TRANSACTIONS OF THE INSTITUTE OF FLUID-FLOW MACHINERY
No. 136, 2017, 3546
Šukasz Zªoty∗ and Damian Pasikowski
Study of characteristic curves of rotodynamic pumps
working as turbines
Institute of Heat Engineering, Faculty of Power and Aeronautical Engineering,
Warsaw University of Technology, Politechniki 1, 00-661 Warsaw, Poland
Abstract
Centrifugal pumps working in reverse mode can be a good alternative for conventional water
turbines.
Prediction of the pumps as turbine characteristic curve is still complicated due to
the lack of information provided by the producers and rare research focusing on this subject.
In some cases of pumping systems it is important to estimate the operating point in turbine
mode basing on pump test data. In this paper the pump characteristics in turbine mode for
ten pumps with a specic speed between 10261 were compared and analyzed. The formulas
used to predict the best performance point and characteristics of pump as turbine was reviewed.
Own formulas for calculating optimum points of pump in the turbine mode was proposed.
Keywords:
Pump as turbine (PAT); Rotodynamic pump; Hydraulic power; Recovery turbine
Nomenclature
BEP
best eciency point
D
g
H
Ns
n
ngt
Q
impeller diameter, m
2
gravitational acceleration, m/s
head, m
pump specic speed
rotational speed, rpm
turbine specic speed
3
ow rate, m /h
∗
Corresponding author. E-mail address: lukasz.zloty@itc.pw.edu.pl
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Š. Zªoty and D. Pasikowski
Greek symbols
αp
βt
γ , αt , βp
η
κ
pump dimensionless specic speed
turbine dimensionless specic speed
dimensionless parameters from [2] equation 8,9,10 respectively
hydraulic eciency
relationship between pump eciency at BEP point and pump
ϕ
ψ
dimensionless head
dimensionless ow
specic speed acc. [3]
Subscripts
h
p
t
1
hydraulic eciency
refers to pump
refers to pump in turbine mode
Intruoduction
The idea of using pumps as turbines is very attractive and can be a good alternative to standard solutions applying water turbines. Rotodynamic pumps have
relatively simple construction what provides long failure-free operation and accessible maintenance. They are readily available due to the multitude of manufacturers and pumps suppliers. Economically it has been found that a pump operating
as a turbine in the range of 1 to 500 kW allows for the return on investment
costs over two years or less, which is considerably shorter than in a conventional
turbine [1].
Choosing the proper pump as a turbine (PAT) requires knowledge of the pump
characteristics working in turbine (reverse) mode. It is a demanding task because
these characteristic curves are not usually supplied with the pump or did not made
available by the producers. In addition the prediction methods of reverse mode
are often focusing on the best eciency point (BEP) and gives many dierent
results. Manufacturers of such equipment often do not have turbine test benches
focusing on determining the typical ow characteristics of the pump. Many researchers, including Stepano [4], Childs [16], Sharma [6], Wong [19], Williams [9],
Alatorre-Frenk [5], show the equations used to predict pump performance as a turbine. The purpose of these formulas is to calculate the BEP of a pump turbine
mode using the characteristics of the pumps provided by the manufacturer.
2
Prediction method overview
This section provides a brief description of several prediction methods available in
the literature. These formulas will be used to compare estimate accuracy of turbine mode characteristics.
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Study of characteristic curves of rotodynamic pumps. . .
37
Childs [16] claimed that the best turbine and pump eciency for the same
machine are practically equal. Equations of the head, H , and the ow rate, Q,
are reported by:
Qt
1
=
,
Qp
ηp
(1)
Ht
1
=
.
Hp
ηp
(2)
Stephano [4] has proposed a method that uses pump eciency. Gives the ratios
of turbine and pump head and ow to the hydraulic eciency of the pump. He
states that the ow of a pump working as a turbine at the same speed would have
the following values:
Qt
1
,
(3)
=
Qp
ηhp
1
Ht
= 2 .
Hp
ηhp
(4)
Because hydraulic eciency is not usually known, the following simplication has
been introduced:
√
ηhp = ηp .
(5)
Taking into account this simplication we get
1
Qt
=√ ,
Qp
ηp
(6)
Ht
1
=
.
Hp
ηp
(7)
Sharma [6] developed a prediction method that also uses coecients depending
on the eciency of the pump:
Qt
1
= 0.8 ,
(8)
Qp
ηp
Ht
1
= 1.2 .
Hp
ηp
(9)
Alatorre-Frenk [5] for calculating head, ow and eciency in reverse mode, used
eciency, head and ow in pump mode. Formulas are as follows:
0.85ηp5 + 0.385
Qt
=
,
Qp
2ηp9.5 + 0.205
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Š. Zªoty and D. Pasikowski
Ht
1
=
,
5
Hp
0.85ηp + 0.385
(11)
ηt = ηp − 0.03 .
(12)
Schmiedl [14] presented forecasting method uses the estimated value of hydraulic
eciency. In this method the eciency of the hydraulic system is calculated from
the following relation:
q
ηhp =
(13)
ηp0.5 ηt0.5 .
The equations for the BEP in Schmiedl method are as follows:
Qt
2.4
= −1.5 + 2 ,
Qp
ηhp
(14)
Ht
2.5
= −1.4 +
.
Hp
ηhp
(15)
Grover [17] has presented the following equations (but they are) limited in their
application to specic speeds in the range of 10 < Ns < 50:
Qt
= 2.379 − 0.0264nqt ,
Qp
(16)
Ht
= 2.693 − 0.0229nqt .
Hp
(17)
Hergt [18] calculates the head and ow in reverse mode using the specic speed
PAT in BEP:
Qt
1.6
= 1.3 −
,
(18)
Qp
nqt − 5
Ht
6
= 1.3 −
.
Hp
nqt − 3
(19)
Derakhaskan and Nourbakhsh [2] formulated a PAT of the BEP prediction method
using pump BEP point based on experimental research of four pumps. Their
recommend to predictions pumps with the specic speed Ns < 60:
γ = 0.0233αp + 0.6464 ,
αt = 0.9413αp − 0.6045 ,
(20)
βt = 0.849βp − 1.2376 .
Nautiyal and his team [3], who relied on their own research and on other researcher's data, performed an analysis to estimate the relationship between pump
ISSN 0079-3205 Trans. Inst. Fluid-Flow Mach.
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Study of characteristic curves of rotodynamic pumps. . .
39
eciency at optimal point and specic speed. They received the following relationship:
ηp − 0.212
κ=
.
(21)
lnNs
Using κ , they determined the relationship between the ow and head in pump
and turbine mode:
Qt
= 30.303κ − 3.424 ,
(22)
Qp
Ht
= 41.667κ − 5.042 .
Hp
3
(23)
Proposed formula
Using the collected data for BEPs in pump and turbine mode, a graph of the
dimensionless turbine ow relative to the pump ow and the dimensionless head
in turbine mode relative to the head in the pump mode was drawn. It is worth
noting that the points of dimensional ow are linear approximation points are
presented in Fig. 1. The equation for this straight line can be represented as
follows:
ϕt = 1.990.5 ϕp + 2−6.48 .
Figure 1. Dimensionless ow at BEP in pump and turbine mode
(24)
ϕ
see Eq. (27).
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Š. Zªoty and D. Pasikowski
Approximation points presented in Fig. 2 is a linear function also proposed for
the prediction head coecient
(25)
ψt = 4.740.5 ψp − 5.720.5 .
Figure 2. Dimensionless head at BEP in pump and turbine mode,
ψ
see Eq. (28).
The following equation gives satisfying results for Ns < 90, which works better for higher specic speeds:
ψ = 1.50.5 ψp + 1.340.5 .
4
(26)
Diagram
Using the research [7,8] conducted to prepare complete characteristic of rotodynamic pump. The results are used to draw diagrams for machine working in pump
mode and reverse mode. The results are shown dimensionless parameters:
• dimensionless ow coecient
ψ=
Q
,
nD3
(27)
ϕ=
gH
.
n2 D 2
(28)
• dimensionless head coecient
Characteristic curves of pump and turbine mode for dierent specic speed from
10 to 261 are presented in Figs. 3 and 4. This diagrams and experiment data
was applied to comparison formulas to PAT's characteristic curves by means of
proposed formula.
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Study of characteristic curves of rotodynamic pumps. . .
Figure 3. Dimensionless head curves for
Figure 4. Dimensionless head curves for
5
41
Ns = 1024.
Ns = 33261.
Comparison prediction method
A comparison of the turbine best performance prediction methods is presented
in Tab. 1. It shows the percentage estimating mistake of the ow coecient,
ϕt , and the head coecient, ψt , obtained from the predictions in relation to the
experimental data. Graphic illustrations of errors are shown in Figs. 5 and 6. By
looking at the results of comparisons, it can be stated that there is no explicit
method of forecasting the operating point on the whole range of pumps with
dierent speed ratings. The Childs method [16] has given satisfactory results in
predicting the ow value.
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9
10
15.1
17.5
19.3
19.9
23.1
24
24.5
30.4
36.4
39.7
42
46.4
55
61.3
64
79.1
94.4
105
209
261
[10]
[7]
[11]
[7]
[12]
[8]
[8]
[7]
[13]
[14]
[13]
[13]
[12]
[13]
[8]
[13]
[11]
[13]
[13]
[8]
[8]
[8]
Pump
Source
Ns
0.069
0.035
0.054
0.063
0.047
0.084
0.088
0.088
0.117
0.122
0.185
0.200
0.190
0.275
0.380
0.414
0.527
0.480
0.400
0.470
0.500
0.910
ϕt
30.91
15.42
7.03
8.59
7.70
7.61
8.70
7.67
11.17
6.86
8.00
6.70
7.84
7.60
6.93
5.75
5.37
4.88
3.82
4.34
2.01
2.34
ψt
Experimental
0.7
-15.9
-19.2
-18.2
19.0
-26.4
20.6
-19.3
-32.1
-13.4
-12.8
-12.9
-7.4
-0.5
-10.9
-10.8
25.6
-6.0
-3.9
4.2
-3.1
-18.9
ϕt [%]
-16.4
-17.3
20.5
-6.9
-5.3
-3.0
12.1
-17.7
-41.8
-13.6
-21.9
-16.2
-31.3
-16.0
-17.0
-4.6
56.1
-13.3
-21.1
-23.1
-34.0
-100.0
ψt [%]
Childs
-27.4
-41.1
-30.3
-32.9
-0.3
-36.7
-13.1
-31.2
-40.0
-24.5
-24.8
-19.7
-18.5
-13.2
-22.8
-24.3
-7.5
-13.9
-12.5
-15.3
-21.9
-33.1
-16.4
-17.3
20.5
-6.9
-5.3
-3.0
12.1
-17.7
-41.8
-13.6
-21.9
-16.2
-31.3
-16.0
-17.0
-4.6
56.1
-13.3
-21.1
-23.1
-34.0
-45.2
Stepano
ψt [%]
ϕt [%]
-11.7
-27.0
-23.8
-24.5
10.9
-30.7
5.8
-24.3
-35.4
-18.1
-17.8
-15.7
-12.0
-5.8
-15.9
-16.4
11.1
-9.2
-7.4
-4.1
-11.1
-24.9
ϕt [%]
-4.7
-4.6
27.9
-0.8
-1.7
-3.1
-27.8
-12.3
-38.8
-8.7
-17.1
-13.4
-27.8
-11.3
-12.1
1.9
76.4
-10.2
-18.1
-16.4
-28.1
-40.8
ψ =t [%]
Sharma
12.1
-12.9
18.9
5.5
56.2
1.0
10.9
2.4
-8.6
3.7
-8.1
-1.4
-8.8
-12.7
-39.8
ϕt [%]
8.2
-0.2
110.2
43.7
49.8
60.7
26.2
28.4
-3.2
31.2
8.1
27.1
-7.8
4.4
-12.1
ψt [%]
Grover
Table 1. Comparison of prediction method accuracy.
-47.2
-86.0
-13.1
-66.4
27.9
-16.4
-3.3
-6.4
-51.3
95.9
-11.6
-23.2
-4.3
6.0
-24.3
-7.1
-14.5
77.7
20.9
25.7
34.8
5.5
7.3
-19.1
9.6
-9.0
7.7
-21.3
-9.4
-19.9
Derakhshan
ψt [%]
ϕt [%]
-9.8
-9.6
5.4
-4.6
41.8
-9.8
1.2
-4.4
-16.0
2.0
-2.5
10.2
7.2
10.8
-2.8
-6.6
-1.7
13.8
15.4
-0.6
-8.9
-20.9
-13.1
-27.3
60.9
8.6
13.8
24.9
-0.6
-0.7
-22.6
8.2
-3.4
19.3
-14.6
8.0
1.0
7.9
40.0
9.2
10.4
-11.2
10.1
-4.9
Prop. formula
ψt [%]
ϕt [%]
42
Š. Zªoty and D. Pasikowski
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Study of characteristic curves of rotodynamic pumps. . .
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Figure 5. Variation between used prediction method of the ow coecient for dierent calculation methods.
Figure 6. Variation between used prediction method of the head coecient for dierent calculation methods.
For several pumps, predictions calculated with formulas are signicantly higher
than for others. For pump with Ns = 15.1, the disproportion for lift height ψt
is from 20% to 110%. Similarly, the situation looks for pump with Ns = 64
for which the predictive dierence is from 39% to 99% above the test outcome.
For pump with Ns = 19.3, the ow coecient, ϕt , for the formulas proposed by
Alaterre-Frenk [5], Grover [7], Derakhshan [2] and given in this work has been
considerably inated.
It is dicult to determine which of the formulas works best for the specic
range because two closely related pump identities, e.g., Ns = 24, and 24.5, have
very dierent deviations from the same prediction formula. Comparison of the
average estimation mistake magnitude for all comparable pumps are in [15], selected are presented in Tab. 2. This table provides a quick view of which of the
formulas generates the smallest variation between turbine mode parameters. The
proposed formulas give satisfactory results for the entire range of pumps being
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Š. Zªoty and D. Pasikowski
compared. The Childs and Grover methods provide a relatively good result only
for the ow coecient. The BEP gives the image of work under xed conditions.
As known, the operating conditions may vary depending on the pressure or ow
available. Another important issue is the possibility of estimating values in terms
other than denominated working conditions.
Table 2. Comparison of accuracy of the prediction methods.
Prediction method
Average estimation of mistake magnitude
ϕt [%]
ψt [%]
Childs
14.0
22.8
Stepano
23.9
20.9
Sharma
17.2
17.9
Alaterre-Frenk
17.0
16.8
Grover
13.5
25.7
Derakhshan
26.7
15.1
Proposed formula
10.8
13.8
The best solution is to have a complete ow characteristic of pump. In paper
[5], a method has been proposed for converting the entire turbine characteristics
to the substitution of the best turbine mode. The use of the proposed formula
for calculation BEP and turbine characteristic for three cases curves is presented
in Fig. 7.
Figure 7. Dimensional ow characteristics of pump reverse mode for the measured data and the
predictions Derakhaskan and Nourbakhsh. Formula for the BEP prediction from this
paper.
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Study of characteristic curves of rotodynamic pumps. . .
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45
Conclusions
Various methods of predicting the best turbine mode are discussed. Their own
formulas have also been proposed, which can be used to predict the operating
point in reverse mode. Presented formulas, they have been checked to what extent they agree with the measurement data. In comparison, thirty pumps were
considered for which the specic speed dierence was in the range of Ns = 9261.
The comparison shows that the available formulas are characterized by large
discrepancies. Also, it is dicult to pinpoint the range of specic speed for which
the formula works best, because for similar specic speed the formulas give significant dierences. Other parameters, such as eciency, rotational velocity, or ow
channel geometry, would have to be considered in order to indicate a particular
formula. For the whole range of pumps compared, the smallest average estimation mistake was obtained based on the formulas proposed in this article. This
indicates the possibility of using them in case of selection of the turbine pump
in a satisfactory part of the cases. However, it should be borne in mind that the
formula may be subject to a large error for specic pumps. If the application
requires thorough knowledge of the course of the characteristics and knowledge
of the ow parameters of the machine, it would be necessary to carry out experimental research.
A good solution to this problem of pump selection and technology development would be to identify suitable for generating energy from rotodynamic pumps
available on the market by dening performance characteristics for the pump series and establishing the general relationship between parameters in pump and
turbine modes. Pump manufacturers should be interested in this area as it would
allow them to expand the market for their products.
Received in September 2017
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