Nuclear Engineering and Technology: Long Yun, Zhu Rongsheng, Wang Dezhong
Nuclear Engineering and Technology: Long Yun, Zhu Rongsheng, Wang Dezhong
Nuclear Engineering and Technology: Long Yun, Zhu Rongsheng, Wang Dezhong
Original Article
a r t i c l e i n f o a b s t r a c t
Article history: Pumps are essential machinery in the various industries. With the development of high-speed and large-
Received 4 January 2020 scale pumps, especially high energy density, high requirements have been imposed on the vibration and
Received in revised form noise performance of pumps, and cavitation is an important source of vibration and noise excitation in
14 February 2020
pumps, so it is necessary to improve pumps cavitation performance. The modern pump optimization
Accepted 7 April 2020
Available online xxx
design method mainly adopts parameterization and artificial intelligence coupling optimization, which
requires direct correlation between geometric parameters and pump performance. The existing cavita-
tion performance calculation method is difficult to be integrated into multi-objective automatic coupling
Keywords:
Pumps
optimization. Therefore, a fast prediction method for pump cavitation performance is urgently needed.
Cavitation performance prediction method This paper proposes a novel cavitation prediction method based on impeller pressure isosurface at
Cavitation single-phase media. When the cavitation occurs, the area of pressure isosurface Siso increases linearly
Pressure isosurface with the NPSHa decrease. This demonstrates that with the development of cavitation, the variation law of
the head with the NPSHa and the variation law of the head with the area of pressure isosurface are
consistent. Therefore, the area of pressure isosurface Siso can be used to predict cavitation performance.
For a certain impeller blade, since the area ratio Rs is proportional to the area of pressure isosurface Siso,
the cavitation performance can be predicted by the Rs. In this paper, a new cavitation performance
prediction method is proposed, and the feasibility of this method is demonstrated in combination with
experiments, which will greatly accelerate the pump hydraulic optimization design.
© 2020 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the
CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
https://doi.org/10.1016/j.net.2020.04.007
1738-5733/© 2020 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/
licenses/by-nc-nd/4.0/).
Please cite this article as: L. Yun et al., A cavitation performance prediction method for pumps PART1-Proposal and feasibility, Nuclear
Engineering and Technology, https://doi.org/10.1016/j.net.2020.04.007
2 L. Yun et al. / Nuclear Engineering and Technology xxx (xxxx) xxx
fluid dynamics, the numerical calculation of cavitation flow based method is still need to be verified. This paper will focus the cavi-
on the appropriate cavitation model [3] has attracted more and tation characteristics of the model pump to find a rapid method to
more attentions [4e8]. predict the cavitation method.
The cavitation model is a mathematical model that describes the
phase transition between the liquid phase and the vapor phase in 2. Pump model and cavitation experiment
the cavitation flow. According to the definition method of ho-
mogenization flow density, the cavitation model is mainly divided 2.1. Design parameters
into two types, namely, the state equation model [9,10] and the
transport equation model (TEM) [11e16]. The state equation model The design parameters of the mixed flow pump are shown in
simulates the cavitation flow field by constructing a functional Table 1.
relationship between density and pressure. The limitation of the The cavitation states from generation, development, critical
practical application of this type model is that the physical meaning cavitation to breakdown cavitation are achieved by changing the
of the functional relationship between assumed density and pres- inlet pressure. A vacuum pump on the closed test bench is applied
sure is not clear. Therefore, the transport equation model is widely to reduce the pressure at the pump inlet and gradually reduce the
used in numerical simulation of cavitation flow [11,16]. NPSHa until the head of the pump decreases by 3%. In the process of
From previous studies, we can find that the current cavitation changing the inlet pressure, the cavitation flow structures during
performance of the pump is mainly obtained by two ways, one is the cavitation development process are observed by the high speed
through experimental measurement, and the other is numerical photography technology from the Plexiglas window at the impeller
calculation. The cost of experimentally measuring the cavitation shell. The Plexiglas window and the pump body are perfectly
performance is too large. If the scale model experiment is adopted, matched, as shown in Fig. 1.
the cavitation scale effect will also occur. In terms of numerical
calculation, the currently used prediction method based on the
cavitation model requires refined calculations, which requires a 2.2. Test devices
high amount of grids and takes time to calculate [17e22], and the
calculation of the head down 3% point is difficult to be found. On Fig. 2 shows the real hydraulic component of the mixed flow
the other hand, it is difficult to find critical cavitation condition. The pump, including the impeller, suction pipe, the guide vane and the
modern optimization design method mainly adopts parameteri- assembly. The inlet diameter of the test section is F270 mm, and
zation and artificial intelligence coupling optimization, which re- the cross-sectional area of the test section is 0.057255 m2. The
quires direct correlation between geometric parameters and pump outlet pipe diameter is F250 mm. There is no shaft bushing in the
performance. In the modern pump optimization design method, outlet pipe during the test, and the outlet cross-sectional area is
the current cavitation numerical calculation method will obviously 0.046445 m2.The difference between the inlet and outlet pressure
increase the number of iterations of the optimization algorithm, sensor from the center of the impeller is 220 mm.
and the algorithm structure will be more complicated. In summary, The cavitation performance test is carried out on the closed test
Firstly, the existing cavitation flow calculation model is difficult to platform. The measurement error of the main measuring instru-
be integrated into multi-objective automatic coupling optimiza- ment is 0.2%. Fig. 3 is the closed-circulation experimental system
tion. Secondly, in the existing pump optimization design, there is for the mixed flow pump, including Motor, Torque meter, Outlet
no method to quickly predict cavitation performance. Therefore, a pressure meter, Model pump, Inlet pressure meter, Vacuum tank,
fast prediction method for pump cavitation performance is ur- Vacuum pump, Valve, Electromagnetic flowmeter, Booster pump,
gently needed. Booster tank, Valve for adjusting, etc. The diameter of the test pipe
In order to solve the problem of cavitation prediction, this paper is 300 mm.
proposes a cavitation performance method for multi-objective
automatic optimization. The prediction method of the pump cavi- 2.3. Experimental cavitation performances
tation performance is based on pressure isosurface area ratio at the
cavitation condition. A pressure isosurface is a surface upon which a The comprehensive cavitation performance of the model pump
particular variable pressure has a constant value, called the level. at 1.000Q, 0.957Q, 0.913Q, 0.870Q and 0.804Q are obtained. The
For instance, an isosurface of pressure would be a surface consisting head values versus NPSHa of the mixed flow pump under different
of all the points in the geometry where the pressure took a given conditions are presented in Fig. 4. Overall, the head curves corre-
value. Pressure isosurface area is the surface area of the pressure sponding to different flows tends to increase with the decrease of
isosurface. The feasibility of this method is demonstrated in com- flow. The head curves of different flow rates vary greatly with
bination with experiments. This will greatly accelerate the speed of NPSHa. As the flow rate decreases, the downward trend of the head
pump hydraulic optimization design. This prediction method is not curve near NPSHr slows down. For example, at 1.000Q, the head
applicable to a single pump, but also applicable to pumps with curve is decreasing faster near NPSHr, the head curve is steep in the
different specific speeds. transition between the horizontal section and the declining section.
The design concept of the method is that when the minimum For example, in the 0.804Q condition, the transition between the
pressure in the liquid is lower than the vaporization pressure, horizontal section and the declining section of the head curve is
pump cavitation inception occurs. Usually cavitation occurs in the relatively gentle. The changing flow rates can cause changes of the
low pressure region in the liquid flow field. When the pressure flow angle, resulting in changes of the attack angles. The attack
increases to a certain extent, cavitation bubble will collapse. This angle will cause the second flow to occur on the pressure side or
hypothesis applies to many experimental phenomena, but the suction side of the blade. This second flow will stimulate the
theoretical basis of the method is less. In the single-phase flow development of cavitation [23].
medium, the flow characteristics of the pump are obtained by According to the cavitation performance curve of Fig. 4, the
computational fluid dynamics method. How to apply the single- NPSHr with a corresponding head drop of 3% at each flow rate is
phase flow calculation to obtain the pressure field and to predict obtained. At this time, the NPSHr ¼ NPSHc. The NPSHr values of the
the pump cavitation performance is still unknown. The method and pump under different flow rates are shown in Table 2. The NPSHr at
theory have not yet been established, and an accurate prediction the design condition is 7.493 m.
Please cite this article as: L. Yun et al., A cavitation performance prediction method for pumps PART1-Proposal and feasibility, Nuclear
Engineering and Technology, https://doi.org/10.1016/j.net.2020.04.007
L. Yun et al. / Nuclear Engineering and Technology xxx (xxxx) xxx 3
Table 1
Design parameters of test pump.
Please cite this article as: L. Yun et al., A cavitation performance prediction method for pumps PART1-Proposal and feasibility, Nuclear
Engineering and Technology, https://doi.org/10.1016/j.net.2020.04.007
4 L. Yun et al. / Nuclear Engineering and Technology xxx (xxxx) xxx
Please cite this article as: L. Yun et al., A cavitation performance prediction method for pumps PART1-Proposal and feasibility, Nuclear
Engineering and Technology, https://doi.org/10.1016/j.net.2020.04.007
L. Yun et al. / Nuclear Engineering and Technology xxx (xxxx) xxx 5
that the pump has a critical cavitation state, pK ¼ pV,NPSHa ¼ NPSHr. Table 3
NPSHa can be calculated by the follow Equation (5) Key parameters definition and methods of single phase cavitation
prediction.
Please cite this article as: L. Yun et al., A cavitation performance prediction method for pumps PART1-Proposal and feasibility, Nuclear
Engineering and Technology, https://doi.org/10.1016/j.net.2020.04.007
6 L. Yun et al. / Nuclear Engineering and Technology xxx (xxxx) xxx
Table 4
Obtained parameters of isosurface at the condition of Qopt ¼ 0.46 m3/s and n ¼ 1450 r/min.
Net Positive Suction Head Pump head Inlet total pressure Isosurface pressure Area of isosurface Area of blade Area ratio
4.3. Discussion
Fig. 8. Isosurface of NPSHc at the condition of Qopt ¼ 0.46 m3/s and n ¼ 1450 r/min.
Please cite this article as: L. Yun et al., A cavitation performance prediction method for pumps PART1-Proposal and feasibility, Nuclear
Engineering and Technology, https://doi.org/10.1016/j.net.2020.04.007
L. Yun et al. / Nuclear Engineering and Technology xxx (xxxx) xxx 7
cavitation prediction hypothesis. That is, the point #4 is the initial (1) The design concept of the method is that when the minimum
cavitation point of the pump. When the pump is under constant pressure in the liquid is lower than the vaporization pressure,
flow and speed, the primary cavitation point is determined by the pump cavitation inception occurs. Usually cavitation occurs
pump impeller itself. At the same time, we find that when cavita- in the low pressure region in the liquid flow field. When the
tion occurs, the variation of noise with cavitation margin is also pressure increases to a certain extent, cavitation will
approximately linear. It is the same as the change law of the pres- collapse. In the single-phase flow medium, the flow charac-
sure isosurface area. This shows that the noise level is closely teristics of the pump are obtained by CFD method. The
related to the cavitation performance. This hypothesis will be relationship between the low pressure isosurface and NPSHa
verified by subsequent cavitation vibration and noise tests, and the is established.
initial cavitation will be assessed by analyzing the vibration or (2) The cavitation performance prediction method based on the
pressure pulsation characteristics by noise measurement or pres- pressure isosurface area ratio is proposed. The feasibility is
sure pulsation measurement. analyzed and demonstrated. When the cavitation occurs in
the design condition, the area of pressure isosurface Siso and
NPSHa satisfy the linear equation Siso ¼ 0.014063NPSHa þ
5. Conclusions 0.123204. The area of pressure isosurface Siso increases lin-
early with the NPSHa. This demonstrates that with the
In order to solve the problem of cavitation fast prediction, this development of cavitation, the variation law of the head with
paper focus research on cavitation prediction method based on the NPSHa and the variation law of the head with the area of
pressure isosurface in single-phase.
Please cite this article as: L. Yun et al., A cavitation performance prediction method for pumps PART1-Proposal and feasibility, Nuclear
Engineering and Technology, https://doi.org/10.1016/j.net.2020.04.007
8 L. Yun et al. / Nuclear Engineering and Technology xxx (xxxx) xxx
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[18] N. Zhang, X. Liu, B. Gao, X. Wang, B. Xia, Effects of modifying the blade trailing
This work was funded by the China Postdoctoral Science Foun- edge profile on unsteady pressure pulsations and flow structures in a cen-
dation Funded Project (Grant No.2019M651734), National Youth trifugal pump, Int. J. Heat Fluid Flow 75 (2019) 227e238.
Natural Science Foundation of China (Grant No.51906085), Jiangsu [19] N. Zhang, X. Liu, B. Gao, B. Xia, DDES analysis of the unsteady wake flow and
its evolution of a centrifugal pump, Renew. Energy 141 (2019) 570e582.
Province Innovation and Entrepreneurship Doctor Project (2019), [20] D. Zhang, L. Shi, W. Shi, R. Zhao, H. Wang, B.P.M.V. Esch, Numerical analysis of
Zhejiang Postdoctor Project (2019). unsteady tip leakage vortex cavitation cloud and unstable suction-side-
perpendicular cavitating vortices in an axial flow pump, Int. J. Multiphas.
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Please cite this article as: L. Yun et al., A cavitation performance prediction method for pumps PART1-Proposal and feasibility, Nuclear
Engineering and Technology, https://doi.org/10.1016/j.net.2020.04.007