this is appropriate for the power failure case, and conservative for the valve closure case. This does not pose a problem for the example scenarios since the pumps are either running full or shut down abruptly. During a transient event, say when a valve is operated or a pump turned off or on, the orderly progression of flow and energy associated with steady state flows is disrupted. In particular, the even and smooth flux of water is usually first disturbed, causing short-term imbalances in the flow continuity. This imbalance cannot be easily accommodated within the confines of the original pressurized flow system; in fact, it is only through the potentially dramatic forces of fluid compressibility and pipe extension that the additional 20

21 (reduced) fluid can be stored at all. But since water and other liquids are not easily compressed, and large pressure forces result, pressures that are quickly created and then rapidly propagate to other portions of the pipeline system, communicating to them information about the change in the rate of flow. Not only are the mass and momentum changes associated with a transient event frequently dramatic, but so are the energy transformations. Consider, for example, that any moderate length and diameter, through its substantial design flow, embodies huge quantities of kinetic energy in the moving water. If flow conditions are changed, at least some portion of this stored energy will be rapidly converted into other forms, such as strain energy, manifested in the pipe system as pressure changes in the water and stress changes in the pipe wall. If uncontrolled, such impressive energy transformations have the potential to do considerable damage, not only to the pipe system, but also to all connected equipment. This damage potential is exactly what makes a proper respect for transient events essential. Specific Mitigation in the Bolney System. Long lines carrying fluid with sometimes quite high velocity characterize the Bolney system. In many applications either of these conditions can create challenges for transient control. What makes this system so interesting is that its possession of both characteristics (i.e., long length and high velocity) to a certain extent relieves many of the transient concerns. In particular, if the flow is suddenly arrested at the downstream end of the system, the upstream propagating surge wave is attenuated by the friction effects, and is thus significantly subdued in its passage through the long pipe system. In a like manner, arresting the flow at the upstream end reduces the flow and thus the friction loss, and a similar attenuation phenomenon occurs. Moreover, the pipes are designed to have considerable strength to be able withstand the steady high pressures required to induce the required flow. Of particular interest here are operations of one of the control or isolation valves within the plants or pump stations, since these valves play a key role in bringing components on and off line. In general, it was found that five-minute valve operation times were sufficient to limit surge pressures within the Bolney system and to limit positive and negative pressure waves well within allowed tolerances. Some attention was also given to the transients associated with bringing a new demand point on or off line within the SAGD plants. As valves are opened or closed at one of the local demand points within the system, the associated transient waves essentially transmit a signal through the rest of the system for it to respond to the change in flow. Since a long pipe system with reasonable velocities is largely dominated by frictional considerations, the decay and reflection of these transient waves is strongly influenced by which other flows and devices are on line, and particularly where other flows are occurring. In general, the first demand within an otherwise quiet system generates the most persistent response, particularly since there may be a number of dead-ends which tend to magnify the magnitude of the pressures waves locally, and because there are a few dissipative elements in the system. However, all demand responses were well controlled, and none of the responses would be characterized as severe, as long as valve operation occurs over an extended period. Figure 40 is typical of the system response for suddenly arresting the flow at one of the SAGD turnouts, and shows a relatively mild and well-behaved transient response. 21

22 Figure 40: Suddenly arresting flow at SAGD facility, creating quite mild transients. : For the operation of inline or isolation valves, the transient response is most sensitive to the final closure of the valve; that is, it is the final closure that effectively breaks the continuity between upstream and downstream conditions at the valve and thus it is this portion that removes any self-mitigation effect associated with the in-line nature of the devices in this system. Thus, a staged closure involving a relatively fast initial closure followed by a more gradual final seating of the valve was found to be preferable in terms of the magnitude of the pressure rise generated. However, overall, valve closure responses are readily controlled under all operating scenarios studied to date. Should any valve be closed suddenly or without proper care, particularly on the main forcemains say at the 4-21 Junction, or should a failure occur, a relatively large transient wave will be initiated that will propagate through the remainder of the connected pipe system. To make matters worse, the steady control system must respond to this event, or the pumps will deliver the high supply pressure throughout the pipeline system, since friction losses would no longer be effective at reducing downstream pressures. To protect against this worst case eventuality, it is recommended that by pass lines be installed at key locations, particular at the 4-21 junction, but indeed at any place where it is conceivable that a quarter turn block valve could be suddenly closed. Our analysis indicates that these by pass lines, with a 3 or 4 internal diameter, have a dramatic effect in improving transient and steady valve closure effects. A comparison of responses with and without by pass makes this abundantly clear. Note that if the steady state control system backs off and reduces the pumping requirements, the pressure rise in the no by pass case will be significantly reduced. However, the point is that the presence of the bypass, simply and inexpensively mitigates against both effects. Figure 41: Suddenly arresting flow at 4-21 Junction in 10 line, creating significant transient along with high pressure build-up with pumps backing up their curves (no steady state control response). 22

23 Figure 42: Suddenly arresting flow at 4-21 Junction in 8 line, with 4 by-pass. Creating mild transient and no significant pump back-up. Pump Control System. 23

24 The last point about valve closure is so important that it is worthwhile restating it from another perspective. When a valve is closed in this system, there is an initial pressure wave that is created that then propagates to other parts of the system, essentially informing these portions of the change in flow state that has occurred. In cases considered in the Bolney system, this initial surge is always expected to be within the pipeline tolerance. However, the system progressively responds to the new state, and the ultimate pressures experienced will depend how the rest of the system responds. In particular, reduced flow will tend to cause the pumps to back-up on their operating curves, an effect that highlights the crucial nature of the pump control system to maximum pressure control. Bulb Unit Vibrations Fourteen bulb units, each 27 MW of the run-of-river plant shown in Fig. 39 are located in the dam forming upper storage, and furthermore have inlet structures, and auxiliary and main inlet wheel gates with three aeration pipes on each intake. (Pejovic et all., 1994) They are Figure 43. Cross Section of the Bulb Unit placed in the middle of the water flowing all around them. Measured vibrations of turbine bearing upon the operating regime (Fig. 40) have been increased with both power output and head, and at the head of 7 m cross the limit line of good vibration operating condition and at the head of 7.6 m and 100 % output, amplitudes reach guarantee. The maintenance cost, if units operate at high head and power output, increases and probability of frequent incidents should be carefully monitored. It is evident that the measured values are large and that they can drastically reduce the units lifetime. The simplified 1 D model (Fig. 41 in which: 1 and 11 are upper tailrace reservoirs, 9 turbine, 2-3 and 4-5 vertical shafts of inlet structure) and transfer matrix method of analysis in the frequency domain are shown in Figure 42 for one phase flow if there is no any air in the water, which never happen in the normal operation, and for the case with the air released in the draft tube. Low frequencies 0.1 and 0.4 Hz are unstable in some domain of operation. 24

25 Figure 44. Measured Bearing Vibrations for Various Power Output P and Heads H Figure 45 A Simplified Linearised Mathematical Model. Figure 46. Natural Frequencies Without Air (Left) and With Air (Right) In The Draft Tube Several key features are obvious: (1) the bulb units are very sensitive to hydraulic vibrations, (2) the mathematical model either 1 D and simplified, can discover some instabilities (3) a draft tube should be as short as possible to decrease amplitudes or pressure fluctuations, (5) specific speed of this turbines should have been higher in order to reduce the vibration (6) maintenance cost of these lower specific speed units is very high (7) life time period is noticeably shorter. Conclusion The aim o hydraulic vibration analysis carried out during design and construction is to find if the machines and associated systems can operate safely avoiding any possible danger to the plant and personnel. Therefore, analysis of resonance and stability is very important. 25

26 Stability and behaviour of the hydraulic system under steady oscillating conditions is dependent upon the characteristics of all its parts. Changing some parameters, such as diameters of penstocks, machines characteristics, or something else, and computing coefficient of attenuation for natural frequencies, as well as responses to the existing forcing exciters, it is possible to reduce amplitudes of oscillations making stability to be better. Reported cases of hydraulic transients and oscillations have shown that this is a serious problem, which should not be overlooked. Therefore, the design of a new plant must contain a complete analysis, covering the whole operating range of the plant. Natural frequencies of the system should be computed and compared with frequencies of the expected excitation forces. The resonance must be avoided in any case. An earthquake might cause serious hydraulic forces within the system, especially if the pipe/penstock is closed. The magnitude of these forces depends both upon earthquake's characteristics and upon the characteristics of the system. The problem is a multi faced one and calls for a collaboration among specialists in seismology, hydraulics and structural analysis. Moreover, the problem is, in a sense, unbounded since the set of possible earthquakes, which might happen in any given region, is not limited. For plants and installations already existing, this analysis should be done also, especially if some difficulties were noticed in a normal operation. The analysis should be performed by mathematical modelling, using digital computers and the theory of transients and confirmed by field measurements and observations. As all the problems are not resolved yet, despite efforts of many scientists in the world, closer collaboration and frequent exchange of the ideas and results are really needed. It is the time the guidelines to be reviewed and accepted as standards, to direct the new designers to apply the new modern methods and economically design the hydraulic systems and plants. Real, measured characteristics of machines and other components must be available for an accurate analysis. Hydraulic systems of airplanes, space shuttles, high pressure oil hydraulic systems as well as internal and external artificial systems of pulsatile human blood systems should be carefully analysed too, to discover instabilities. References Gajic A., Pejovic S., 1980 Hidraulicki udar i vibracije hidropostrojenja (Waterhammer and Hydraulic Oscillations), Konsultacije "Prelazne pojave u hidroelektranama sa cevnim i Kaplanovim turbinama", Ljubijana. Gajic A., Pejovic S, Obradovic D., 1986, Hydraulic Loads in Hydraulic Systems during an Earthquake (in Serbo-Croatian), XVU Yugoslav Congress of Rational and Applied Mechanic, Zadar, Vol. 2, pp Jemcov. R., Krsmanovic, L., Pejovic, S., 1980, Excitations of Vibrations in Pumped Storage Power Plant "Chapljina", (in Serbo-Croatian), JUG EL, Ljubljana, pp McInnis D., Karney B.W., 1995, Transient in Distribution Networks: Field Tests and Demand Models, Journal of Hydraulic Engineering, Vol No. 3. March, pp

27 Obradovic D., Arnautovic D., Pejovic S., Gajic A., 1988, Mathematical Model of Transient Regimes in Multi-Unit Hydro Power Plants, IAHR Symposium, Trondheim, pp Obradovic D, Pejovic S., Gajic A-, 1986, Analysis of Earthquake Effects upon Hydraulic Structures, 5th International Conference on Pressure Surges, Hannover, pp Pejovic S, 1989, Pressure Surges and Vibrations in Hydropower Plants -Experiences in Yugoslavia, The Current State of Technology in Hydraulic Machinery. International Editorial Committee Book Series on Hydraulic Machinery, Gower Technical, pp Pejovic S. 1980, Vitbracije sislema pumpne hidroelektrane "Capljina", (Vibrations in the Pumped Storage Power Plant "Capljina"), Masinski fakultet, Beograd. Pejovic, S., Boldy, A. F-, Obradovic, D, 1987, Guidelines to Hydraulic Transient Analysis, Technical Press, England. Pejovic, S., Boldy, A. P., 1992, Guioeline.s to Hydraulic Transient Analysis of Pumping systems, P&B Press, Belgrade - Coventry. Pejovic S., Gajic A., 1992, Sensitivity and Stability Analysis of Pumping Systems and Air Chamber Influence on Hydraulic Vibrations, International Conference on Unsteady Flow and Fluid Transients, Durham, England, pp 10. Pejovic S., Gajic A., 1992, Cases and Incidents Due to Hydraulic Transients Yugoslav Experiences, Int. Congress on Cases and Accidents in Fluid Systems, Sao Paulo, pp Pejovic S., Gajic A-, Savic Z., Stojanonic Z., 1994b, Hydraulic Stability of Bulb Turbines, 17th IAHR Symposium. Beijing, paper J2, pp Pejovic S., Krsmanovic Lj., Jemcov R., Crnkovic P., 1976, Unstable Operation on High-head Reversible Pump-turbines, 8th IAHR Symposium, Leningrad. Pejovic S., Vukosavic D., 1991, Vibration and Economy of Hydropowerplant Operation, Work Group on Behaviour of Hydr Machinery under Steady Oscillatory Condition, Milano, paper 1, pp