Positive slope characteristics are very important for the safe and stable operation of a pump-turbine. In this study, the unsteady flows in a pump-turbine at pump mode are investigated numerically. To predict the positive slope characteristics with an improved accuracy, a modified Partially-Averaged Navier-Stokes (MPANS) model is employed to capture the unstable physics in a pump-turbine. It is confirmed that the present numerical method predicts the positive slope characteristics in the pump-turbine fairly well compared with the experimental data. It is noted that at the drooping point of the performance curve (positive slope), there are three sets of rotating stall cells in the flow passages of both the guide vanes and stay vanes. In the guide vane region, the flow is completely shut off by the rotating stall, whereas in the stay vane region, the flow passage is partly blocked at the drooping point. The numerical results also reveal that the remarkable variation and high angle of attack (AOA) values upstream the leading edge of the guide vane contribute to the flow separation at the vane suction side and induce rotating stall in the flow passage within the positive slope region. Furthermore, the propagation of the rotating stall is depicted by both Eulerian and Lagrangian viewpoints: the rotating stall blocks the flow passage between two neighboring guide vanes and pushes the flow toward the leading edge of the subsequent guide vane. The rotating stall cell shifts along the rotational direction with a much lower frequency (0.146
the National Natural Science Foundation of China(Grant,No.,51536008)
Beijing Natural Science Foundation(Grant,No.,3182014)
Science and Technology on Water Jet Propulsion Laboratory(Grant,No.,61422230103162223004)
and State Key Laboratory for Hydroscience and Engineering(Grant,No.,sklhse-2017-E-02)
This work was supported by the National Natural Science Foundation of China (Grant No. 51536008), Beijing Natural Science Foundation (Grant No. 3182014),
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Figure 1
Computational domain of the pump-turbine.
Figure 2
Mesh generation of each flow component
Figure 3
Mesh independence test.
Figure 4
(Color online) Characteristic curves near the positive slope.
Figure 5
(Color online) Streamline and static pressure distributions on the blade mid-span surface at different operating points.
Figure 6
(Color online) Streamlines on the mid-span surface at different operating points.
Figure 7
(Color online) Swirling strength distribution at different operating points.
Figure 8
(Color online) AOA distributions at different operating points.
Figure 9
Flow and AOA/
Figure 10
(Color online) Streamlines on the mid-span during two runner revolutions at OP1.
Figure 11
(Color online) FTLE distribution at one typical runner revolution (
Figure 12
(Color online) Tracer particles at one typical runner revolution (
Figure 13
(Color online) FTLE distribution at one typical runner revolution (
Figure 14
(Color online) Tracer particles at one typical runner revolution (
Figure 15
Illustration of the mechanism of rotating stall at OP1.
Figure 16
Pressure fluctuation at time domain in the vaneless region.
Figure 17
Pressure fluctuation at frequency domain in the vaneless region.
Parameter | Value |
Runner outlet diameter | 547 mm |
Runner inlet diameter | 250 mm |
Runner blade number | 7 |
Stay vane number | 20 |
Guide vane number | 20 |
Height of guide vane | 37.75 mm |
Runner rotational speed |
Component | Minimum | Maximum | Average |
Runner blade | 8.87 | 336.54 | 96.69 |
Stay vane | 1.63 | 127.87 | 35.90 |
Guide vane | 2.34 | 160.44 | 53.28 |
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