pressure. The approach has been shown to be mathematically acceptable, but sacrifices the geometric similitude of the closed surge tank. Compared with the two alternative approached, the advantages of the new method include the lower cost and complexity, and the preservation of the geometry of the closed surge tank. It is concluded that the new method involves serious manipulations at the cost of the geometric similitude of the water conduit geodetic height. However, under these circumstances, the similitude of the hydraulics and the thermodynamics is preserved, and the approach is feasible for scaling closed surge tanks.
C3: An evaluation of the accuracy of a hydraulic scale model of a hydropo wer plant with a closed surg e tank s (P2)
A hydraulic scale model of an existing hydropower plant with a closed surge tank was constructed and applied to determine the accuracy by comparing the results with field measurements from the prototype. Hydraulic scale models are usually constructed for the design of new hydropower plants, and the accuracy is rarely quantified. The main reasons for this include differences between the actual constructed prototype and the hydraulic scale model, and dismantling of the model before the prototype is constructed to clear laboratory space for new models. The accuracy was tested with field measurements from the prototype during an emergency shutdown from full load. The prototype is the 150 MW Torpa hydropower plant in southern Norway, and technical data of the power plant and the measurements are found in P2 and P4. Fig. 5 presents a comparison of the measured pressure in front of the turbine in the hydraulic scale model and in the prototype.
As can be seen from the comparison, the pressure in front of the turbine in the model and the prototype is different during the steady-state operation in the first 100 s. The reason is different velocity heads owing to the fact that the bifurcation pipe of the prototype has not been included in the model. However, the sum of the velocity head, pressure and geodetic height is equal. The comparison of the results from the hydraulic scale model and field measurements show a deviation of approximately 4% in the first (maximum) pressure amplitude, and a deviation of less than 1% for the oscillation period. There is a significantly higher dampening of the oscillations in the hydraulic scale model compared with the prototype, resulting in a 20% deviation for the second amplitude.
The deviations of both the first and subsequent amplitudes may be caused by one or several of the following reasons; heat transfer in the closed surge tank, errors in the power plant drawings, scaling errors, scaling effects, construction errors, and measurement errors. The author believes that one of the following four error sources are most likely; a limited capacity of the overflow weir in the upper reservoir, lingering air bubbles in the water pipes, simplification of frictional losses by the means of singular losses through valves, or the thermodynamics of the air. Regarding the overflow weir in the upper reservoir, the water discharge and level is varying due to the alternating flow direction in the headrace tunnel during the mass oscillations. The variable water level in the upper reservoir may thus have increased the dampening of the mass oscillations, but this has not been confirmed at the time of writing. Regarding the air bubbles in the pipes, flushing of air was necessary to obtain the presented results. The flushing was
___________________________________________________________________ 25
Fig. 5. Comparison of (a) pressure upstream the turbine and (b) air pressure in the closed surge tank in the prototype and the hydraulic scale model
conducted by running the maximum possible water velocity through the pipes (0.4 m/s) for 8 h. Additional flushing time did not result in improvements, but it is possible that the maximum velocity was insufficient to flush all air in the system. Air in the system is a known problem in hydraulic scale modelling of closed conduit flow and explains a higher dampening. Regarding the frictional losses, these were simplified with singular losses through valves in the model, to enable easier control of the head loss. This approach was accurate for steady-state conditions, but may have yielded higher energy dissipation during transients. Regarding the thermodynamic behavior, this may not have been fully adiabatic. Hydraulic scale modelling of closed surge tanks was only possible by assuming adiabatic behavior, and heat transfer out of the closed surge tank may have enhanced the energy dissipation during the mass oscillations.
For the design of closed surge tanks, it is the first (maximum) amplitude that is of highest importance. This amplitude will determine the design pressure and water levels in the surge tank. Accuracy of 4% is regarded as acceptable, and it is concluded that hydraulic scale models can be applied to the evaluation of the important first (maximum) amplitude. The 20% deviation in the subsequent amplitudes is too high to recommend hydraulic scale modelling to determine anything other than the first (maximum) amplitude. It is possible that future studies will identify and mitigate the error sources and enable hydraulic scale modelling with higher accuracy.
___________________________________________________________________ 26