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The method for determining blade inlet angle of special impeller using in turbine mode of centrifugal pump as turbine
Accepted Manuscript The method for determining blade inlet angle of special impeller using in turbine mode of centrifugal pump as turbine
Tao Wang, Fanyu Kong, Bin Xia, Yuxing Bai, Chuan Wang PII:
S0960-1481(17)30245-8
DOI:
10.1016/j.renene.2017.03.054
Reference:
RENE 8647
To appear in:
Renewable Energy
Received Date:
13 October 2016
Revised Date:
23 January 2017
Accepted Date:
18 March 2017
Please cite this article as: Tao Wang, Fanyu Kong, Bin Xia, Yuxing Bai, Chuan Wang, The method for determining blade inlet angle of special impeller using in turbine mode of centrifugal pump as turbine, Renewable Energy (2017), doi: 10.1016/j.renene.2017.03.054
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ACCEPTED MANUSCRIPT Highlights:
The innovative impeller with the forward-curve blade is designed.
The forward-curve impeller in the PAT has obvious superiority
The calculation equation of critical flow is deduced.
The value of blade inlet angle is recommended in a reasonable range in PAT.
ACCEPTED MANUSCRIPT 1
The method for determining blade inlet angle of special impeller using in
2
turbine mode of centrifugal pump as turbine
3
Tao Wanga*, Fanyu Kongb, Bin Xiab, Yuxing Baib and Chuan Wanga, b*
4 5
a Key
Laboratory of Fluid and Power Machinery, Ministry of Education, School of Energy and Power
6 7 8 9 10
Engineering , Xihua University, Chengdu, Sichuan 610039, China b
Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang, Jiangsu 212013, China * Corresponding
author:
E-mail address: [email protected] (T. Wang) and [email protected] (C. Wang)
11 12
Abstract: Due to that the conventional backward-curve centrifugal impellers do not effectively match the turbine’s
13
running, the performance of the pump-as-turbine (PAT) was usually not ideal. Therefore, to improve significantly the
14
performance of PAT, one kind of special impeller with forward-curved blades was desigened for the turbine’s working
15
condition, and the method for determining blade inlet angle that played important role in the energy conversion was
16
also stduied deeply in this paper. Moreover, four forward-curve impellers with different blade inlet angles were
17
numerically investigated by using a verified computational fluid dynamics (CFD) technique, and relevant external
18
characteristic experiments were also conducted to benchmark the numerical calculation. Based on the results, the flow
19
rate of numerical best efficiency point (BEP) is very close to that of theoretical BEP, and the flow rate of BEP
20
increases with extending the blade inlet angles. Additionally, the energy loss within the impeller reaches the minimum
21
if suitable blade inlet angle is selected, so the value of blade inlet angle is recommended in a reasonable range in
22
special impeller used in turbine mode of PAT. Furthermore, compared with the original backward-curve impeller, the
23
maximum efficiency of the forward-curve impeller increases from 59.98% to 67.91%, and the flow-efficiency curve is
24
more flat, which reflects that the forward-curve impeller in the PAT has obvious superiority. This paper is very
25
instructive to the design of the special impeller using in the PAT. 1
ACCEPTED MANUSCRIPT 26
Keywords: Pump as turbine, CFD, Blade inlet angle, Forward-curved blades.
27
1 Introduction
28
With the development of the social economy, there is an increasing demand for the energy, while energy shortage is
29
becoming the remarkable restriction of the development [1-6]. The use of renewable energy and new energy is of great
30
significance to solve the energy shortage. Moreover, liquid-pressure-energy (LPE) is a kind of clean renewable energy,
31
and the utilization of small power LPE is one of the energy’s development directions in future. Pumps are a kind of
32
reversible rotating machinery, which can be reversely used and called pump as turbine (PAT) [7-10]. Compared with
33
other small power LPE, PAT has the advantages of small size, low cost, simple maintenance and wide applications.
34
Over the last several years, considerable efforts have been made in the PAT performance prediction, optimization
35
and performance improvement through using theoretical, experimental and numerical methods. Pugliese et al. [11]
36
tried to assess the performance of pumps operating in reverse model, and two centrifugal pumps such as a centrifugal
37
horizontal single-stage pump and a vertical multi-stage pump were investigated by some experiments. Tan et al. [12]
38
presented a comprehensive correlation aimed to bring out the accurate prediction of the turbine model operations of
39
centrifugal pumps, and used experimental data of wide range of pumps representing the centrifugal pump
40
configurations in terms of specific speed. Fecarotta et al. [13] presented the reliability of the affinity law to predict the
41
behavior of a PAT under various speeds, and found that the difference between the theoretical model and the
42
experimental results was significant. Barbarelli et al. [14] put forward to the predictive model estimating the
43
performances of centrifugal pumps used as turbines, and obtained that the estimation error was much small and
44
acceptable for this kind of application. Derakhshan et al. [15–16] redesigned the blade shapes by gradient-based
45
optimization technique to gain higher efficiency. Singh et al [17] and Derakhshan et al [18] provided a number of
46
simple modifications, such as blade/hub/shroud rounding and the impeller tip to improve the performance of PAT.
47
Doshi et al. [19] made an experimental study to investigate the relative effects of blade and shroud rounding for the 2
ACCEPTED MANUSCRIPT 48
inlet impeller round in PAT. Qian et al. [20] studied an axial-flow pump in both pump and turbine modes, and found
49
that the adjustable guide vane provided a cost-effective solution to considerably improve the efficiency of the PAT
50
under partial loading. In summary, most previous studies focus on the overall performance prediction of the PAT by
51
using various methods, which reflecting that the relevant prediction methods are rather credible, while a small number
52
of studies concentrate on the performance improvement of the PAT through optimizing the blade, rounding the
53
impeller and adjusting the suitable guide vane. Few scholars tried to design the special impeller to improve the
54
efficiency of the PAT.
55
Single-stage centrifugal pump is mostly equipped with the spiral volute. Because of space size restriction, there
56
are usually no adjustable guide vanes, which leads to fluid directly flowing into impeller inlet from volute outlet when
57
pump operates in turbine mode. Furthermore, the blade inlet and outlet angles of original impeller designed for pump
58
working condition, not for turbine mode; do not match well with turbine running condition. Thus the turbine mode of
59
PAT efficiency is universally not high and the high efficiency range is usually narrow when pump reversely operates as
60
turbine directly. A convenient suitable way of solving this problem is to redesign the blade for turbine working
61
condition while the other components do not undergo any modifications. Unfortunately, little work is available about
62
PAT special impeller with forward curved blades before. And the blade inlet and outlet angles are two important
63
factors which directly determine the fluid flow characteristics. Especially blade inlet angle plays a decisive role in
64
energy conversion. Therefore, it is significant to research how to determine the blade inlet angle of special impeller and
65
how the blade inlet angle influences the performance of PAT.
66
In this paper, a PAT special impeller with forward curved blades was designed to improve PAT efficiency.
67
Based on the comparison of experimental data between original and special impellers, the results show that the best
68
efficiency is increased by 7.93 percentage points and the special impeller can better satisfy the turbine operating
69
conditions. Then, blade inlet angles of four different blades are calculated at corresponding rated flow rates
70
respectively. The performances of four PATs are analyzed respectively based on CFD results, whose accuracy can be 3
ACCEPTED MANUSCRIPT 71
validated through an open test rig established in Jiangsu University. At last, the reasonable range of blade inlet angle is
72
recommended.
73
2 Design method of forward curved blade using in PAT
74
2.1 Volute Outflow
75
When a centrifugal pump reverses as a turbine, the rotational direction is reverse and volute is used as flume of
76
turbine mode. In order to calculate the velocity moment before impeller inlet, the fluid flow laws in volute should be
77
investigated. The spiral volute cross sections are mainly designed in accordance with the theorem of angular
78
momentum conservation. Namely, fluid is idealized and flow movement is assumed to axisymmetric potential flow.
79
The flow movement in spiral volute satisfies vur=k, as shown in Fig.1.
80 81 82 83 84 85
Fig.1
Notes: v is the absolute velocity in volute, m·s-1; vu is the circumferential component of absolute velocity, m·s-1; vm is the meridional component of absolute velocity, m·s-1; δ is flow angle of volute, （°）; a0 is distance from the first cross section center of spiral volute to the PAT axis, m; ρ0 is first cross section radius of spiral volute, m; φ0 is wrap angle of volute, （°）.
The velocity moment in volute can be expressed as [21]:
Qr
0
86
k
87
where Qr is the rated flow rate，(m3/s).
88
Water flow movement in spiral volute
2(a0 a ) 360 2 0
2 0
,
(1)
We assume that
4
ACCEPTED MANUSCRIPT k1 89
0 720( a0 a02 02 )
90
Then,
91
k k1Qr
92 93 94
(2)
.
(3)
The object of study in this case is a single stage centrifugal PAT with pump specific speed ns=18.1. Table 1 lists the main parameters of original pump. Table 1 Main parameters of original pump as turbine Name
Impeller
Volute
95 96
.
Parameters
Value
Impeller inlet diameter D1 (mm)
235
Impeller outlet diameter D2 (mm)
102
Impeller hub diameter Dh (mm)
30
Length of wear ring L (mm)
15
Impeller inlet width b1 (mm)
15.14
Blade number Z
6
Volute wrap angle, φ0 (deg)
345
The distance from the center of inlet cross section to PAT axis, a0 (mm)
163.5
The radius of inlet cross section of volute, ρ0 (mm)
24.5
Volute cross section shape
round
According to geometric parameters of original pump, the volute constant can be calculated, k=82.6216Qr. 2.2 Blade Inlet Angle
97
In this paper, the velocity moment at impeller inlet vu1r1 is equal to k which is proportional to the rated flow rate Qr,
98
when the energy conversion between volute outlet and impeller inlet is neglected at the rated flow rate condition. Thus
99
inlet velocity triangle will show three different shapes under corresponding rated flow rates. As shown in Fig.2, inlet
100
relative flow angle β1 is related to rated flow rates.
101 102
(a)
103
Fig.2
(b)
(c)
Inlet velocity triangles at different rated flow rates: (a) β1>90°, (b) β1=90°, and (c) β1<90°
104
Notes: v1 is inlet absolute velocity, m·s-1; u1 is inlet circumferential velocity, m·s-1; vu1 is circumferential velocity component of
105
inlet absolute velocity, m·s-1; vm1 is meridional velocity component of inlet absolute velocity, m·s-1; w1 is inlet relative velocity, m·s-
106
1;
β1 is relative flow angle at blade inlet, (°); α1 is absolute flow angle at blade inlet, (°). 5
ACCEPTED MANUSCRIPT 107
108 109 110
When impeller diameter and rotational speed are constant, inlet rotational speed, u1, is constant:
u1
D1 n 60
.
The circumferential velocity componet at impeller inlet can be calculated as:
vu1
2k
.
D1
(5)
111
Let k k1Q .
112
Then
113
u1 vu 1
114
(4)
n D1 60
2k D1
n D1 120 k1Q 2
60 D1
.
(6)
When vu1= u1, the critical flow rate, Qc, in accordance with β1=90° can be deduced as:
n D1
2
115
Qc
120 k1
.
(7)
116
As shown in Fig. 2(b), if the rated flow rate is equal to the critical flow rate (Qr=Qc), vu1=u1. In other situations, the
117
circumferential component, vu1, increases with increasing flow rate Q. Inlet relative flow angle, β1, also increases with
118
increase of vu1 while inlet rotational speed u1 is invariable. Fig. 2(a) shows β1>90° with Qr>Qc. Whereas, with the
119
decrease of rated flow rate, β1<90°with u1>vu1, simultaneously, as shown in Fig.2(c).
120 121
In this paper, critical flow rate, Qc=94.5 m3/h, can be obtained under present parameters, D1=0.235 m, n=1500 rpm, and k1=82.6216.
122
In order to study the influences of blade inlet angle on performance of PAT with forward curved blades, four blade
123
inlet angles corresponding to four different rated flow rates (90 m3/h , 94.5 m3/h, 100 m3/h, and 110 m3/h) including the
124
critical flow rate are investigated in this paper.
125
The meridional velocity component, vm1, at impeller inlet can be calculated as:
Qr
126
vm 1
127
where b1 is width of impeller inlet (m), ψ1 is blade inlet blockage coefficient, which can be expressed as:
D1b1 1
,
(8)
6
ACCEPTED MANUSCRIPT su 1 Z
128
1 1
129
where su1 is the circumferential thickness of blade leading edge (m).
D1
,
(9)
130
The corresponding inlet triangles at different rated flow rates and inlet relative flow angles β1 can be obtained, under
131
the present parameters, b1=16 mm, Z=11 and ψ1≈0.85. The inlet angle is equal to inlet flow angle (βb1=β1) under the
132
assumption that there is no incidence loss at rated flow rate condition. Table 2 lists four blade inlet angles (βb1) at four
133
different rated flow rates (Qr).
134
135 136 137
138 139 140 141 142 143 144
145
Table 2
Blade inlet angles at four rated flow rates Qr (m3/h)
βb1 (°)
90
71
94.5
90
100
111
110
135
2.3 Blade Outlet Angle When the fluid out of impeller is non-swirling flow, outlet rotational speed u2 is orthogonal to v2 and the outlet absolute flow angle is equal to 90 degree, as shown in Fig.3.
Fig.3 Notes: v2 is outlet absolute velocity,
m·s-1;
Outlet velocity triangle at blade trailing edge u2 is outlet circumferential velocity, m·s-1; vm2 is meridional velocity component of
outlet absolute velocity, m·s-1; w2 is outlet relative velocity, m·s-1; β2 is outlet relative flow angle, (°); α2 is outlet absolute flow angle, (°).
The outlet flow angle, β2, is deduced as:
2 ac tan
vm 2 u2
.
The outlet meridional component, vm2, is calculated as:
Qr
146
vm 2
147
where A2 is actual area of outlet flow cross section (m2).
148
(10)
A2
,
(11)
Due to relatively small diameter and relatively excessive blade numbers of special impeller, fluid basically follows 7
ACCEPTED MANUSCRIPT 149
along blade surfaces out of impeller. Therefore, the blade outlet angle can be assumed to be equal to outlet flow angle
150
(βb2=β2). Table 3 lists the blade outlet angle βb2 at different rated flow rates Qr.
151
152
Table 3
Blade outlet angles at four rated flow rates Qr (m3/h)
βb2 (°)
90
36
94.5
39
100
37
110
41
2.4 Impeller model
153
According to four sets of blade angles, four special impellers with forward curved blades were designed using
154
ANSYS BladeGen software. The blade wrap angle at middle streamline is determined as 42.7°. The dimensions of
155
impeller inlet diameter, outlet diameter, impeller hub diameter and length of wear ring are all as same as those of
156
original pump. The blade thickness is 5mm at leading edge while 2mm at trailing edge. The radius of rounding is half
157
of blade thickness at blade inlet and outlet respectively. The 3D models of blades with different inlet angles and special
158
impeller (Qr=94.5 m3/h, βb1=90°) by BladeGen software are shown in Fig.4 and Fig.5 respectively.
159 160 161
Fig.4
3D models of blades with different inlet angles
162 163
Fig.5
Special impeller model (βb1=90°) 8
ACCEPTED MANUSCRIPT 164
3 Numerical investigations
165
ANSYS CFX is a commercial 3D Navier-stokes CFD code that utilizes a finite-element based finite-volume method
166
to discrete the transport equations. It is a fully-implicit solver and also a coupled solver. Thus it creates no time step
167
limitation and is considered easy to implement. And the momentum and continuity equations are solved
168
simultaneously. This approach reduces the number of iterations required to obtain convergence and no pressure
169
correction term is required to retain mass conversion, leading to a more robust and accurate solver. In this case,
170
ANSYS CFX was used to simulate the flow within the PAT.
171
3.1 Numerical model
172
The whole computational domain consists of the following five parts, as shown in Fig.6: volute, impeller, front
173
chamber, back chamber and draft tube. In order to get a relatively stable inlet and outlet flow, the volute inlet and draft
174
tube outlet section have been extended by four times of the pipe diameter.
175 176
Fig.6
Numerical model of PAT
177 178
3.2 Mesh generation
179
Structured hexahedral grids for each component part were generated in ICEM CFD. Fluid domains were divided into
180
several blocks and the correlation was established between the geometry and blocks, the hexahedral grids were finally
181
realized. Fig.7 shows the total grids of the computational domains. In viscous layer, especially blade surface, the
182
leading edges, trailing edges, shroud surface, hub surface, volute tongue and volute inner surface, the near-wall grids 9
ACCEPTED MANUSCRIPT 183
were densified to ensure that the value of y+ near boundary wall is around 40. The independence of the numerical
184
performance predictions from grid number was performed as depicted in Fig.8. Both turbine head and torque increased
185
with the increase of grid number while turbine efficiency decreased with the increase of grid number. It was observed
186
that the head, torque and efficiency vary by less than 0.5% when the grid numbers are more than approximately
187
1.2106. Thus the final selected grid numbers of volute, impeller, front chamber, back chamber, draft tube and total
188
elements are 448,110, 429,088, 99,720, 50,400, 192,726, and 1,220,044, respectively.
189 190 191
Fig.7
Computational domain grids of PAT
Fig.8
Grid independence
3.3 Solution parameters
192
Considering the computational accuracy, consuming time and computational stability, the Standard k-ε turbulence
193
model was selected for the simulation [22]. Clear water at 25ºC was chosen as the working fluid. Impeller and volute
194
were set in different coordinate systems with the former in rotating frame and the latter in stationary one. The interface
195
between rotational and stationary components was set to a frozen rotor interface while the interface between two
196
stationary components was set to a general grid interface. All the wall surface roughness within the control volume was
197
set to 50 um similar to the real surface. Convergence criterion was 10-6 for all of the momentum and mass equations.
198
The advection scheme was set to high resolution. The turbulence numerics were set to high resolution. Inlet boundary
199
was set to mass flow rate inlet while outlet boundary was set to static pressure outlet. The PAT performance curves
200
were achieved by changing the mass flow rate.
10
ACCEPTED MANUSCRIPT 201
4 Experimental investigation
202
In order to investigate the performances of PAT and verify the accuracy of CFD results, a complete PAT open-
203
circuit rig was set up and utilized in Jiangsu University, as shown in Fig.9. A feed pump was installed to supply high
204
pressure fluid required for PAT energy recovery. An electric eddy current dynamometer (EECD) was installed to
205
measure and consume energy generated by PAT and to regulate rotational speed of PAT. The inlet and outlet pressures
206
were obtained using pressure transmitters. The flow rate was measured by a turbine flow meter.
207
All the measuring instruments were calibrated before put in use. The standard used in experiments was ISO
208
9906:1999. The required pressure head, shaft power, and efficiency of PAT were obtained after measuring all
209
parameters. The relative uncertainty in experimental measurement of speed, discharge, head, torque, and efficiency is
210
±0.07%, ±0.5%, ±0.72%, ±0.93% and ±1.28% respectively among tested PAT with special impeller at BEP (a detailed
211
description of uncertainties in Appendix).
212 213
214 215
Fig.9
Fig.10
An open PAT test rig established in Jiangsu University
Performance curves of PAT obtained by experimental and numerical results 11
ACCEPTED MANUSCRIPT 216
Figure 10 shows the performance curves of PAT obtained by experimental and numerical results. As illustrated in
217
Fig.10, the numerically predicted performance curves well reflect the tendency of PAT’s experimental results.
218
Comparing the numerical shaft power with the experimental one, the difference is marginal. The Q-H curve predicted
219
by CFD is positioned below the experimental one. Meanwhile, the efficiency curve obtained by experiment is
220
positioned below the CFD one. The difference between the numerical and experimental results is mainly due to the
221
neglect of the mechanical loss caused by mechanical seals and bearings, the volumetric loss caused by balancing holes
222
and the manufacturing and installation errors which was not taken into account in the simulation.
223
The deviation of predicted efficiency from experimental data is 1.8%~3.6% in the range of 70 m3/h~115 m3/h.
224
Compared with the experimental data, the predicted performance curves by numerical computation have an acceptable
225
accuracy. The good agreement between CFD prediction and experiment results in the present study demonstrates that
226
the grid quality and turbulence model are suitable for the PAT performance prediction. It is reasonable to believe that
227
CFD can be used in the prediction of PAT’s performance.
228
5 Results and analyses
229
Numerical simulations of four special impellers with different blade angles were performed. Table 4 lists their
230
performance parameters at best efficiency points (BEP) and Fig.11 shows the four PATs performance curves obtained
231
by CFD.
232 233 234 235 236 237 238
Table 4
Numerical predicted BEPs of PATs with different blade inlet angles βb1 (°)
Q (m3/h)
H (m)
P (kW)
Η (%)
71
90
33.60
5.79
70.31
90
94.5
35.98
6.53
70.57
111
97
37.54
7.02
70.85
135
105
41.83
8.45
70.67
Comparison of four PATs performance curves, we can find that in the whole operating range, the change tendencies
239
of four PATs performance curves are similar. The PAT flow versus power (Q-P) and flow versus head (Q-H) curves
240
increase in accordance with increasing the flow rate while the flow versus efficiency (Q-η) curve increases with the 12
ACCEPTED MANUSCRIPT 241
increase of the flow rate, reaches maximum at BEP, and then decreases. The blade inlet angles have an obvious
242
influence on the PAT performances. The flow rate, required pressure head, generated shaft power, and efficiency at
243
best-efficiency point (BEP) increased with increasing the blade inlet angle. The flow rates of four PATs at BEP are
244
about 90, 94.5, 97 and 105 m3/h, respectively, as inlet angle varied from 71 to 90 and 111 then 135 degree.
245 246
Fig.11
Performance curves of four PATs with different blade inlet angles
247
The numerical flow rate of best efficiency point (BEP) is very close to the theoretical flow rate, reflecting that the
248
relavant numerical method is rather credible. Based on this, the flow rate of BEP increases with extending the blade
249
inlet angles. That is, smaller angle matches with relatively lower flow rate of BEP while bigger angle with higher flow
250
rate. Moreover, the deep analyses of the pressure head, generated shaft power, and efficiency with the change of flow
251
rate are presented in section 5.1 and 5.2.
252
5.1 Head and Shaft Power
253
While the fluid is no-swirling outflow at the rated flow rate, the outlet circumferential component of velocity
254
becomes zero (vu2=0). At this condition, the Euler equation can be given as:
255
He
g
vu 1 r1
g
k
g
k1Qr .
(12)
256
The theoretical head, He increases with increasing the rated flow rate Qr given in Table 2.
257
The head required by PAT can be represented as: 13
ACCEPTED MANUSCRIPT 258
H H e h ,
259
where △h (m) is the total hydraulic loss within PAT.
(13)
260
Figure 12 shows the total hydraulic loss in PATs which increases with the increase of the flow rate. The loss
261
increases with increasing the blade inlet angle at flow rate lower than 110 m3/h while decreases after higher than 110
262
m3/h which results in different four H-Q curves (as shown in Fig.11).
263 264 265
Fig.12
Total hydraulic loss in four PATs with different blade inlet angles
The output shaft power can be represented as:
266
P gQH e Pv Pm ,
267
where Pv is the volumetric loss power (kW), Pm is the mechanical loss power (kW).
(14)
268
As the four PATs have the same dimensions and structures except for the blade inlet and outlet angles, we treat Pv
269
and Pm as the same value at the same flow rate. And the theoretical head of PAT has the same value at the same flow
270
rate. Therefore, it results the four Q-P curves are almost overlapped, as shown in Fig.11.
271
5.2 Efficiency
272 273
The efficiency relies on the ratio of output power to input power which can be expressed as:
P
gQH
100% .
(15)
274
As shown in Fig.11, the PAT efficiency increases with the increase of flow rate, reaches maximum at BEP, and
275
then decreases. At above 110 m3/h flow rate, the PAT efficiency increases with increasing blade inlet angle. When flow 14
ACCEPTED MANUSCRIPT 276
is not along with blade spine at impeller inlet, the incidence loss will increase which leads to efficency decreasing. The
277
inlet flow angle is less than blade inlet angle at operating flow rate lower than the rated flow rate while the inlet flow
278
angle greater at higher flow rate. The off-design is further, the more hydraulic loss. Comparing the four efficiency
279
curves, the efficiency of impeller with 135 degree inlet angle is significantly lower than the other three impellers from
280
lower flow rate to BEP which is caused by further off-design condition. For the same reason, the impeller with 71
281
degree inlet angle has mostly unfavorable performance at higher flow rate. In addition, the 71 degree impeller is
282
observed to have the lowest maximum efficiency among the four impellers. However, the common range of the blade
283
outlet angle of a centrifugal pump impeller is usually from 22 degree to 30 degree. As shown in Fig.13, the blade inlet
284
angle of original pump impeller is only 25 degree, so the efficiency of original PAT is dramatically lower than the
285
special impeller with forward curved blades. And this conclusion can been proved by published experimental results
286
for the validation. We choose pumps with the similar specific speeds to compare the efficiency of special impeller with
287
the turbine mode performance of other pumps published results available. Table 5 lists the PAT experimental BEP
288
efficiency and comparisons with the published data. It is shown that the special impeller is more efficient in these
289
pumps even though the specific speed of pump with special impeller is the lowest among the five cases.
290 291 292
Fig.13
3D model of original pump impeller
Table 5 PATs experimental BEPs efficiencies and comparisons with the published data Original pump specific speed ns (r/min)
Impeller
η (%)
18.1
Special impeller
67.91
18.1[Yang et al. 9]
Original impeller
59.98
19.9[Doshi et al. 19]
Original impeller
63.4
19.9[Doshi et al. 19]
Rounded impeller
64.5
20.6[Yang et al. 10]
Original impeller
62.53 15
ACCEPTED MANUSCRIPT 293 294
In order to compare the high-efficiency operating range, we carried out the experiments of original impeller and special impeller in the same test rig. The experimental performance curves of two impellers are shown in Fig14.
295 296
Fig.14
Experimental performance curves of two impellers
297
Comparing the two PAT performance curves obtained by experiment, the Q-P curve of special impeller is positioned
298
above the original one which means that the special impeller can output more shaft power than the original one at the
299
same flow rate. At the same time, the required pressure head of special impeller is higher than that of the original
300
impeller below the 105 m3/h flow rate range. The Q-η curve of special impeller is also positioned above the original
301
one in the whole working range. Compared the two Q-η curves, the efficiency curve of PAT with the special impeller
302
is more flat than that of the original one. The efficiency variation of PAT with forward curved blades is only within
303
1.5% between 0.9QBEP and 1.2QBEP operating range. Therefore, the high-efficiency operating range of the special
304
impeller with forward-curved blades is wider than that of the conventional forward-curved impeller. Moreover, the
305
flow rates of BEPs of two PATs are 81.64 m3/h and 95.24 m3/h, and the maximum efficiencies are 59.98% and
306
67.91%, respectively, which reflects that the forward-curve impeller in the PAT has obvious superiority.
307
5.3 The Turbulence Kinetic Energy Distribution
308
The turbulence kinetic energy is a criterion of the turbulence intensity, which is related to energy loss within fluid
309
domain. The larger the turbulence kinetic energy is, the more the energy loss becomes. The turbulence kinetic energy
310
distribution of blade to blade surface at impeller inlet is non-uniform circumferentially because the spiral volute is
311
unsymmetrical structure as shown in Fig.15 and Fig.16. 16
ACCEPTED MANUSCRIPT
Turbulence
312
kinetic
energy
[m2s-2]
Ⅲ
a)
Ⅲ
b)
Ⅳ
Ⅳ
Ⅱ
Ⅱ
Ⅰ
Volute tongue
Ⅴ
Ⅴ
Ⅰ
313
Ⅲ
c)
Ⅲ
d)
Ⅳ
Ⅳ
Ⅱ
Ⅱ
Ⅰ
Ⅴ
Ⅰ
Ⅴ
314 315 316
Fig.15
Turbulence kinetic energy distribution of blade to blade surface within impellers with different inlet angles at Q=90m3/h: (a) βb1=71°, (b) βb1=90°, (c) βb1=111°, and (d) βb1=135°
317
Figure 15 shows the turbulence kinetic energy distribution of blade to blade surface within impellers with different
318
inlet angle at 90 m3/h flow rate. The rotational direction of PAT impeller is clockwise, and the position of the volute
319
tongue is depicted in Fig. 15 (a). The blade inlet angles have an obvious influence on the turbulence kinetic energy in
320
the blade inlet zones. The turbulence kinetic energy increases with the increase of the blade inlet angles. Comparing the
321
Fig.15(d) with Fig.15(a), when the blade inlet angle is equal to 135°, the turbulence kinetic energy in blade inlet zones
322
increases significantly. Turbulent kinetic energy mainly comes from the mean-flow and the turbulence is supplied 17
ACCEPTED MANUSCRIPT 323
energy by Reynolds shear stress working. Therefore, the energy loss in βb1=135° impeller inlet is larger than that in
324
βb1=71°, which leads to the efficiency of the former is less than the later at Q=90m3/h, as shown in the performance
325
curves (Fig.11).
Turbulence
326
kinetic
energy
[m2s-2] a)
b)
Volute tongue 327
c)
d)
328 329 330
Fig.16
Turbulence kinetic energy distribution of blade to blade surface within impellers with different inlet angles at Q=120 m3/h: (a) βb1=71°, (b) βb1=90°, (c) βb1=111°, and (d) βb1=135°
331
Figure 16 shows the turbulence kinetic energy distribution of blade to blade surface within impellers with different
332
inlet angle at 120 m3/h flow rate. With the increase of the flow rate from 90 m3/h to 120 m3/h, the value of turbulence
333
kinetic energy at impeller inlet increases obviously. Comparing the turbulence kinetic energy distribution in Fig.16 18
ACCEPTED MANUSCRIPT 334
with Fig.15, in contrast to Q=90 m3/h, at Q=120 m3/h operating condition, the turbulence kinetic energy decreases with
335
the increase of the blade inlet angles. The blade inlet angle varies from 71° to 90°, 110° and 135°, the turbulence
336
kinetic energy of blade inlet decreases gradually. The turbulence kinetic energy in Fig.16(a) is quite obviously higher
337
than that in Fig.16(d), which means that the energy loss in βb1=71° impeller inlet is larger than that in βb1=135°. The
338
results can further be explained by the velocity triangle change with flow rate at impeller inlet, as shown in Fig.17.
339 340 341 342
Fig.17 Velocity triangle change with flow rate at impeller inlet
When the flow rate increases, the approach meridional component vm1 grows to v＇ m1 and the circumferential velocity component vu1 grows to v＇ u1so that the approach flow relative angle increases from β1 to β＇ 1.
343
If PAT flow rate is not equal to the rated flow rate, the flow angle is not equal the blade angle (β1≠βb1). The
344
difference between blade angle βb1 and flow angle β1 is known as incidence angle Δβ. The more the flow rate deviates
345
from the rated rate, the bigger incidence angle and the more turbulence kinetic energy at the impeller inlet. As shown in
346
Fig.15 and Fig.16, the energy loss within impeller of βb1=135° is more than that within the other three impellers at the
347
flow rate of 90 m3/h while the loss is least in the four impellers at 120 m3/h flow rate operating condition.
348
These results are well consistent with the performance curve analysis. It indicates that the energy loss within
349
impeller reaches the minimum when the rated flow rate matches suitable inlet angle. Smaller angle matches with
350
relatively lower rated flow rate while bigger angle with higher rated flow rate.
351
5.4 Recommendation
352
Table 4 shows that the predicted flow rates of BEPs by CFD are all very close to the rated flow rates given in table 2.
353
It indicates that the theoretical calculating method of blade inlet angle and the design method of special impeller are
354
reasonable. The maximum efficiency of the impeller with βb1=90° is similar to that with βb1=111°. And the high 19
ACCEPTED MANUSCRIPT 355
efficiency operating range of the two impellers is wider than that of the other two. The efficiency of the two PATs
356
maintains more than 70% at the flow rates varying from 90 m3/h to 110 m3/h, thus the two efficiency curves are more
357
flat. Therefore, blade inlet angle is recommended in a range of 70 degree and 135 degree when the spiral volute of this
358
low specific speed pump is used as turbine flume.
359
6 Conclusions
360
In this paper, in order to improve greatly the efficiency of the PAT, the blade inlet angle of one typical PAT with
361
forward-curve impeller was theoretically and numerically investigated deeply, and the conclusions can be obtained as
362
follows:
363
(1) The relationship formula between the volute constant, wrapping angle and geometric dimension of volute inlet are
364
obtained. Moreover, the velocity moment at the impeller inlet is also deduced based on the angular momentum
365
conservation. And then, the blade inlet angle and blade out angle are gained for the impeller with the non-impingement
366
velocity inlet and normal velocity outlet. Finally, a kind of special impeller with forward-curved blades is succefully
367
desigened for the PAT.
368
(2) The numerical flow rate of best efficiency point (BEP) is very close to the theoretical flow rate, reflecting that the
369
relavant numerical method is rather credible. Based on this, the flow rate of BEP increases with extending the blade
370
inlet angles. That is, smaller angle matches with relatively lower flow rate of BEP while bigger angle with higher flow
371
rate. The performance of PAT is better and the high efficiency range is wider when the blade inlet angle is designed in
372
a reasonable range.
373
(3) Compared with the performance curve of the original PAT with the backward-curve impeller, the efficiency curve
374
of PAT with the forward-curve impeller is more flat, showing that the high-efficiency operating range of the forward-
375
curve impeller is wider than that of the conventional backward-curve impeller. Moreover, the flow rates of BEPs of
376
two PATs are 81.64 m3/h and 95.24 m3/h, and the maximum efficiencies are 59.98% and 67.91%, respectively, which 20
ACCEPTED MANUSCRIPT 377
reflects that the forward-curve impeller in the PAT has obvious superiority.
378
Appendix. Experimental Uncertainty Analysis
379
Table 6 lists the instrumentation and their accuracy. Table 7 presents the measurement uncertainties at BEP of
380
special impeller for PAT test rig.
381
Table 6
Instrumentation and their accuracy
Test instrumentation
Make
Range
Turbine flow meter of LWGYB-100
Beijing flow meter factory
20-200
Pressure sensor1 of WT2000GP7S (Inlet pressure)
Welltech
0-1.0 MPa
±0.1%
Pressure sensor2 of WT2000GP6S (Outlet pressure)
Welltech
-300-300 kPa
±0.1%
Electric eddy current dynamometer of CWF25D
Zhongcheng Test Equipment
0-120 Nm
±0.4Nm
0-10,000 rpm
±1 rpm
Speed sensor
382
Table 7
△n
△n/n
Q
△Q
△Q/Q
H
△H
△H/H
T
△T
△T/T
(%)
(m3/h)
(m3/h)
(%)
(m)
(m)
(%)
(Nm)
(Nm)
(%)
1500
±1
±0.07
95.24
±0.48
±0.5
38.32
±0.27
±0.72
42.97
±0.4
±0.93
The pressure head of the turbine is calculated from Eq. (16). △Z is zero because the pressure transmitters are put on
H
389
390 391
Torque
rpm
385
388
Head
n
one plane.
387
discharge
rpm
384
386
±0.5%
Measurement uncertainties at BEP of special impeller for PAT test rig
speed
383
Accuracy m3/h
p1 p2
z
g
v12 v22 100% 2g
(16)
The uncertainty in pressure head is determined from
H / H
(p1 / p ) 2 (p2 / p ) 2 (Q1 / Q) 2 (Q2 / Q) 2 100% 0.72%
(17)
The PAT efficiency is calculated from
T
gQH
100%
(18)
The uncertainty in turbine efficiency is determined from
/
(
n 2 Q 2 H 2 T 2 ) ( ) ( ) ( ) 100% 1.28% n Q H T
(19)
21
ACCEPTED MANUSCRIPT 392
Acknowledgments
393
This work was supported by the Natural Science Foundation of China (grant numbers 51609105, 51379179,
394
51279172, and 11602097), Postgraduate Innovation Foundation of Jiangsu Province of China (grant number
395
CXZZ13_0678), the Open Research Fund of Key Laboratory of Xihua University (grant numbers szjj2015-029, and
396
szjj2016-061), and Sichuan Provincial Department of Education(grant number 16ZB0157).
397
Nomenclature
398 399 400 401 402 403 404 405 406 407 408 409 410 411
H = head (m)
412 413
kW = Kilowatt
414
Abbreviations
415 416 417
PAT = pump as turbine
418
Greek symbols
419 420 421 422 423
η
efficiency
ρ
density (kg/m3)
α
absolute flow angle (deg)
β
relative flow angle (deg)
ψ
blockage coefficient
424
Subscripts
425 426
1
high pressure side
2
low pressure side
D = diameter (m) g = acceleration due to gravity (m/s2) n = rotational speed (r/min) ω = rotational speed (rad/s) v = velocity (m/s) vu = circumferential component of absolute velocity (m/s) vr = radial component of absolute velocity (m/s) vm = meridional velocity component (m/s) w = relative velocity (m/s) u = peripheral velocity (m/s) Q =the flow rate (m3/s) ns = specific speed (r/min) ns =n·Q0.5·H-0.75 (where n is in r/min, Q in m3/s and H in m) P = power (W, kW)
BEP =at best efficiency point CFD = computational fluid dynamics
22
ACCEPTED MANUSCRIPT 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469
References [1] Wang C, Shi W, Wang X, et al. Optimal design of multistage centrifugal pump based on the combined energy loss model and computational fluid dynamics[J]. Appl Enegy 2017;187:10-26. [2] Su XH, Huang S, Zhang XJ, Yang SS. Numerical research on unsteady flow rate characteristics of pump as turbine. Renew Energy 2016;94(8): 488-495. [3] Jain S, Patel R. Investigations on pump running in turbine mode: a review of the state-of-the-art. Renew Sustain Energy Rev 2014;30:841-68. [4] Arriaga M. Pump as turbine-A pico-hydro alternative in Lao People‘s Democratic Republic. Renew Energy 2010;35:110915. [5] Singh P, Nestman F. An Optimization Routine on a Prediction and Selection Model for the Turbine Operation of Centrifugal Pumps. Exp Therm Fluid Sci 2010;34(2):152–164. [6] Giosion DR, Henderson AD, Walker JM. Brandner PA, Sargison JE. Gautam P. Design and performance evaluation of a pump-as-turbine micro-hydro test facility with incorporated inlet flow control. Renew Energy 2015;78:1-6. [7] Derakhshan S, Nourbakhsh A. Experimental Study of Characteristic Curves of Centrifugal Pumps Working as Turbines in Different Specific Speeds. Exp Therm Fluid Sci. 2008;32(3): 800–807. [8] Bozorgi A, Riasi E, Nourbakhsh A. Numerical and experimental study of using axial pump as turbine in Pico hydropower plants. Renew Energy 2013;53:258-64. [9] Yang SS, Derakhshan S, Kong FY. Theoretical, numerical and experimental prediction of pump as turbine performance. Renew Energy 2012;48:507-13. [10] Yang SS, Liu HL, Kong FY, et al. Experimental, numerical, and theoretical research on impeller diameter influencing centrifugal pump-as-turbine[J]. J Energ Eng 2013;139:299-307. [11] Pugliese F, Paola F D, Fontana N, et al. Experimental characterization of two Pumps As Turbines for hydropower generation[J]. Renew Energy 2016;99:180-187. [12] Xu T, Engeda A. Performance of centrifugal pumps running in reverse as turbine: Part Ⅱ- systematic specific speed and specific diameter based performance prediction[J]. Renew Energy 2016;99:188-197. [13] Fecarotta O, Carravetta A, Ramos H M, et al. An improved affinity model to enhance variable operating strategy for pumps used as turbines[J]. J Hydraul Res 2016;(3):1-10. [14] Barbarelli S, Amelio M, Florio G. Predictive model estimating the performances of centrifugal pumps used as turbines[J]. Energy 2016;107:103-121. [15] Derakhshan S, Mohammadi B. The comparison of incomplete sensitivities and genetic algorithms applications in 3D radial turbo machinery blade optimization. Comput Fluid 2010;39( 10) :2022-29． [16] Derakhshan S, Kasaeian N. Optimization, Numerical, and Experimental Study of a Propeller Pumps Turbine. ASME J Energ Resour 2014;136(1): 012005-1-7. [17] Singh P, Nestmann F. Internal hydraulic analysis of impeller rounding in centrifugal pumps as turbines. Exp Therm Fluid Sci 2011;35:121-34. [18] Derakhshan S, Nourbakhsh A, Mohammadi B. Efficiency improvement of centrifugal reverse pumps. ASME J Fluids Eng 2009;131:21103-9. [19] Doshi A, Channiwala S, Singh P. Inlet impeller rounding in pumps as turbines: An experimental study to investigate the relative effects of blade and shroud rounding[J]. Exp Therm Fluid Sci 2017; 82:333-348. [20] Qian Z, Wang F, Guo Z, et al. Performance evaluation of an axial-flow pump with adjustable guide vanes in turbine mode[J]. Renew Energy 2016;99: 1146-1152. [21] Wang T, Kong FY, Yuan SQ, Yang SS, et al. Design and experiment on pump as turbine with forward curved blades[J]. Transactions of the Chinese Society for Agricultural Machinery 2014;45(12): 75-79.
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[22] Wang T, Kong FY., Yang SS, et al. Numerical study on hydraulic performances of pump as turbine with forward-curved blades[C]. Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting, 2014;FEDSM 2014-21347.
24
Tao Wang, Fanyu Kong, Bin Xia, Yuxing Bai, Chuan Wang PII:
S0960-1481(17)30245-8
DOI:
10.1016/j.renene.2017.03.054
Reference:
RENE 8647
To appear in:
Renewable Energy
Received Date:
13 October 2016
Revised Date:
23 January 2017
Accepted Date:
18 March 2017
Please cite this article as: Tao Wang, Fanyu Kong, Bin Xia, Yuxing Bai, Chuan Wang, The method for determining blade inlet angle of special impeller using in turbine mode of centrifugal pump as turbine, Renewable Energy (2017), doi: 10.1016/j.renene.2017.03.054
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.
ACCEPTED MANUSCRIPT Highlights:
The innovative impeller with the forward-curve blade is designed.
The forward-curve impeller in the PAT has obvious superiority
The calculation equation of critical flow is deduced.
The value of blade inlet angle is recommended in a reasonable range in PAT.
ACCEPTED MANUSCRIPT 1
The method for determining blade inlet angle of special impeller using in
2
turbine mode of centrifugal pump as turbine
3
Tao Wanga*, Fanyu Kongb, Bin Xiab, Yuxing Baib and Chuan Wanga, b*
4 5
a Key
Laboratory of Fluid and Power Machinery, Ministry of Education, School of Energy and Power
6 7 8 9 10
Engineering , Xihua University, Chengdu, Sichuan 610039, China b
Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang, Jiangsu 212013, China * Corresponding
author:
E-mail address: [email protected] (T. Wang) and [email protected] (C. Wang)
11 12
Abstract: Due to that the conventional backward-curve centrifugal impellers do not effectively match the turbine’s
13
running, the performance of the pump-as-turbine (PAT) was usually not ideal. Therefore, to improve significantly the
14
performance of PAT, one kind of special impeller with forward-curved blades was desigened for the turbine’s working
15
condition, and the method for determining blade inlet angle that played important role in the energy conversion was
16
also stduied deeply in this paper. Moreover, four forward-curve impellers with different blade inlet angles were
17
numerically investigated by using a verified computational fluid dynamics (CFD) technique, and relevant external
18
characteristic experiments were also conducted to benchmark the numerical calculation. Based on the results, the flow
19
rate of numerical best efficiency point (BEP) is very close to that of theoretical BEP, and the flow rate of BEP
20
increases with extending the blade inlet angles. Additionally, the energy loss within the impeller reaches the minimum
21
if suitable blade inlet angle is selected, so the value of blade inlet angle is recommended in a reasonable range in
22
special impeller used in turbine mode of PAT. Furthermore, compared with the original backward-curve impeller, the
23
maximum efficiency of the forward-curve impeller increases from 59.98% to 67.91%, and the flow-efficiency curve is
24
more flat, which reflects that the forward-curve impeller in the PAT has obvious superiority. This paper is very
25
instructive to the design of the special impeller using in the PAT. 1
ACCEPTED MANUSCRIPT 26
Keywords: Pump as turbine, CFD, Blade inlet angle, Forward-curved blades.
27
1 Introduction
28
With the development of the social economy, there is an increasing demand for the energy, while energy shortage is
29
becoming the remarkable restriction of the development [1-6]. The use of renewable energy and new energy is of great
30
significance to solve the energy shortage. Moreover, liquid-pressure-energy (LPE) is a kind of clean renewable energy,
31
and the utilization of small power LPE is one of the energy’s development directions in future. Pumps are a kind of
32
reversible rotating machinery, which can be reversely used and called pump as turbine (PAT) [7-10]. Compared with
33
other small power LPE, PAT has the advantages of small size, low cost, simple maintenance and wide applications.
34
Over the last several years, considerable efforts have been made in the PAT performance prediction, optimization
35
and performance improvement through using theoretical, experimental and numerical methods. Pugliese et al. [11]
36
tried to assess the performance of pumps operating in reverse model, and two centrifugal pumps such as a centrifugal
37
horizontal single-stage pump and a vertical multi-stage pump were investigated by some experiments. Tan et al. [12]
38
presented a comprehensive correlation aimed to bring out the accurate prediction of the turbine model operations of
39
centrifugal pumps, and used experimental data of wide range of pumps representing the centrifugal pump
40
configurations in terms of specific speed. Fecarotta et al. [13] presented the reliability of the affinity law to predict the
41
behavior of a PAT under various speeds, and found that the difference between the theoretical model and the
42
experimental results was significant. Barbarelli et al. [14] put forward to the predictive model estimating the
43
performances of centrifugal pumps used as turbines, and obtained that the estimation error was much small and
44
acceptable for this kind of application. Derakhshan et al. [15–16] redesigned the blade shapes by gradient-based
45
optimization technique to gain higher efficiency. Singh et al [17] and Derakhshan et al [18] provided a number of
46
simple modifications, such as blade/hub/shroud rounding and the impeller tip to improve the performance of PAT.
47
Doshi et al. [19] made an experimental study to investigate the relative effects of blade and shroud rounding for the 2
ACCEPTED MANUSCRIPT 48
inlet impeller round in PAT. Qian et al. [20] studied an axial-flow pump in both pump and turbine modes, and found
49
that the adjustable guide vane provided a cost-effective solution to considerably improve the efficiency of the PAT
50
under partial loading. In summary, most previous studies focus on the overall performance prediction of the PAT by
51
using various methods, which reflecting that the relevant prediction methods are rather credible, while a small number
52
of studies concentrate on the performance improvement of the PAT through optimizing the blade, rounding the
53
impeller and adjusting the suitable guide vane. Few scholars tried to design the special impeller to improve the
54
efficiency of the PAT.
55
Single-stage centrifugal pump is mostly equipped with the spiral volute. Because of space size restriction, there
56
are usually no adjustable guide vanes, which leads to fluid directly flowing into impeller inlet from volute outlet when
57
pump operates in turbine mode. Furthermore, the blade inlet and outlet angles of original impeller designed for pump
58
working condition, not for turbine mode; do not match well with turbine running condition. Thus the turbine mode of
59
PAT efficiency is universally not high and the high efficiency range is usually narrow when pump reversely operates as
60
turbine directly. A convenient suitable way of solving this problem is to redesign the blade for turbine working
61
condition while the other components do not undergo any modifications. Unfortunately, little work is available about
62
PAT special impeller with forward curved blades before. And the blade inlet and outlet angles are two important
63
factors which directly determine the fluid flow characteristics. Especially blade inlet angle plays a decisive role in
64
energy conversion. Therefore, it is significant to research how to determine the blade inlet angle of special impeller and
65
how the blade inlet angle influences the performance of PAT.
66
In this paper, a PAT special impeller with forward curved blades was designed to improve PAT efficiency.
67
Based on the comparison of experimental data between original and special impellers, the results show that the best
68
efficiency is increased by 7.93 percentage points and the special impeller can better satisfy the turbine operating
69
conditions. Then, blade inlet angles of four different blades are calculated at corresponding rated flow rates
70
respectively. The performances of four PATs are analyzed respectively based on CFD results, whose accuracy can be 3
ACCEPTED MANUSCRIPT 71
validated through an open test rig established in Jiangsu University. At last, the reasonable range of blade inlet angle is
72
recommended.
73
2 Design method of forward curved blade using in PAT
74
2.1 Volute Outflow
75
When a centrifugal pump reverses as a turbine, the rotational direction is reverse and volute is used as flume of
76
turbine mode. In order to calculate the velocity moment before impeller inlet, the fluid flow laws in volute should be
77
investigated. The spiral volute cross sections are mainly designed in accordance with the theorem of angular
78
momentum conservation. Namely, fluid is idealized and flow movement is assumed to axisymmetric potential flow.
79
The flow movement in spiral volute satisfies vur=k, as shown in Fig.1.
80 81 82 83 84 85
Fig.1
Notes: v is the absolute velocity in volute, m·s-1; vu is the circumferential component of absolute velocity, m·s-1; vm is the meridional component of absolute velocity, m·s-1; δ is flow angle of volute, （°）; a0 is distance from the first cross section center of spiral volute to the PAT axis, m; ρ0 is first cross section radius of spiral volute, m; φ0 is wrap angle of volute, （°）.
The velocity moment in volute can be expressed as [21]:
Qr
0
86
k
87
where Qr is the rated flow rate，(m3/s).
88
Water flow movement in spiral volute
2(a0 a ) 360 2 0
2 0
,
(1)
We assume that
4
ACCEPTED MANUSCRIPT k1 89
0 720( a0 a02 02 )
90
Then,
91
k k1Qr
92 93 94
(2)
.
(3)
The object of study in this case is a single stage centrifugal PAT with pump specific speed ns=18.1. Table 1 lists the main parameters of original pump. Table 1 Main parameters of original pump as turbine Name
Impeller
Volute
95 96
.
Parameters
Value
Impeller inlet diameter D1 (mm)
235
Impeller outlet diameter D2 (mm)
102
Impeller hub diameter Dh (mm)
30
Length of wear ring L (mm)
15
Impeller inlet width b1 (mm)
15.14
Blade number Z
6
Volute wrap angle, φ0 (deg)
345
The distance from the center of inlet cross section to PAT axis, a0 (mm)
163.5
The radius of inlet cross section of volute, ρ0 (mm)
24.5
Volute cross section shape
round
According to geometric parameters of original pump, the volute constant can be calculated, k=82.6216Qr. 2.2 Blade Inlet Angle
97
In this paper, the velocity moment at impeller inlet vu1r1 is equal to k which is proportional to the rated flow rate Qr,
98
when the energy conversion between volute outlet and impeller inlet is neglected at the rated flow rate condition. Thus
99
inlet velocity triangle will show three different shapes under corresponding rated flow rates. As shown in Fig.2, inlet
100
relative flow angle β1 is related to rated flow rates.
101 102
(a)
103
Fig.2
(b)
(c)
Inlet velocity triangles at different rated flow rates: (a) β1>90°, (b) β1=90°, and (c) β1<90°
104
Notes: v1 is inlet absolute velocity, m·s-1; u1 is inlet circumferential velocity, m·s-1; vu1 is circumferential velocity component of
105
inlet absolute velocity, m·s-1; vm1 is meridional velocity component of inlet absolute velocity, m·s-1; w1 is inlet relative velocity, m·s-
106
1;
β1 is relative flow angle at blade inlet, (°); α1 is absolute flow angle at blade inlet, (°). 5
ACCEPTED MANUSCRIPT 107
108 109 110
When impeller diameter and rotational speed are constant, inlet rotational speed, u1, is constant:
u1
D1 n 60
.
The circumferential velocity componet at impeller inlet can be calculated as:
vu1
2k
.
D1
(5)
111
Let k k1Q .
112
Then
113
u1 vu 1
114
(4)
n D1 60
2k D1
n D1 120 k1Q 2
60 D1
.
(6)
When vu1= u1, the critical flow rate, Qc, in accordance with β1=90° can be deduced as:
n D1
2
115
Qc
120 k1
.
(7)
116
As shown in Fig. 2(b), if the rated flow rate is equal to the critical flow rate (Qr=Qc), vu1=u1. In other situations, the
117
circumferential component, vu1, increases with increasing flow rate Q. Inlet relative flow angle, β1, also increases with
118
increase of vu1 while inlet rotational speed u1 is invariable. Fig. 2(a) shows β1>90° with Qr>Qc. Whereas, with the
119
decrease of rated flow rate, β1<90°with u1>vu1, simultaneously, as shown in Fig.2(c).
120 121
In this paper, critical flow rate, Qc=94.5 m3/h, can be obtained under present parameters, D1=0.235 m, n=1500 rpm, and k1=82.6216.
122
In order to study the influences of blade inlet angle on performance of PAT with forward curved blades, four blade
123
inlet angles corresponding to four different rated flow rates (90 m3/h , 94.5 m3/h, 100 m3/h, and 110 m3/h) including the
124
critical flow rate are investigated in this paper.
125
The meridional velocity component, vm1, at impeller inlet can be calculated as:
Qr
126
vm 1
127
where b1 is width of impeller inlet (m), ψ1 is blade inlet blockage coefficient, which can be expressed as:
D1b1 1
,
(8)
6
ACCEPTED MANUSCRIPT su 1 Z
128
1 1
129
where su1 is the circumferential thickness of blade leading edge (m).
D1
,
(9)
130
The corresponding inlet triangles at different rated flow rates and inlet relative flow angles β1 can be obtained, under
131
the present parameters, b1=16 mm, Z=11 and ψ1≈0.85. The inlet angle is equal to inlet flow angle (βb1=β1) under the
132
assumption that there is no incidence loss at rated flow rate condition. Table 2 lists four blade inlet angles (βb1) at four
133
different rated flow rates (Qr).
134
135 136 137
138 139 140 141 142 143 144
145
Table 2
Blade inlet angles at four rated flow rates Qr (m3/h)
βb1 (°)
90
71
94.5
90
100
111
110
135
2.3 Blade Outlet Angle When the fluid out of impeller is non-swirling flow, outlet rotational speed u2 is orthogonal to v2 and the outlet absolute flow angle is equal to 90 degree, as shown in Fig.3.
Fig.3 Notes: v2 is outlet absolute velocity,
m·s-1;
Outlet velocity triangle at blade trailing edge u2 is outlet circumferential velocity, m·s-1; vm2 is meridional velocity component of
outlet absolute velocity, m·s-1; w2 is outlet relative velocity, m·s-1; β2 is outlet relative flow angle, (°); α2 is outlet absolute flow angle, (°).
The outlet flow angle, β2, is deduced as:
2 ac tan
vm 2 u2
.
The outlet meridional component, vm2, is calculated as:
Qr
146
vm 2
147
where A2 is actual area of outlet flow cross section (m2).
148
(10)
A2
,
(11)
Due to relatively small diameter and relatively excessive blade numbers of special impeller, fluid basically follows 7
ACCEPTED MANUSCRIPT 149
along blade surfaces out of impeller. Therefore, the blade outlet angle can be assumed to be equal to outlet flow angle
150
(βb2=β2). Table 3 lists the blade outlet angle βb2 at different rated flow rates Qr.
151
152
Table 3
Blade outlet angles at four rated flow rates Qr (m3/h)
βb2 (°)
90
36
94.5
39
100
37
110
41
2.4 Impeller model
153
According to four sets of blade angles, four special impellers with forward curved blades were designed using
154
ANSYS BladeGen software. The blade wrap angle at middle streamline is determined as 42.7°. The dimensions of
155
impeller inlet diameter, outlet diameter, impeller hub diameter and length of wear ring are all as same as those of
156
original pump. The blade thickness is 5mm at leading edge while 2mm at trailing edge. The radius of rounding is half
157
of blade thickness at blade inlet and outlet respectively. The 3D models of blades with different inlet angles and special
158
impeller (Qr=94.5 m3/h, βb1=90°) by BladeGen software are shown in Fig.4 and Fig.5 respectively.
159 160 161
Fig.4
3D models of blades with different inlet angles
162 163
Fig.5
Special impeller model (βb1=90°) 8
ACCEPTED MANUSCRIPT 164
3 Numerical investigations
165
ANSYS CFX is a commercial 3D Navier-stokes CFD code that utilizes a finite-element based finite-volume method
166
to discrete the transport equations. It is a fully-implicit solver and also a coupled solver. Thus it creates no time step
167
limitation and is considered easy to implement. And the momentum and continuity equations are solved
168
simultaneously. This approach reduces the number of iterations required to obtain convergence and no pressure
169
correction term is required to retain mass conversion, leading to a more robust and accurate solver. In this case,
170
ANSYS CFX was used to simulate the flow within the PAT.
171
3.1 Numerical model
172
The whole computational domain consists of the following five parts, as shown in Fig.6: volute, impeller, front
173
chamber, back chamber and draft tube. In order to get a relatively stable inlet and outlet flow, the volute inlet and draft
174
tube outlet section have been extended by four times of the pipe diameter.
175 176
Fig.6
Numerical model of PAT
177 178
3.2 Mesh generation
179
Structured hexahedral grids for each component part were generated in ICEM CFD. Fluid domains were divided into
180
several blocks and the correlation was established between the geometry and blocks, the hexahedral grids were finally
181
realized. Fig.7 shows the total grids of the computational domains. In viscous layer, especially blade surface, the
182
leading edges, trailing edges, shroud surface, hub surface, volute tongue and volute inner surface, the near-wall grids 9
ACCEPTED MANUSCRIPT 183
were densified to ensure that the value of y+ near boundary wall is around 40. The independence of the numerical
184
performance predictions from grid number was performed as depicted in Fig.8. Both turbine head and torque increased
185
with the increase of grid number while turbine efficiency decreased with the increase of grid number. It was observed
186
that the head, torque and efficiency vary by less than 0.5% when the grid numbers are more than approximately
187
1.2106. Thus the final selected grid numbers of volute, impeller, front chamber, back chamber, draft tube and total
188
elements are 448,110, 429,088, 99,720, 50,400, 192,726, and 1,220,044, respectively.
189 190 191
Fig.7
Computational domain grids of PAT
Fig.8
Grid independence
3.3 Solution parameters
192
Considering the computational accuracy, consuming time and computational stability, the Standard k-ε turbulence
193
model was selected for the simulation [22]. Clear water at 25ºC was chosen as the working fluid. Impeller and volute
194
were set in different coordinate systems with the former in rotating frame and the latter in stationary one. The interface
195
between rotational and stationary components was set to a frozen rotor interface while the interface between two
196
stationary components was set to a general grid interface. All the wall surface roughness within the control volume was
197
set to 50 um similar to the real surface. Convergence criterion was 10-6 for all of the momentum and mass equations.
198
The advection scheme was set to high resolution. The turbulence numerics were set to high resolution. Inlet boundary
199
was set to mass flow rate inlet while outlet boundary was set to static pressure outlet. The PAT performance curves
200
were achieved by changing the mass flow rate.
10
ACCEPTED MANUSCRIPT 201
4 Experimental investigation
202
In order to investigate the performances of PAT and verify the accuracy of CFD results, a complete PAT open-
203
circuit rig was set up and utilized in Jiangsu University, as shown in Fig.9. A feed pump was installed to supply high
204
pressure fluid required for PAT energy recovery. An electric eddy current dynamometer (EECD) was installed to
205
measure and consume energy generated by PAT and to regulate rotational speed of PAT. The inlet and outlet pressures
206
were obtained using pressure transmitters. The flow rate was measured by a turbine flow meter.
207
All the measuring instruments were calibrated before put in use. The standard used in experiments was ISO
208
9906:1999. The required pressure head, shaft power, and efficiency of PAT were obtained after measuring all
209
parameters. The relative uncertainty in experimental measurement of speed, discharge, head, torque, and efficiency is
210
±0.07%, ±0.5%, ±0.72%, ±0.93% and ±1.28% respectively among tested PAT with special impeller at BEP (a detailed
211
description of uncertainties in Appendix).
212 213
214 215
Fig.9
Fig.10
An open PAT test rig established in Jiangsu University
Performance curves of PAT obtained by experimental and numerical results 11
ACCEPTED MANUSCRIPT 216
Figure 10 shows the performance curves of PAT obtained by experimental and numerical results. As illustrated in
217
Fig.10, the numerically predicted performance curves well reflect the tendency of PAT’s experimental results.
218
Comparing the numerical shaft power with the experimental one, the difference is marginal. The Q-H curve predicted
219
by CFD is positioned below the experimental one. Meanwhile, the efficiency curve obtained by experiment is
220
positioned below the CFD one. The difference between the numerical and experimental results is mainly due to the
221
neglect of the mechanical loss caused by mechanical seals and bearings, the volumetric loss caused by balancing holes
222
and the manufacturing and installation errors which was not taken into account in the simulation.
223
The deviation of predicted efficiency from experimental data is 1.8%~3.6% in the range of 70 m3/h~115 m3/h.
224
Compared with the experimental data, the predicted performance curves by numerical computation have an acceptable
225
accuracy. The good agreement between CFD prediction and experiment results in the present study demonstrates that
226
the grid quality and turbulence model are suitable for the PAT performance prediction. It is reasonable to believe that
227
CFD can be used in the prediction of PAT’s performance.
228
5 Results and analyses
229
Numerical simulations of four special impellers with different blade angles were performed. Table 4 lists their
230
performance parameters at best efficiency points (BEP) and Fig.11 shows the four PATs performance curves obtained
231
by CFD.
232 233 234 235 236 237 238
Table 4
Numerical predicted BEPs of PATs with different blade inlet angles βb1 (°)
Q (m3/h)
H (m)
P (kW)
Η (%)
71
90
33.60
5.79
70.31
90
94.5
35.98
6.53
70.57
111
97
37.54
7.02
70.85
135
105
41.83
8.45
70.67
Comparison of four PATs performance curves, we can find that in the whole operating range, the change tendencies
239
of four PATs performance curves are similar. The PAT flow versus power (Q-P) and flow versus head (Q-H) curves
240
increase in accordance with increasing the flow rate while the flow versus efficiency (Q-η) curve increases with the 12
ACCEPTED MANUSCRIPT 241
increase of the flow rate, reaches maximum at BEP, and then decreases. The blade inlet angles have an obvious
242
influence on the PAT performances. The flow rate, required pressure head, generated shaft power, and efficiency at
243
best-efficiency point (BEP) increased with increasing the blade inlet angle. The flow rates of four PATs at BEP are
244
about 90, 94.5, 97 and 105 m3/h, respectively, as inlet angle varied from 71 to 90 and 111 then 135 degree.
245 246
Fig.11
Performance curves of four PATs with different blade inlet angles
247
The numerical flow rate of best efficiency point (BEP) is very close to the theoretical flow rate, reflecting that the
248
relavant numerical method is rather credible. Based on this, the flow rate of BEP increases with extending the blade
249
inlet angles. That is, smaller angle matches with relatively lower flow rate of BEP while bigger angle with higher flow
250
rate. Moreover, the deep analyses of the pressure head, generated shaft power, and efficiency with the change of flow
251
rate are presented in section 5.1 and 5.2.
252
5.1 Head and Shaft Power
253
While the fluid is no-swirling outflow at the rated flow rate, the outlet circumferential component of velocity
254
becomes zero (vu2=0). At this condition, the Euler equation can be given as:
255
He
g
vu 1 r1
g
k
g
k1Qr .
(12)
256
The theoretical head, He increases with increasing the rated flow rate Qr given in Table 2.
257
The head required by PAT can be represented as: 13
ACCEPTED MANUSCRIPT 258
H H e h ,
259
where △h (m) is the total hydraulic loss within PAT.
(13)
260
Figure 12 shows the total hydraulic loss in PATs which increases with the increase of the flow rate. The loss
261
increases with increasing the blade inlet angle at flow rate lower than 110 m3/h while decreases after higher than 110
262
m3/h which results in different four H-Q curves (as shown in Fig.11).
263 264 265
Fig.12
Total hydraulic loss in four PATs with different blade inlet angles
The output shaft power can be represented as:
266
P gQH e Pv Pm ,
267
where Pv is the volumetric loss power (kW), Pm is the mechanical loss power (kW).
(14)
268
As the four PATs have the same dimensions and structures except for the blade inlet and outlet angles, we treat Pv
269
and Pm as the same value at the same flow rate. And the theoretical head of PAT has the same value at the same flow
270
rate. Therefore, it results the four Q-P curves are almost overlapped, as shown in Fig.11.
271
5.2 Efficiency
272 273
The efficiency relies on the ratio of output power to input power which can be expressed as:
P
gQH
100% .
(15)
274
As shown in Fig.11, the PAT efficiency increases with the increase of flow rate, reaches maximum at BEP, and
275
then decreases. At above 110 m3/h flow rate, the PAT efficiency increases with increasing blade inlet angle. When flow 14
ACCEPTED MANUSCRIPT 276
is not along with blade spine at impeller inlet, the incidence loss will increase which leads to efficency decreasing. The
277
inlet flow angle is less than blade inlet angle at operating flow rate lower than the rated flow rate while the inlet flow
278
angle greater at higher flow rate. The off-design is further, the more hydraulic loss. Comparing the four efficiency
279
curves, the efficiency of impeller with 135 degree inlet angle is significantly lower than the other three impellers from
280
lower flow rate to BEP which is caused by further off-design condition. For the same reason, the impeller with 71
281
degree inlet angle has mostly unfavorable performance at higher flow rate. In addition, the 71 degree impeller is
282
observed to have the lowest maximum efficiency among the four impellers. However, the common range of the blade
283
outlet angle of a centrifugal pump impeller is usually from 22 degree to 30 degree. As shown in Fig.13, the blade inlet
284
angle of original pump impeller is only 25 degree, so the efficiency of original PAT is dramatically lower than the
285
special impeller with forward curved blades. And this conclusion can been proved by published experimental results
286
for the validation. We choose pumps with the similar specific speeds to compare the efficiency of special impeller with
287
the turbine mode performance of other pumps published results available. Table 5 lists the PAT experimental BEP
288
efficiency and comparisons with the published data. It is shown that the special impeller is more efficient in these
289
pumps even though the specific speed of pump with special impeller is the lowest among the five cases.
290 291 292
Fig.13
3D model of original pump impeller
Table 5 PATs experimental BEPs efficiencies and comparisons with the published data Original pump specific speed ns (r/min)
Impeller
η (%)
18.1
Special impeller
67.91
18.1[Yang et al. 9]
Original impeller
59.98
19.9[Doshi et al. 19]
Original impeller
63.4
19.9[Doshi et al. 19]
Rounded impeller
64.5
20.6[Yang et al. 10]
Original impeller
62.53 15
ACCEPTED MANUSCRIPT 293 294
In order to compare the high-efficiency operating range, we carried out the experiments of original impeller and special impeller in the same test rig. The experimental performance curves of two impellers are shown in Fig14.
295 296
Fig.14
Experimental performance curves of two impellers
297
Comparing the two PAT performance curves obtained by experiment, the Q-P curve of special impeller is positioned
298
above the original one which means that the special impeller can output more shaft power than the original one at the
299
same flow rate. At the same time, the required pressure head of special impeller is higher than that of the original
300
impeller below the 105 m3/h flow rate range. The Q-η curve of special impeller is also positioned above the original
301
one in the whole working range. Compared the two Q-η curves, the efficiency curve of PAT with the special impeller
302
is more flat than that of the original one. The efficiency variation of PAT with forward curved blades is only within
303
1.5% between 0.9QBEP and 1.2QBEP operating range. Therefore, the high-efficiency operating range of the special
304
impeller with forward-curved blades is wider than that of the conventional forward-curved impeller. Moreover, the
305
flow rates of BEPs of two PATs are 81.64 m3/h and 95.24 m3/h, and the maximum efficiencies are 59.98% and
306
67.91%, respectively, which reflects that the forward-curve impeller in the PAT has obvious superiority.
307
5.3 The Turbulence Kinetic Energy Distribution
308
The turbulence kinetic energy is a criterion of the turbulence intensity, which is related to energy loss within fluid
309
domain. The larger the turbulence kinetic energy is, the more the energy loss becomes. The turbulence kinetic energy
310
distribution of blade to blade surface at impeller inlet is non-uniform circumferentially because the spiral volute is
311
unsymmetrical structure as shown in Fig.15 and Fig.16. 16
ACCEPTED MANUSCRIPT
Turbulence
312
kinetic
energy
[m2s-2]
Ⅲ
a)
Ⅲ
b)
Ⅳ
Ⅳ
Ⅱ
Ⅱ
Ⅰ
Volute tongue
Ⅴ
Ⅴ
Ⅰ
313
Ⅲ
c)
Ⅲ
d)
Ⅳ
Ⅳ
Ⅱ
Ⅱ
Ⅰ
Ⅴ
Ⅰ
Ⅴ
314 315 316
Fig.15
Turbulence kinetic energy distribution of blade to blade surface within impellers with different inlet angles at Q=90m3/h: (a) βb1=71°, (b) βb1=90°, (c) βb1=111°, and (d) βb1=135°
317
Figure 15 shows the turbulence kinetic energy distribution of blade to blade surface within impellers with different
318
inlet angle at 90 m3/h flow rate. The rotational direction of PAT impeller is clockwise, and the position of the volute
319
tongue is depicted in Fig. 15 (a). The blade inlet angles have an obvious influence on the turbulence kinetic energy in
320
the blade inlet zones. The turbulence kinetic energy increases with the increase of the blade inlet angles. Comparing the
321
Fig.15(d) with Fig.15(a), when the blade inlet angle is equal to 135°, the turbulence kinetic energy in blade inlet zones
322
increases significantly. Turbulent kinetic energy mainly comes from the mean-flow and the turbulence is supplied 17
ACCEPTED MANUSCRIPT 323
energy by Reynolds shear stress working. Therefore, the energy loss in βb1=135° impeller inlet is larger than that in
324
βb1=71°, which leads to the efficiency of the former is less than the later at Q=90m3/h, as shown in the performance
325
curves (Fig.11).
Turbulence
326
kinetic
energy
[m2s-2] a)
b)
Volute tongue 327
c)
d)
328 329 330
Fig.16
Turbulence kinetic energy distribution of blade to blade surface within impellers with different inlet angles at Q=120 m3/h: (a) βb1=71°, (b) βb1=90°, (c) βb1=111°, and (d) βb1=135°
331
Figure 16 shows the turbulence kinetic energy distribution of blade to blade surface within impellers with different
332
inlet angle at 120 m3/h flow rate. With the increase of the flow rate from 90 m3/h to 120 m3/h, the value of turbulence
333
kinetic energy at impeller inlet increases obviously. Comparing the turbulence kinetic energy distribution in Fig.16 18
ACCEPTED MANUSCRIPT 334
with Fig.15, in contrast to Q=90 m3/h, at Q=120 m3/h operating condition, the turbulence kinetic energy decreases with
335
the increase of the blade inlet angles. The blade inlet angle varies from 71° to 90°, 110° and 135°, the turbulence
336
kinetic energy of blade inlet decreases gradually. The turbulence kinetic energy in Fig.16(a) is quite obviously higher
337
than that in Fig.16(d), which means that the energy loss in βb1=71° impeller inlet is larger than that in βb1=135°. The
338
results can further be explained by the velocity triangle change with flow rate at impeller inlet, as shown in Fig.17.
339 340 341 342
Fig.17 Velocity triangle change with flow rate at impeller inlet
When the flow rate increases, the approach meridional component vm1 grows to v＇ m1 and the circumferential velocity component vu1 grows to v＇ u1so that the approach flow relative angle increases from β1 to β＇ 1.
343
If PAT flow rate is not equal to the rated flow rate, the flow angle is not equal the blade angle (β1≠βb1). The
344
difference between blade angle βb1 and flow angle β1 is known as incidence angle Δβ. The more the flow rate deviates
345
from the rated rate, the bigger incidence angle and the more turbulence kinetic energy at the impeller inlet. As shown in
346
Fig.15 and Fig.16, the energy loss within impeller of βb1=135° is more than that within the other three impellers at the
347
flow rate of 90 m3/h while the loss is least in the four impellers at 120 m3/h flow rate operating condition.
348
These results are well consistent with the performance curve analysis. It indicates that the energy loss within
349
impeller reaches the minimum when the rated flow rate matches suitable inlet angle. Smaller angle matches with
350
relatively lower rated flow rate while bigger angle with higher rated flow rate.
351
5.4 Recommendation
352
Table 4 shows that the predicted flow rates of BEPs by CFD are all very close to the rated flow rates given in table 2.
353
It indicates that the theoretical calculating method of blade inlet angle and the design method of special impeller are
354
reasonable. The maximum efficiency of the impeller with βb1=90° is similar to that with βb1=111°. And the high 19
ACCEPTED MANUSCRIPT 355
efficiency operating range of the two impellers is wider than that of the other two. The efficiency of the two PATs
356
maintains more than 70% at the flow rates varying from 90 m3/h to 110 m3/h, thus the two efficiency curves are more
357
flat. Therefore, blade inlet angle is recommended in a range of 70 degree and 135 degree when the spiral volute of this
358
low specific speed pump is used as turbine flume.
359
6 Conclusions
360
In this paper, in order to improve greatly the efficiency of the PAT, the blade inlet angle of one typical PAT with
361
forward-curve impeller was theoretically and numerically investigated deeply, and the conclusions can be obtained as
362
follows:
363
(1) The relationship formula between the volute constant, wrapping angle and geometric dimension of volute inlet are
364
obtained. Moreover, the velocity moment at the impeller inlet is also deduced based on the angular momentum
365
conservation. And then, the blade inlet angle and blade out angle are gained for the impeller with the non-impingement
366
velocity inlet and normal velocity outlet. Finally, a kind of special impeller with forward-curved blades is succefully
367
desigened for the PAT.
368
(2) The numerical flow rate of best efficiency point (BEP) is very close to the theoretical flow rate, reflecting that the
369
relavant numerical method is rather credible. Based on this, the flow rate of BEP increases with extending the blade
370
inlet angles. That is, smaller angle matches with relatively lower flow rate of BEP while bigger angle with higher flow
371
rate. The performance of PAT is better and the high efficiency range is wider when the blade inlet angle is designed in
372
a reasonable range.
373
(3) Compared with the performance curve of the original PAT with the backward-curve impeller, the efficiency curve
374
of PAT with the forward-curve impeller is more flat, showing that the high-efficiency operating range of the forward-
375
curve impeller is wider than that of the conventional backward-curve impeller. Moreover, the flow rates of BEPs of
376
two PATs are 81.64 m3/h and 95.24 m3/h, and the maximum efficiencies are 59.98% and 67.91%, respectively, which 20
ACCEPTED MANUSCRIPT 377
reflects that the forward-curve impeller in the PAT has obvious superiority.
378
Appendix. Experimental Uncertainty Analysis
379
Table 6 lists the instrumentation and their accuracy. Table 7 presents the measurement uncertainties at BEP of
380
special impeller for PAT test rig.
381
Table 6
Instrumentation and their accuracy
Test instrumentation
Make
Range
Turbine flow meter of LWGYB-100
Beijing flow meter factory
20-200
Pressure sensor1 of WT2000GP7S (Inlet pressure)
Welltech
0-1.0 MPa
±0.1%
Pressure sensor2 of WT2000GP6S (Outlet pressure)
Welltech
-300-300 kPa
±0.1%
Electric eddy current dynamometer of CWF25D
Zhongcheng Test Equipment
0-120 Nm
±0.4Nm
0-10,000 rpm
±1 rpm
Speed sensor
382
Table 7
△n
△n/n
Q
△Q
△Q/Q
H
△H
△H/H
T
△T
△T/T
(%)
(m3/h)
(m3/h)
(%)
(m)
(m)
(%)
(Nm)
(Nm)
(%)
1500
±1
±0.07
95.24
±0.48
±0.5
38.32
±0.27
±0.72
42.97
±0.4
±0.93
The pressure head of the turbine is calculated from Eq. (16). △Z is zero because the pressure transmitters are put on
H
389
390 391
Torque
rpm
385
388
Head
n
one plane.
387
discharge
rpm
384
386
±0.5%
Measurement uncertainties at BEP of special impeller for PAT test rig
speed
383
Accuracy m3/h
p1 p2
z
g
v12 v22 100% 2g
(16)
The uncertainty in pressure head is determined from
H / H
(p1 / p ) 2 (p2 / p ) 2 (Q1 / Q) 2 (Q2 / Q) 2 100% 0.72%
(17)
The PAT efficiency is calculated from
T
gQH
100%
(18)
The uncertainty in turbine efficiency is determined from
/
(
n 2 Q 2 H 2 T 2 ) ( ) ( ) ( ) 100% 1.28% n Q H T
(19)
21
ACCEPTED MANUSCRIPT 392
Acknowledgments
393
This work was supported by the Natural Science Foundation of China (grant numbers 51609105, 51379179,
394
51279172, and 11602097), Postgraduate Innovation Foundation of Jiangsu Province of China (grant number
395
CXZZ13_0678), the Open Research Fund of Key Laboratory of Xihua University (grant numbers szjj2015-029, and
396
szjj2016-061), and Sichuan Provincial Department of Education(grant number 16ZB0157).
397
Nomenclature
398 399 400 401 402 403 404 405 406 407 408 409 410 411
H = head (m)
412 413
kW = Kilowatt
414
Abbreviations
415 416 417
PAT = pump as turbine
418
Greek symbols
419 420 421 422 423
η
efficiency
ρ
density (kg/m3)
α
absolute flow angle (deg)
β
relative flow angle (deg)
ψ
blockage coefficient
424
Subscripts
425 426
1
high pressure side
2
low pressure side
D = diameter (m) g = acceleration due to gravity (m/s2) n = rotational speed (r/min) ω = rotational speed (rad/s) v = velocity (m/s) vu = circumferential component of absolute velocity (m/s) vr = radial component of absolute velocity (m/s) vm = meridional velocity component (m/s) w = relative velocity (m/s) u = peripheral velocity (m/s) Q =the flow rate (m3/s) ns = specific speed (r/min) ns =n·Q0.5·H-0.75 (where n is in r/min, Q in m3/s and H in m) P = power (W, kW)
BEP =at best efficiency point CFD = computational fluid dynamics
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