G

N

To

WI

a

ARRA

1

Tsptc

imnooi

saplsth

0d

ARTICLE IN PRESSModel

ED-5993; No. of Pages 8

Nuclear Engineering and Design xxx (2010) xxx–xxx

Contents lists available at ScienceDirect

Nuclear Engineering and Design

journa l homepage: www.e lsev ier .com/ locate /nucengdes

he transient flow in a centrifugal pump during the discharge valve rapidpening process

u Dazhuan ∗, Wu Peng, Li Zhifeng, Wang Leqinnstitute of Process Equipment, Zhejiang University, 38 Zheda Road, Hangzhou 310027, PR China

r t i c l e i n f o

rticle history:eceived 6 May 2010eceived in revised form 29 July 2010ccepted 16 August 2010

a b s t r a c t

During the rapid opening period of the discharge valve in the pump system commonly used in nuclearreactor operation, the flow-rate of the pump increases impulsively. In this paper, we report on experimentand numerical simulations which were implemented to investigate the external transient hydrodynamicperformance and the internal flow mechanism of the pump during this transient process. External andinternal characteristics under different flow-rates were measured with an experimental system. The

simulation for steady conditions was based on detached eddy simulation (DES) and sliding mesh wasverified by comparing the simulation with test results. More importantly, the transient characteristicsduring the valve’s rapid opening process were simulated using a similar method. Results show that theQ–H curve deviates from the steady-state value. The external characteristics are further explained byanalyzing the relative velocity on the middle stream surfaces S1 m and S2 m between blades. The pumpperformance during the valve’s rapid opening process is influenced both by the fluid acceleration and

of th

instantaneous evolutions

. Introduction

Pumps play important roles in nuclear reactor coolant systems.ransient operations are commonly found, such as the pump’starting and stopping, the flow-rate increasing and decreasing, andower failures in the centrifugal pump motors. The responses ofhe pump system in these operations show transient effects due tohanges in the operating conditions.

Boyd et al. (1961) performed a mathematical simulation for var-ous transient conditions of coolant flow and pump speeds in a

ultiloop nuclear reactor system. They studied the transient phe-omena due to power failure, starting pumps in idle loops, and thepening of an active pump’s discharge valve. They emphasized thatne must consider all the components offering resistance changen the full primary coolant flow.

Rapid changes in flow-rate will lead to sudden changes in pres-ure which propagate from the change point to the pipe systemt the speed of sound in a liquid. This is called the water hammerhenomenon. In some pipeline systems, where a pump is used to

Please cite this article in press as: Wu, D., et al., The transient flow in a centEng. Des. (2010), doi:10.1016/j.nucengdes.2010.08.024

ift liquid into a reservoir with a static head, the check valve down-tream of the pump does not open until the static head is higherhan the reservoir. Joseph and Hamill (1972) investigated the waterammer effects caused by valve openings in these operations.

∗ Corresponding author. Tel.: +86 139 89880802; fax: +86 571 87952406.E-mail address: wudazhuan@zju.edu.cn (D. Wu).

029-5493/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2010.08.024

e vortex structure.© 2010 Elsevier B.V. All rights reserved.

For theoretical analysis, many researchers have used hybridmodels to solve the water hammer problem. Among them, themethod of characteristics line (MOC) is the most popular one inmodeling the valve-induced water hammer equations, because ofits feasibility and advantages for complex systems (Kaliatka etal., 2007; Werner et al., 2008). Wenxi et al. (2008) evaluated thevalve-induced water hammer phenomena in a parallel pumps feed-water system (PPFS) during the alternate startup process of parallelpumps. A code was developed to compute the transient phenom-ena, including the pressure wave vibration, local flow velocity,slamming of the check valve disc, etc.

Most studies have focused on the water hammer in pipes whenthe valve is opening or closing, while the flow status in pumpshas been given little attention. In a valve’s opening process, theflow-rate increases from zero to maximum rapidly, so most of thetime pumps operate under off-design conditions. The flow fieldsunder off-design conditions are influenced by complex separa-tion and recirculation, thus making them highly turbulent andunsteady. Numerical calculations of performance for off-designconditions are extremely difficult using traditional steady-statemethods, because of the need to control complex physical phe-nomena such as the boundary layer separation, vortex dynamics,

rifugal pump during the discharge valve rapid opening process. Nucl.

interactions between rotational and stationary components, vibra-tions and noise, etc. (Felix et al., 2002; Rikke et al., 2003).

There are many ways that cause the flow-rate increasing ordecreasing. In this paper, rapid opening of the discharge valve ischosen as a way to achieve the process that flow-rate is increas-

ARTICLE IN PRESSG Model

NED-5993; No. of Pages 8

2 D. Wu et al. / Nuclear Engineering and Design xxx (2010) xxx–xxx

Nomenclature

A0 cross sectional area (m2)CFL Courant Friedrichs Lewy number, CFL = W�t/�xd2 outer diameter of the impeller (mm)H total head of the pump (m)Hc apparent static head (m)Hd total head of the pump at design condition (m)Hi indicated total head (m)Leq length of equivalent pipe (m)n rotational speed (rpm)ns specific speed, ns = 3.65n

√Q /H3/4

Q flow-rate (m3/h)Qd flow-rate at design condition (m3/h)Qi instantaneous flow-rate (m3/h)R radius (m)Re Reynolds number, Re = U2D2/vt time (s)

isaspc

ap1comstmttnesid

tdacicossaa

2

2

c

�t time step size (s)�h hydraulic efficiency

ng rapidly. During this period, the valve is opened within a feweconds, the flow rate of the pump increases rapidly. Numericalnd experimental results of external and internal characteristicshow significant transient effects, which differ from steady-staterocesses. These unsteady phenomena are not predictable with theonventional steady-state simulation approach.

During recent years, with the expansion of centrifugal pumppplications, studies on transient characteristics during start-uperiod have received increased attention (Lefebvre and Barker,995; Kazem et al., 2007). Analysis methods for transient pro-esses can be understood for flow-rate changes caused by fastpening and closing valves. Wang et al. (2008) used the dynamicesh method for 2D simulation of a centrifugal pump during the

tart-up period, but this method requires considerable computa-ional resources for the large deformation and update load of the

esh in rotational regions. Wu et al. (2009) developed a methodo simulate the flow field during the start-up period, based onhe sliding mesh technique, in which interfaces were used to con-ect the rotational impeller and the stationary components. Andxperiments were also carried out to verify the reliability of theimulation. Wu et al. (2010) also reported some experimental stud-es on hydrodynamic performance of a cavitating centrifugal pumpuring transient operation.

In order to improve the accuracy of the numerical simula-ions and better understand the flow in the centrifugal pumpsuring transient processes, a numerical method for simulationst off-design conditions is proposed and then the simulation isarried out. The method is validated by comparing with the exper-mental results both from the aspects of external and internalharacteristics. Based on the experimental and numerical resultsf steady-state performances, a simulation model of the unsteadytate is built, and a similar simulation method is applied for theimulation of the valve’s rapid opening processes. Both the externalnd internal characteristics are analyzed. The results can be useds references for future studies and applications.

. Numerical simulations at steady flow-rate

Please cite this article in press as: Wu, D., et al., The transient flow in a centEng. Des. (2010), doi:10.1016/j.nucengdes.2010.08.024

.1. Model and parameter

The pump under investigation, shown in Fig. 1, is a shroudedentrifugal pump with a specific speed of ns = 103 and hydraulic

Fig. 1. Geometry of the centrifugal pump.

efficiency of �h = 70%. The impeller has an outer diameter ofd2 = 238 mm and four backswept blades. In order to measure theflow field by the particle image velocimetry (PIV) technique, thecase is designed like a box with a diffuser. The diameter of inletpipe is 200 mm and outlet is 156 mm.

The pump is designed to rotate at n = 1475 rpm, operate at aflow-rate of Qd = 332 m3/h and provide a pressure rise equivalentto a head of Hd = 7.1 m. The rated Reynolds number (Re = U2D2/v)based on the outer diameter of the impeller is 4.4 × 106.

2.2. CFD code

The flow fields at off-design conditions are highly turbulent andunsteady. Due to the complex separation and recirculation, numer-ical simulations of the performances for off-design conditions willbe extremely difficult. Therefore, a reliable turbulence model mustbe chosen to simulate the performances more accurately.

Most of the numerical simulations for engineering applicationsat high Reynolds numbers are performed using the Reynolds aver-aged Navier–Stockes (RANS) turbulence models. Tutar and Hold(2001) and Benim et al. (2008) have pointed out, however, thatthe RANS model is not appropriate for computations of transientturbulent separated flow. While the RANS models are appropriatefor simulations of attached flows, they fail to accurately capture thecomplex flow structures in regimes substantially different from thethin shear and attached boundary layers. Thus, they are not suitablefor calculating the flow with separation and recirculation underoff-design conditions.

Simulation strategies such as direct numerical simulation (DNS)and large eddy simulation (LES) are attractive as an alternative forpredictions of flow fields where RANS is deficient. But they willcarry a prohibitive computational cost for resolving boundary layerturbulence at high Reynolds numbers.

The detached eddy simulation (DES) has been recently devel-oped, and is one of the most widely used models for high speedturbulent flows with massive separations. The DES model wasdeveloped to combine RANS in the attached boundary layers withLES in the shear layers and separated flow regions (Spalart et al.,1997). It is a unified approach based on the adoption of a singleturbulence model. It functions as a sub-grid scale LES model in theseparated flow regions where the grid is nearly isotropic, and as

rifugal pump during the discharge valve rapid opening process. Nucl.

a RANS model in the attached boundary layer regions (Basu et al.,2005). It retains the essential features of LES type method as well asemploys a computationally cheaper RANS method in regions whereit is appropriate.

IN PRESSG

N

ring and Design xxx (2010) xxx–xxx 3

lden

6parc

2

agtga

2

pesddtfi

ttimmmuSs

2

trt

2lIi

n

3

somu

i

Table 1Characteristics of the mesh structure, boundary conditions, and numerical setup ofthe steady flow simulations.

Mesh structure

Total number of cells 3,702,328 2,334,914 1,436,774Cells in inlet section 395,116 226,818 118,694Cells in impeller 518,836 329,344 171,570Cells in diffuser 319,287 183,893 97,985Cells in outlet section 80,512 43,266 20,500Cells in case section 2,388,577 1,551,593 1,028,025

Boundary condition

Velocity inlet (m/s) 0.619 1.149 1.644 2.060 2.935Pressure outlet (Pa) 0 0 0 0 0Wall No-slip

Numerical setup

Number of time steps 2000Time step (s) 5e−4Time steps per revolution 80CPU time per time step (min) 10 4.5 3.3Total computational time (h) 333 150 110

Table 2numerical setup of the unsteady flow simulations.

Numerical setup 1 s 0.5 s 0.25 s

Number of time steps 2400 1200 600Time step (s) 5e−4 5e−4 5e−4

ARTICLEModel

ED-5993; No. of Pages 8

D. Wu et al. / Nuclear Enginee

Applications of the DES models for a wide variety of prob-ems involving separated flow configurations have shown certainegrees of success relative to the RANS predictions. But DES mod-ls have not been so widely used in pumps, thus further trials areecessary for pump applications.

Realizable-DES is available in the software package FLUENT.3. The time dependent term scheme is 2nd-order implicit. Theressure–velocity coupling is calculated through the SIMPLEClgorithm. A second-order upwind scheme with numerical under-elaxation is applied for the discretization of convection term andentral difference schemes for diffusion terms.

.3. Computational domain and grid

The pump is divided into four parts: inlet, impeller, diffusernd case. Impeller is rotary and the other parts are stationary. Theeometry of the centrifugal pump is discretized by unstructuredetrahedral meshes. In order to check the influence of differentrids on the results, meshes with different quantities of elementsre tested.

.4. Boundary conditions at operating conditions

Simulations are carried out over a wide range of operatingoints, from shutoff to the maximum flow rate. Walls are mod-led using the standard wall functions. Velocity in axial direction ispecified as inlet boundary, while the average static pressure field isefined as the outlet boundary. The inlet and outlet boundary con-itions are placed far away from the impeller component in ordero minimize the influence of the boundary conditions on the floweld.

The flow in the impeller is defined as moving mesh zone, whilehe flow in the inlet pipe, diffuser, and outlet pipe is calculated inhe stationary reference frame. The connection between the rotarympeller and the stationary components is linked by interfaces. That

eans that the node of each side of the interface does not have toatch while the meshes are moved. This method is called slidingesh method which is commonly used for unsteady flow field sim-

lation of pumps (Croba and Kueny, 1996; Gonzalez et al., 2002).ix different flow-rates with a rotational speed of 1475 rpm areimulated: 0, 70, 130, 186, 233, and 332 m3/h.

.5. Numerical setup

In order to resolve the real temporal variation of the flow, theime-step has been adjusted to �t = 5 × 10−4 s, which ensures aeasonable CFL number based on physical time less than 1.0. Thisime-step is equivalent to 80 time-steps per impeller revolution.

The flow fields at different flow-rates have been iterated for000 time-steps, respectively, equivalent to 24 revolutions. Simu-

ations have been parallelly performed on a Linux PC cluster of eightntel Xeon processors (3.2 GHz) at institute of process equipmentn Zhejiang University.

An overview of mesh structure, boundary conditions, andumerical setup of the simulations is provided in Table 1.

. Numerical simulations of valve rapid opening process

In practical applications, flow-rate may be increased impul-ively from shutoff to maximum. In these operations, pumps

Please cite this article in press as: Wu, D., et al., The transient flow in a centEng. Des. (2010), doi:10.1016/j.nucengdes.2010.08.024

perate under off-design conditions. Based on the simulatedethod above, this special transient operation can be simulated

sing a similar method.To compare different phenomena between steady flow-rate and

ncreasing flow-rate operations, all of the numerical setups are the

Time steps per revolution 80 80 80CPU time per time step (min) 10 10 10Total computational time (h) 400 200 100

same except the inlet velocity, which is defined by a UDF pro-gram. During the period of increasing flow-rate in a centrifugalpump, the flow-rate increases rapidly from shut-off to its operat-ing flow-rate and then remains at this flow-rate. Variations of theflow-rate under three different valve’s opening times are definedby functions (1)–(3). The previously calculated result of flow fieldat shut-off condition is used as the initial flow field for unsteadyflow simulations.

Q (t) =

⎧⎪⎨⎪⎩

0 t < 0.07 s

233(t − 0.07) (m3/h) 0.07 s ≤ t < 1.07 s

233 t ≥ 1.07 s

(1)

Q (t) =

⎧⎪⎨⎪⎩

0 t < 0.07 s

466(t − 0.07) (m3/h) 0.07 s ≤ t < 0.57 s

233 t ≥ 0.57 s

(2)

Q (t) =

⎧⎪⎨⎪⎩

0 t < 0.07 s

932(t − 0.07) (m3/h) 0.07 s ≤ t < 0.32 s

233 t ≥ 0.32 s

(3)

An overview of the numerical setup is provided in Table 2.

4. Results and discussion

4.1. Comparison of external characteristics between steadyflow-rate simulations and experimental results

rifugal pump during the discharge valve rapid opening process. Nucl.

Six different operating conditions at a flow-rate of 0, 70, 130,186, 233 and 332 m3/h are simulated under a rotational speed of1475 rpm. Because the simulation method is unsteady, rotor–statorinteraction phenomena between impeller and case can be captured(Gonzalez et al., 2002). One impeller revolution has 80 time-steps

Please cite this article in press as: Wu, D., et al., The transient flow in a centrifugal pump during the discharge valve rapid opening process. Nucl.Eng. Des. (2010), doi:10.1016/j.nucengdes.2010.08.024

ARTICLE IN PRESSG Model

NED-5993; No. of Pages 8

4 D. Wu et al. / Nuclear Engineering and Design xxx (2010) xxx–xxx

Fig. 2. Fluctuant curve of the instantaneous head.

Fig. 3. General view of the pump.

Fig. 4. Comparison between experimental result and simulated results with differ-ent grid quantity.

Fig. 5. Internal flow comparison between simulation and PIV test.

Fig. 6. Comparison between steady and unsteady flow-rate simulation.

Fig. 7. Total head comparison between steady and unsteady flow-rate simulation.

ING

N

ring an

atTf1npudiiAdd

n

increases, simulated results are well in agreement with experimen-

ARTICLEModel

ED-5993; No. of Pages 8

D. Wu et al. / Nuclear Enginee

nd the impeller has four vanes, so the period of head oscilla-ions caused by rotor–stator interaction is about 20 time-steps.ake the curve of Q = 233 m3/h in Fig. 2 as an example. There areour obvious peaks which are nearly 14 m, and the time-steps are26, 150, 173 and 190. So the period of the curve oscillation isearly 20 time steps, it is equal to the rotor–stator interactioneriod. Beside, the amplitude of the instantaneous head grad-ally increases as the flow-rate increases. This is because fluidischarged from diffuser includes two parts: fluid circularly flow-

ng in diffuser and that discharged from impeller. The former flows steady and the latter fluctuates, which causes a fluctuant head.s the flow-rate is decreased, fluid which flows from impeller to

Please cite this article in press as: Wu, D., et al., The transient flow in a centEng. Des. (2010), doi:10.1016/j.nucengdes.2010.08.024

iffuser is also decreased. Accordingly, the fluctuation of head isecreased.

In order to compare with experimental results, the instanta-eous head was averaged in a rotational period of impeller, which

Fig. 8. Velocity vector graphs at unstead

PRESSd Design xxx (2010) xxx–xxx 5

is called available head. Steady performance of the pump was testedin a test rig, and the case part is shown in Fig. 3. The accuracy ofthe flow rate and pressure sensor is 0.5%. Fig. 4 shows simulatedresults of three different grid quantities and the correspondingexperimental results. Through comparison, one concludes that agrid quantity of 3.7 × 106 can accurately simulate the external char-acteristics.

As shown in Fig. 4, the maximum error comparing between sim-ulated and experimental results is about 7% at shut-off condition.This is because the flow field at shutoff condition is so complexthat some vortices cannot be captured accurately. As the flow-rate

rifugal pump during the discharge valve rapid opening process. Nucl.

y condition of different flow-rate.

tal results. At the flow rate of 70 m3/h, the error is 3%. The steadystate simulation is only used for method validation, such accu-racy is enough for unsteady flow rate simulation and engineeringapplications.

ING

N

6 ring an

4s

FtFtwadwcptb

pcr

4o

eos

aflTiaflhaaWpasols

rpattsh1

H

wti

L

wt

process of variable flow-rates, simulated results of flow-rate at1.163, 82.44, 164.14 and 251.72 m3/h were undertaken. Compar-ison between different flow-rates of velocity vector graphs oncross-section near the diffuser is shown in Fig. 8. As can be seenfrom the graphs, large-scale vortices exist in impeller and diffuser at

ARTICLEModel

ED-5993; No. of Pages 8

D. Wu et al. / Nuclear Enginee

.2. Internal flow comparison of steady flow-rate betweenimulations and experiments

The velocity vector graph on cross-section of the pump shown inig. 3 is caught by a 2D PIV device. The comparison between simula-ions and PIV experimental results at shutoff condition is shown inig. 5. The maximum velocity in simulation is about 3 m/s, while athe same position of the measured velocity is 2 m/s. An anticlock-ise vortex exists above the diffuser in the two graphs, because

t shut-off condition the fluid is blocked off by valves and cannotischarge out. It continues to circulate in the pump. Comparingith the flow structure of simulated results shown in Fig. 5, flow

aptured by the PIV method is a little flat. This is because bubblesroduced in the pump at start-up affect the PIV results. In addition,he simulated model has its own error. So the PIV result can onlye a qualitative comparison.

By comparing the internal and external characteristics of theump between experiment and simulation, this simulation methodan be used for pump simulation from shutoff to maximum flow-ate.

.3. External characteristic simulation result of valve rapidpening process

The method mentioned above can accurately calculate thexternal characteristics and internal flow at conditions from shut-ff to maximum flow-rate. Based on this method, unsteady flow isimulated with the shut-off condition as the initial flow field.

Similarly, instantaneous head is also averaged to obtain thevailable head. Simulated results of steady state and increasedow-rate with different valve opening times are shown in Fig. 6.he unsteady Q–H curve lies under the steady Q–H curve. Withncreases in flow-rate, the velocity of the fluid in pipes increases,nd part of the energy exported by the pump is used to provideuid acceleration. Thus, the faster the valve opens, the greater theead loss. With increases in flow-rate, the transient head curvepproaches the steady-state curve gradually. This phenomenongrees well with the experimental results of Wang et al. (2003).ith increases in flow-rate, velocity of the fluid in pipes increases,

art of the energy exported by the pump is used to provide fluidcceleration, so at the same flow-rate unsteady flow process has amaller head. This is because the flow-rate increases to the designperating point, the flow separation phenomenon in the impelleressens, causing the transient curves to move closer to the steady-tate curve.

In order to analyze the transient effect in the process of flow-ate increases, it is necessary to differentiate the total head of theump H(t) from the indicated total head between the suction portnd the discharge of the pump Hi(t). The total head is affected byhe acceleration of the water contained in the pump casing. So therue total head rise H(t) is obtained by subtracting the apparenttatic head Hc(t) due to the acceleration from the indicated totalead Hi(t), as the following equation shows (Tsukamoto and Ohashi,982):

(t) = Hi(t) − Hc(t) = Hi(t) +{

Leq

gA0

}dQi(t)

dt(4)

here the pump is represented by a straight pipe with cross sec-ional area A0 and length Leq. The equivalent pipe Leq of the pumps calculated by the equation:

∫

Please cite this article in press as: Wu, D., et al., The transient flow in a centEng. Des. (2010), doi:10.1016/j.nucengdes.2010.08.024

eq =L

s=0

{A0

A(s)

}ds (5)

here s is the distance measured from the suction port, and L is theotal path length.

PRESSd Design xxx (2010) xxx–xxx

In the present paper, as shown in Fig. 1, the passage area of thepump does not change so significantly, so the average of the areais taken as the passage area A(s), and length of the middle stream-line is taken as Leq. Following Eq. (4), the total head of the pumpscan be calculated. As shown in Fig. 7, at low flow-rate, the headof 1 s opening time is the lowest and is highest at 0.25 s, with 0.5 sbeing intermediate. Meanwhile, at high flow-rates, the three differ-ent opening ways are nearly the same. To explain this phenomenon,the internal flow of the pump must be analyzed.

4.4. Internal flow simulation result of valve rapid opening process

To analyze the transient evolution of the flow field during the

rifugal pump during the discharge valve rapid opening process. Nucl.

Fig. 9. Relative velocity evolutions of different conditions on the middle streamsurfaces S1 m.

ARTICLE ING Model

NED-5993; No. of Pages 8

D. Wu et al. / Nuclear Engineering an

Fs

lvvittra

itfrsalrst

istoa

afa

ig. 10. Relative velocity evolutions of different conditions on the middle streamurfaces S2 m.

ow flow-rate. As the flow-rate increases gradually, more compactortices are generated in the flow passage of the impeller, whileortices in the case are smaller, fluid flowing to the outlet morentensively. The main reason is that at off-design conditions, due tohe liquid viscosity, flow separation occurs on the blade surface, andhus vortices are generated. As the flow-rate increases, flow sepa-ation on the blade surface decreases, and vortices in the impellerre also decreased.

Fig. 9 shows the relative velocity evolutions of different open-ng times at flow-rate of 100 m3/h (left) and 233 m3/h (right) onhe middle stream surfaces S1 m in the impeller. As can be seenrom the graphs, when the valve is opened in 0.25 s, at a flow-ate of 100 m3/h, vortices on the middle stream surfaces S1 m aremall and compact; when valve is opened in some vortices developt the trailing edge of the suction face; when valve is opened inarge vortices can be observed on the pressure face. At the flow-ate of 233 m3/h, there is almost no difference on the middletream surfaces S1 m, and the internal flow is very smooth alonghe blades.

Fig. 10 shows the relative velocity evolutions of different open-ng times at a flow-rate of 100 m3/h and 233 m3/h on the middletream surfaces S2 m in the impeller. As the opening time increases,he structure of the vortices becomes more complex at a flow-ratef 100 m3/h, while the internal flow is very smooth along the blades

3

Please cite this article in press as: Wu, D., et al., The transient flow in a centEng. Des. (2010), doi:10.1016/j.nucengdes.2010.08.024

t a flow rate of 233 m /h.As was stated above, the internal flow shown in Figs. 9 and 10

grees with Q–H curve shown in Fig. 7 on the whole. Pump per-ormances in valve opening processes are both influenced by thecceleration of the fluid and transits effect of flow revolution.

PRESSd Design xxx (2010) xxx–xxx 7

5. Conclusion

Based on the experimental and simulated results of internal andexternal characteristics at steady operation from shutoff conditionto design condition, DES and silding mesh were used to explorethe transient characteristic of the process when valve was rapidlyopened. The results show that:

(1) Simulated results of steady operation using DES model agreewell with the experimental results, and the phenomenon ofhead fluctuation caused by the impeller–volute interation iswell predicted. The results indicate that the proposed method iscapable of solving complex flow in the centrifugal pump underoff-design conditions.

(2) The Q–H curve of valve opening process lies under the steadyQ–H curve, which reflects the acceleration effect when the flow-rate is increasing.

(3) Besides the acceleration effect, a transits effect of the vorticsrevolution is also a main factor which influences the perfor-mance of the pump.

In this context, flow-rate variations are defined as linear func-tions and outlet pressure is set to constant, which is differentfrom the actual situation. the pipelines and pump should be cou-pled together for further study so that the boundary conditionsof flow-rate and pressure better approximate the actual situation.The contents and conclusions of the current work can provide ref-erences for the performance prediction, design optimization andfluid control of the pump used in the transient process of valverapid opening.

Acknowledgement

This study was performed as part of National Natural ScienceFoundation of China, the project numbers are 50776077, 50979095and 50906074. This support is gratefully acknowledged.

References

Basu, D., Hamed, A., Das, K., 2005. DES Hybrid RANS/LES and PANS model forunsteady separated turbulent flow simulations. In: Proceedings of FEDSM 5,pp. 19–23.

Benim, A.C., Pasqualotto, E., Suh, S.H., 2008. Modeling turbulent flow past a cir-cular cylinder by RANS, URANS LES and DES. Progress in Computational FluidDynamics 8, 299–307.

Boyd, G.M., Rosser, R.M., Cardwell, B.B., 1961. Transients flow performance in amultiloop nuclear reactor system. Nuclear Science and Engineering 9, 442–454.

Croba, D., Kueny, J., 1996. Numerical calculation of 2D, unsteady flow in centrifu-gal pumps: impeller and volute interaction. International Journal for NumericalMethod in Fluids 22, 467–481.

Felix, A., Peter, H., Philippe, D., 2002. CFD calculation of a mixed flow pump char-acteristic from shutoff to maximum flow. Journal of Fluid Engineering 124,798–802.

Gonzalez, J., Fernandez, J., Blanco, E., 2002. Numerical simulation of the dynamiceffects due to impeller–volute interaction in a centrifugal pump. Journal of FluidEngineering 124, 348–354.

Joseph, L., Hamill, F.A., 1972. Start-up pressures in short pump discharge lines. Jour-nal of the Hydraulic Division, Proceedings of ASCE 98, 1117–1125.

Kaliatka, A., Uspuras, E., Vaisnoras, M., 2007. Benchmarking analysis of water ham-mer effects using RELAP5 code and development of RBMK-1500 reactor maincirculation circuit model. Annals of Nuclear Energy 34, 1–12.

Kazem, F., Anis, B., Franscesco, D., 2007. A model for the analysis of pump start-uptransients in Tehran Research Reactor. Progress in Nuclear Energy 49, 499–510.

Lefebvre, P.J., Barker, W.P., 1995. Centrifugal pump performance during transientoperation. Journal of Fluid Engineering 117, 123–128.

Rikke, K., Christian, B., Nicholas, P., 2003. Flow in a centrifugal pump impeller atdesign and off-design conditions. Part II. Large eddy simulations. Journal of Fluid

rifugal pump during the discharge valve rapid opening process. Nucl.

Engineering 125, 73–83.Spalart, P.R., Jou, W.H., Allmaras, S.R., 1997. Comments on the feasibility of LES

for wings, and on a hybrid RANS/LES approach. In: First AFOSR InternationalConference on DNS/LES.

Tsukamoto, H., Ohashi, H., 1982. Transient characteristics of a centrifugal pumpduring starting period. Journal of Fluid Engineering 104, 6–13.

ING

N

8 ring an

T

W

W

W

Wu, D., Xu, B., Li, Z., et al., 2009. Numerical simulation on internal flow of centrifu-

ARTICLEModel

ED-5993; No. of Pages 8

D. Wu et al. / Nuclear Enginee

utar, M., Hold, A.E., 2001. Computational modelling of flow around a circular cylin-der in sub-critical flow regime with various turbulence models. InternationalJournal for Numerical Methods in Fluids 35, 763–784.

ang, L., Wu, D., Zheng, S., 2003. Experimental study on transient performance of amixed-flow-pump. Fluid Machinery 31, 1–3.

Please cite this article in press as: Wu, D., et al., The transient flow in a centEng. Des. (2010), doi:10.1016/j.nucengdes.2010.08.024

ang, L., Li, Z., Dai, W., et al., 2008. 2-D numerical simulation on transient flow incentrifugal pump during starting period. Journal of Engineering Thermophysics29, 1319–1322.

enxi, T., Su, G.H., Wang, G., 2008. Numerical simulation and optimization on valve-induced water hammer characteristics for parallel pump feedwater system.Annals of Nuclear Energy 35, 2280–2287.

PRESSd Design xxx (2010) xxx–xxx

Werner, B., Audrius, J., Annalisa, M., 2008. Analysis of the capability of system codesto model cavitation water hammers: simulation of UMSICHT water hammerexperiments with TRACE and RELAP5. Nuclear Engineering and Design 238,1129–1145.

rifugal pump during the discharge valve rapid opening process. Nucl.

gal pump during transient operation. Journal of Engineering Thermophysics 30,1319–1322.

Wu, D., Wang, L., Hao, Z., et al., 2010. Experimental study on hydrodynamic perfor-mance of a cavitating centrifugal pump during transient operation. Journal ofMechanical Science and Technology 24, 575–582.