Numerical study on characteristics of unsteady flow in a centrifugal ...

Engineering Computations Numerical study on characteristics of unsteady flow in a centrifugal pump volute at partial load condition Lei Tan Baoshan Zhu Yuchuan Wang Shuliang CAO Shaobo Gui

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Numerical study on characteristics of unsteady flow in a centrifugal pump volute at partial load condition Lei Tan Downloaded by TSINGHUA UNIVERSITY At 00:35 08 August 2015 (PT)

Institute of Fluid Machinery and Fluid Engineering, Tsinghua University, Beijing, China

Unsteady flow in a centrifugal pump volute 1549 Received 10 May 2014 Revised 29 October 2014 31 October 2014 26 November 2014 Accepted 26 November 2014

Baoshan Zhu Department of Thermal Engineering, Tsinghua University, Beijing, China

Yuchuan Wang College of Water Resources and Architectural Engineering, Northwest A&F University, Xian, China

Shuliang Cao Department of Thermal Engineering, Tsinghua University, Beijing, China, and

Shaobo Gui Changjiang Institute of Survey, Planning, Design and Research, Wuhan, China Abstract Purpose – The purpose of this paper is to elucidate the detailed flow field and cavitation effect in the centrifugal pump volute at partial load condition. Design/methodology/approach – Unsteady flows in a centrifugal pump volute at non-cavitation and cavitation conditions are investigated by using a computation fluid dynamics framework combining the re-normalization group k-e turbulence model and the mass transport cavitation model. Findings – The flow field in pump volute is very complicated at part load condition with large pressure gradient and intensive vortex movement. Under cavitation conditions, the dominant frequency for most of the monitoring points in volute transit from the blade passing frequency to a lower frequency. Generally, the maximum amplitudes of pressure fluctuations in volute at serious cavitation condition is twice than that at non-cavitation condition because of the violent disturbances caused by cavitation shedding and explosion. Originality/value – The detailed flow field and cavitation effect in the centrifugal pump volute at partial load condition are revealed and analysed. Keywords Cavitation, Centrifugal pump, Partial load condition, Unsteady flow, Computation fluid dynamics, Pressure fluctuations Paper type Research paper

This work has been supported by the Tsinghua University Initiative Scientific Research Program (Grant numbers 2014z21041 and 20141081231), the State Key Laboratory of Hydroscience and Engineering (Grant number 2014-KY-05), the Open Research Subject of Key Laboratory of Fluid and Power Machinery, Ministry of Education (Grant number szjj2015-021), and the National Natural Science Foundation of China (Grant numbers 51176088 and 51179090).

Engineering Computations: International Journal for ComputerAided Engineering and Software Vol. 32 No. 6, 2015 pp. 1549-1566 © Emerald Group Publishing Limited 0264-4401 DOI 10.1108/EC-05-2014-0109

EC 32,6

Nomenclature b2 Cvap Ccon

1550 D2 Di


Do fi fBPF H k NPSHA n p Q

Notation blade width at exit (mm) coefficient of vapourization rate coefficient of condensation rate diameter of impeller outlet (mm) pipe diameter of pump inlet (mm) pipe diameter of pump outlet (mm) rotational frequency (Hz) blade passing frequency (Hz) head (m) the turbulent kinetic energy (m2/s2) net positive suction head available (m) rotational speed of impeller (r/min) pressure (Pa) flow rate (m3/s)

Rb u Zi Greek symbols αl αv αnuc ε η μl μv μm μt ρl ρv ρm

bubble radius (m) velocity (m/s) number of blade volume fraction of liquid volume fraction of vapour volume fraction of nucleation site turbulent kinetic energy dissipation rate (m2/s3) efficiency of pump dynamic viscosity of liquid (Pa∙s) dynamic viscosity of vapour (Pa∙s) dynamic viscosity of mixture (Pa∙s) turbulent viscosity (Pa∙s) density of liquid (kg/m3) density of vapour (kg/m3) density of mixture (kg/m3)

1. Introduction Turbulent flow in a centrifugal pump is highly complicated, especially when the pump works at partial load condition with cavitation. The rotor-stator interaction between impeller and volute in a centrifugal pump generates pressure fluctuations and induces operation instability. Considerable attention has already been paid to study the unsteady interaction in centrifugal pumps. Both experimental and numerical approaches have contributed to the understanding of the complex flow fluctuations due to the rotor-stator interaction. Arndt et al. (1990) first reported the unsteady pressure measurement of both impeller blade and diffuser vane in a diffuser pump by experiments. The results showed that the largest pressure fluctuations on the diffuser vanes were observed to occur on the vane suction side close to the vane leading edge. Hajem et al. (2001) investigated detailed flow field in a centrifugal pump by using a laser Doppler velocimeter. Measurements indicated that the vane had a significant effect on the impeller flow structure when the blade suction side is facing the diffuser vane. Parrondo-Gayo et al. (2002) conducted a systematic series of experiments to measure the pressure fluctuations on 36 points around the centrifugal pump volute for different operating points. Majidi (2005) numerically calculated the unsteady pressure distribution in the impeller and volute of a centrifugal pump, and found that the pressure fluctuations were strong at impeller outlet and in vicinity of the tongue due to the interaction between impeller and volute. Pei et al. (2012) numerically investigated the periodically unsteady pressure field caused by rotor-stator interaction in a single-blade pump for various operation conditions.


Cavitation occurs when the liquid reaches a state at which vapour cavities or bubbles are formed and then grow due to a decrease in local pressure to the vapour pressure of the liquid. These formed and growing cavities will collapse implosively and disappear as soon as they reach higher pressure regions in the flowing liquid (Escaler et al., 2006; He and Liu, 2011). Cavitation induces pressure pulsation and uneven load distribution, thereby seriously reducing the efficiency of pumps and affecting their operational stability (Brennen, 1994; Wang and Zhu, 2010). Therefore, characteristics of unsteady flow under cavitation condition in the centrifugal pump should be investigated deeply. Friedrichs and Kosyna (2002) conducted an experimental investigation on the rotating cavitation in two centrifugal pumps. The results showed that the onset of rotating cavitation can be assigned to the cavitation number and blade incidence angle. Medvitz et al. (2002) calculated cavitation flows in a centrifugal pump at small cavitation numbers by using the cavitation model proposed by Kunz et al. (2000). Coutier-Delgosha et al. (2003) experimentally and numerically investigated the types of cavitation and the spatial distribution of vapour structures in a centrifugal pump impeller with a two-dimensional curved blade. Stroboscopic light was used for standard imaging, and high-speed video with light-sheet illumination was applied to observe the self-oscillating states of the cavitation. Hosangadi et al. (2004) used an acoustically accurate, compressible multiphase model to simulate a cavitating inducer at design flow conditions with different inflow pressures. The computational results indicated that the loss in performance directly correlates with the amount of blockage in blade to blade passages caused by cavitation. Luo et al. (2008) investigated the impeller inlet geometry effect on centrifugal pump performance, and found that the larger blade angle and uniform flow at impeller inlet can improve the pump cavitation performance. Wu et al. (2011) used stereo PIV to observe the structure of cavitation in development of a tip leakage vortex in an axial water jet pump rotor from its initial rollup to breakdown. Unsteady flows have significant effect on the centrifugal pump operation stability, especially under the cavitation condition. Although numerous numerical and experimental investigations have been conducted on the centrifugal pump cavitation, the unsteady characteristics of cavitation flows are still difficult to capture accurately (Bachert et al., 2010), especially under partial load condition where large-scale unsteadiness and high dynamic pressure loads may occur. In this paper, unsteady flows in a centrifugal pump under partial load condition are simulated by using the re-normalization group (RNG) k-ε turbulence model coupled with the mass transport cavitation model. This study aims to elucidate the detailed flow field and cavitation effect in the centrifugal pump volute at partial load condition. 2. Mathematical model and numerical algorithm The fluid in the cavitation flow field is considered a homogeneous and compressible mixed medium of liquid and vapour. The continuity and momentum equations in the Cartesian coordinates are as follows: @rm @ rm ui þ ¼0 (1) @xi @t @ui @uj 2 @uk @ rm u i @ rm u i u j @p @ þ ¼ þ mm þ mt þ dij ; @xi @xi @t @xj @xj @xi 3 @xk

(2)

Unsteady flow in a centrifugal pump volute 1551

EC 32,6


1552

where ρ and μ are respectively the density and dynamic viscosity, calculated by the weighted average of each phase volume fraction α; ρm ¼ ρlαl + ρvαv, μlαl + μvαv; subscripts l, v and m denote the liquid phase, the vapour phase and the mixture, respectively; u is the velocity; p is the pressure; μt is the turbulent viscosity. Subscripts i, j and k denote the axis directions. The RNG k-ε turbulence model, which is widely applied in numerical simulation of hydraulic rotation machinery, is employed by considering the influence of fluid compressibility on the cavitation flow. The turbulent viscosity μt is modified with a function f( ρm) (Coutier-Delgosha et al., 2003; Tan et al., 2012a,b; Liu et al., 2012), such that: k2 mt ¼ f rm cm ; e

(3)

where k and ε are the turbulent kinetic energy and turbulent kinetic energy dissipation rate, respectively; the empirical constant cμ ¼ 0.09. The density function f (ρm) is defined as: " #n rm rv U rl rv ; f rm ¼ r v þ (4) rl rv where n is a constant and set to 10 (Coutier-Delgosha et al., 2003; Tan et al., 2012a,b; Liu et al., 2012). The liquid-vapour mass transfers due to cavitation are solved by the mass transport cavitation model: @ rn a n _ vap m _ con ; þ rU rn an u ¼ m (5) @t in which the mass transfers for vapourization and condensation rates proposed by Zwart et al. (2004) are modelled as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3anuc ð1av Þrv 2 maxðpv p; 0Þ _ vap ¼ C vap (6) m 3 rl Rb

_ con m

3av rv ¼ C con Rb

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 maxðppv ; 0Þ ; 3 rl

(7)

where Cvap and Ccon are the empirical calibration coefficients for vapourization and condensation rates, respectively; Rb is the bubble radius; pv is the vapour pressure; αnuc is the nucleation site volume fraction. The vapour pressure pv in most cavitation models is chosen as a constant according to test temperature. However, pv is actually influenced by the local turbulent pressure fluctuation (Liu et al., 2009). Thus, this influence is considered in the cavitation model by expressing the modified vapour pressure pv as follows: pv ¼ psat þ 0:195rm k; where psat is the saturation pressure at the test temperature.

(8)


The computation fluid dynamics code CFX is employed in this numerical study. Unsteady Navier-Stokes equations are solved by CFX coupled with the RNG k-ε turbulence model and mass transport cavitation model. The spatial domain is discretized by using an element-based finite volume method in CFX. The second-order backward Euler scheme is used in the unsteady numerical simulation. To make the pump inlet pressure become consistent with the experimental operation, the total pressure at the pump inlet is specified and the velocity direction is taken to be normal to the boundary. The mass flow at the pump outlet is selected. Scalable wall functions are imposed to solve the near-wall flow close to the no-slip wall over the impeller blades, sidewalls, volute casing and inlet and outlet pipe walls. In steady cavitation flow calculation, the initial calculation is converged at a given operating condition. Then the subsequent calculations are taken with the pressure at pump inlet decreasing step by step. The results of the steady calculation are taken as the initial flow field in unsteady flow calculation. The methods of frozen rotor and transient rotor stator are applied to couple the rotation and station domains for steady and unsteady calculations, respectively. 3. Problem statement and numerical parameters 3.1 Parameters of centrifugal pump and computational domain The test pump is a conventional single suction centrifugal pump (see Figure 1). The main parameters of the pump are listed in Table I. The impeller is shrouded and the blade is backswept. The partial load condition Q/Qd ¼ 0.76 is chosen in the following unsteady calculations. Figure 1(a) shows that the computation domain consists of three modules, namely, suction pipe, impeller and volute. Structural hexahedral meshes are used in the entire flow domains, and finer meshes are adopted near the blade surface and volute tongue to capture the flow details and to improve calculation accuracy (Figures 1(c) and (d)). As shown in Figure 1(b), 13 monitoring points are set at the middle-span plane of the volute, including three dense points VA-VC around the volute tongue to analyse the extremely complicated flow field in this narrow region. 3.2 Independence test of mesh density and time step Five mesh densities (Table II) are used for steady flow calculations under noncavitation conditions to test the mesh independence. Simulated results indicate the weak influence of the mesh density on the pump head H and efficiency η in the present simulations. Therefore, the coarsest mesh with 1,804,742 elements is employed for optimal calculation load. Here, H1 and η1 are the pump head and efficiency calculated by using mesh 1, respectively. The effects of time step Δt on the simulations are also tested. Different time steps, including Δt ¼ 1.08 × 10−4, 2.15 × 10−4 and 4.31 × 10−4 s, are used (equivalently Tb/64, Tb/32 and Tb/16), where Tb is the time between two sequential blades passing through a fixed position on the volute. Figure 2 shows the time history of pressure fluctuations on monitoring points V2, V5 and V10 for the three time steps. Minimal differences are found among the three time steps. Therefore, by considering the balance between the spectrum accuracy and the computation cost, we denote the final time step as Δt ¼ 2.15 × 10−4 s.


EC 32,6

(a)

(b)

XI

V11

X V10

1554

IX VIII

V9 VB VA

VC II

V8


V2

VII

V7

V3

V4

V6

III

IV

VI V5 V

(c)

Figure 1. Computation meshes of centrifugal pump and monitoring points in volute

(d)

Notes: (a) Whole passage; (b) monitoring points in volute; (c) impeller; (d) volute tongue

Parameter

Value 3

Table I. Parameters for the test centrifugal pump

Rated discharge Qd (m /h) Rated head H (m) Rotational speed n (r/min) Number of blade Zi Impeller diameter D2 (mm) Blade width at exit b2 (mm) Pipe diameter of pump inlet Di (mm) Pipe diameter of pump outlet Do (mm)

340 30 1,450 6 329 34.6 200 150

3.3 Validation of calculation results Net positive suction head available (NPSHA), defined in Equation (9), is the difference between the total energy and vapourization energy for the unit weight of the fluid at the pump inlet: p u2 p þ v rl g 2g rl g

(9)

1555

The performances of the calculated centrifugal pump are tested by using laboratory measurements in previous studies (Tan et al., 2010, 2012a,b, 2014). Figure 3 compares the experimental and calculated results of pump head and efficiency. The calculated head and efficiency of the pump are time averaged from the total sampling time of 0.54 s, corresponding to 13 rotational periods of the impeller. A good quantitative agreement exists in the wide discharge range, with the maximum relative errors smaller than 5 per cent. The numerical results of cavitation characteristics are also in good agreement with the experimental data, especially the sudden decline in the head corresponding to the decrease in NPSHA (see Figure 4). 4. Results and discussion 4.1 Flow characteristics under non-cavitation condition Figure 5 shows the frequency characteristics of pressure fluctuations at monitoring points VA-V11 under non-cavitation condition. The dominant frequencies of pressure Item Suction pipe Impeller Volute Whole passage H/H1 η/η1

Mesh 1

Mesh 2

Mesh 3

Mesh 4

Mesh 5

723,855 417,396 663,491 1,804,742 1 1

723,855 1,048,831 663,491 2,436,177 0.99428 1.00331

723,855 1,942,195 663,491 3,329,541 0.99455 1.00336

723,855 2,714,058 663,491 4,101,404 0.99394 1.00361

723,855 3,696,570 663,491 5,083,916 0.99355 1.00380

420,000

Table II. Pump head H and efficiency η vs mesh elements

V10

Δt =1.08 × 10–4 s

390,000

Δt =2.15 × 10–4 s –4 Δt =4.31 × 10 s

V5 360,000 p/Pa


NPSHA ¼

Unsteady flow in a centrifugal pump volute

V2 330,000

300,000

270,000 0.05

0.06

0.07 t/s

0.08

0.09

Figure 2. Time histories of pressure fluctuations on V2, V5 and V10 for three time steps

EC 32,6

/%

H/m 36

80 30

70 60

1556

24 50 18

40 30

12

6

Experiment /% Calculation /%

Experiment H/m Calculation H/m

10

0 0

60

120

180

240

300

360

420

0 480

3 –1 Q /m ·h

33

32

31

H /m


20

Figure 3. Experimental and calculated performances of the pump

30

29

Figure 4. Experimental and calculated cavitation performances of the pump

Q =260m3/h, Experiment Q =260m3/h, Calculation

28

27 1

2

3

4

5

6

7

8

NPSHA /m

fluctuations on those monitoring points are the blade passing frequency fBPF ¼ n × z/ 60 ¼ 145 Hz or 2fBPF. The blade passing frequency is the consequence of the non-uniform flow coming out the impeller from both sides of each blade, due to the differences between pressure and suction sides (jet-wake flow pattern) (Majidi, 2005). The pressure fluctuation amplitudes of fBPF or 2 fBPF are obviously stronger than that of other high harmonics. At the low frequency range from 0 to 145 Hz, characteristics of frequency domain are fairly complicated with irregular pressure amplitude jitter on several monitoring points, such as VC and V2. The pressure fluctuation amplitudes on monitoring points VC and V2 are extraordinarily larger than that on other points. In order to understand this physical phenomenon, the flow field in this region should be investigated. Figures 6 and 7 show the instantaneous pressure distribution and streamline at middle-span plane of the

100

200

300

400

Frequency/Hz

0

(c)

500

100

600

200

300

400

Frequency/Hz

VA

VB

0 VC

5,000

10,000

15,000

20,000

25,000

p/Pa 500

0

(b)

600

100

200

300

400

V7

V9 V8

0 V11 V10

2,000

4,000

6,000

8,000

Frequency/Hz

Notes: (a) Monitor points VA-VC; (b) monitor points V2-V6; (c) monitor points V7-V11

0

(a)

p/Pa

500


600

V2

V3

V4

V5

0

V6

2,000

4,000

6,000

8,000

p/Pa


Figure 5. Spectrums of monitor points at non-cavitation condition

EC 32,6


1558

Figure 6. Instantaneous pressure distribution at middle-span plane

(a)

(b)

Pressure/Pa 400,000 360,000 320,000 280,000 240,000 200,000 160,000 120,000 80,000 40,000 0

Pressure/Pa 400,000 360,000 320,000 280,000 240,000 200,000 160,000 120,000 80,000 40,000 0

VC V2

(c)

(d)

Pressure/Pa 400,000 360,000 320,000 280,000 240,000 200,000 160,000 120,000 80,000 40,000 0

Pressure/Pa 400,000 360,000 320,000 280,000 240,000 200,000 160,000 120,000 80,000 40,000 0

VC V2

VC V2

VC V2

Notes: (a) t=0.5121 s; (b) t=0.5138 s; (c) t=0.5155 s; (d) t=0.5172 s

centrifugal pump from t ¼ 0.5121 to 0.5172 s corresponding to 3/4 Tb. The four sequent maps in Figures 6 and 7 demonstrate the process that a blade passes through the volute tongue, and the interaction between the impeller and the volute in details. As one specific blade approaches and departs the tongue, obvious pressure variations in the vicinity of the tongue can be observed. In the volute screw section, pressure gradually increases from the volute tongue to the outlet along the flow direction, but the pressure gradient near the volute tongue is higher than that of downstream region. The time-varying pressure gradient near the monitoring points VC and V2 are relatively obvious, whereas they almost remain the same at the second half of the screw section. It should be noted that though the highest pressure gradient occurs on point VB, the time evolution of pressure gradient around this point is unconspicuous. The similar variation tendency of streamline close to points VC and VB can be observed in Figure 8. There are reverse flows and vortex around the point VC corresponding four successive positions, and the flow near point V2 is also uneven and varies with time. Therefore, the complicated and time-varying flow field around points VB and V2 induce large pressure fluctuation amplitudes.

(a)

VC

VC

1559

V2

V2


Unsteady flow in a centrifugal pump volute

(b)

(c)

(b)

VC

VC

V2

V2

Notes: (a) t=0.5121 s; (b) t=0.5138 s; (c) t=0.5155 s; (d) t=0.5172 s

Figure 8 shows the instantaneous streamlines at cross-section of point VC from t ¼ 0.5121 to 0.5172 s corresponding to 3/4 Tb as shown in Figures 6 and 7. The second flows are considerably pronounced at the VC cross-section, which are caused by pressure gradients perpendicular to the flow direction and related to the volute centre line curvature. The flow field is uneven at t ¼ 0.5121 s at VC cross-section with a potential vortex inception at the centre of the cross-section. Then this vortex core develops to an intensive vortex at t ¼ 0.5121 s at the top middle of the cross-section. This counter clockwise vortex disturbs the flow field within about 1/3 area of the cross-section. At t ¼ 0.5155 s, the counter clockwise vortex separates into an counter rotating vortex pair at the section bottom and top, respectively. The counter rotating vortex pair then moves to the middle height of the cross-section, and their vortex centres are nearly symmetric about the vertical middle line of the section. The location, shape and intensity of the vortex are changing with time at the VC cross-section, which induces the strong flow fluctuations near the monitoring point VC. 4.2 Flow characteristics under cavitation conditions Figure 9 shows the development of cavitation in impeller as the pressure gradually drops at pump inlet according to the experimental measurement. For the non-cavitation

Figure 7. Instantaneous streamline at middle-span plane

EC 32,6

(a)

1560


(b)

(c)

(d)

Figure 8. Instantaneous streamline at VC cross-section

Notes: (a) t=0.5121 s; (b) t=0.5138s; (c) t=0.5155 s; (d) t=0.5172 s

condition in Figure 9(a), the pressure at pump inlet is high enough to suppress the appearance of cavitation. As the inlet pressure drops to NPSHA ¼ 2.2 m, the cavitation develops to occupy the blade leading edge and make the pump head begin to decrease as shown in Figure 4. For the more lower inlet pressure according to the NPSHA ¼ 1.5 m, the cavitation has already occupied the blade to blade passages, and blockage the normal flow in the impeller and results in the pump head decline in Figure 4. Figures 10 and 11 show the frequency characteristics of pressure fluctuations at monitoring points VA-V11 under cavitation conditions of NPSHA ¼ 2.2 and 1.5 m. For both cavitation conditions, only the dominant frequencies of the pressure

(a)

(b)

(c)



Notes: (a) Non-cavitation; (b) NPSHA=2.2 m; (c) NPSHA=1.5m

fluctuations on monitoring points VC and V2 remain the same as that of non-cavitation condition. On other monitoring points the dominant frequencies transit from fBPF or 2fBPF to a fairly low frequency of 9.67 Hz, about 1/15fBPF. This phenomenon indicates that the flow field in volute becomes more complex as cavitation develops. The low frequency is mainly related to the cavitation bubble shedding, and breaking downstream the impeller. Table III shows the maximum amplitude of pressure fluctuations for both noncavitation and cavitation flows. Generally, the pressure fluctuation amplitudes for cavitation flows are larger than that for non-cavitation. In the entire volute casing, the pressure amplitudes are noticeable strong from points VA to V3, especially the point VC, whereas they reduce to a relatively low value from points V4 to V7, and then they rebound to a high value from points V8 to V11. The maximum amplitude among those 13 monitoring points for both non-cavitation and cavitation conditions appears at point VC, where the flow is uneven at the middle-span plan and there is a time-varying intensive vortex pair at the cross-section. The relatively low-pressure fluctuation amplitudes at points V4-7 are mainly contributed by the position far away from the volute tongue, and more fluent diffused flow due to a larger curvature radius of this section. The pressure fluctuation amplitudes at points V8-11 in the diffuser section of the volute are nearly at the level of 3,000 pa for non-cavitation and NPSHA ¼ 2.2 m, and at the level of 6,000 pa for NPSHA ¼ 1.5 m. 5. Conclusions A numerical simulation combination of RNG k-ε turbulence model and mass transport cavitation model is employed to calculate the unsteady flows in a centrifugal pump at partial load. The satisfied agreement with experimental and calculated results guarantees the reliability and accuracy of the numerical simulation framework. For the non-cavitation flows, the dominant frequencies of pressure fluctuations on monitoring points in pump volute are fBPF or 2fBPF. Four successive time-varying maps of pressure contour, streamline and second flow provide details on interaction of impeller and volute when one blade passes the volute tongue. High-pressure gradient and intensive second flow near the monitoring point VC induce the most violent pressure fluctuations of all the monitoring points. In comparison with the non-cavitation flow, the maximum amplitudes of pressure fluctuations increase on most of monitoring points for cavitation condition of

Figure 9. Development of cavitation in impeller

100

200

0

(c)

400

Frequency/Hz

300

100

500

200

600

400

VB

Frequency / Hz

300

VA

0 VC

5,000

500

10,000

15,000

20,000

25,000

p/Pa 0

600

(b)

100

V7

V8

200

400

V9

0 V11 V10

2,000

4,000

6,000

8,000

10,000

12,000

Frequency/ Hz

300


0

(a)

Figure 10. Spectrum of monitor points under cavitation condition NPSHA ¼ 2.2 m 500

600

V2

V3

V4

V5

0

V6

2,000

4,000

6,000

8,000

10,000

12,000

p/Pa


1562

p/Pa

EC 32,6

100

200

300

400

Frequency/Hz

0

(c)

500

100

600

200

400

Frequency /Hz

300

VB

500

0

(b)

600

100

V7

200

300

400

V8

V9

0 V11 V10

3,000

6,000

9,000

12,000

15,000

Frequency / Hz


0

VA

0 VC

5,000

10,000

15,000

20,000

25,000

p/Pa

(a)

p/Pa

500


600

V2

V3

V4

0 V6 V5

3,000

6,000

9,000

12,000

15,000

p/Pa


Figure 11. Spectrum of monitor points under cavitation condition NPSHA ¼ 1.5 m


EC 32,6

Monitoring point

VA VB VC V2 1564 V3 V4 V5 V6 Table III. Maximum amplitude V7 V8 of pressure V9 fluctuations of V10 monitor points V11 in volute

Maximum amplitude of pressure fluctuation (pa) Non-cavitation NPSHA ¼ 2.2 m NPSHA ¼ 1.5 m 5,123.88 4,038.84 26,180.79 10,372.69 7,031.20 1,785.85 2,484.82 1,788.26 1,617.42 3,472.76 3,350.90 3,398.61 3,408.30

5,344.38 4,012.87 22,285.08 14,387.46 7,665.94 2,392.08 1,891.19 2,102.08 2,028.34 3,194.44 3,294.84 3,340.80 3,352.07

6,456.17 5,976.31 26,024.45 16,555.02 8,530.95 5,544.26 5,662.33 5,878.50 6,072.47 6,187.40 6,031.29 5,720.80 5,715.45

NPSHA ¼ 2.2 m, while for several points the variation is not obvious. As the cavitation develops seriously, the dominant frequency transition and amplitude increasing demonstrate the remarkable influence of cavitation on unsteady turbulent flow in the centrifugal pump.

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Baoshan Zhu, born in 1967, is currently an Associate Professor at the State Key Laboratory of Hydroscience and Engineering, Tsinghua University, China. He received his PhD Degree from the Yokohama National University, Japan. His research interests include fluid machinery and engineering. Yuchuan Wang, born in 1983, is currently an Assistant Professor at the College of Water Resources and Architectural Engineering, Northwest A&F University, China. He received his PhD Degree from the Tsinghua University, China. His research interests include fluid machinery and engineering. Shuliang Cao, born in 1955, is currently a Professor at the State Key Laboratory of Hydroscience and Engineering, Tsinghua University, China. He received his PhD Degree from the Tohoku University, Japan. His research interests include fluid machinery and engineering. Shaobo Gui, born in 1982, is currently an Associate Professor at the Changjiang Institute of Survey, Planning, Design and Research, Wuhan, China. He received his PhD Degree from the Tsinghua University, China. His research interests include fluid machinery and engineering.

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