Performance measurements on a Pelton turbine model

Performance measurements on a Pelton turbine modelF G Stamatelos, J S Anagnostopoulos∗, and D E PapantonisSchool of Mechanical Engineering, National Technical University of Athens, Athens, Greece

The manuscript was received on 19 May 2010 and was accepted after revision for publication on 22 September 2010.

DOI: 10.1177/2041296710394260

Abstract: Pelton hydraulic turbines are impulse-type turbomachines commonly used in hydro-electric plants with medium-to-high water head and in various energy recovery applications. Theaim of the present work is to provide detailed performance measurements on a Pelton turbinemodel, along with the design and geometrical dimensions of its runner/buckets and injectors.Such a complete set of data would be useful for further development and evaluation of numericalmodelling tools of the complex unsteady free-surface flow developed in the turbine, and is miss-ing from the literature. The two-nozzle Pelton model was designed using standard guidelines andwas fully constructed in the Laboratory of Hydraulic Turbomachines, NTUA. The measurementsinclude the net water head and flowrate, the injector characteristic curves, and the torque androtation speed of the runner, from which the corresponding overall efficiency and shaft powerare computed. The model was tested with one injector (upper or lower) and with both injectors inoperation, using either constant or variable rotation speed mode. The comparative results weresatisfactory and in line with the theory, verifying similarity and repeatability, and allowing for anestimation of mechanical losses. The measurements covered the entire operation range of theturbine, in order to draw complete hillcharts for various operation modes.

Keywords: Pelton turbine model, performance measurements, runner geometry, turbinehillcharts, mechanical losses

1 INTRODUCTION

In 1879, Lester Pelton developed an impulse hydrotur-bine runner with double-bucket design that exhaustedthe water to the side, decreasing the correspond-ing kinetic energy losses. Later on, in 1895, WilliamDoble improved Pelton’s idea and created an ellipti-cal bucket with a cut, allowing the water jet to enterthe bucket smoothly. The current bucket design prac-tices are based mainly on the accumulated experience;however, in recent years significant effort has beendirected towards a better understating of the detailsof the complex unsteady flow in the runner, with theaid of modern numerical modelling and experimen-tal techniques. Now, all Pelton turbine componentsare analysed by calculation and the research aims ata complete design optimization of the buckets and thedistribution system.

∗Corresponding author: School of Mechanical Engineering,

National Technical University of Athens, 9 Heroon Polytechniou

Str., Zografou, Athens 15780, Greece.

email: [email protected]

The experimental studies on Pelton hydroturbinesthat have been published in the literature are notmany. The high complexity of the unsteady jet–bucketinteraction in the rotating runner and, moreover, thecontaminating effects of the outflow that splasheson the casing walls make the measurements of theflow in the interior of the casing practically impossi-ble. Hence, the existing experimental works concerneither flow visualization studies [1, 2] or flow–bucketinteraction in non-rotating buckets [3, 4].

Perrig et al. [1, 2] used flow observation techniquesto study the unsteady evolution of the free-surfaceflow in a single-injector Pelton runner. They found thatthe impact of the droplets released from the bucketscauses perturbations on the jet surface, which mayresult in reduced bucket efficiency. Also, some morecomplex and not well understood mechanisms dur-ing the jet cut process were identified and showedthat they can influence considerably the subsequentevolution of the flow in the bucket and the energyexchange efficiency (compressibility effects, spray andwater threads formation, Coanda effect, etc.).

The measurements of Kvicinsky et al. [3] includepressure distribution and water layer thickness in a

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F G Stamatelos, J S Anagnostopoulos, and D E Papantonis

steady jet–bucket interaction, whereas in a similar testrig Zoppe et al. [4] conducted experiments for variousjet incident angles and present additional data for totaltorque and thrust variation versus the jet diameter andangle.

Kvicinsky et al. [5, 6] used 32 pressure sensors onthe inner surface of a rotating bucket and performedunsteady pressure measurements, defining five dif-ferent pressure zones on the surface. The transientpressure distribution on a rotating bucket was mea-sured in the works of Mack et al. [7] and Perrig et al. [8].The comprehensive experimental study of Perrig [9]also includes measurements of the water film thick-ness evolution and the pressure coefficient variationat various zones of the bucket during the runner rota-tion, and analyses the contribution of each zone to theenergy transfer. Also, the importance of some complexmechanisms developed in the jet impact and the back-side flow was identified, and the energy losses duringthe jet–bucket interaction were analysed. The authoremphasizes the need for additional measurements toquantify these effects.

Flow visualization studies have also been conductedin the jet discharged from the nozzle of Pelton turbineinjectors, and several parameters that can influencethe jet quality and cause reduction of runner perfor-mance and efficiency were examined. The influenceof the injector design on the unsteady and divergentbehaviour of the jet is studied by Staubli and Hauser[10], whereas the significant role of secondary flowsgenerated at the bends of the distribution piping onthe jet shape, orientation, and surface disturbancesand instabilities was identified by Zhang and Parkin-son [11] and Zhang and Casey [12], and supported bylaser Doppler anemometry (LDA) velocity measure-ments. Finally, the effect on the runner efficiency ofthe jet interference in multi-jet Pelton turbines and ofthe casing dimensions were investigated in the exper-imental works of Fuji et al. [13] and Matthias et al.[14], respectively.

An extended flow mechanical analysis was done inthe theoretical work of Zhang [15] for a better under-standing of the flow in a rotating bucket. The particularcontribution of the flow frictions in the bucket surfaceto the total losses, as well as of the jet impact work tothe total energy transfer during the jet–bucket inter-action, are investigated and quantified in subsequentstudies [16].

The computer modelling of the flow in Pelton run-ners is taking advantage from the progress in computerpower and the development of advanced softwaretools [17–19]. Computational fluid dynamics (CFD)is being increasingly used with Reynolds averagedNavier–Stokes equations (RANS) solvers and commer-cial software. Among the latest such studies are theworks of Kvicinsky [6], Mack et al. [17], Zoppe et al. [4],Perrig et al. [8, 20], and Santolin et al. [21], concern-ing from a stationary bucket, to a complete single- or

multi-injector system and rotating runner includingpenstock and casing. Also, CFD dynamic results canbe used as input for the structural analysis of Peltonrunners [18].

Although these computations can simulate theentire working cycle of the bucket, the accuracy ofthe torque predictions is still not adequate, due to thedevelopment of complex secondary flow mechanismsmentioned above that are not modelled [9, 22]. More-over, the traditional mesh-based Eulerian approachesface significant numerical diffusion problems due tothe complex evolution of the free-surface flow pat-tern, whereas the unsteadiness of the flow requiresextended and fine meshes with enormous compu-tations, which are still not feasible for industrialdesign [17].

Other numerical approaches alternative to mesh-based flow simulation methods have recently beendeveloped and applied for flow modelling in rotat-ing Pelton runners aiming at reducing the computerdemands, like the use of streamlines in the Animated-Cartoon Frames method [23], and the integration offluid particle motion equations in the Fast LagrangianSolution method [24]. The fully Lagrangian mesh-less simulation approaches adopt the Moving ParticleSemi-Implicit method [25] or the Smoothed ParticleHydrodynamics method [26–29]. These methods arebased on the incompressible Navier–Stokes equationsand among their advantages are the inherent simula-tion of the surface pattern, and the capability to predictthe behaviour of the flow after the exit from the bucketand its interaction with the casing. However, their per-formance and accuracy are still not satisfactory andfurther development and improvements are needed.

From the above survey it can be deduced that, dueto the high complexity of the flow and the implica-tion of various flow mechanisms in the jet–bucketinteraction, the numerical simulation and design toolsneed experimental support to validate and improvetheir capability to reproduce as close as possible the

Fig. 1 Laboratory Pelton turbine model


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Performance measurements on a Pelton turbine model

performance of a real Pelton turbine. The present workaims at providing comprehensive measurements ofthe performance characteristic curves in the wholeworking range of a laboratory model turbine, alongwith the detailed geometrical data of its injector, run-ner, and buckets. Such complete set of data is missingfrom the published literature; hence, it could be usefulto the continuing research effort in the area.

2 EXPERIMENTAL SET-UP

The design and construction of the Pelton turbinemodel shown in Fig. 1 were carried out completely

Table 1 Pelton original and model’s main features

Pelton turbine(Aoos River)

Pelton model(scale 1:6)

Runner pitch diameter 2407 mm 400 mmJet diameter 188 mm 31 mmRotation speed 428.6 r/min 1150 r/minFlowrate (nominal) 18.3 m3/s 270.6 m3/hNet head 653 mWG 129.6 mWGMechanic power 110 MW 83 kWBuckets 22 22Injectors 6 2

within the Laboratory of Hydraulic Turbomachinesfacilities. The model corresponds to a real turbine ofthe Greek Public Power Corporation, installed at thesprings of Aoos River, and it was constructed in a1:6 scale. A comparison of the main characteristicsbetween the original and the model turbine is givenin Table 1.

Fig. 2 Three-stage centrifugal pump

Fig. 3 Model turbine bucket design and main dimensions

Fig. 4 Model injectors design and main dimensions


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Table 2 Nozzle and spear geometry

Injector inlet diameter 81.5 mmNozzle length 53.4 mmNozzle outlet diameter 36 mmNozzle outlet angle 90◦Nozzle profile radius 75.6 mmSpear body diameter 47 mmSpear length 50 mmSpear angle 50◦Spear travel distance 40 mm

The opening of the two injectors is regulated manu-ally by a precision screw. The front cover of the model ismade of Plexiglas permitting the visual observation ofthe flow field (Fig. 1). The turbine’s brake is a 75 kW DCgenerator, which provides the capability of continuousadjustment of the rotation speed of the runner.

Water supply is provided by a 200 kW, three-stagecentrifugal pump (Fig. 2), the rotation speed of whichis controlled by a hydraulic coupler. At its Best Effi-ciency point the pump rotates at 1800 r/min, providing320 m3/h flowrate and 117 mWG net head.

The cast-iron-made buckets are mounted on therunner hub and their design details and geometricaldimensions are given in Fig. 3. The bucket’s splitterline deviates 10◦ from the radial direction of the run-ner (Fig. 3(c)). The bucket design is based on availabletheoretical guidelines [30, 31], and the same was donewith the injectors, the dimensions of which are shown

in Fig. 4 and summarized in Table 2. The spear valveopening fraction is defined as the distance �x fromthe close valve position, divided by the nozzle exitdiameter DN = 36 mm (Fig. 4).

3 MEASURING APPARATUS AND PROCEDURE

The performance data of the turbine model areobtained in the form of characteristic operation curvesof the net head, and the shaft power and the overallefficiency as a function of the flowrate and rotationspeed, varied within a broad operating range. The cor-responding physical quantities were measured at eachoperation point with the following instrumentation:

(a) rotational speed of the turbine by an electronicpulse meter (Fig. 5(a)), with measurement error±0.5 per cent;

(b) flowrate, Q, by an electromagnetic flow meter(Fig. 5(b)), which was calibrated by the volumet-ric tank of the test stand, with relative uncertainty±0.5 per cent;

(c) relative static pressure of the water right beforethe injectors, using a differential pressure trans-ducer (0–20 bar), with relative uncertainty ±0.25per cent;

(d) torque, M , developed at the shaft between theturbine and the brake, by a torque transducer

Fig. 5 Photos of the instruments used in the laboratory: (a) pulse meter; (b) flow meter; (c) torquemeter; and (d) monitoring environment


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with strain gage sensing (Fig. 5(c)), and maximumexperimental error ±0.2 per cent.

The laboratory test rig and the measuring proce-dure comply with the international electrotechnicalcommission (IEC) model test standards (TC 4/WG23). Prior to the experiments all measuring instru-ments were calibrated according to their manuals.The pressure transducer was calibrated accordingto the method of hydraulic deadweight testers. Thereferred measurement errors of the instruments corre-spond to their manufacturing and/or calibration data.According to the error propagation theory, the errorprobability of turbine performance results obtainedfrom the primary experimental data can be assessed.The flowrate and net head parameters, � and �, aswell as the turbine efficiency η are the parametersused throughout the present article, and from theirdefinition relations (1) and (2) given in section 4.2 itemerges that their relative uncertainties are within ±1per cent, ±1.25 per cent, and ±1.5 per cent, respec-tively. Furthermore, the repeatability of the measureddata was thoroughly tested for several operating pointsof the turbine on daily and weekly basis, and the calcu-lated overall efficiency results showed deviation below±1 per cent, except for the smallest spear opening,where in some particular cases it exceeded ±2 per cent.

The produced signals from the instruments were allanalog; hence, an A/D card was used for their gath-ering and digitization. The LabView 8.6� graphicalprogramming software was implemented for the dataacquisition of the analog signals and their conver-sion into digital. The dimensionless quantities of theflowrate, net head, and efficiency are calculated andthe developed graphical environment, an example ofwhich is given in Fig. 5(d), allows for continuous mon-itoring of the pump and turbine operating conditionsand real-time evaluation of every measured value, withrespect to the performance characteristic curves.

4 EXPERIMENTAL RESULTS

Several sets of measurements were conducted in orderto acquire a more reliable and comprehensive picture

of the turbine model performance. The characteristicoperation curves were obtained for nine consecutiveopening positions of the spear valve, and separatelyfor the lower and for the upper injector, as well as withboth injectors in operation.

4.1 Injector performance

Indicative views from the turbine operation are givenin Fig. 6. The photo on the left shows the opera-tion of only the upper injector at increased runnerspeed quite above the optimum to allow for bet-ter observation inside the casing. The right picturepresents a more detailed view of the free jet formationat the nozzle outlet and of its downstream diametervariation. The jet diameter takes its minimum valueabout one nozzle diameter from the exit (Vena con-tracta) and then exhibits a slight expansion becauseof the friction with the air, a typical behaviour forthis type of injectors [12]. It must be noted how-ever that the distance between the nozzle exit andthe runner, which is depicted also in Fig. 4(a), isquite larger than in full-scale turbines. This can resultin substantial spreading of the jet before its impactto the bucket, and must be taken into account innumerical simulation studies of the present turbinemodel. Moreover, it may increase the jet degradationeffects of secondary flows developed in the distri-bution branches, especially towards the closed valveposition.

The flowrate through a Pelton turbine spear valvedepends on the opening position of the valve and thefluid pressure. The corresponding performance curvescorrelate the flowrate variation with the spear openingat constant pressure. These quantities are measured atthe lower injector of the laboratory turbine model, andthe obtained performance curves are given in Fig. 7for two differential pressure values, 50 and 110 mWG.The pattern is typical for spear valves, having linearrelation at small openings and asymptotic flowrateincrease towards full opening [10]. Also, according tothe theory, the flowrate increases with the square rootof pressure.

Fig. 6 Operating turbine model: (a) view through the casing and (b) jet at the nozzle exit


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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.010

30

50

70

90

110

130

P = 50 mWGP = 110 mWG

Flo

w R

ate,

Q [m

3 /h]

Nozzle opening portion, Dx/DN

Fig. 7 Injector performance curves for two fluid pres-sures

4.2 Runner performance

In order to facilitate comparison and generalize theirusage, the flowrate and the head measurements areexpressed in dimensionless form, using the flowrateparameter � and the net head parameter �, respec-tively

� = QπR3ω

and � = 2gHR2ω2

(1)

where Q denotes the measured flowrate (m3/h), H isthe measured manometric pressure before the noz-zles, R is the runner pitch radius (R = 200 mm), ω itsangular speed, and g the gravitational acceleration.

For a given opening of the spear valve(s), the varia-tion range of the above quantities can be covered bytwo different methods: either by keeping constant theoperation point (flowrate, head, and speed of rota-tion) of the feeding pump and varying the rotationspeed of the runner, or by keeping constant the tur-bine runner speed and adjusting the pump flowrateby varying its rotation speed. These two measuringprocedures should produce equivalent results for theabove quantities � and �, as also for the correspond-ing efficiency values. In order to verify the reliabilityand the repeatability of the experimental results, thelatter were obtained with both the above procedures,and will be compared in the next section.

The overall efficiency of the turbine is calculatedfrom the ratio of the mechanical power developed onthe shaft over the hydraulic power of the fluid at theinjector inlet, as follows

η = Nm

Ni= Mω

ρgHQ(2)

where M denotes the measured torque at the shaft(kpm) and ρ is the water density. The above quantities

0,000 0,003 0,006 0,009 0,012 0,015 0,018 0,021 0,0240

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Spear opening, a 0.11 0.22 0.33 0.44 0.55 0.66 0.77 0.88 1.00

Net

Hea

d Pa

ram

eter

, y

0,000 0,003 0,006 0,009 0,012 0,015 0,018 0,021 0,0240.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Spear opening, a 0.11 0.22 0.33 0.44 0.55 0.66 0.77 0.88 1.00

Ove

rall

Eff

icie

ncy,

h

Flow Rate Parameter, F

Flow Rate Parameter, F(a)

(b)

Fig. 8 Turbine performance curves for the lower injec-tor: (a) net head parameter and (b) overall effi-ciency versus flowrate parameter, �

�, �, and η will be used for graphical presentation andanalysis of the measurements. Some indicative sets arealso given in numeric form in the Appendix.

The characteristic performance curves of the Peltonturbine model obtained with one injector (the lower)in operation and by the constant-pump/variable-turbine rotation speed method are shown in Fig. 8,where the spear valve opening, �x/DN is the draw-ing parameter. The net head parameter, �, exhibitsa smooth correlation with the flowrate parameter, �,for all openings (Fig. 8(a)), thus verifying the normaloperation of the test rig in the entire flow range. Someminor scattering of the data at high flowrates are due todifficulties in the exact regulation of the turbine speed.The scattering increases in the corresponding resultsof the overall efficiency in Fig. 8(b), because its valueobtained by equation (2) includes the perturbations ofthe torque developed at the shaft.

The pattern of the efficiency characteristic curvesin Fig. 8(b) is in agreement with the theory and with


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the known performance of Pelton turbines: for a giveninjector opening there is an optimum flowrate thatmaximizes efficiency, at which the remaining angularmomentum of the bucket outflow becomes minimum.The maximum efficiency is achieved for an inter-mediate injector opening, whereas there is a smalldecrease towards full opening, due to the increase ofthe jet diameter and the entailed reduction of buck-ets accommodation effectiveness. On the other hand,efficiency exhibits a drastic drop below certain injec-tor opening (here below 20 per cent), but this timebecause of the degradation of the jet quality (devi-ation from the axis, surface disturbances, or otherinstabilities).

The corresponding turbine performance with theupper injector in operation was found to be almostthe same with the lower one. Also, the � − � and η − �

characteristic curves have the same pattern when bothinjectors are operating, as shown in Figs 9(a) and (b),

0.000 0.006 0.012 0.018 0.024 0.030 0.036 0.042 0.0480

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Spear opening, a 0.11 0.22 0.33 0.44 0.55 0.66 0.77 0.88 1.00

Net

Hea

d P

aram

eter

, y


(b)Flow Rate Parameter, F

0.000 0.006 0.012 0.018 0.024 0.030 0.036 0.042 0.0480.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Spear opening, a 0.11 0.22 0.33 0.44 0.55 0.66 0.77 0.88 1.00

Ove

rall

Effi

cien

cy, h

Fig. 9 Turbine performance curves with both injectors:(a) net head parameter and (b) overall efficiencyversus flowrate parameter, �

respectively, where only the total flowrate rangeis now double. Some differences in the maximumefficiency values can be observed compared to thesingle-injector operation in Fig. 8(b), which will bediscussed later.

4.3 Constant turbine speed operation mode

The above measurements were repeated followingthe second, variable-pump/constant-turbine rotationspeed method, in which the runner speed is fixed to700 r/min and the characteristic curves are obtainedby varying the feeding pump rotation speed. Theobtained experimental data were close to the first-method ones for both single- and two-injector opera-tion, but they are not identical as the similarity ruleswould require. As shown in Fig. 10 for three indicativespear openings, the measurements with the secondmethod exhibit increased fluctuations and scattering.

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.0350

2

4

6

8

10

12

a = 1.0a = 0.33

Variable Turbine Speed Constant Turbine Speed

Net

Hea

d P

aram

eter

, y


(b)

a = 0.11

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.0350.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

a = 1.0

a = 0.33a = 0.11

Variable Turbine Speed Constant Turbine Speed

Ove

rall

Effi

cien

cy, h


Fig. 10 Comparison of different measuring procedureswith both injectors in operation: (a) net headparameter and (b) overall efficiency versusflowrate parameter


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This is mainly due to difficulties in regulating the pumprotation speed, which in turn cause deviations fromthe desired flowrate and corresponding fluctuationsin turbine loading and runner speed. Consequently,the first measuring procedure is preferable, since itrequires control of the runner rotation speed only.

4.4 Turbine efficiency analysis

The maximum attainable efficiency of the model tur-bine over the entire loading range is the envelope ofthe particular efficiency curves for various openings ofthe injectors, like the ones in Figs 8(b) and 9(b). Theseenvelope curves for one and two injectors in opera-tion are drawn in Fig. 11. The best efficiency pointis obtained with both injectors at about 60 per centof nominal flowrate and reaches a maximum valueof almost 87 per cent. The overall efficiency curveremains quite flat, with values above 80 per cent forloads between 20 per cent and 100 per cent, providingthat the unit operates with one injector at loads belowabout 45 per cent and with both injectors above thisthreshold value. The efficiency differences betweenupper and lower injector curves can be attributed topossible injector manufacturing deviations, as also tothe non-symmetric branches of the distributor, whichinduce different secondary flow structures at noz-zle inlet and consequently produce jets of not thesame quality. The second explanation seems morevalid because the discrepancy becomes much smallertowards full nozzle opening, where the influence ofsecondary flow structures is expected to reduce.

A more detailed comparative view of the turbineperformance measurements can be obtained from theefficiency data drawn in Fig. 12 for three different spearopenings and with the lower, upper, and both injectorsin operation. In order to compare the two-nozzle casewith the single-nozzle cases, the flowrate of the formeris divided by 2.

0 20 40 60 80 100 1200.65

0.70

0.75

0.80

0.85

0.90

Lower injector Upper injector Both injectors

Tur

bine

effi

cien

cy, h

Turbine load, Q/QN (%)

Fig. 11 Attainable efficiency curves of the Pelton model

0.000 0.003 0.006 0.009 0.012 0.015 0.018 0.021 0.0240.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

a = 1.0

a = 0.33

Upper nozzle Lower nozzle Both nozzles

Ove

rall

Effi

cien

cy, h


a = 0.11

Fig. 12 Comparison of overall efficiency curves forinjectors at various loadings

At the same, intermediate opening position of theinjectors (�x/DN = 0.33) the three corresponding effi-ciency curves are quite close, except for the bestefficiency region, where the two-nozzle operationshows better performance. However, for smaller open-ings this difference becomes much more pronouncedand the two-nozzle efficiency near the closing posi-tion (α = 0.11) is almost 10 percentage units greater(Fig. 12). This behaviour can be explained consider-ing that the overall turbine efficiency includes bothhydraulic and mechanical power losses. The latterconsist of the bearing losses and the windage lossesof the rotating runner, and remain about the samewhen the turbine operates at a given speed with eitherone or both injectors. However, in the second case thetotal water hydraulic power is double and hence thepercentage fraction of mechanical losses is about half.

Based on this remark, the comparative results ofFig. 12 can be used to obtain an assessment of themagnitude of turbine mechanical power losses, whichcannot be directly measured. Overall efficiency forsingle and both injectors in operation is given byequations (3) and (4)

ηsingle = Njet − Ns − Nh − Nm

Njet(3)

ηboth ≈ 2Njet − 2Ns − 2Nh − Nm

2Njet(4)

where Njet = γ QH is the net water power measuredupstream of a single injector, Nh and Ns are thehydraulic power losses at the injector and at therunner, and Nm the mechanical power losses, takenconstant in both cases. In equation (4) it was assumedthat the hydraulic losses of two-injector operationare double those of single injector. Although in two-injector operation the bifurcation introduces someadditional disturbance into the flow, the changes inflow path direction, which are mainly responsible forthe creation of secondary flow structures (cross-flow


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vortices), are similar to the ones during single-injectoroperation in each corresponding branch. Therefore,for a given spear opening the flow field in the nozzleand the produced jet quality are expected to be similarfor both operation modes.

From the above relations it can be deduced bysubtraction that

Nm

Njet≈ 2(ηboth − ηsingle) (5)

Consequently, using the experimental data of Fig. 12for the smallest opening (�x/DN = 0.11), the mechan-ical losses are about 14.5 per cent of the average ofthe corresponding water input power at a single injec-tor (overall efficiency difference from the two-injectoroperation is about 6.5 percentage units for the upperand about 8 for the lower injector).

Next, using the results of Figs 8(a) and (b), andassuming that the absolute value of the mechanicalpower losses are about the same in the entire loadrange of the runner (at fixed rotation speed), one canestimate the fraction of mechanical losses at the bestefficiency region of the turbine. For example, compari-son of the operating conditions (net head and flowrate)for maximum efficiency at the spear openings �x/DN

0.11 and 0.33 gives

Nm

Njet − 0.33= Nm

Njet − 0.11

Njet − 0.11

Njet − 0.33

≈ 0.145 · (HQ)jet−0.11

(HQ)jet−0.33≈ 0.065 (6)

Since the overall turbine efficiency for the 0.33 spearopening is about 86 per cent (Figs 8(b) and 12), thecorresponding hydraulic losses in the injector and therunner can be estimated as

Nh

Njet−0.33= Njet−0.33 − N − Nm

Njet−0.33

≈ 1 − η − Nm

Njet−0.33≈ 0.075 (7)

On the other hand, Fig. 12 shows that at largerspear valve openings the efficiency of the two-injectoroperation mode exhibits an opposite trend, becomingsubstantially less than the single-injector one (about 4percentage units at fully open position, Fig. 12). Thisunexpected behaviour cannot be attributed to eitherhydraulic or mechanical reasons. The only reasonableexplanation is that it is caused by the outflow fromthe buckets, part of which may re-enter the runnersection after exiting from the cutout notch lips or afterimpacting on the casing walls, and may also interferewith the nozzle jets and cause surface perturbations. Inaddition, the water mist environment inside the caseincreases the average density of the air surroundingthe runner and hence the windage losses. Such effectscan cause substantial reduction of the efficiency of the

runner [1, 32], and the phenomenon is expected tobecome worse as the total flowrate in the turbine (tur-bine loading) increases, a behaviour that is evident inthe experimental results (Figs 8(b), 9(b), and 12).

4.5 Losses in turbine components

In order to analyse the turbine efficiency and thepower losses in the machine further it is necessary toestimate the hydraulic losses of the spear valve. Sincemeasuring the discharged jet properties is not possiblein this case, it can be achieved only by numerical sim-ulation of the flow in the injector. Such studies havebeen carried out in the laboratory using the SmoothedParticle Hydrodynamics, as also the commercial soft-ware Fluent� [33]. Applying the latter tool the totalpower losses as the flow passes through the spear valveare numerically computed for the entire spear traveldistance in order to discriminate between the feedinglosses in the injector and the losses in the jet–bucketinteraction.

Next, considering also the mechanical losses esti-mation of section 4.4, a more detailed picture of thelosses distribution between the components of theturbine can be obtained, as demonstrated by the effi-ciency curves of Fig. 13. Increasing the measuredoverall efficiency curve by the corresponding mechan-ical losses results in the total hydraulic efficiency curveof the turbine.Then, adding to this the calculated spearvalve losses, the resulting curve represents the effi-ciency of the jet–bucket interaction mechanism andenergy exchange in the runner. This curve includesthe friction losses during the free-surface flow in thebucket, the kinetic energy of the outflow (of the orderof 1 per cent), the minor losses at the jet impact points,as well as any jet degradation and interference effects.As discussed in section 4.4, the latter become signif-icant at low and high load operation conditions. The

0 20 40 60 80 100 1200.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

Effi

cien

cy d

egre

e

Turbine Load, Q/QN

(%)

Jet-bucket interaction efficiency Total hydraulic efficiency Overall efficiency

Fig. 13 Efficiency curves of various machine compo-nents


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Fig. 14 Hillcharts of the turbine model at constant runner speed: (a) upper injector and (b) bothinjectors in operation

Fig. 15 Hillcharts of the turbine model with variable runner speed: (a) upper injector and (b) bothinjectors in operation

results in Fig. 13 indicate efficiency reduction up toabout 5 per cent and 10 per cent, respectively.

4.6 Turbine hillcharts

The complete performance hillcharts of the Peltonmodel turbine are finally constructed and presentedin Figs 14 and 15. Figure 14 presents the experimen-tal data obtained with constant runner rotating speed(700 r/min), whereas Fig. 15 presents the correspond-ing ones with the constant-pump/variable-turbinespeed method. The diagrams include � − � lines forvarious spear openings, lines of constant shaft power,and turbine efficiency contours. The general patternof all these charts is quite similar, verifying the properand qualitative design and construction process of themodel turbine followed in the laboratory. According to

the aforementioned analysis, the best efficiency areais somewhat larger in case of two-injector operation(Figs 14(b) and 15(b)), and the corresponding maxi-mum values are about 2 percentage units higher. Also,as expected, overall efficiency maximizes at aboutthe same net head value in all cases. However, thebucket outflow interferences discussed in the previ-ous section cause a displacement of the best efficiencyarea towards smaller flowrates through each nozzlein the two-injector operation case (e.g. at � ≈ 0.9 inFig. 15(a) and at � ≈ 0.14 = 2 × 0.7 in Fig. 15(b)).

5 CONCLUSIONS

The performance of a Pelton turbine model designedand constructed in the laboratory is thoroughly


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examined. The turbine has the ability to function withone or both injectors, and the measurements covera wide range of operation conditions, allowing forthe drawing of complete turbine hillcharts. The over-all efficiency results and the effects of the loading(flowrate) and spear valve opening are in agreementwith the theory. Maximum attainable efficiency isaround 86 per cent, which is a satisfactory perfor-mance for this power range (∼ 80 kW) and in line withthe literature references, verifying the turbine modeldesign effectiveness.

On the other hand, the similarity of the results whenonly one or both nozzles were open verifies the qual-ity and reliability of model construction. The observeddifferences in overall efficiency between single- andtwo-nozzle operation in the low flowrate region canbe used to estimate the mechanical losses of the run-ner, a quantity that is not directly measurable. Also,the corresponding differences in the high flowrateregion reveal and quantify the interference effects ofthe bucket outflow and the influence of the casing.

The obtained experimental data set can be used tocompare the results of numerical modelling tools inorder to improve their accuracy in predicting the per-formance data of a real Pelton turbine. This constitutesa difficult task, not only because of the high complex-ity of the unsteady jet–bucket interaction flow but alsobecause of the involvement of several complex flowmechanisms that are not completely understood andcannot be adequately modelled. Such simulation toolsare currently under development also by the presentauthors based on the Lagrangian meshless approach,and their adjustment with the aid of the obtainedmeasurements will be the objective of a future work.

© Authors 2011

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APPENDIX

Indicative experimental data for turbine operationwith the lower, the upper and with both injectors fora fixed spear valve opening fraction, α = 0.33. Thesedata correspond to the intermediate curves of Fig. 12,and they are also included in the graphs of Figs 8 to 10,as well as in the hillcharts of Figs 13 and 14. Notice thatthe � values for both injectors have been divided by 2to compare with the single-injector curves in Fig. 12.

Lower injector Upper injector Both injectors

� � η � � η � � η

0.015 61 21.68 0.5651 0.019 10 33.41 0.4778 0.029 81 20.29 0.58840.014 80 19.33 0.5989 0.017 71 28.76 0.5089 0.027 92 17.91 0.61290.013 66 16.74 0.6265 0.016 58 25.19 0.5338 0.026 16 15.82 0.64020.012 70 14.24 0.6605 0.015 50 22.05 0,5613 0.023 78 13.22 0.67280.011 84 12.38 0.6900 0.014 36 18,93 0.5953 0.022 80 11.89 0.68260.011 37 11.46 0.6985 0.013 58 16.90 0.6183 0.021 40 10.44 0.72460.010 65 10.13 0.7391 0.012 75 14.89 0.6410 0.019 82 9.224 0.76240.010 14 9.020 0,8025 0.012 08 13.50 0.6638 0.018 89 8.317 0.79510.009 598 8.233 0.7741 0.011 61 12.35 0.6849 0.017 93 7.490 0.83820.009 068 7.289 0.7930 0.010 99 11.05 0.7093 0.016 93 6.644 0.83050.008 684 6.671 0.8121 0.010 42 9.985 0.7331 0.016 47 6.210 0.84360.008 296 6.182 0.8243 0.010 01 9.201 0.7524 0.015 68 5.715 0.86540.007 917 5.572 0.8309 0.009 499 8.245 0.7734 0.014 81 5.178 0.87380.007 665 5.225 0.8270 0.009 224 7.824 0.7864 0.014 30 4.744 0.87360.007 373 4.795 0.8335 0.008 866 7.223 0.8017 0.013 81 4.430 0.85140.007 051 4.421 0.8184 0.008 523 6.637 0.8118 0.013 23 4.082 0.83070.006 784 4.118 0.8081 0.008 252 6.201 0.8200 0.012 75 3.755 0.80030.006 650 3.908 0.7922 0.007 997 5.848 0.8272 0.012 40 3.562 0.76600.006 332 3.557 0.7530 0.007 714 5.441 0.8286 0.011 97 3.301 0.73040.006 149 3.396 0.7371 0.007 386 5.009 0.8288 0.011 61 3.110 0.70490.005 952 3.159 0.7083 0.007 195 4.726 0.8251 0.011 33 2.921 0.67750.005 739 2.922 0.6748 0.006 903 4.363 0.8050 0.010 83 2.744 0.63240.005 690 2.782 0.6483 0.006 744 4.155 0.7901 0.010 57 2.600 0.56980.005 455 2.662 0.6128 0.006 551 3.925 0.7868 0.010 19 2.446 0.48900.005 231 2.451 0.5630 0.006 369 3.710 0.7604 0.009 959 2.303 0.4419


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Performance measurements on a Pelton turbine model

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