Annals of Nuclear Energy 97 (2016) 190–197
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
A systematic investigation on flow characteristics of impeller passage in a nuclear centrifugal pump under cavitation state Qiang Fu a, Fan Zhang a, , Rongsheng Zhu a, Bo He b ⇑
a b
National Research Center of Pumps, Jiangsu University, 212013 Zhenjiang, China POWERCHINA SPEM LIMITED COMPANY, Shanghai 201316, China
a r t i c l e
i n f o
Article history: Received 24 May 2016 Received in revised form 27 June 2016 Accepted 6 July 2016 Available online 27 July 2016 Keywords: Nuclear centrifugal pump Flow characteristic Fluctuation Cavitation Numerical simulation simulation
a b s t r a c t
Cavita Cavitatio tion n is a greatl greatly y harmfu harmfull flow flow phenom phenomeno enon n for nuclea nuclearr centri centrifug fugal al pumps, pumps, and it should should be attach attached ed importance when the pump is designed. Under cavitating conditions the flow patterns in the pump are complex and highly turbulent flow can be induced. In this paper the flow characteristics in the impeller passag passage e of a nuclea nuclearr centri centrifug fugal al pump pump model model were were system systemati atical cally ly invest investiga igated ted under under steady steady and transi transient ent cavitation conditions. At moderate cavitation levels the results show that the fluctuations of the radial force on the impeller are mainly affected by rotor-stator interaction effects, but are strongly influenced by cavitation cavitation under developed developed cavitatio cavitation n condition conditions. s. At inception inception vapor is mainly mainly generated generated near the leading edge of the blade, and spreads on the suction side of the impeller at higher cavitation levels. The vapor generation, development and burst under transient cavitation conditions have a strong influence on the flow patterns in the impeller passage. The trends of the simulations are in accordance with the measured results, thus confirming the validity of the numerical model used for predicting the characteristics of the flow through the impeller. 2016 Elsevier Ltd. All rights reserved.
1. Introduction Centrifugal pumps have been widely used in many areas for a long time, but their operational requirements are now becoming stricter stricter and stricter. For example example,, in centrifug centrifugal al pumps pumps used in nuclear nuclear reactors reactors not only only adequat adequate e hydrauli hydraulic c performa performance nce but also also stabl stable e and reliab reliable le opera operatio tion n under under some some extre extreme me opera operatin ting g condiconditions tions must must be attain attained ed.. The The centri centrifug fugal al chargi charging ng pump pumps s are parts parts of the Chemical and Volume Control System (CVCS) and designed to provide provide normal charging charging service service to the Reactor Reactor Coolant System (RCS), which makes them extremely important in nuclear power plants plants.. When When the pump pump opera operates tes at a suffici sufficien ently tly lowpressure lowpressure,, cavcavitation itation is generate generated, d, and its developm development ent inevitab inevitably ly affects affects the safety safety operatio operation n of the nuclear nuclear pumps. pumps. This flow phenom phenomeno enon n takes takes place place in almost almost all kinds kinds of pump pumps s and has docum documen ental tal effects on the performance of the machine, and therefore should be avoided as much as possible. In recent recent years years an increa increasin sing g amou amount nt of inform informati ation on is has been been made available in the open literature on cavitation in centrifugal pumps. Cout Coutier-D ier-Delgo elgosha sha et al. (200 (2003) 3) numerica numerically lly and experim experimenentally investigated investigated the performa performances nces of a centrifug centrifugal al pump pump with
⇑
Corresponding Corresponding author.
E-mail address:
[email protected] (F.
[email protected] (F. Zhang). http://dx.doi.org/10.1016/j.anucene.2016.07.011 0306-4549/ 2016 Elsevier Ltd. All rights reserved.
two-dim two-dimens ensiona ionall curved curved blades blades under under the cavitatin cavitating g operated operated condition. Yanxia dition. Yanxia et al. (2015) used used high high speed speed digit digital al mov movies ies to study study the flow visualization of internal cavitating flow patterns in a centrifugal pump at low flow rates. Xiaojun et al. (2013) analyzed (2013) analyzed the periodically unsteady pressure field and head-drop phenomenon caused caused by leading leading edge cavitatio cavitation n in a single single stage centrifugal centrifugal pump pump.. They They poin pointe ted d out out that that the the vorte vortex x flow flow gene genera rati tion on in the the rear rear of the cavitatin cavitating g region is the main main reason of the head-dro head-drop. p. Vapor usually is generated and bursts for a short time in the cavitating region of the flow, resulting in the possible onset of flow instabilities caused by cavitatio cavitation. n. Many Many researche researchers rs analyzed analyzed the flow mecha mechanis nism m of cavita cavitatio tion-i n-indu nduced ced flow flow instab instabili ilitie ties s in order order to supsupply theoretical information for optimal design of pumps operating with better better cavitatio cavitation n performa performance nce (Tsujimoto Tsujimoto,, 2001; Yongpeng et al. al.,, 201 2014; 4; Slo Slotem teman an et al. al.,, 200 2004; 4; Ya Yama mamo moto to and Ts Tsuji ujimo moto, to, 2009; Lee et al., 2009). 2009). In addition, a number of other investigations on the cavitating two-phase flow in pumps have been documented in Medvitz in Medvitz et al. (2002), Dular et al. (2005), Zuchao et al. (2008), Poullikkas (2003) and Long et al. (2009) . Transi Transient ent flow flow is also also a comm common on flow flow pheno phenome menon non occur occurrin ring g in turbo turbopum pumps ps under under a wide wide range range of condit conditio ions, ns, usuall usually y durin during g startstartup, shut-down and variable load operation, and has been the focus of a numb number er of invest investiga igatio tions. ns. Tsuk Tsukamo amoto to and Oha Ohashi shi (198 (1982) 2) and Li et al. (2010 (2010)) studied the instantaneous flow characteristics of centrifugal pumps during the start-up period. Wu et al. (2013, 2010)
Q. Fu et al. / Annals of Nuclear Energy 97 (2016) 190–197
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Nomenclature
b2 C p C v D1 D2 F x F y F z F cond F vap H K p N P
p0 Q Q d Q max
outlet width of impeller, mm static pressure coefficient absolute velocity coefficient inlet diameter of impeller, mm outlet diameter of impeller, mm radial force on X axial direction radial force on Y axial direction axial force condensation coefficient, 0.01 correction factor of evaporation, 50 head, m pressure coefficient, 5000 impeller rotation speed, rpm power, kW pressure when cavitation starts, pa flow rate, m3/s design flow rate, m3/s maximum flow rate, m3/s
investigated the transient flow induced by speed-changes and rapid openings of the discharge valve in centrifugal pumps. Zhang et al. (2014a,b) numerically simulated the transient flow patterns of a nuclear centrifugal pump during changes of its operating conditions at constant rotating speed. The above investigations only represent a small fraction of the information available in open literature on transient cavitation in centrifugal pumps. However, the adverse effects induced by transient cavitation in pumps are extremely serious, and cannot be ignored in the design process. Therefore, the flow characteristics under both steady and transient cavitation conditions are investigated in our present study, whose results hopefully represent a useful reference for further research work.
Re Rc RB R T t 0 T u2 v Z U
steam generation rate steam condensation rate bubble radius, m radius of impeller, m time, s initial time, s temperature, C impeller outlet circumferential velocity, m/s absolute velocity, m/s number of blades wrap angle, deg efficiency nucleation volume fraction vapor volume fraction vapor density, kg/m3 liquid density, kg/m3 time step net positive suction head required, m
g anuc avap qvap ql Dt NPSH r
a suitable number of grid elements is very important for the simulation. The predicted head performance of the pump with 4 different numbers of grid elements are compared in Fig. 2 and the detail of various grid meshes are reported in Table 2. In general, the head of the model pump increases with the number of grid elements increases. However, the head obtained for grid number 4 only increases by less than 1 m with the respect to the results of grid number 3, while the head discrepancies for the other grids are significantly larger. Therefore grid number 3 was selected in the present simulations. Fig. 3 shows an overview of partial mesh of the flow passage, especially the main parts of the geometric structure. The Zwart-Gerber-Belamri model, as expressed by (1) and (2), proved to yield better precision for cavitation simulation ( Zwart et al., 2004), has and therefore been selected in the present work.
2. Physical model The pump model is a centrifugal charging pump, which is an important component of the reactor coolant system of nuclear power plants. Cavitation usually occurs in the first stage of the multi-stage centrifugal charging pumps. Therefore, in the present study, only the stationary domains including the annual suction chamber and the double-channel volute, the rotating domain of the first impeller stage have been selected as the physical model in order to investigate its cavitation characteristics. The main geometric andhydraulic specifications of the pump are reported in Table 1. It is required NPSH r 6 7.8 m accordingto theCVCsystem ina nuclear power plant at the maximum flow rate Q max = 160 m3/h. The flow domains of the centrifugal charging pump with its first stage impeller have been modeled by Pro/E, as shown in Fig. 1.
3. Numerical approach The RANS equations have been performed by using the ANSYS CFX 14.5 software, which uses a multi-block technique to couple the separate numerical domains. A high mesh quality is required in the numerical simulations for improving the precision of the results and reducing the computational time. All parts of the pump model have been meshed with structured hexahedral grids, and the meshes of boundary layers have been thickened. Generally speaking, the calculated error caused by the mesh are reduced by increasing the number of gird elements, but excessive computer memory and running time are required in the numerical simulation if the grid number is too large. Hence the selection of
Re ¼ F
3anuc ð1 av ap Þqv ap ap
v
Rc ¼ F cond
RB 3av ap qv ap
RB
s ffiffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 2 pv ap p 3
s ffiffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 2 p pv ap 3
ql
;
ql
p > p
;
p < p
ap
v
ap
v
ð1Þ
ð2Þ
The SST k-x turbulence model is a hybrid model combining the advantages of the standard k-x and k-e turbulence models. The viscous flow near the wall and the turbulence fully developed turbulent region can be accurately modeled using the standard k-x and standard k -e turbulence models, respectively. As a result, the SST k-x turbulence model was applied in this investigation to solve the RANS functions. The average static pressure has been specified at the inlet of the suction chamber, with uniform normal flow running into the inlet section. The mass flow rate has been assigned at the outlet of the double-channel volute. The impeller domain rotated with speed
Table 1
Specifications of the pump model. Geometric specifications Inlet diameter (mm) Outlet diameter (mm) Outlet width (mm) Wrap angle (deg) Blade number
Hydraulic specifications
D1 140 Nominal speed (r/min) D2 236 Design flow rate (m3/h) b2 12 Maximum efficiency u 135 Maximum flow rate (m3/h) Z 4 Net positive suction head required(m)
n 4500 Q d 110 g P60% Q max 160 NPSH r 67.8
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192
Table 3
Test precision standard of grade 2 in China. Contents
Q
H
P
g
Uncertainty
6±2.0%
6±1.5%
6±1.5%
6±2.8%
In order to resolve the actual temporal variation of the flow, the time step size of the computation has been adjusted to correspond to an impeller rotation of 3 degrees. Hence, for a rotation speed of 4500 r/min the time step Dt has been set to be 1.111 10 4 s. The impeller completed 9 revolutions during each computation, so the total simulation time has been 0.12 s. The results of the last 3 revolutions of the impeller have been used to analyze the periodic characteristics of the flow.
Fig. 1. Flow domains of the pump model.
4. Experimental results The test has been carried out at Jiangsu University according to Chinese National Precision Grade No. 2 regulations, whose standard is reported in Table 3. The original model pump has been tested in the open test bench, shown in Fig. 4. The flow rate of fluid has been measured by the turbine flow meter, with 0.5% uncertainty. The pressure in the inlet and outlet has been measured by pressure sensor, whose uncertainty is 0.1%. An integrated measuring instrument platform has been used to acquire the test data with ±0.5% uncertainty in the test. Both the hydraulic and the cavitation performance at the large flow rate have been measured in this test, and the affinity laws have been applied to obtain the final test data.
Fig. 2. Head comparison under 4 grid numbers.
Table 2
4.1. Hydraulic performance
Grid detail of 4 schemes. Schemes
Scheme 1
Scheme 2
Scheme 3
Scheme 4
Grid number Heads/m
954372 109.6
1572531 118.3
2067148 122.1
2611692 122.9
n = 4500 r/min, while the other domains were stationary. A medium turbulence intensity of 5% has been set at the inlet section and a non-slipping boundary condition has been imposed on all solid surfaces. The steady simulated results supplied the suitable initial conditions for transient runs.
The measured head and efficiency are compared in Fig. 5 with their simulated values, and the uncertainty of the measured head, efficiency is 0.51%, 0.65% respectively. Both the measured head and efficiency exceed the designed values at the 1.0Q d operating condition. The measured head is larger than its design head H d over most of the flow rate range, and the measured efficiency is also higher than its design value at flow rates from 0.85 Q d to 1.6Q d. The simulated results of the head and efficiency are both higher than their test values and the maximum deviation is about 6% of
Fig. 3. Partial mesh overview of the flow passage.
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193
Fig. 4. Test bench of the centrifugal pump.
rate, but nevertheless, the tendency of the measured and simulated results in the whole flow range is good. The geometrical structure of the charging pump is complicated and the pump should operate at multi flow rates. Thus the internal flow characteristics are extremely intense at the low flow rates. The disk leakages were not included in the computational domain in order to simplify the geometrical structure, and this is the main reason that the test results are lower than the simulated results. Although some discrepancies are manifest in Fig. 12, good overall agreement has been attained between the simulated and tested results. The hydraulic performance comparison illustrated in Fig. 5 verifies the validity of the adopted model for simulating the flow characteristics of the impeller.
4.2. Cavitation performance Fig. 5. Hydraulic performance comparison of simulated and measured results.
Fig. 6 shows the simulated and measured results of the pump’s cavitation performance at maximum flow rate of Q = 160 m3/h, and the uncertainty of the measured NPSH is 0.58%. Both the simulated and measured values of NPSH do not exceed NPSH r, the required value for the pump system. The simulated NPSH is 0.782NPSH r and the measured NPSH is 0.821NPSH r at H = 0.97H d. Here the required experimental NPSH of the pump is defined with a 3% head drop criterion. As a whole, the simulated results are in good accordance with the measured data with a reasonable value (3.8%) of the
1.08 1.04 1.00
Simulated result
d
H / 0.96 H
Measured result
0.92 0.88 0.84 0.7
0.8
0.9
1.0
1.1
1.2
1.3
NPSH / NPSH
r
Fig. 6. Simulated and measured results of the pump cavitation performance at Q = 160 m3/h.
the design value. The cavitation requirement at the maximum flow rate has been the driving design factor of the pump, and therefore the best efficiency point has been located at higher flow rates than the design value 1.0Q d. With the increase of flow rate, the tested results approach the simulated results and almost coincide at the larger flow rates. The deviation between the measured and simulated results at the high flow rate is smaller than the low flow
Fig. 7. Schematic view of X and Y axis.
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194
relative error. The main reason for the deviation is that the leakage, frictions and other flow loss were not considered in the simulation.
cavitation (3% head drop), serious cavitation (6% head drop) and fractured cavitation (head breakdown), respectively corresponding to the NPSH values equal to 7.2 m, 6.5 m, 6.12 m, 5.9 m and 5.8 m. Fig. 7 shows the schematic view of the X and Y axes in the impeller axial plane. The radial force along X and Y axes under the different cavitation regimes are discussed in this section, and all the results were obtained from numerical simulation. Fig. 8 shows the radial force fluctuations along the X and Y axial directions under the above five different cavitation regimes. Fig. 8 (a), (b) and (c) indicate a certain level of periodicity of the radial force fluctuations, with the force along the Y direction larger than in the X direction. The two tongues of the double-channel volute are located along the Y axis. Most of the flow unsteadiness occurs
5. Results and discussion 5.1. Radial forces along the X and Y axes According to the specifications of the nuclear power plant the required NPSH r of the centrifugal charging pump cannot exceed 7.8 m at the maximumflow rate of Q = 160 m3/h. The development of cavitation in the pump at Q = 160 m3/h has been conventionally divided into five regimes, indicated here as incipient cavitation (0% head drop), developing cavitation (1% head drop), critical
Fx
200
Fy
150
150
100
100
50
50
N /
N /
0
F
Fx
200
Fy
0
F
-50
-50
-100
-100
-150
-150 -200
-200 0.00
0.01
0.02
0.03
0.00
0.04
0.01
/s t
0.04
Fx
Fy
(b) Developing cavitation (1% head drop) Fx
200
150
150
100
100
50
50
0
0 N /
N /
0.03
t /s
(a) Incipient cavitation (0% head drop) 200
0.02
F
Fy
F
-50
-50
-100
-100
-150
-150
-200
-200
0.00
0.01
0.02
0.03
0.04
0.00
0.01
t /s
0.02
0.03
0.04
/s t
(c) Critical cavitation (3% head drop) 200
(d) Serious cavitation (6% head drop)
Fx
Fy
150 100 50
N /
F
0 -50
-100 -150 -200 0.00
0.01
0.02
0.03
0.04
/s t
(e) Fractured cavitation (head breakdown) Fig. 8. Radial forces on the X and Y axes under different cavitation conditions.
Q. Fu et al. / Annals of Nuclear Energy 97 (2016) 190–197
in the proximity of each tongue, and as a result the fluctuation of the radial force is more intense along the Y axial than in the X-direction. Before the intensity of cavitation increases to the critical regime, the interaction between the rotor and stator is the main source of the flow unsteadiness, as can be inferred from the periodicity of the radial force. When cavitation reaches to the serious cavitation regime, large amounts of vapor are generated in the flow passage and their motion and development greatly influence the radial forces along the X and Y axes, which become disorderly and aperiodic. Beyond the critical cavitation regime the effects on the flow pattern become dominant, and finally in the fractured cavitation regime the flow unsteadiness is mainly caused by cavitation rather than rotor-stator interaction phenomenon.
p0 t < 0 :04s p0 k p ðt t 0 Þ t P 0:04s
ð 3Þ
where t 0 is initial time, t 0 = 0.04s; p 0 is the pressure when cavitation starts, Pa; k p is pressure coefficient, k p = 50000, Pa/s. The steady flow field obtained from previously calculations has been used to initialize the transient simulation. Also in this case the time step Dt has been taken equal to 1.111 10 4 s and the total simulation time is 0.68 s. Four typical monitoring points A, B, C and D have been defined inside the impeller in order to analyze the characteristics of the flow in the centrifugal pump under transient cavitation operation. All monitoring points have been located along the mean streamline of the impeller and their relative positions are shown in Fig. 9. The pressure coefficient C p and the velocity coefficient C v defined as:
C p ¼ p=ð0:5qu22 Þ
ð 4Þ
C ¼ 2 v =u2
ð 5Þ
v
B
C
D
0.5 0.4 p
C
0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
t /s
Fig. 10. Transient static pressure in the impeller.
In order to further investigate the flow patterns in the impeller of the centrifugal pump under transient cavitation conditions, the evolution of the flow characteristics from inception to the fractured cavitation regime are discussed in the following. All of the numerical setups are the same as for the analysis of steady cavitation except for the inlet pressure, which has been defined by the CEL program of CFX. The variation of the inlet static pressure under cavitating conditions has been defined by means of function (3).
pðt Þ ¼
A
0.6
5.2. Flow characteristics in the transient cavitation regime
195
These two equations have been used to describe the flow pressure and velocity under the transient cavitation conditions. Fig. 10 presents the transient static pressure fluctuations at the four monitoring points in the impeller under cavitation conditions.
The pressure increases from the inlet to the outlet of the impeller and the fluctuations in the outer part of the impeller are stronger than in the inner part. This is because the fluid gets energy from the rotating impeller and the outer part of the impeller is more affected by rotor-stator interaction effects. When cavitation starts, the pressure in the inlet part remains nearly constant up to t = 0.12 s and then nearly decreases to 0 for a very short time, as can be seen from the pressure characteristics at points A and B. The pressures at points C and D decrease slightly at t = 0.15 s, then remain almost constant up to t = 0.5 s, and finally drop to 0 afterwards. The main reason of this behavior is that vapor is generated in the inner part of the impeller at incipient cavitation conditions, and then is convected to the outer part when cavitation becomes more intense. The pressure of the impeller is strongly influenced by the generation and burst of the vapor phase. The transient velocity fluctuations at the four monitoring points in the impeller during the development of cavitation are shown in Fig. 11. Consistently with previous trends illustrated in Fig. 10, the amplitudes of the pressure and velocity fluctuations in the impeller are larger at points C and D than at points A and B. The velocity fluctuation in the outer part of impeller is prone to be affected by the rotor-stator interaction effects. It remains almost constant at all monitoring points before t = 0.12 s, then increases rapidly at points A and B and decreases slightly at points C and D. In this time range cavitation occurs in the inlet part of the impeller and does not reach the outer part. The velocities at points A and B are larger than at C and D up to t = 0.56 s. At this time cavitation reaches the outer part of the impeller and the velocities rise up suddenly at points C and D, indicating that the cavitation extend through the whole flow passage of the impeller at the end of the transient cavitation run.
1.6
A
B
C
D
1.5 1.4 1.3 v
C 1.2 1.1 1.0 0.9 0.8 0.0
0.1
0.2
0.3
0.4
0.5
0.6
t /s
Fig. 9. Monitoring points on the impeller.
Fig. 11. Transient relative velocity in the impeller.
0.7
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The generation, development and burst of the vapor in the impeller flow passage are typical features of cavitation, and Fig. 12 shows the variation of the vapor volume fraction variation at the four monitoring points in the impeller during the transient run. It can be seen clearly that the vapor fraction starts to increase after t = 0.13 s at points A and B and after t = 0.58 s at points C and D. Although the vapor variation trends at points A and B are nearly the same, the vapor fraction at point A is much larger than at point B. In addition, the vapor moves rapidly towards the outer part of the impeller, and therefore the falling speed at A is more pronounced than at B after the vapor volume fraction has reached its maximum value. The vapor fraction at points C and D increases significantly and even exceeds the vapor fraction in inlet part of the impeller at the end of transient cavitation run. When cavitation reaches the fractured cavitation regime, the flow in the impeller passage becomes disorderly and highly turbulent, generating the second rise of the vapor fractions at the four monitoring points in the impeller. Since vibrations and other unsteady flow phenomena occur in conjunction with cavitation, especially under the transient conditions, the operation stability of the centrifugal pump system cannot be ignored. The axial force on the centrifugal pump impeller under the transient cavitation run is shown in Fig. 13. At the beginning of the transient run, cavitation is light and has almost no influence on the axial force, which fluctuates in the 330–365 N range with no sudden changes. The axial force on the impeller starts to increase from t = 0.12 s and nearly reaches to 475 N at t = 0.22 s. Then, it falls down to 370 N, rises up again to a high value, and finally decreases at the end of the transient cavitation run. The generation and motion of the vapor phase and its bursting in the fractured cavitation regime lead to a change of flow patterns in the blade passages, which is a main reason for rising and falling of the axial force on the impeller. 0.5
A
B
C
6. Conclusions The flow characteristics on the impeller of a nuclear centrifugal pump model operating under cavitating conditions at high flow rates have been systematically investigated. Both the results under the steady and transient cavitation have been discussed. Although some deviation has been observed between the simulated and measured results, both trends are consistent and the relative error remains with acceptable limits. The overall good agreement between the simulations and experimental measurements confirms the validity of the model adopted for predicting the flow characteristics of the impeller. At slight cavitation development conditions the fluctuations of radial force are mainly affected by the rotor-stator interaction phenomenon, but become more and more dominated by cavitation when its intensity increases towards the fractured cavitation regime, and finally the flow unsteadiness is mainly caused by cavitation rather than rotor-stator interaction. Under transient cavitation conditions the vapor generation, development and burst have a strong influence on the flow patterns in the impeller passage. At cavitation inception vapor is mainly generated near the leading edge of the blades, and progressively extends on the suction side of the impeller at increasing levels of cavitation. At the end of transient cavitation regime, vapor nearly blocks the whole flow passage of the impeller and leads to the development of a highly turbulent flow in the trailing regions of the blade passages. The generation and motion of the vapor phase and its bursting in the fractured cavitation regime lead to a change of flow patterns in the blade passages, which is a main reason for rising and falling of the axial force on the impeller.
Conflict of interest The authors declare that there is no conflict of interest regarding the publication of this paper.
D
0.4
Acknowledgement
0.3
f v
This study is financially supported by the National Natural Science Foundation of China (Grant No. 51379091, No. 51239005 and No. 51509108), Natural Science Foundation of Jiangsu Province of China (Grant No. BK20140554, No. SBK2015042921), Postdoctoral Science Foundation of China (Grant No. 156993) and Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). The supports are gratefully acknowledged.
0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
t /s
Fig. 12. Transient vapor volume fraction in the impeller.
References
480 460 440 420 N / 400 z
F
380 360 340 320 0.0
0.1
0.2
0.3
0.4
0.5
0.6
t /s
Fig. 13. Axial force in the transient cavitation process.
0.7
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