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Evolutions of flow patterns and pressure fluctuations in a prototype pump-turbine during the runaway transient process after pump-trip
Journal Pre-proof Evolutions of flow patterns and pressure fluctuations in a prototype pump-turbine during the runaway transient process after pump-trip Zhiyan Yang, Yongguang Cheng, Linsheng Xia, Wanwan Meng, Ke Liu, Xiaoxi Zhang PII:
S0960-1481(20)30098-7
DOI:
https://doi.org/10.1016/j.renene.2020.01.079
Reference:
RENE 12942
To appear in:
Renewable Energy
Received Date: 26 January 2019 Revised Date:
10 January 2020
Accepted Date: 18 January 2020
Please cite this article as: Yang Z, Cheng Y, Xia L, Meng W, Liu K, Zhang X, Evolutions of flow patterns and pressure fluctuations in a prototype pump-turbine during the runaway transient process after pumptrip, Renewable Energy (2020), doi: https://doi.org/10.1016/j.renene.2020.01.079. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Zhiyan Yang：Conceptualization, Writing - Original Draft, Writing- Reviewing and Editing. Yongguang Cheng: Supervision, Resources, Writing - Original Draft, Writing- Reviewing and Editing. Linsheng Xia: Writing Original Draft, Investigation. Wanwan Meng: Writing - Original Draft, Validation. Ke Liu: Methodology, Validation. Xiaoxi Zhang: Investigation, Validation, Methodology.
1
Evolutions of flow patterns and pressure fluctuations in a prototype pump-turbine
2
during the runaway transient process after pump-trip
3 4
Zhiyan Yanga, Yongguang Chenga*, Linsheng Xiab, Wanwan Menga, Ke Liua and
5
Xiaoxi Zhangc
6 7
a. State Key Laboratory of Water Resources and Hydropower Engineering Science,
8
Wuhan University, Wuhan 430072, China
9
b. China Ship Development and Design Center, Wuhan 430064, China
10
c. School of Environmental Science and Engineering, Xiamen University of
11
Technology, Xiamen 361024, China
12 13
Corresponding author: Yongguang Cheng; E-mail: [email protected]
14 15
Abstract: The runaway after pump-trip is a fast transient process, during which unit
16
vibrations, water-hammer fluctuations, pressure pulsation changes and flow pattern
17
transitions happen violently, endangering pump-turbine units of pumped-storage
18
power stations. In this paper, based on validated CFD data from 1D-3D coupled
19
simulation, we describe the evolutions of flow patterns and pressure fluctuations in a
20
prototype pump-turbine during this working point fast sliding process, and try to
21
reveal the influence mechanism of flow pattern transitions on pressure fluctuation
22
changes. The results show that the general evolutions of flow patterns are dominated
23
by the changes of the runner velocity triangles, which are controlled by the changes of
24
the discharge and rotational speed. Inhomogeneous local flow also contributes to
25
abundant local vortex structures, such as rotating-stall vortices in the vane and runner
26
regions, skirt and helical vortices in the draft-tube, separation vortices in the blade
27
channels, and the impinging jets on the blade surfaces. These unstable vortices appear,
28
change, and vanish in a fast transitional and uneven manner, leading to great
29
differences in pressure and runner force fluctuations in different working regions.
30 1
31
Key words: pump-turbine, runaway transient process, 1D-3D coupled simulation,
32
flow patterns, pressure fluctuations, runner forces
33 34
1. Introduction
35
Pumped-storage power is the largest and best regulator in the power grid for its
36
irreplaceable capacities of peak fitting, valley filling, frequency regulating, phase
37
modulating, and spinning reserving. With the development of intermittent renewable
38
energies, the complementary functions of pumped-storage become more and more
39
important. Because a pumped-storage plant has many operating conditions and
40
transformations between different operations, violent pressure fluctuations and
41
machine vibrations in pump-turbines can be encountered in many pumped-storage
42
plants. During transient processes, such problems will become more severe, because
43
the working point passes through various working modes, which may include the
44
hump and S-shaped characteristic regions where unstable flow structures develop and
45
change abruptly [1-2]. The pump-trip runaway, an accident process when the
46
motor-generator is rejected from the power grid but the guide vane servomotor fails to
47
close, is the most violent one because both the hump- and S-shaped regions are
48
experienced [3]. During this process, the runner will be decelerated and accelerated by
49
dynamic working head, and complex flow pattern transitions and severe pressure
50
fluctuations will happen, which could endanger the safety of units. Therefore, despite
51
the probability of the pump-trip runaway is small, it is one of the must studied
52
transient processes in the design stage of pumped-storage plants. To analyze this fast
53
changing phenomenon, considering the superposition of water-hammer in water
54
conveyance system and pressure pulsations in pump-turbine, and understanding the
55
relationship of flow patterns, pressure pulsations and runner forces, are important,
56
because their interactions, correlations and evolutions are the main cause of a series of
57
unit vibration problems [4].
58
Many studies on flow patterns and pressure pulsations in pump-turbines have
59
been conducted based on computational fluid dynamics (CFD) simulations or model
60
tests, and some correlations between them have been clarified [5-7]. However, the 2
61
attentions of the existing investigations were mainly focused on the flow
62
characteristics of a certain steady working condition. Xia [8] and Pacot [9] analyzed
63
the rotating-stall instabilities of a pump-turbine in the pump mode and concluded that
64
the rotating-stall could cause periodical high pressure. Liu [10] found that the
65
cavitation on the suction side of runner inlet could lead to great changes of pressure
66
distributions on blade surface, when the pump-turbine worked in the hump-shaped
67
region. Foroutan [11] reported that the pressure fluctuations in a simplified draft-tube
68
due to the vortex rope could have a large amplitude, as high as twice the local mean
69
pressure value. Hasmatuchi [12] presented the experimental evidence of the
70
rotating-stall in a model pump-turbine working in the S-shaped region, and found that
71
the pressure pulsating amplitude increased when the discharge decreased. Recently,
72
Xia [19] found the backflow patterns at the runner inlet in the pump-turbines working
73
in the S-shaped region, and discussed the correlation between the working points
74
located along the guide vane opening curves and their corresponding flow patterns.
75
As for transient processes, studying the flow characteristics by model tests is
76
very difficult and CFD simulation becomes the basic tool. A few studies on this topic
77
have already been reported [13] and the evolutions of pressure fluctuations
78
corresponding to the flow transitions have been discussed [14-16]. However, they
79
were limited by only considering some specific working conditions, and most
80
questionably ignoring water-hammer pressure effects [17], without which the dynamic
81
characteristics of pump-turbine cannot be fully considered. In addition, the generation
82
mechanism of special flow patterns has not been discussed in depth, and the
83
coexistence of multiple vertex structures has been neglected. Li [18] investigated the
84
transient process in pump mode, in which the guide vanes were closing and the
85
rotational speed was constant, and found that the obvious flow separations in the
86
runner and vanes could result in significant pressure fluctuations. Staubli [19]
87
predicted the unstable flow fields during turbine starting-up process in the turbine
88
mode, and found time-varying inflow and outflow from the runner into the vaneless
89
space could be the cause of instability. Liu [20] simulated a load rejection transient
90
process of a prototype pump-turbine, and found that the vortex ropes in the draft-tube 3
91
had large deviations from the results in steady working conditions. Li [21] simulated
92
the normal shutdown process of a prototype pump-turbine in turbine mode, and
93
investigated the global characteristics and pressure fluctuations under the emergence
94
of flow separation and vortex formation. Xia [22] studied the runaway transient
95
process from a turbine working point, and concluded that the locally distributed
96
backflow vortices at the runner inlet could enhance the local rotor-stator interaction,
97
and the evolving rotating-stall could induce asymmetrical pressure distribution on
98
runner blades.
99
From the above works, we know that the flow patterns in pump-turbines working
100
in different modes show quite different features, contributing to great differences in
101
pressure fluctuations. This is an obvious conclusion for both steady conditions and
102
transient processes. But how the flow patterns change during the transient processes
103
that experience different working regions, and how they influence the alterations of
104
pressure pulsations and runner forces, need to be clearly stated.
105
In this study, the runaway transient process after pump-trip in a prototype
106
pumped-storage power station was simulated, and the evolutions and correlations of
107
pressure fluctuations, runner forces and flow structures were analyzed. The paper will
108
describe the basic simulation model and parameters; the resulting histories of macro
109
parameters; the evolutions of flow structures, pressure pulsations, and runner forces.
110
The results are discussed according to the trajectory curve in the characteristic plane,
111
and related by the short term Fourier transformation.
112 113
2. Numerical Methods
114
2.1 The pumped-storage station and its simulation model
115
A low-head pumped-storage power station with two 150MW units in one water
116
conveyance system was considered. As shown in Fig.1, the system includes an
117
upstream reservoir (water level 397.67m), a diversion tunnel, two penstocks, two
118
pump-turbine units (rated head 126.7m in the pump mode), two downstream conduits,
119
and a downstream reservoir (water level 291.28m). The setting elevation of the units
120
is 264.00m. The pumping condition with one unit in operation was simulated in this 4
121
study. The 1D-3D coupling method [23] was adopted, in which the diversion tunnel,
122
penstock and downstream conduit were simulated by the one-dimensional (1D)
123
method of characteristics (MOC), while the pump-turbine was simulated by
124
three-dimensional (3D) CFD. The profile and parameters of computational domain are
125
shown in Fig. 1, while the 3D model of pump-turbine and the layout of several
126
monitoring points are shown in Fig. 2. The basic parameters of the pump-turbine are
127
given in Table 1, in which D1 denotes the runner outlet diameter (pump mode), D2 the
128
runner inlet diameter (pump mode), nr the rated rotational speed, Zb the number of
129
runner blades, ngv the number of guide vanes, nsv the number of stay vanes, ns the
130
specific-speed (pump mode), and Hr the rated head (pump mode).
131
Fig. 1. Profile of the computational domain
132
Fig. 2. 3D model of pump-turbine and schematic of monitoring points and sections
133 134
Table 1. Main parameters of the prototype pump-turbine Parameter
Value
Parameter
Value
D1 (m)
5.2265
Zb
7
D2 (m)
4.132
ngv
20
nr (rpm)
200
nsv
20
ns (m,m3/s)
59.9
Hr (m)
126.7
135 5
136
2.2 Numerical schemes
137
Commercial software ANSYS FLUENT 15.0 was used in the 1D-3D simulations.
138
The 3D geometry in Fig. 2 was discretized into structured meshes with multiple
139
blocks by ANSYS ICEM 15.0. A grid refinement evaluation was performed and we
140
found that the relative differences in macro parameters from 6.9 million to 8.0 million
141
grid elements are negligible. Therefore, the mesh with 6.9 million grid elements was
142
finally chosen (Table 2), in which fine boundary layers are set up in the regions of
143
stay vanes, guide vanes, and runner.
144 145
Table 2. Number of grid elements (million) Draft-tube with
Spiral casing with Runner
Stay vanes Guide vanes 1.2
Total extended tube
extended tube 1.0
1.1
2.3
1.3
6.9
146 147
We selected the SAS-SST turbulence model, and specified the transient
148
simulation timestep as 0.00125s, which corresponds to 1.5 degrees of runner rotation
149
at the rated speed. For both steady and unsteady working conditions, the SIMPLEC
150
algorithm was chosen to achieve the coupling solution of the velocity and pressure
151
equations. The second order discretization in time and in space was used.
152
Boundary conditions were defined as follows. The outlet and inlet of pipes in 3D
153
model were set as static pressure and total pressure boundary conditions by 1D MOC,
154
respectively. At the 1D-3D interfaces, the partly overlapping coupling method in
155
reference [23] was used and the compressibility of water was simulated by defining
156
the pressure depended density, as shown in Eq. 1. The friction and local head losses in
157
each pipe were considered in the 1D model. ρ = ρ0 e(p-p0 )/ρ0 a
158
2
(1)
159
where ρ and p are the density and pressure of water, respectively; ρ0 and p0 are the
160
initial values of ρ and p, respectively; e (-) is the base of natural logarithms; a is the
161
acoustic speed in water. 6
162
2.3 Computation of the varying speed of turbine unit
163
The rotation of the runner was simulated by the sliding mesh model during
164
runaway process. The angular speed ω of the runner varies with time in accordance to
165
angular momentum equation, as shown in Eq. 2, and a User-Defined-Function (UDF)
166
program in ANSYS FLUENT 15.0 was used to realize the variation of rotational
167
speed.
168
T
ωt = ∆t + ωt-∆t J
(2)
169
where J is the total rotational inertia of runner and motor-generator; T is the hydraulic
170
torque acting on the runner; ωt and ωt-Δt are the rotational speed at the current and
171
previous timesteps, respectively; ∆t is the timestep.
172 173
2.4 Validation of the simulation model
174
Before simulating the runaway transient process, the 1D-3D coupling model
175
should be validated. Because the data of a field test for the pump-trip transient process
176
with a designed closing law of guide vanes from the original opening (GVO) 23.6
177
degrees was available, we simulated the same condition for comparison. Fig. 3 shows
178
the resulting macro parameters, in which the field test curves provided by the test
179
engineer are filtered. Compared to the field test values, the simulated pressure history
180
has stronger fluctuations, which should be the signals of water-hammer in pipelines
181
and complex flow structures in the pump-turbine. The water-hammer cycle in the
182
upstream pipeline is around 1.25s, corresponding to the pressure fluctuating cycle at
183
P1 after guide vanes have closed. The relatively high frequency fluctuations at P4
184
should be caused by vortices in draft-tube and runner passages. Generally speaking,
185
the simulation results are in good agreement with the field test results, and the
186
reliability of the 1D-3D coupled approach is validated. Then, the runaway process
187
without guide vane closing after the pump-trip from the same steady working point
188
was simulated, which will be explained in later sections.
7
189
Fig. 3 Validation of the 1D-3D coupled CFD model by field test results
190 191
3 Results of the runaway transient process after pump-trip
192
3.1 Macro parameters during the runaway process
193
During the runaway process, the working point passes through the pump,
194
pump-braking, turbine, and turbine-braking modes, and its dynamic trajectory travels
195
across these regions and finally revolves around a zero-torque point with fluctuations,
196
as shown by the red curve in the n11-Q11 plane of Fig. 4, in which the unit speed
197
n11 = -nD1 / √H and unit discharge Q11 = -Q / (D21 √H) are defined. The dynamic
198
curve has a good agreement with the static characteristic curve (black curve, obtained
199
by model tests) in the pump, pump-braking and turbine modes, excepting near the
200
static zero-torque point. Not following the static characteristic curve, the dynamic
201
trajectory fluctuates and gradually converges to a speed-no-load region, which is on
202
the left of the static zero-torque point. If the errors in model tests and simulation are
203
considered, the remaining deviations of the dynamic and static curves should be
204
owing to the unstable vortex structures developed in the whole runaway process,
205
which are marked in Fig. 4.
206
The histories of the key macro parameters during the runaway are shown in Fig.
207
5, in which the process has been divided into six modes: pump (P), pump-braking
208
(PB), turbine (T1), turbine-braking (TB), turbine (T2), and no-load runaway (NL). The
209
transition from the P mode to PB mode is defined by the sign of discharge Q changing
210
from positive to negative, namely the flowing direction changes from pump direction
211
to turbine direction but the runner rotates still in pump direction. The transition from 8
212
the PB mode to T1 mode is defined by the sign of rotational speed n changing from
213
positive to negative, namely the rotating direction changes from pump direction to
214
turbine direction and the runner works in normal turbine condition. The transition of
215
T1 mode and TB mode is defined by the sign of torque T changing from negative to
216
positive, namely the water driving power is surpassed by the water dissipating power.
217
The NL mode defined by the small and fluctuating turbine output power when the
218
working point revolves around the zero-torque point. These definitions are
219
corresponding to the characteristic regions in Fig. 4(b).
220
Due to the specific-speed of this pump-turbine is relative large, there is no larger
221
fluctuations in rotational speed and discharge during the last no-load runaway mode,
222
which is obviously different from the unstable fluctuations in the S-shaped region for
223
many low specific-speed pump-turbines [24]. The torque T varies with normal laws in
224
the P, PB and T1 modes, and becomes unstable in the TB, T2 and NL modes. The
225
axial force of runner (Fz) in the P and PB modes is mainly affected by the
226
water-hammer and increases quickly at the beginning of the P mode. However, in the
227
T1 mode, Fz decreases sharply before the working point is approaching to the rated
228
turbine point. Once entering the last three modes, Fz becomes unstable and fluctuates
229
with high frequencies and large amplitudes. For the radial force (Fx and Fy) of runner,
230
the variation range is not large and the fluctuations in the last TB, T2 and NL modes
231
are also severe. Obviously, all the severe fluctuations in torque and runner forces
232
begin after the working point enters the so-called S region, although the S-shaped
233
shape is not obvious for this low-head pump-turbine.
(a) Original data
9
(b) Low-pass filtered data in S-shaped region Fig. 4. Dynamic trajectory curve in the n11 – Q11 plane
234
(a) Histories of torque, discharge and speed
(b) Histories of runner forces
235
Fig. 5. Histories of macro parameters during the pump-trip runaway process. (P:
236
pump; PB: pump-braking; T1 and T2: turbine; TB: turbine-braking; NL: no-load
237
runaway)
238 239
3.2 Pressure fluctuations during the runaway process
240
The pressure fluctuations at points P1, P2, P3 and P4 during the runaway
241
transient process are shown in Fig. 6. On the whole, regional variation features are
242
obvious as the working point passes through the six modes successively. In the P
243
mode, the rapidly decreasing discharge after the sudden power loss causes a negative
244
water-hammer wave upstream the runner and a positive water-hammer wave
245
downstream the runner (Fig. 6(b)). Accordingly, the pressure histories at monitoring
246
points P1, P2 and P3 show rapid decrease and the pressure at point P4 shows rapid
247
increase (Fig. 6). When the working point enters the PB mode, the flow direction
248
reverses and the torque turns to increase again (Fig. 5(a)), leading to the gradual
249
restorations of pressure values at the monitoring points (Fig. 6). The pressures recover
250
roughly to their initial values when the working point gets into the T1 mode. In the 10
251
TB mode, the torque value becomes positive, meaning energy dissipation (Fig. 5(a)),
252
accordingly the pressures at P1, P2 and P3 begin to decrease and that at P4 begins to
253
increase (Fig. 6). These pressure decreases and increases during the first four modes
254
are mainly related to the water-hammer in water conveyance system and the
255
pump-turbine characteristics transferring between the operating modes. After the T2
256
mode, the discharge and speed are approaching to a steady level, therefore the pipe
257
water-hammer effect becomes weak and turbine pressure pulsation effect becomes
258
dominant (Fig. 6). It can be seen that the pressure fluctuation amplitudes increase
259
rapidly once the working point leaves the turbine best efficiency point (t = 21.5 s), and
260
they approach to the maximum values after entering the TB mode. The violent
261
fluctuations continue in the T2 and NL modes, showing no damping tendency. The
262
fluctuation frequencies and amplitudes at P3 are much higher than at other points,
263
because the pressure pulsations by the rotor-stator interaction are superimposed.
(a) Original pressure data 264 265
(b) Low-pass filtered data
Fig. 6. Histories of pressure fluctuations at different monitoring points 3.3 Evolutions of flow patterns during the runaway process
266
To investigate the mechnism of large pressure fluctuation amplitudes, the
267
evolutions of flow patterns in the vane, runner and draft-tube regions were analyzed.
268
Three stream surfaces with spanwise ratios 0.1, 0.5, and 0.9 across the vane and
269
runner (Fig. 2) were selected to show the flow patterns. At the same time, the velocity
270
triangles at the inlet (adjacent to the guide vanes) and outlet (connected to the
271
draft-tube) of runner were borrowed to interpret the general development trends of
272
flow patterns, even though it cannot describe local vertex structures accurately. 11
273
When the unit is in a steady pumping operation, the flow fields in the
274
pump-turbine are smooth, and there are no obvious vortex structures and flow
275
blockages (Fig. 7, t = 0.0 s). Accordingly, the pressure pulsations are stable and have
276
no high amplitude signals. However, during the runaway process, the pressure
277
fluctuations vary quickly and the flow patterns evolve with various vortex structures.
278
(1) Pump mode (t < 6.5 s)
279
When the pump is suddenly powered off, the rotational speed, discharge and
280
head begin to decrease simultaneously, because the runner is decelerated by the
281
resisting torque of water. In addition, because the water pumping force is proportional
282
to the square of rotational speed, the decrease of discharge is faster than that of
283
rotational speed (Fig. 5(a)), leading to the reduction of outflow angle α1, which is
284
defined by the angle between the absolute flow velocity V1 and the peripheral velocity
285
U1, as shown Fig. 7. Because U1 in the vaneless region is still high and the water in
286
the vane region is slowed down, the enhanced shearing action and the large attack
287
angle to the vanes generate several rotating-stall vortices. The existing studies [5,8]
288
showed that when the rotating stalls occur, the disturbed flow and blockage can only
289
be observed in part of blade and vane channels (Fig. 7, t = 5.5, 6.0 s), which result in
290
uneven circumferential outflow and pressure distributions.
291
As for the inflow triangle, the absolute flow velocity V2 near the pressure surface
292
of runner blades decreases sharply, resulting in the increase of the inflow attack angle
293
β2, which is defined by the exterior angle between the relative velocity W2 and the
294
peripheral velocity U2. When the inflow water impacts with runner blades, it separates
295
from blades and contributes to large-scale separation vortices in the blade passages
296
(Fig. 8(a)). Overall, the main axes of vortices in the vane and runner regions are
297
approximately perpendicular to the stream surfaces. For the flow in the draft-tube,
298
previous studies showed that when water flows into the runner region, it is disturbed
299
by the runner and has circumferential components [25]. And the decrease of runner
300
discharge will result in the increase of the circumferential components of draft-tube
301
water. Here, to identify the vortex structures accurately, a newly proposed omega
302
method was used [26], which considers vortex as a region where vorticity overtakes 12
303
deformation and are superior to other methods (e.g., vorticity tube, Q-criterion and
304
Lambda-2 method) [27,28]. In this case, once the pump is tripped, due to the decrease
305
of runner flow capacity and the inertia of water in the draft-tube, the inflow water will
306
impinge on the pressure surfaces of runner blades, forming backflows on the shroud
307
side (Fig. 8(b)). The upward main flow in the draft-tube center moves shearing with
308
these backflows, generating backflow vortex structures near the draft-tube wall.
309
Under the disturbance of the runner, these vortices further separate into several skirt
310
shaped vortices (Fig. 7, t = 5.5, 6.0 s).
311
Generally speaking, the smaller the discharge, the more complex the flow
312
patterns. Also, the velocity triangles can only show the developing trend of flowing
313
state, but the local backflows and vortices cannot be accurately described, which
314
reflects the complexity and inhomogeneity of the flow patterns.
315
Fig. 7. Velocity triangles and flow patterns in the pump mode
(a)
(b) 13
316 317
Fig. 8. Separations in runner passages (a) and backflows in the draft-tube (b) (t = 6.0 s)
(2) Pump-braking mode (6.5 s < t < 13.7 s)
318
Due to the recovering pressure head on the turbine (Fig. 6(b)), the flowing
319
direction begins to reverse to the turbine direction, but the rotating direction remains
320
in the pump direction, even though the rotational speed continues to decrease (Fig.
321
5(a)). In the initial stage of pump-braking mode, because the rotational speed, inflow
322
angle β1 (defined by the exterior angle between the relative velocity W1 and the
323
peripheral velocity U1) and centrifugal force at the runner inlet are still large, flowing
324
into the runner passages is not smooth. The inflow strongly impacts the pressure
325
surfaces of the blades. The impact makes some water turning left and returning to the
326
vaneless space, some water jumping over and impacting the next blade, and some
327
water turning right and entering the blade passages, which form large separation
328
vortices around the suction surfaces of the blades (Fig. 9, t = 9.0 s).
329
At the runner outlet, the increasing outflow angle α2 (defined by the angle
330
between the absolute flow velocity V2 and the peripheral velocity U2) pushes the main
331
flow near the draft-tube wall to develop stronger, with the reverse flow in the center
332
also intensified (Fig. 9, t = 13.0 s). In detail, a part of the outflow goes into the
333
draft-tube directly, and the rest goes round to suction surfaces, which intensifies the
334
shearing actions with the upward flow in draft-tube center and produces separation
335
vortices near suction surfaces (Fig. 10).
336
In the later period of the pump-braking mode, with the increase of discharge, the
337
main flow in the vane region gradually becomes strong and steady, depressing the
338
local small vortex structures between vanes. Also, the large separation vortices in
339
runner passages are decreasing in scale but not in intensity.
340
According to the above two working regions, the different flow patterns have
341
different influences on pressure fluctuations. Generally speaking, the formation of
342
vortex structures can produce higher amplitude pressure fluctuations, which should be
343
weakened if the vortex structures disappear. However, the pressure fluctuating
344
amplitudes increase obviously in pump-braking mode, far larger than in the pump
345
mode (Fig. 6(a)). The reason is that the vortex structures in the pump mode are 14
346
generated by shearing action. Due to low energy dissipation, these vortices are
347
difficult to produce higher amplitude signals. But in pump-braking mode, the strong
348
impacts on the runner blade pressure surfaces and the large separating vortices on
349
suction surfaces are high energy dissipated, which can produce high amplitude signals.
350
Therefore, it is not the number and size of vortices that determines the amplitudes of
351
pressure fluctuations, but the strengths of impacting on the solid walls and interacting
352
between vortices.
353
Fig. 9. Velocity triangles and flow patterns in pump-braking mode
354
(a) 355 356
(b)
Fig. 10. Flow patterns in runner passages and draft-tube in pump-braking mode (t = 9.0 s)
(3) Turbine mode T1 (13.7 s < t < 28 s)
357
Affected by the increasing resisting torque, the runner begins to rotate in the
358
direction of turbine mode, companied by increase of discharge. In the initial stage,
359
because of the relatively small peripheral velocity U1 and the small inflow attack
360
angle β1, the impacting of inflow on blade pressure surfaces accelerates the rotational
361
speed of runner, and the separation vortices on the suction surfaces still exist (Fig. 11,
362
t = 16.0 s). With the increase of rotational speed, namely the increase of peripheral 15
363
velocity U1, β1 becomes larger gradually and fits to the blade inlet angle, contributing
364
to scale and intensity decreases of the separation vortices. At the optimal working
365
point (about t = 21.5 s), the inflow enters the runner passages without any hindrance,
366
and the outflow at the runner outlet flows vertically and smoothly down to the
367
draft-tube (Fig. 11, t = 21.5 s). However, after t = 21.5 s, when the working point
368
passes through the optimal, the rotational speed and the inflow attack angle β1 at the
369
runner inlet continues to increase, and separation vortices occur again on the blade
370
suction surfaces (Fig. 11, t = 27 s). Fig. 12 shows the flow patterns in a single runner
371
passage. Once the working point leaves the optimal, obvious backflows occur on the
372
shroud side due to the centrifugal force and the increasing impact on the runner blade.
373
A part of the backflows jumps into the nearby runner channel, and a part goes back to
374
the vaneless space. On the hub side, the water flows into the blade passage easily.
375
As for the draft-tube, in the turbine mode with different discharges, flow patterns
376
have a developing manner, which are corresponding to the findings in references
377
[11,29]. Fig. 13 shows vortex structure evolutions in the draft-tube at different times.
378
As flow rate increases, backflows in the draft-tube center weakens, resulting in the
379
shrinking of skirt vortex structures near the wall and the developing of a single thick
380
eccentric vortex belt in the center. When the working point is before the optimal, the
381
larger the discharge, the finer the vortex shape, which is approaching a conical
382
cucumber shape from a helical rope shape. Once the working point leaves the optimal
383
the optimal, skirt vortices are re-generated and overspread the whole wall.
384
It is evident from the pressure fluctuation diagram (Fig. 6(a)) that when the unit
385
enters the turbine mode, especially before t = 21.5 s, the pressure fluctuations
386
gradually decrease at P2 and P3 due to the disappearance of the unstable vortex
387
structures. However, high amplitude pressure fluctuations at P4 and runner radial
388
forces (Fig. 5(b)) still keep exist during this time, it should be due to the existence of
389
the vortices in the runner passages and draft-tube (Fig. 11, t = 16 s). After t = 21.5s,
390
the pressure amplitudes begin to increase again because of the backflows at the runner
391
inlet [30]. Due to backflows in the vaneless space, the recirculation inside the blade
392
passages, and the impact by the runner blades, the rotor-stator interaction is 16
393
intensified and the pressure fluctuating amplitudes increase greatly (Fig. 6(a)).
394
Fig. 11. Velocity triangles and flow patterns in the pump-braking mode
395
t = 21.5 s 396
t = 27.0 s
Fig. 12 Flow patterns in a single runner passage at different times
397
398
t = 16.0 s
t = 17.0 s
t = 18.0 s
t = 20.0 s
t = 21.0 s
t = 21.5 s
t = 25.0 s
t = 27.0 s
Fig. 13. Evolutions of the vortices in the draft-tube 17
399
(4) Turbine-braking mode TB, turbine mode T2 and no-load mode NL (t > 28 s)
400
From the histories of pressure fluctuations in Fig. 6, it can be seen that the last
401
three working regions are similar because of the constant trends of rotational speed
402
and discharge. In these three stages, the pressure pulsating amplitudes are the largest
403
in the vaneless space. The vaneless space should be the area where energy is
404
dissipated during runaway process, because the increase of amplitudes can be
405
considered as the increase of energy dissipation. Fig. 14 shows flow patterns in a
406
single runner passage and draft-tube, which are similar to those in the turbine mode
407
after the optimal working point.
408
To better investigate the internal flow patterns when the runaway is approaching
409
to the NL point, three stream sections cutting through the runner and vane regions at t
410
= 70 s are shown in Fig. 15. Obviously, on the hub side and middle span, there are
411
only a few separation vortices near the blade suction surfaces. However, on the shroud
412
side, more vortices exist near the blade pressure surfaces, accompanied with
413
backflows at the runner inlet. As a result, the stronger shearing action induced by the
414
high-speed flow in the vaneless space and the low-speed flow in the vane region,
415
contribute to the formation of separation vortices on the abdomen of guide vanes.
(a)
(b)
416
Fig. 14. Flow patterns in a single runner passage (a) and draftt-ube (b) (t = 70.0 s)
417
Fig. 15. Flow patterns on the three stream sections at t = 70.0 s
418 419
3.4 Frequency spectrum A time-frequency analysis of the transient pressure fluctuations at the monitoring 18
420
points is performed by using the Short Time Fourier Transform (STFT) [31], and the
421
results are shown in Fig. 16. At the beginning of the runaway process, the
422
characteristics of pressure fluctuations are mainly influenced by the runner. The
423
dominant frequency in the spectrograms is the blade passing frequency (BPF), and the
424
rest high frequencies are the integer multiples of the BPF. Due to the decreases of the
425
rotational speed and discharge, the vortex structures generated in the vane and runner
426
regions cause the generation of relatively low frequency signals with relatively higher
427
amplitudes (4.0 s < t < 6.5 s). In the transferring process from pump mode to
428
pump-braking mode, it is obvious that, due to the separation vortices and the impact
429
on runner blades, higher frequency signals and low frequency signals mix up and
430
display no clear boundary, and changing trends of the frequencies are in accordance
431
with the change of the rotational speed (6.5 s < t < 13.7 s). When the unit enters the
432
turbine mode, the frequency distinction becomes clear, and the amplitudes decrease
433
greatly near the better operation region (13.7 s < t < 21.5 s). These are because the
434
vortices in the vane region become weak or disappear. Once the working point leave
435
the optimal, the amplitudes increase gradually because of the violent rotor-stator
436
interaction induced by backflows (21.5 s < t < 28 s). After t = 28 s, the unit goes into
437
TB, T2 and NL modes in turn. All the low frequency and high frequency signals joint
438
again, and the amplitudes become very strong. These should be due to the various
439
vortices in the vane region, vaneless space, runner, and draft-tube.
(a) Point P1
(b) Point P2
19
(c) Point P3 440 441
(d) Point P4
Fig. 16. Frequency spectra for pressures at the monitoring points 4. Conclusions
442
The flow patterns, pressure pulsations, and runner force fluctuations during the
443
runaway transient process after pump-trip experience rapid and dynamic evolutions,
444
because the working point slides across the pump, pump-braking, turbine 1,
445
turbine-braking, turbine 2, and no-load runaway modes successively. In this study, we
446
analyzed the evolutional phenomena in this process and found that the changes in
447
pressure pulsations and runner force fluctuations are correlated to the transition of the
448
flow patterns, which have distinct features in different modes. Apart from the
449
rotating-stall vortices in the vane and runner regions in the pump mode, the impact
450
and separation vortices in the blade channels, the skirt and backflow vortices in the
451
draft-tube in the pump-braking and turbine 1 modes, along with the backflow vortices
452
at the runner inlet in the turbine-braking, turbine 2, and no-load runaway modes, are
453
the main causes that make the fluctuating magnitudes of pressure and runner forces
454
larger. The main findings are summarized as follows.
455
(1) When the discharge becomes small in the pump mode, the rotating-stall
456
vortices in the runner and vane regions develop due to the shearing action, and the
457
skirt vortices near the draft-tube wall appear due to the back and rotating flow around
458
the circumference.
459
(2) In the pump-braking mode, the flowing direction changes to the turbine
460
direction but the rotating direction is still in the pump direction. The vortices in the
461
vane region disappear completely as the discharge increases. The distinguish flow
462
structures in this mode are the strong impact jets on the blade pressure surfaces and 20
463
the large separation vortices near the suction surfaces. In the draft-tube, the runner
464
outflow around the tube wall and the backflow in the center are enhanced with the
465
increase of discharge, resulting in larger skirt vortices distributed in the circumference.
466
These flow structures make the pressure and runner force fluctuations intensified.
467
(3) As the rotating direction turns to the turbine direction, the pump-turbine is
468
operating in the turbine mode. Before the working point is approaching to the best
469
efficiency point, the impact jets on the blade pressure surfaces and the separation
470
vortices near the suction surfaces, along with the skirt vortices and backflow in the
471
draft-tube are suppressed as the rotational speed increases. In the best efficiency point
472
all flow patterns become smooth. After the working point leaves this optimal point,
473
the runner and draft-tube vortices appear again. The shroud side backflows at the
474
runner inlet become visible before the working point is approaching to the
475
turbine-braking mode. The runner inlet backflows make the rotor-stator interaction
476
obvious, resulting in the increasing pressure pulsations and runner force fluctuations.
477
(4) In the turbine-braking to no-load runaway modes, the working point comes
478
back to the turbine mode many times. The flow characteristics during this last
479
oscillating and converging process are similar. Apart from the separation vortices in
480
the vane and runner regions, the skirt vortices in the draft-tube, the backflow vortices
481
at the runner inlet are the distinguished phenomenon. It is the backflow vortices that
482
make the pressure and runner force fluctuations more violent.
483
(5) During this runaway transient process, the pressure pulsations in the vaneless
484
space are the largest in the pump-turbine. This phenomenon is caused by the
485
rotor-stator interaction, which are intensified by the impact jets on blades and the
486
backflow vortices at the runner inlet. The skirt and helical vortices in the draft-tube
487
and the rotating-stall vortices in the runner and vane regions are the main source of
488
low frequency pressure fluctuations.
489 490
Funding
491
This work was supported by the National Natural Science Foundation of China
492
(NSFC) (Grant Nos. 51839008 and 51579187), the Natural Science Foundation of 21
493
Hubei Province (Grant No. 2018CFA010), and the Natural Science Foundation of
494
Fujian Province (Grant No. 2018J01525).
495 496
Acknowledgments
497 498
The numerical simulations were conducted on the supercomputing system in the Supercomputing Center of Wuhan University.
499 500
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25
•Evolutions of flow patterns and pressure fluctuations during runaway process were described. •Evolutions of flow patterns are dominated by changes of velocity triangles. •Inhomogeneous local flow contributes to vortex structures. •Different vortices lead to great differences in pressure fluctuations in different working regions.
Conflict of interest statement: Yongguang Cheng and other co-authors have no conflict of interest.
S0960-1481(20)30098-7
DOI:
https://doi.org/10.1016/j.renene.2020.01.079
Reference:
RENE 12942
To appear in:
Renewable Energy
Received Date: 26 January 2019 Revised Date:
10 January 2020
Accepted Date: 18 January 2020
Please cite this article as: Yang Z, Cheng Y, Xia L, Meng W, Liu K, Zhang X, Evolutions of flow patterns and pressure fluctuations in a prototype pump-turbine during the runaway transient process after pumptrip, Renewable Energy (2020), doi: https://doi.org/10.1016/j.renene.2020.01.079. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Zhiyan Yang：Conceptualization, Writing - Original Draft, Writing- Reviewing and Editing. Yongguang Cheng: Supervision, Resources, Writing - Original Draft, Writing- Reviewing and Editing. Linsheng Xia: Writing Original Draft, Investigation. Wanwan Meng: Writing - Original Draft, Validation. Ke Liu: Methodology, Validation. Xiaoxi Zhang: Investigation, Validation, Methodology.
1
Evolutions of flow patterns and pressure fluctuations in a prototype pump-turbine
2
during the runaway transient process after pump-trip
3 4
Zhiyan Yanga, Yongguang Chenga*, Linsheng Xiab, Wanwan Menga, Ke Liua and
5
Xiaoxi Zhangc
6 7
a. State Key Laboratory of Water Resources and Hydropower Engineering Science,
8
Wuhan University, Wuhan 430072, China
9
b. China Ship Development and Design Center, Wuhan 430064, China
10
c. School of Environmental Science and Engineering, Xiamen University of
11
Technology, Xiamen 361024, China
12 13
Corresponding author: Yongguang Cheng; E-mail: [email protected]
14 15
Abstract: The runaway after pump-trip is a fast transient process, during which unit
16
vibrations, water-hammer fluctuations, pressure pulsation changes and flow pattern
17
transitions happen violently, endangering pump-turbine units of pumped-storage
18
power stations. In this paper, based on validated CFD data from 1D-3D coupled
19
simulation, we describe the evolutions of flow patterns and pressure fluctuations in a
20
prototype pump-turbine during this working point fast sliding process, and try to
21
reveal the influence mechanism of flow pattern transitions on pressure fluctuation
22
changes. The results show that the general evolutions of flow patterns are dominated
23
by the changes of the runner velocity triangles, which are controlled by the changes of
24
the discharge and rotational speed. Inhomogeneous local flow also contributes to
25
abundant local vortex structures, such as rotating-stall vortices in the vane and runner
26
regions, skirt and helical vortices in the draft-tube, separation vortices in the blade
27
channels, and the impinging jets on the blade surfaces. These unstable vortices appear,
28
change, and vanish in a fast transitional and uneven manner, leading to great
29
differences in pressure and runner force fluctuations in different working regions.
30 1
31
Key words: pump-turbine, runaway transient process, 1D-3D coupled simulation,
32
flow patterns, pressure fluctuations, runner forces
33 34
1. Introduction
35
Pumped-storage power is the largest and best regulator in the power grid for its
36
irreplaceable capacities of peak fitting, valley filling, frequency regulating, phase
37
modulating, and spinning reserving. With the development of intermittent renewable
38
energies, the complementary functions of pumped-storage become more and more
39
important. Because a pumped-storage plant has many operating conditions and
40
transformations between different operations, violent pressure fluctuations and
41
machine vibrations in pump-turbines can be encountered in many pumped-storage
42
plants. During transient processes, such problems will become more severe, because
43
the working point passes through various working modes, which may include the
44
hump and S-shaped characteristic regions where unstable flow structures develop and
45
change abruptly [1-2]. The pump-trip runaway, an accident process when the
46
motor-generator is rejected from the power grid but the guide vane servomotor fails to
47
close, is the most violent one because both the hump- and S-shaped regions are
48
experienced [3]. During this process, the runner will be decelerated and accelerated by
49
dynamic working head, and complex flow pattern transitions and severe pressure
50
fluctuations will happen, which could endanger the safety of units. Therefore, despite
51
the probability of the pump-trip runaway is small, it is one of the must studied
52
transient processes in the design stage of pumped-storage plants. To analyze this fast
53
changing phenomenon, considering the superposition of water-hammer in water
54
conveyance system and pressure pulsations in pump-turbine, and understanding the
55
relationship of flow patterns, pressure pulsations and runner forces, are important,
56
because their interactions, correlations and evolutions are the main cause of a series of
57
unit vibration problems [4].
58
Many studies on flow patterns and pressure pulsations in pump-turbines have
59
been conducted based on computational fluid dynamics (CFD) simulations or model
60
tests, and some correlations between them have been clarified [5-7]. However, the 2
61
attentions of the existing investigations were mainly focused on the flow
62
characteristics of a certain steady working condition. Xia [8] and Pacot [9] analyzed
63
the rotating-stall instabilities of a pump-turbine in the pump mode and concluded that
64
the rotating-stall could cause periodical high pressure. Liu [10] found that the
65
cavitation on the suction side of runner inlet could lead to great changes of pressure
66
distributions on blade surface, when the pump-turbine worked in the hump-shaped
67
region. Foroutan [11] reported that the pressure fluctuations in a simplified draft-tube
68
due to the vortex rope could have a large amplitude, as high as twice the local mean
69
pressure value. Hasmatuchi [12] presented the experimental evidence of the
70
rotating-stall in a model pump-turbine working in the S-shaped region, and found that
71
the pressure pulsating amplitude increased when the discharge decreased. Recently,
72
Xia [19] found the backflow patterns at the runner inlet in the pump-turbines working
73
in the S-shaped region, and discussed the correlation between the working points
74
located along the guide vane opening curves and their corresponding flow patterns.
75
As for transient processes, studying the flow characteristics by model tests is
76
very difficult and CFD simulation becomes the basic tool. A few studies on this topic
77
have already been reported [13] and the evolutions of pressure fluctuations
78
corresponding to the flow transitions have been discussed [14-16]. However, they
79
were limited by only considering some specific working conditions, and most
80
questionably ignoring water-hammer pressure effects [17], without which the dynamic
81
characteristics of pump-turbine cannot be fully considered. In addition, the generation
82
mechanism of special flow patterns has not been discussed in depth, and the
83
coexistence of multiple vertex structures has been neglected. Li [18] investigated the
84
transient process in pump mode, in which the guide vanes were closing and the
85
rotational speed was constant, and found that the obvious flow separations in the
86
runner and vanes could result in significant pressure fluctuations. Staubli [19]
87
predicted the unstable flow fields during turbine starting-up process in the turbine
88
mode, and found time-varying inflow and outflow from the runner into the vaneless
89
space could be the cause of instability. Liu [20] simulated a load rejection transient
90
process of a prototype pump-turbine, and found that the vortex ropes in the draft-tube 3
91
had large deviations from the results in steady working conditions. Li [21] simulated
92
the normal shutdown process of a prototype pump-turbine in turbine mode, and
93
investigated the global characteristics and pressure fluctuations under the emergence
94
of flow separation and vortex formation. Xia [22] studied the runaway transient
95
process from a turbine working point, and concluded that the locally distributed
96
backflow vortices at the runner inlet could enhance the local rotor-stator interaction,
97
and the evolving rotating-stall could induce asymmetrical pressure distribution on
98
runner blades.
99
From the above works, we know that the flow patterns in pump-turbines working
100
in different modes show quite different features, contributing to great differences in
101
pressure fluctuations. This is an obvious conclusion for both steady conditions and
102
transient processes. But how the flow patterns change during the transient processes
103
that experience different working regions, and how they influence the alterations of
104
pressure pulsations and runner forces, need to be clearly stated.
105
In this study, the runaway transient process after pump-trip in a prototype
106
pumped-storage power station was simulated, and the evolutions and correlations of
107
pressure fluctuations, runner forces and flow structures were analyzed. The paper will
108
describe the basic simulation model and parameters; the resulting histories of macro
109
parameters; the evolutions of flow structures, pressure pulsations, and runner forces.
110
The results are discussed according to the trajectory curve in the characteristic plane,
111
and related by the short term Fourier transformation.
112 113
2. Numerical Methods
114
2.1 The pumped-storage station and its simulation model
115
A low-head pumped-storage power station with two 150MW units in one water
116
conveyance system was considered. As shown in Fig.1, the system includes an
117
upstream reservoir (water level 397.67m), a diversion tunnel, two penstocks, two
118
pump-turbine units (rated head 126.7m in the pump mode), two downstream conduits,
119
and a downstream reservoir (water level 291.28m). The setting elevation of the units
120
is 264.00m. The pumping condition with one unit in operation was simulated in this 4
121
study. The 1D-3D coupling method [23] was adopted, in which the diversion tunnel,
122
penstock and downstream conduit were simulated by the one-dimensional (1D)
123
method of characteristics (MOC), while the pump-turbine was simulated by
124
three-dimensional (3D) CFD. The profile and parameters of computational domain are
125
shown in Fig. 1, while the 3D model of pump-turbine and the layout of several
126
monitoring points are shown in Fig. 2. The basic parameters of the pump-turbine are
127
given in Table 1, in which D1 denotes the runner outlet diameter (pump mode), D2 the
128
runner inlet diameter (pump mode), nr the rated rotational speed, Zb the number of
129
runner blades, ngv the number of guide vanes, nsv the number of stay vanes, ns the
130
specific-speed (pump mode), and Hr the rated head (pump mode).
131
Fig. 1. Profile of the computational domain
132
Fig. 2. 3D model of pump-turbine and schematic of monitoring points and sections
133 134
Table 1. Main parameters of the prototype pump-turbine Parameter
Value
Parameter
Value
D1 (m)
5.2265
Zb
7
D2 (m)
4.132
ngv
20
nr (rpm)
200
nsv
20
ns (m,m3/s)
59.9
Hr (m)
126.7
135 5
136
2.2 Numerical schemes
137
Commercial software ANSYS FLUENT 15.0 was used in the 1D-3D simulations.
138
The 3D geometry in Fig. 2 was discretized into structured meshes with multiple
139
blocks by ANSYS ICEM 15.0. A grid refinement evaluation was performed and we
140
found that the relative differences in macro parameters from 6.9 million to 8.0 million
141
grid elements are negligible. Therefore, the mesh with 6.9 million grid elements was
142
finally chosen (Table 2), in which fine boundary layers are set up in the regions of
143
stay vanes, guide vanes, and runner.
144 145
Table 2. Number of grid elements (million) Draft-tube with
Spiral casing with Runner
Stay vanes Guide vanes 1.2
Total extended tube
extended tube 1.0
1.1
2.3
1.3
6.9
146 147
We selected the SAS-SST turbulence model, and specified the transient
148
simulation timestep as 0.00125s, which corresponds to 1.5 degrees of runner rotation
149
at the rated speed. For both steady and unsteady working conditions, the SIMPLEC
150
algorithm was chosen to achieve the coupling solution of the velocity and pressure
151
equations. The second order discretization in time and in space was used.
152
Boundary conditions were defined as follows. The outlet and inlet of pipes in 3D
153
model were set as static pressure and total pressure boundary conditions by 1D MOC,
154
respectively. At the 1D-3D interfaces, the partly overlapping coupling method in
155
reference [23] was used and the compressibility of water was simulated by defining
156
the pressure depended density, as shown in Eq. 1. The friction and local head losses in
157
each pipe were considered in the 1D model. ρ = ρ0 e(p-p0 )/ρ0 a
158
2
(1)
159
where ρ and p are the density and pressure of water, respectively; ρ0 and p0 are the
160
initial values of ρ and p, respectively; e (-) is the base of natural logarithms; a is the
161
acoustic speed in water. 6
162
2.3 Computation of the varying speed of turbine unit
163
The rotation of the runner was simulated by the sliding mesh model during
164
runaway process. The angular speed ω of the runner varies with time in accordance to
165
angular momentum equation, as shown in Eq. 2, and a User-Defined-Function (UDF)
166
program in ANSYS FLUENT 15.0 was used to realize the variation of rotational
167
speed.
168
T
ωt = ∆t + ωt-∆t J
(2)
169
where J is the total rotational inertia of runner and motor-generator; T is the hydraulic
170
torque acting on the runner; ωt and ωt-Δt are the rotational speed at the current and
171
previous timesteps, respectively; ∆t is the timestep.
172 173
2.4 Validation of the simulation model
174
Before simulating the runaway transient process, the 1D-3D coupling model
175
should be validated. Because the data of a field test for the pump-trip transient process
176
with a designed closing law of guide vanes from the original opening (GVO) 23.6
177
degrees was available, we simulated the same condition for comparison. Fig. 3 shows
178
the resulting macro parameters, in which the field test curves provided by the test
179
engineer are filtered. Compared to the field test values, the simulated pressure history
180
has stronger fluctuations, which should be the signals of water-hammer in pipelines
181
and complex flow structures in the pump-turbine. The water-hammer cycle in the
182
upstream pipeline is around 1.25s, corresponding to the pressure fluctuating cycle at
183
P1 after guide vanes have closed. The relatively high frequency fluctuations at P4
184
should be caused by vortices in draft-tube and runner passages. Generally speaking,
185
the simulation results are in good agreement with the field test results, and the
186
reliability of the 1D-3D coupled approach is validated. Then, the runaway process
187
without guide vane closing after the pump-trip from the same steady working point
188
was simulated, which will be explained in later sections.
7
189
Fig. 3 Validation of the 1D-3D coupled CFD model by field test results
190 191
3 Results of the runaway transient process after pump-trip
192
3.1 Macro parameters during the runaway process
193
During the runaway process, the working point passes through the pump,
194
pump-braking, turbine, and turbine-braking modes, and its dynamic trajectory travels
195
across these regions and finally revolves around a zero-torque point with fluctuations,
196
as shown by the red curve in the n11-Q11 plane of Fig. 4, in which the unit speed
197
n11 = -nD1 / √H and unit discharge Q11 = -Q / (D21 √H) are defined. The dynamic
198
curve has a good agreement with the static characteristic curve (black curve, obtained
199
by model tests) in the pump, pump-braking and turbine modes, excepting near the
200
static zero-torque point. Not following the static characteristic curve, the dynamic
201
trajectory fluctuates and gradually converges to a speed-no-load region, which is on
202
the left of the static zero-torque point. If the errors in model tests and simulation are
203
considered, the remaining deviations of the dynamic and static curves should be
204
owing to the unstable vortex structures developed in the whole runaway process,
205
which are marked in Fig. 4.
206
The histories of the key macro parameters during the runaway are shown in Fig.
207
5, in which the process has been divided into six modes: pump (P), pump-braking
208
(PB), turbine (T1), turbine-braking (TB), turbine (T2), and no-load runaway (NL). The
209
transition from the P mode to PB mode is defined by the sign of discharge Q changing
210
from positive to negative, namely the flowing direction changes from pump direction
211
to turbine direction but the runner rotates still in pump direction. The transition from 8
212
the PB mode to T1 mode is defined by the sign of rotational speed n changing from
213
positive to negative, namely the rotating direction changes from pump direction to
214
turbine direction and the runner works in normal turbine condition. The transition of
215
T1 mode and TB mode is defined by the sign of torque T changing from negative to
216
positive, namely the water driving power is surpassed by the water dissipating power.
217
The NL mode defined by the small and fluctuating turbine output power when the
218
working point revolves around the zero-torque point. These definitions are
219
corresponding to the characteristic regions in Fig. 4(b).
220
Due to the specific-speed of this pump-turbine is relative large, there is no larger
221
fluctuations in rotational speed and discharge during the last no-load runaway mode,
222
which is obviously different from the unstable fluctuations in the S-shaped region for
223
many low specific-speed pump-turbines [24]. The torque T varies with normal laws in
224
the P, PB and T1 modes, and becomes unstable in the TB, T2 and NL modes. The
225
axial force of runner (Fz) in the P and PB modes is mainly affected by the
226
water-hammer and increases quickly at the beginning of the P mode. However, in the
227
T1 mode, Fz decreases sharply before the working point is approaching to the rated
228
turbine point. Once entering the last three modes, Fz becomes unstable and fluctuates
229
with high frequencies and large amplitudes. For the radial force (Fx and Fy) of runner,
230
the variation range is not large and the fluctuations in the last TB, T2 and NL modes
231
are also severe. Obviously, all the severe fluctuations in torque and runner forces
232
begin after the working point enters the so-called S region, although the S-shaped
233
shape is not obvious for this low-head pump-turbine.
(a) Original data
9
(b) Low-pass filtered data in S-shaped region Fig. 4. Dynamic trajectory curve in the n11 – Q11 plane
234
(a) Histories of torque, discharge and speed
(b) Histories of runner forces
235
Fig. 5. Histories of macro parameters during the pump-trip runaway process. (P:
236
pump; PB: pump-braking; T1 and T2: turbine; TB: turbine-braking; NL: no-load
237
runaway)
238 239
3.2 Pressure fluctuations during the runaway process
240
The pressure fluctuations at points P1, P2, P3 and P4 during the runaway
241
transient process are shown in Fig. 6. On the whole, regional variation features are
242
obvious as the working point passes through the six modes successively. In the P
243
mode, the rapidly decreasing discharge after the sudden power loss causes a negative
244
water-hammer wave upstream the runner and a positive water-hammer wave
245
downstream the runner (Fig. 6(b)). Accordingly, the pressure histories at monitoring
246
points P1, P2 and P3 show rapid decrease and the pressure at point P4 shows rapid
247
increase (Fig. 6). When the working point enters the PB mode, the flow direction
248
reverses and the torque turns to increase again (Fig. 5(a)), leading to the gradual
249
restorations of pressure values at the monitoring points (Fig. 6). The pressures recover
250
roughly to their initial values when the working point gets into the T1 mode. In the 10
251
TB mode, the torque value becomes positive, meaning energy dissipation (Fig. 5(a)),
252
accordingly the pressures at P1, P2 and P3 begin to decrease and that at P4 begins to
253
increase (Fig. 6). These pressure decreases and increases during the first four modes
254
are mainly related to the water-hammer in water conveyance system and the
255
pump-turbine characteristics transferring between the operating modes. After the T2
256
mode, the discharge and speed are approaching to a steady level, therefore the pipe
257
water-hammer effect becomes weak and turbine pressure pulsation effect becomes
258
dominant (Fig. 6). It can be seen that the pressure fluctuation amplitudes increase
259
rapidly once the working point leaves the turbine best efficiency point (t = 21.5 s), and
260
they approach to the maximum values after entering the TB mode. The violent
261
fluctuations continue in the T2 and NL modes, showing no damping tendency. The
262
fluctuation frequencies and amplitudes at P3 are much higher than at other points,
263
because the pressure pulsations by the rotor-stator interaction are superimposed.
(a) Original pressure data 264 265
(b) Low-pass filtered data
Fig. 6. Histories of pressure fluctuations at different monitoring points 3.3 Evolutions of flow patterns during the runaway process
266
To investigate the mechnism of large pressure fluctuation amplitudes, the
267
evolutions of flow patterns in the vane, runner and draft-tube regions were analyzed.
268
Three stream surfaces with spanwise ratios 0.1, 0.5, and 0.9 across the vane and
269
runner (Fig. 2) were selected to show the flow patterns. At the same time, the velocity
270
triangles at the inlet (adjacent to the guide vanes) and outlet (connected to the
271
draft-tube) of runner were borrowed to interpret the general development trends of
272
flow patterns, even though it cannot describe local vertex structures accurately. 11
273
When the unit is in a steady pumping operation, the flow fields in the
274
pump-turbine are smooth, and there are no obvious vortex structures and flow
275
blockages (Fig. 7, t = 0.0 s). Accordingly, the pressure pulsations are stable and have
276
no high amplitude signals. However, during the runaway process, the pressure
277
fluctuations vary quickly and the flow patterns evolve with various vortex structures.
278
(1) Pump mode (t < 6.5 s)
279
When the pump is suddenly powered off, the rotational speed, discharge and
280
head begin to decrease simultaneously, because the runner is decelerated by the
281
resisting torque of water. In addition, because the water pumping force is proportional
282
to the square of rotational speed, the decrease of discharge is faster than that of
283
rotational speed (Fig. 5(a)), leading to the reduction of outflow angle α1, which is
284
defined by the angle between the absolute flow velocity V1 and the peripheral velocity
285
U1, as shown Fig. 7. Because U1 in the vaneless region is still high and the water in
286
the vane region is slowed down, the enhanced shearing action and the large attack
287
angle to the vanes generate several rotating-stall vortices. The existing studies [5,8]
288
showed that when the rotating stalls occur, the disturbed flow and blockage can only
289
be observed in part of blade and vane channels (Fig. 7, t = 5.5, 6.0 s), which result in
290
uneven circumferential outflow and pressure distributions.
291
As for the inflow triangle, the absolute flow velocity V2 near the pressure surface
292
of runner blades decreases sharply, resulting in the increase of the inflow attack angle
293
β2, which is defined by the exterior angle between the relative velocity W2 and the
294
peripheral velocity U2. When the inflow water impacts with runner blades, it separates
295
from blades and contributes to large-scale separation vortices in the blade passages
296
(Fig. 8(a)). Overall, the main axes of vortices in the vane and runner regions are
297
approximately perpendicular to the stream surfaces. For the flow in the draft-tube,
298
previous studies showed that when water flows into the runner region, it is disturbed
299
by the runner and has circumferential components [25]. And the decrease of runner
300
discharge will result in the increase of the circumferential components of draft-tube
301
water. Here, to identify the vortex structures accurately, a newly proposed omega
302
method was used [26], which considers vortex as a region where vorticity overtakes 12
303
deformation and are superior to other methods (e.g., vorticity tube, Q-criterion and
304
Lambda-2 method) [27,28]. In this case, once the pump is tripped, due to the decrease
305
of runner flow capacity and the inertia of water in the draft-tube, the inflow water will
306
impinge on the pressure surfaces of runner blades, forming backflows on the shroud
307
side (Fig. 8(b)). The upward main flow in the draft-tube center moves shearing with
308
these backflows, generating backflow vortex structures near the draft-tube wall.
309
Under the disturbance of the runner, these vortices further separate into several skirt
310
shaped vortices (Fig. 7, t = 5.5, 6.0 s).
311
Generally speaking, the smaller the discharge, the more complex the flow
312
patterns. Also, the velocity triangles can only show the developing trend of flowing
313
state, but the local backflows and vortices cannot be accurately described, which
314
reflects the complexity and inhomogeneity of the flow patterns.
315
Fig. 7. Velocity triangles and flow patterns in the pump mode
(a)
(b) 13
316 317
Fig. 8. Separations in runner passages (a) and backflows in the draft-tube (b) (t = 6.0 s)
(2) Pump-braking mode (6.5 s < t < 13.7 s)
318
Due to the recovering pressure head on the turbine (Fig. 6(b)), the flowing
319
direction begins to reverse to the turbine direction, but the rotating direction remains
320
in the pump direction, even though the rotational speed continues to decrease (Fig.
321
5(a)). In the initial stage of pump-braking mode, because the rotational speed, inflow
322
angle β1 (defined by the exterior angle between the relative velocity W1 and the
323
peripheral velocity U1) and centrifugal force at the runner inlet are still large, flowing
324
into the runner passages is not smooth. The inflow strongly impacts the pressure
325
surfaces of the blades. The impact makes some water turning left and returning to the
326
vaneless space, some water jumping over and impacting the next blade, and some
327
water turning right and entering the blade passages, which form large separation
328
vortices around the suction surfaces of the blades (Fig. 9, t = 9.0 s).
329
At the runner outlet, the increasing outflow angle α2 (defined by the angle
330
between the absolute flow velocity V2 and the peripheral velocity U2) pushes the main
331
flow near the draft-tube wall to develop stronger, with the reverse flow in the center
332
also intensified (Fig. 9, t = 13.0 s). In detail, a part of the outflow goes into the
333
draft-tube directly, and the rest goes round to suction surfaces, which intensifies the
334
shearing actions with the upward flow in draft-tube center and produces separation
335
vortices near suction surfaces (Fig. 10).
336
In the later period of the pump-braking mode, with the increase of discharge, the
337
main flow in the vane region gradually becomes strong and steady, depressing the
338
local small vortex structures between vanes. Also, the large separation vortices in
339
runner passages are decreasing in scale but not in intensity.
340
According to the above two working regions, the different flow patterns have
341
different influences on pressure fluctuations. Generally speaking, the formation of
342
vortex structures can produce higher amplitude pressure fluctuations, which should be
343
weakened if the vortex structures disappear. However, the pressure fluctuating
344
amplitudes increase obviously in pump-braking mode, far larger than in the pump
345
mode (Fig. 6(a)). The reason is that the vortex structures in the pump mode are 14
346
generated by shearing action. Due to low energy dissipation, these vortices are
347
difficult to produce higher amplitude signals. But in pump-braking mode, the strong
348
impacts on the runner blade pressure surfaces and the large separating vortices on
349
suction surfaces are high energy dissipated, which can produce high amplitude signals.
350
Therefore, it is not the number and size of vortices that determines the amplitudes of
351
pressure fluctuations, but the strengths of impacting on the solid walls and interacting
352
between vortices.
353
Fig. 9. Velocity triangles and flow patterns in pump-braking mode
354
(a) 355 356
(b)
Fig. 10. Flow patterns in runner passages and draft-tube in pump-braking mode (t = 9.0 s)
(3) Turbine mode T1 (13.7 s < t < 28 s)
357
Affected by the increasing resisting torque, the runner begins to rotate in the
358
direction of turbine mode, companied by increase of discharge. In the initial stage,
359
because of the relatively small peripheral velocity U1 and the small inflow attack
360
angle β1, the impacting of inflow on blade pressure surfaces accelerates the rotational
361
speed of runner, and the separation vortices on the suction surfaces still exist (Fig. 11,
362
t = 16.0 s). With the increase of rotational speed, namely the increase of peripheral 15
363
velocity U1, β1 becomes larger gradually and fits to the blade inlet angle, contributing
364
to scale and intensity decreases of the separation vortices. At the optimal working
365
point (about t = 21.5 s), the inflow enters the runner passages without any hindrance,
366
and the outflow at the runner outlet flows vertically and smoothly down to the
367
draft-tube (Fig. 11, t = 21.5 s). However, after t = 21.5 s, when the working point
368
passes through the optimal, the rotational speed and the inflow attack angle β1 at the
369
runner inlet continues to increase, and separation vortices occur again on the blade
370
suction surfaces (Fig. 11, t = 27 s). Fig. 12 shows the flow patterns in a single runner
371
passage. Once the working point leaves the optimal, obvious backflows occur on the
372
shroud side due to the centrifugal force and the increasing impact on the runner blade.
373
A part of the backflows jumps into the nearby runner channel, and a part goes back to
374
the vaneless space. On the hub side, the water flows into the blade passage easily.
375
As for the draft-tube, in the turbine mode with different discharges, flow patterns
376
have a developing manner, which are corresponding to the findings in references
377
[11,29]. Fig. 13 shows vortex structure evolutions in the draft-tube at different times.
378
As flow rate increases, backflows in the draft-tube center weakens, resulting in the
379
shrinking of skirt vortex structures near the wall and the developing of a single thick
380
eccentric vortex belt in the center. When the working point is before the optimal, the
381
larger the discharge, the finer the vortex shape, which is approaching a conical
382
cucumber shape from a helical rope shape. Once the working point leaves the optimal
383
the optimal, skirt vortices are re-generated and overspread the whole wall.
384
It is evident from the pressure fluctuation diagram (Fig. 6(a)) that when the unit
385
enters the turbine mode, especially before t = 21.5 s, the pressure fluctuations
386
gradually decrease at P2 and P3 due to the disappearance of the unstable vortex
387
structures. However, high amplitude pressure fluctuations at P4 and runner radial
388
forces (Fig. 5(b)) still keep exist during this time, it should be due to the existence of
389
the vortices in the runner passages and draft-tube (Fig. 11, t = 16 s). After t = 21.5s,
390
the pressure amplitudes begin to increase again because of the backflows at the runner
391
inlet [30]. Due to backflows in the vaneless space, the recirculation inside the blade
392
passages, and the impact by the runner blades, the rotor-stator interaction is 16
393
intensified and the pressure fluctuating amplitudes increase greatly (Fig. 6(a)).
394
Fig. 11. Velocity triangles and flow patterns in the pump-braking mode
395
t = 21.5 s 396
t = 27.0 s
Fig. 12 Flow patterns in a single runner passage at different times
397
398
t = 16.0 s
t = 17.0 s
t = 18.0 s
t = 20.0 s
t = 21.0 s
t = 21.5 s
t = 25.0 s
t = 27.0 s
Fig. 13. Evolutions of the vortices in the draft-tube 17
399
(4) Turbine-braking mode TB, turbine mode T2 and no-load mode NL (t > 28 s)
400
From the histories of pressure fluctuations in Fig. 6, it can be seen that the last
401
three working regions are similar because of the constant trends of rotational speed
402
and discharge. In these three stages, the pressure pulsating amplitudes are the largest
403
in the vaneless space. The vaneless space should be the area where energy is
404
dissipated during runaway process, because the increase of amplitudes can be
405
considered as the increase of energy dissipation. Fig. 14 shows flow patterns in a
406
single runner passage and draft-tube, which are similar to those in the turbine mode
407
after the optimal working point.
408
To better investigate the internal flow patterns when the runaway is approaching
409
to the NL point, three stream sections cutting through the runner and vane regions at t
410
= 70 s are shown in Fig. 15. Obviously, on the hub side and middle span, there are
411
only a few separation vortices near the blade suction surfaces. However, on the shroud
412
side, more vortices exist near the blade pressure surfaces, accompanied with
413
backflows at the runner inlet. As a result, the stronger shearing action induced by the
414
high-speed flow in the vaneless space and the low-speed flow in the vane region,
415
contribute to the formation of separation vortices on the abdomen of guide vanes.
(a)
(b)
416
Fig. 14. Flow patterns in a single runner passage (a) and draftt-ube (b) (t = 70.0 s)
417
Fig. 15. Flow patterns on the three stream sections at t = 70.0 s
418 419
3.4 Frequency spectrum A time-frequency analysis of the transient pressure fluctuations at the monitoring 18
420
points is performed by using the Short Time Fourier Transform (STFT) [31], and the
421
results are shown in Fig. 16. At the beginning of the runaway process, the
422
characteristics of pressure fluctuations are mainly influenced by the runner. The
423
dominant frequency in the spectrograms is the blade passing frequency (BPF), and the
424
rest high frequencies are the integer multiples of the BPF. Due to the decreases of the
425
rotational speed and discharge, the vortex structures generated in the vane and runner
426
regions cause the generation of relatively low frequency signals with relatively higher
427
amplitudes (4.0 s < t < 6.5 s). In the transferring process from pump mode to
428
pump-braking mode, it is obvious that, due to the separation vortices and the impact
429
on runner blades, higher frequency signals and low frequency signals mix up and
430
display no clear boundary, and changing trends of the frequencies are in accordance
431
with the change of the rotational speed (6.5 s < t < 13.7 s). When the unit enters the
432
turbine mode, the frequency distinction becomes clear, and the amplitudes decrease
433
greatly near the better operation region (13.7 s < t < 21.5 s). These are because the
434
vortices in the vane region become weak or disappear. Once the working point leave
435
the optimal, the amplitudes increase gradually because of the violent rotor-stator
436
interaction induced by backflows (21.5 s < t < 28 s). After t = 28 s, the unit goes into
437
TB, T2 and NL modes in turn. All the low frequency and high frequency signals joint
438
again, and the amplitudes become very strong. These should be due to the various
439
vortices in the vane region, vaneless space, runner, and draft-tube.
(a) Point P1
(b) Point P2
19
(c) Point P3 440 441
(d) Point P4
Fig. 16. Frequency spectra for pressures at the monitoring points 4. Conclusions
442
The flow patterns, pressure pulsations, and runner force fluctuations during the
443
runaway transient process after pump-trip experience rapid and dynamic evolutions,
444
because the working point slides across the pump, pump-braking, turbine 1,
445
turbine-braking, turbine 2, and no-load runaway modes successively. In this study, we
446
analyzed the evolutional phenomena in this process and found that the changes in
447
pressure pulsations and runner force fluctuations are correlated to the transition of the
448
flow patterns, which have distinct features in different modes. Apart from the
449
rotating-stall vortices in the vane and runner regions in the pump mode, the impact
450
and separation vortices in the blade channels, the skirt and backflow vortices in the
451
draft-tube in the pump-braking and turbine 1 modes, along with the backflow vortices
452
at the runner inlet in the turbine-braking, turbine 2, and no-load runaway modes, are
453
the main causes that make the fluctuating magnitudes of pressure and runner forces
454
larger. The main findings are summarized as follows.
455
(1) When the discharge becomes small in the pump mode, the rotating-stall
456
vortices in the runner and vane regions develop due to the shearing action, and the
457
skirt vortices near the draft-tube wall appear due to the back and rotating flow around
458
the circumference.
459
(2) In the pump-braking mode, the flowing direction changes to the turbine
460
direction but the rotating direction is still in the pump direction. The vortices in the
461
vane region disappear completely as the discharge increases. The distinguish flow
462
structures in this mode are the strong impact jets on the blade pressure surfaces and 20
463
the large separation vortices near the suction surfaces. In the draft-tube, the runner
464
outflow around the tube wall and the backflow in the center are enhanced with the
465
increase of discharge, resulting in larger skirt vortices distributed in the circumference.
466
These flow structures make the pressure and runner force fluctuations intensified.
467
(3) As the rotating direction turns to the turbine direction, the pump-turbine is
468
operating in the turbine mode. Before the working point is approaching to the best
469
efficiency point, the impact jets on the blade pressure surfaces and the separation
470
vortices near the suction surfaces, along with the skirt vortices and backflow in the
471
draft-tube are suppressed as the rotational speed increases. In the best efficiency point
472
all flow patterns become smooth. After the working point leaves this optimal point,
473
the runner and draft-tube vortices appear again. The shroud side backflows at the
474
runner inlet become visible before the working point is approaching to the
475
turbine-braking mode. The runner inlet backflows make the rotor-stator interaction
476
obvious, resulting in the increasing pressure pulsations and runner force fluctuations.
477
(4) In the turbine-braking to no-load runaway modes, the working point comes
478
back to the turbine mode many times. The flow characteristics during this last
479
oscillating and converging process are similar. Apart from the separation vortices in
480
the vane and runner regions, the skirt vortices in the draft-tube, the backflow vortices
481
at the runner inlet are the distinguished phenomenon. It is the backflow vortices that
482
make the pressure and runner force fluctuations more violent.
483
(5) During this runaway transient process, the pressure pulsations in the vaneless
484
space are the largest in the pump-turbine. This phenomenon is caused by the
485
rotor-stator interaction, which are intensified by the impact jets on blades and the
486
backflow vortices at the runner inlet. The skirt and helical vortices in the draft-tube
487
and the rotating-stall vortices in the runner and vane regions are the main source of
488
low frequency pressure fluctuations.
489 490
Funding
491
This work was supported by the National Natural Science Foundation of China
492
(NSFC) (Grant Nos. 51839008 and 51579187), the Natural Science Foundation of 21
493
Hubei Province (Grant No. 2018CFA010), and the Natural Science Foundation of
494
Fujian Province (Grant No. 2018J01525).
495 496
Acknowledgments
497 498
The numerical simulations were conducted on the supercomputing system in the Supercomputing Center of Wuhan University.
499 500
Reference
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•Evolutions of flow patterns and pressure fluctuations during runaway process were described. •Evolutions of flow patterns are dominated by changes of velocity triangles. •Inhomogeneous local flow contributes to vortex structures. •Different vortices lead to great differences in pressure fluctuations in different working regions.
Conflict of interest statement: Yongguang Cheng and other co-authors have no conflict of interest.