in

hran

Computational uid dynamicsExperimentalPump as turbine

turestntaeraas tts oect

ical and numerical results, the pump was tested as a turbine in a test rig. All required parameters were

alternreversainta

researcWith

Numerous papers have been published on this subject, but therehas been comparably limited use of this knowledge. Stepanoff[2], Sharma [3], Wong [4], Gantar [5], Williams [6], Alatorre-Frenk[7], Ramos and Borga [8], Derakhshan and Nourbakhsh. [9], havepresented some relations to predicate the best efciency point(BEP) of a PAT. The results obtained by these relations had almost20% deviation from experimental data [10].

a turbine in this test rig. All required parameters were measuredto achieve complete characteristic curves of the reverse pump.The theoretical and numerical results were compared with exper-imental data and some other methods.

2. Theoretical analysis

When a centrifugal pump operates as a turbine, ow and rotat-ing directions are reverse. There is one passage with two oppositeows and rotating directions. Using area ratio method [5,13], a

* Corresponding author. Tel.: +98 21 82 08 48 31; fax: +98 21 88 33 86 48.

Experimental Thermal and Fluid Science 32 (2008) 16201627

Contents lists availab

a

.eE-mail address: shhoureh@ut.ac.ir (S. Derakhshan).mands, it will be more economical to exploit such energy sourcesin the future. Experiments have shown that in relatively low poweroutputs, pumps with high technological standards in reverseoperation can compete with conventional turbines in respect tomaximum efciency [1]. Pump manufacturers do not normallyprovide characteristic curves of their pumps working as turbines.This makes it difcult to select an appropriate pump to run as aturbine for a specic operating condition.

Since behavior of a pump running as a turbine changes, predic-tion of characteristic curves of pump as turbine (PAT) is difcult.

Anderson [13]. This method estimates turbine mode hydrauliccomponents based on pump characteristics. Also, this pump wassimulated in reverse and direct modes using computational uiddynamics. 3D full NavierStokes equations were solved using Fine-Turbo V.7 ow solver. Using numerical results, complete character-istic curves of the pump in direct and reverse modes wereobtained.

A complete mini hydropower test rig established in laboratory[9] was used for experimental verication of theoretical andnumerical results. The simulated centrifugal pump was tested as1. Introduction

One of the cheap and attractivepower resources is using pumps inrelatively simple machines, easy to min most developing countries. Theturbines was started around 1930.0894-1777/$ - see front matter 2008 Elsevier Inc. Adoi:10.1016/j.expthermusci.2008.05.004measured to achieve complete characteristic curves of the reverse pump. The theoretical and numericalresults were compared with experimental data and some other methods.

2008 Elsevier Inc. All rights reserved.

atives in small water-e operation. Pumps arein and readily availableh on using pumps-as-increasing energy de-

Most recent attempts to predict performance of PAT, have beenmade using computational uid dynamics (CFD) [11,12]. However,without verifying the CFD results by experimental data, they arenot reliable.

In this paper, the best efciency point of an industrial centrifu-gal pump running as turbine was achieved using theoretical anal-ysis based on area ratio method developed by Williams [5] andBest efciency pointCharacteristic curves equations were solved using FineTurbo V.7 ow solver. Using numerical results, complete characteristic

curves of the pump in direct and reverse modes were obtained. For experimental verication of theoret-Theoretical, numerical and experimentalreverse operation

Shahram Derakhshan *, Ahmad NourbakhshDepartment of Mechanical Engineering, Faculty of Engineering, University of Tehran, Te

a r t i c l e i n f o

Article history:Received 1 December 2007Received in revised form 13 May 2008Accepted 14 May 2008

Keywords:

a b s t r a c t

When a pump works as adeveloped to predict the bcoincidence with experimeior of pumps in reverse opcentrifugal pump runningmate hydraulic componenpump was simulated in dir

Experimental Therm

journal homepage: wwwll rights reserved.vestigation of centrifugal pumps in

, P.O. Box 11365/4563, Iran

bine, its hydraulic behavior will be changed. Several methods have beenefciency of pumps running as turbines but their results are not in goodl data for all pumps. Therefore, study and investigation of hydraulic behav-tion can be useful. In this study, the best efciency point of an industrialurbine was achieved using a theoretical analysis. This method tries to esti-f reverse (turbine) mode using direct (pump) mode. In the next step, theand reverse modes by computational uid dynamics. 3D full NavierStokes

lsev ier .com/ locate/et fsle at ScienceDirect

l and Fluid Science

Thercorrelation passage between direct and reverse modes of a centrif-ugal pump may be found. To calculate head, discharge and ef-ciency of PAT at BEP, hydraulic losses in volute and impeller,mechanical losses related to power losses due to gland packingand bearing cases, disc friction losses in gaps between rotor andstator, volumetric losses related to leakage from clearances be-tween rotor and stator shall be detected.

Fig. 1 shows inlet and outlet velocity triangles in pump and tur-

Nomenclature

a area, m2

b impeller passage widthc absolute velocity, m/sD diameter, me impeller blade thickness, mg gravitational acceleration, m/s2

H head, mm diameter ratio, D2D1

N rotational speed, rpmn rotational speed, rpsNs specic speed, (m, m3/s)P power, W, kWQ discharge, m3/su peripheral velocity, m/sw relative velocity, m/sz impellers blade number

Greek symbolsa absolute velocity angle (rad)b relative velocity angle (rad)b0 blade angle (rad)e utilization factoru discharge numberl slip factor

S. Derakhshan, A. Nourbakhsh / Experimentalbine modes. In Fig. 1.a, the gray velocity triangle is related to slipphenomenon (l is slip factor) on pump mode, since in impelleroutlet, real relative ow angle (b2) is smaller than blade angle(b02). The absolute ow angle in position 2, a2, is approximatelythe same for both modes of operation in respect to the shape ofthe volute. A good estimation of this angle is the volute angle, av.In reverse mode, the ow angle in blade outlet (b3) can be assumedclose to the blade inlet angle (b01) (no whirl at exit). Using momen-tum theorem and turbine inlet and outlet velocity triangles, Eulerhead in turbine mode is [2]

H00t u2cu2 u3cu3

g1

Using velocity triangles Eq. (1) can be changed to

H00t u3Q

00t

gm cotav

a2 cotb

01

a1

u

23

g2

Shockless discharge Q 00t is obtained as

Q 00t Cm a2 u2 a2

cotav cotb023

To avoid shock losses, the inlet relative velocity angle (b2) should beas much as possible close to the blade inlet angle.

Flow reaches the impeller after hydraulic losses in volute. Theselosses must be added to Euler head. Since computing of hydrauliclosses is difcult, these losses were estimated using pump mode.The hydraulic efciency of a pump at BEP can be computed usingits overall efciency [2]:

ghp gp

p 4Leakage value for pump operation is estimated using Thorne meth-od [14]. Volumetric efciency is

glp 1Q lp

Qp Q lp5

The important parameter is the overall mechanical efciencyincluding power losses due to disc friction, gland packing and bear-ing losses. Overall mechanical efciency is determined using:

g efciencyp power numberq density, kg/m3

x rotational speed, rad/sw head number

Superscript theoretical

Subscriptsb best efciency pointe blade exith hydraulici impellerl leakagem meridianme mechanicaln netu peripheralp pumpv volutet turbine

mal and Fluid Science 32 (2008) 16201627 1621gmep gp

glpghp:

Hydraulic efciencies in impeller and volute can be dened as

gip H0

H00; gvp

HH0

6

where H00;H0, H are Euler, impeller and real heads, respectively. Itcan be assumed friction losses in impeller and volute are the same,besides, the shock losses in impeller are approximately close to thediffusion losses in volute [5]. So, total losses in volute and impellerare equal: H00 H0 H0 H.

Impeller and volute efciencies are computed as follows:

H0

H00 HH0

HH00

) ghp gip gvp

1 gip H00H0H00

1 gvp H0HH0

H00 H0 H0 H

8>: ) 1 gip 1 gvpgipThen

gvp 2ghp

1 ghp; gip

1 ghp2

7

In general, contraction losses are less than expansion losses (insame shapes) [5]. Therefore, volute hydraulic losses in reverse modeare less than direct mode (in same conditions). In other words:

1 gvt k1 gvp; k < 1 8

and pump modes are the same. Power losses due to leakage arecomputed as

Plt c Q lt Ht gvt 12Volute power losses of turbine mode are

Pvt 1 gvt c Q t Ht 13Using Eqs. (12) and (13), kinetic energy losses in turbine impelleroutlet is calculated as

Pet 1 e c Q t Ht Pvt Plt 14In same procedure of volute (Eq. (8)), hydraulic efciencies of

impeller in turbine and pump modes are

1 git 0:91 gip 15Hydraulic losses of impeller in turbine mode are evaluated as

Pit 1 git c Q t Ht Pvt Plt Pet 16Turbine net power is

Pnt c Q t Ht Pvt Plt Pet Pit Pmt 17

Thermal and Fluid Science 32 (2008) 162016272cm2

cu2

w22c

2(1-)u

c22w

a

b

1622 S. Derakhshan, A. Nourbakhsh / ExperimentalThere are no empirical equations for the contraction losses and ksubsequently. However, Williams [5] assumed: k = 0.9.

In turbine impeller outlet, a little no-recovered energy exists inform of kinetic energy. The utilization factor is dened as

e utilized energy by impelleravailable energy for impeller

;

using Fig. 1.a, the utilization factor is:

e H00t

H00t c2u32g

; cu3 Q00t

a1 tanb01 u3 9

Real head at BEP of turbine operation is

Ht e gvt H00t 10Turbine discharge at BEP can be evaluated as shockless dischargeand leakage value. Using pump leakage value, turbine leakage valuecan be estimated by

Q lt Q lp HtHp

s11

Discharge at BEP of turbine mode is Q t Q 00t Q lt .To calculate maximum efciency of PAT, total losses shall be

evaluated. In same rotational speeds, mechanical losses in turbine

2 vm2c

u2c2u

1

u3

w3

3c

cu3

cm3

Fig. 1. (a) Pump impeller outlet velocity triangle, (b) turbine impeller inlet andoutlet velocity triangles.Turbine maximum efciency is

gt Pnt

c Q t Ht c Q t Ht Pvt Plt Pet Pit Pmt

c Q t Ht18

Using simple assumptions, the BEP of PAT was achieved.

3. Numerical simulation

A 3D model of the pump was generated where the model in-cludes the whole impeller and the volute since a single blade chan-nel model of the impeller alone is not enough to study thecircumferential variation of the ow caused by volute (Fig. 2).The model does not include the ow eld in the space betweenimpeller hub/shroud and casing nor the sealing gap. The grid sizewas approximately 700,000 cells. The FineTurbo V.7 ow solverdeveloped by Numeca was used and grid was generated usingIGG5.5 for the volute and Autogrid5 for the impeller.

FineTurbo is an integrated software based on nite volume dis-cretization for multi-block structured grids. The multi-block struc-tured grids on the blades were prepared by IGG5.5 and AutoGrid5[15,16]. The physical model used in the solver is the Reynolds-Fig. 2. 3D model of simulated centrifugal pump.

Averaged NavierStokes equations in rotating frames of referencecoupled with various turbulence models and near-wall treatmentfor low-Reynolds modeling. Without any restriction, the standardhigh Reynolds ke turbulence model can be chosen with extendedwall functions [1618]. The discrete schemes are physically basedsecond order [18]. For fast convergence, mass ow rate, velocitydirection, turbulence kinetic energy k and turbulent dissipation ewere imposed at inlet boundary while at outlet boundary condi-tion, static pressure was prescribed. Finally, periodic boundarycondition was applied between two blades.

To check if the grid used in the whole pumpmodel is too coarse,simulations were made with one impeller channel and two differ-ent grids. The rst grid had the same grid coarseness with 70,000cells for one impeller channel and the second one consisted ofabout 200,000 cells. The simulation results showed less than 1%difference in calculated efciencies and heads.

4. Experimental setup

A complete laboratory model of mini hydropower plant was in-stalled in University of Tehran [9] as shown in Fig. 3. The dischargeand head for pump working as turbine were generated in theexperimental setup by each tested pump. When a pump is working

as turbine, a control system is needed to regulate the frequency.The classical governor used for standard turbines are expensiveand not always recommended for small hydropower plants. Sincethese types of plants are more used in remote areas, an electronicload controller with ballast loads was built and used for keepingthe frequency of generator in these tests. A conventional synchro-nous generator was installed to produce electricity. To measure theturbine shaft torque, generator is changed to suspense state andusing a scaled arm and several weights, turbine shaft torque canbe measured. The discharge was measured by the discharge lawand using various orice plates for each test. Pressures were mea-sured by some barometers ranging from 0 to 5 bar. An industriallow specic speed centrifugal pump with specic speed 23.5 (m,m3/s) was selected for testing as turbine. This pump has the max-imum input turbine shaft power, the maximum head and the max-imum discharge of 20 kW, 25 m and 120 l/s, respectively. For thePAT testing, feed pump, several pipes, an orice, a generator andballast loads were selected and installed in the test rig. In thePAT applications, it should be considered: that if a generator is cou-pled directly, a nominal speed corresponding to one of synchro-nous speeds (e.g. 750, 1000, 1500 or 3000 rpm) should bechosen. For induction generators and also induction motors, slipmust be taken into account (the tested pump rotates with

Consumer

FlowMeterValve

MotorPumpTurbine

Torque Meter

Generator

Controller

Vessel

Barometer

Fig. 3. The mini hydropower established in University of Tehran.

.06

S. Derakhshan, A. Nourbakhsh / Experimental Thermal and Fluid Science 32 (2008) 16201627 16230

2

4

6

8

10

0 0.02 0.04 0

ExpCFDFig. 4. Measured and numerical head numb0.08 0.1 0.120

20

40

60

80

100

(%

)er and efciency curves of pump mode.

1450 rpm in pump mode). Practically, synchronous generators areusually used. The PAT was tested in Nt = 1500 rpm.

After measuring all parameters, PAT head, discharge, outputpower and efciency were obtained. A rst-order uncertainty anal-ysis is performed using constant odds combination method, basedon a 95% condence level as described by Moffat [19]. The uncer-tainty of head, ow rate, power and efciency are, 5.5%, 3.4%,5.1% and 5.5%, respectively.

5. Results

Table 1 shows BEP of the pump predicted by theory andexperiment.

Here, w, u, p are dened as

w gHn2D2

; / QnD3

; p Pqn3D5

19

Theoretical method predicted 1.1%, 4.7%, 5.25% and 2.1% lower dis-charge number, head number, power number and efciency thanexperimental data at BEP, respectively. The head and power pre-dicted by this method are lower than experimental data due tothe volute and the impeller losses evaluation.

The characteristic curves of head, discharge, power and ef-ciency in pump and turbine modes achieved by experimental andCFD methods were shown in Figs. 47. CFD could not simulateleakage, disc friction and mechanical losses since numerical modeldid not include ow eld in the space between impeller hub/shroud and casing nor the sealing gap. To compare CFD results

with experimental data, leakage value estimated using Thornemethod [14] was reduced from CFD discharges in pumpmode. Alsomechanical and disc friction losses evaluated using Stepanoffmethod [2] were added to the pump input power obtained byCFD. The results resemble the experimental data as Figs. 4 and 5.Table 2 shows the BEP of the pump predicted by CFD and experi-ment. CFD predicted 4.1%, 0.3% and 4.2% and 1.3% higher dischargenumber, head number, power number and efciency than experi-mental data at BEP, respectively.

CFD results for turbine mode were not in good coincidence withexperimental data. In turbine mode, the measured discharge ismore than real discharge passing from impeller. Using Eq. (11), tur-bine leakage value was added to CFD discharges of turbine mode.Mechanical and disc friction losses in reverse mode are close to di-rect mode in same rotational speeds [5]. These losses were reducedfrom turbine output power computed by CFD. Figs. 6 and 7 showresults for PAT.

Table 3 compares the values of BEPCFD and BEPExp of turbinemode. The deviations of CFD results from experimental data atBEP are 1.1%, 22.9%, 16.4% and +5.5% for discharge number,head number, power number and efciency, respectively. Thesedeviations maybe in respect to the loss mechanisms in variouszones of the PAT control volume and rotational momentum theoryacross the impeller.

Deviations of the CFD results for the PAT also suggest a lowerdetermination of the net rotational momentum compared to mis-

Table 1PAT dimensionless BEP predicted by theoretical method and experiment

Theoretical Experimental. Theoretical error (%)

/ 0.089 0.09 1.1

0.0

1624 S. Derakhshan, A. Nourbakhsh / Experimental Thermal and Fluid Science 32 (2008) 16201627w 9.15 9.6 4.7p 0.578 0.61 5.25g 0.71 0.725 2.1

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04

ExpCFDFig. 5. Measured and numerical power numbcalculation of hydraulic losses. However, the miscalculation oflosses cannot be ruled out. CFD results of pump mode resembleexperimental data. In turbine mode, numerical results and experi-mental data are not in good coincidence. These deviations are con-rmed by other published numerical results [12]. Differencebetween real geometry and CFD model is only in interaction be-tween volute and impeller according to Fig. 8, since the model doesnot include ow zone in the space between impeller hub/shroudand casing. There are some miscalculation losses by CFD wherehead and output power show lower rotational momentum for allregions of discharges. Maybe there are two phenomena in Fig. 8,

6 0.08 0.1 0.120

20

40

60

80

100

(%

)er and efciency curves of pump mode.

TherS. Derakhshan, A. Nourbakhsh / Experimentalchanging the ow angle in impeller inlet (zone A) and additionallosses related to zone B.

0246

810121416182022

24262830

0 0.02 0.04 0.06

ExpCFD

Fig. 6. Measured and numerical head numbe

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 0.02 0.04 0.06

ExpCFD

Fig. 7. Measured and numerical power numb

Table 2Pump dimensionless BEP predicted by CFD and experiment

CFD Experimental CFD error (%)

/ 0.067 0.064 +4.1w 5.66 5.64 +0.3p 0.49 0.47 +4.2g 0.78 0.77 +1.3mal and Fluid Science 32 (2008) 16201627 1625In pumpmode, ow enters from impeller outlet zone into great-er zone as volute inlet. Therefore there are no miscalculated losses

0.08 0.1 0.12 0.140

20

40

60

80

100

(%

)

r and efciency curves of turbine mode.

0.08 0.1 0.12 0.140

20

40

60

80

100

(%

)

er and efciency curves of turbine mode.

Table 3PAT dimensionless BEP predicted by CFD and experiment

CFD Experimental CFD error (%)

/ 0.089 0.09 1.1w 7.4 9.6 22.9p 0.51 0.61 16.4g 0.765 0.725 +5.5

Table 5 compares the results of theoretical and numericalmethods with experimental data and some other methods. Numer-ical and theoretical methods estimated the discharge adequately.Predicting the head by theoretical methods is nearly close toexperimental data. Numerical method cannot estimate the

1626 S. Derakhshan, A. Nourbakhsh / Experimental Thermal and Fluid Science 32 (2008) 16201627AAB Bin CFD simulation. On the other hand, the effect of geometric sim-plication is likely to be greater in turbine mode, because its effecton downstream ow is more than upstream ow, i.e. ow throughthe impeller. Table 4 shows the deviations of numerical resultsfrom experimental data at a part-load point. In simulation, ow en-ters to the impeller by greater absolute ow angle especially at BEP(Fig. 9). Losses of zone B are miscalculated by CFD in all dischargeregions.

a bFig. 8. Volute and impeller interaction: (a) real- and (b) CFD-model.

Table 4PAT dimensionless part-load point at same discharge predicted by CFD andexperiment

CFD Experimental CFD error (%)

/ 0.06 0.06 w 4.6 6.0 23.3p 0.18 0.2 10g 0.633 0.55 +15.1

2real

u2real

2real

c

2CFDw

w 2CFDc

CFDreal

m2c

u2CFDc

c

2u

Fig. 9. Turbine mode inlet velocity triangles in real (derived from theory andexperimental head and ow) and CFD.

Table 5PATs dimensionless BEP predicted by various methods

Pump Experimental CFD Theoretical

Ns (m, m3/s) wt/wp /t//p wt/wp /t//p wt/wp /t//

23.5 1.7 1.41 1.31 1.40 1.62 1.39head accurately. The validity of any prediction method isbased on accurate predictions of both head and the dischargeaccurately.

Stepanoff [2], Sharma [3] and Alatorre-Frenk [7] did not showacceptable results in comparing with the experimental data forboth of the head and the discharge.

6. Conclusions

In this paper, a theoretical method was presented to calculatebest efciency point of reverse pump based on pumping modecharacteristics (geometric and hydraulic). This methods predictedvalues are slightly lower than experimental data. In fact, the lossesin volute and impeller must be evaluated exactly. In the next step,a centrifugal pump (NS = 23.5 (m, m3/s)) was simulated using CFDin direct and reverse modes. To verify numerical results, simulatedpump was tested as a turbine in the test rig. CFD results were ingood coincidence with experimental data for pump mode not onlyat best efciency point but also in part-load and over-load zones.But numerical results were not in acceptable coincidence withexperimental data for turbine mode. Turbine head and power val-ues achieved by CFD were lower than experimental data at samedischarges. The only difference between direct and reverse modeswas in ow and in rotating directions. The difference between realgeometry and CFD model was in interaction between volute andimpeller since ow zone in the space between impeller hub/shroudand casing was not included in the model. The effect of geometricsimplication is likely to be greater in turbine mode, because its ef-fect on downstream ow is more than upstream ow, i.e. owthrough the impeller.

Characteristics of best efciency point predicted by numericalmethods were not in good coincidence with experimental data. Fu-ture works on CFD application can be improved, since the applica-tion of CFD fails in the turbine boundary as proved with this study.

References

[1] J.M. Chapallaz, P. Eichenberger, G. Fischer, Manual on Pumps used as Turbines,Vieweg, Braunschweig, 1992.

[2] A.J. Stepanoff, Centrifugal and Axial Flow Pumps, Design and Applications, JohnWiley and Sons, Inc., New York, 1957.

[3] K. Sharma, Small hydroelectric project-use of centrifugal pumps as turbines,Technical , Report, Kirloskan Electric Co., Bangalore, India, 1985..

[4] W. Wong, Application of centrifugal pumps for powers generation, WorldPump (1987) , pp. 348381.

[5] M. Gantar, Propeller pumps running as turbines, in: Conference on HydraulicMachinery, September 1315, 1988, Ljubljana, Slovenia, pp. 237248.

[6] A. Williams, Pumps as turbines used with induction generations of stand-alonemicro-hydroelectric power plants, Ph.D.M.E. Thesis, Nottingham Polytechnic,1992.

[7] C. Alatorre-Frenk, Cost minimization in microhydro systems using pumps-as-turbines, Ph.D.M.E. Thesis, University of Warwick, 1994.

[8] H. Ramos, A. Borga, Pump as turbine: an unconventional solution to energyproduction, Urban Water 1 (1999) 261263.

[9] S. Derakhshan, A. Nourbakhsh, Experimental study of characteristic curves ofcentrifugal pumps working as turbines in different specic speeds,Experimental Thermal and Fluid Science 32 (2008) 800807.

Stepanoff [2] Sharma [3] Alatorre- Frenk [7]p wt/wp /t//p wt/wp /t//p wt/wp /t//p

1.30 1.14 1.37 1.23 1.65 1.63

[10] A. Williams, Pumps as Turbines Users Guide, International TechnologyPublications, London, 1995.

[11] A. Tomm, A. Braten, B. Stoffel, G. Ludwig, Analysis of a standard pump inreverse operation using CFD, in: 20th IAHR Symposium, 2000, Charlotte NorthCarolina, USA, Paper No. 5.

[12] A. Rodrigues, P. Singh, A. Williams, F. Nestmann, E. Lai, Hydraulic analysis of apump as a turbine with CFD and experimental data, in: ImechE, Seminar Proc.of Advances of CFD in Fluid Machinery Design, 2003, London, England.

[13] H.H.Anderson, Anderson, Modern developments in the use of large singleentry centrifugal pumps, Proc. Inst. Mech. Eng. 177 (31) (1993).

[14] E.W. Thorne, Design by the area ratio method, in: Sixth Technical Conferenceof the BPMA, 1979.

[15] AutoGrid v.5 User Guide, Numeca, 2006.[16] N. Hakimi, Preconditioning methods for time dependent NavierStokes

equations, PhD thesis, Vrije Universiteit Brussel, 1997.[17] B. Launder, D. Spalding, The numerical computation of turbulent ow,

Computer Methods in Applied Mechanics and Engineering 3 (1974) 269289.[18] FineTurbo v.7 User Guide, Numeca, 2006.[19] R.J. Moffat, Contributions to the theory of single-sample uncertainty analysis,

ASME J. Fluids Eng. 104 (1982) 250260.

S. Derakhshan, A. Nourbakhsh / Experimental Thermal and Fluid Science 32 (2008) 16201627 1627

Theoretical, numerical and experimental investigation of centrifugal pumps in reverse operationIntroductionTheoretical analysisNumerical simulationExperimental SetupsetupResultsConclusionsReferences