design, modeling, and cfd analysis of a micro hydro pelton ...design, modeling, and cfd analysis of...

Research ArticleDesign Modeling and CFD Analysis of a Micro Hydro PeltonTurbine Runner For the Case of Selected Site in Ethiopia

Tilahun Nigussie1 Abraham Engeda2 and Edessa Dribssa1

1School of Mechanical and Industrial Engineering Addis Ababa Institute of Technology Addis Ababa Ethiopia2Department of Mechanical Engineering Michigan State University East Lansing USA

Correspondence should be addressed to Tilahun Nigussie tilahunnigussieaaiteduet

Received 4 June 2017 Revised 17 August 2017 Accepted 29 August 2017 Published 12 October 2017

Academic Editor Rafat Al-Waked

Copyright copy 2017 Tilahun Nigussie et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper addresses the design modeling and performance analysis of a Pelton turbine using CFD for one of the selected microhydro potential sites in Ethiopia to meet the requirements of the energy demands The site has a net head of 475m and flow rate of014m3s The design process starts with the design of initial dimensions for the runner based on different literatures and directedtowards the modeling of bucket using CATIA V5 The performance of the runner has been analyzed in ANSYS CFX (CFD) undergiven loading conditions of the turbine Consequently the present study has also the ambition to reduce the size of the runner tohave a cost effective runner designThe case study described in this paper provides an example of how the size of turbine can affectthe efficiency of the turbine These were discussed in detail which helps in understanding of the underlying fluid dynamic designproblem as an aid for improving the efficiency and lowering the manufacturing cost for future study The result showed that themodel is highly dependent on the size and this was verified and discussed properly using flow visualization of the computed flowfield and published result

1 Introduction

Despite the fact that many rural communities have goodaccess to plenty of water resources the most serious problemfaced by a country like Ethiopia is that of rural electrificationOne of the most important and achievable methods toproduce electricity is to introduce a standalone electric powergeneration using renewable resources Rural ElectrificationFund (REF) which is operating under the Ministry ofWater Irrigation and Energy (MWIE) is working to controlthe energy crisis in the country [1ndash3] In its effort it hasidentified some potential micro hydro sites in the countryThis potential for small-scale hydro power is estimated to be10 of the total potential (1500ndash3000MW) [3 4] So far outof the total potentials for micro hydro power (MHPs) in thecountry (over 1000MW)only aminute portion of it (less than1) is developed [4] If these water resources were properlyharnessed it will help Ethiopia tomeet its power demand andmaintain her economic growth for the next decade Due tothe existence of these numerous sites in Ethiopia suitable for

micro hydro turbine installations the need for developmentof micro hydro turbines using locally available materials andwith local manufacturing capability has been identified forthose sites which have been evaluated and proved to be viablethe aim being to cut the equipment cost which is importedfrom various countries from Europe and Asia As a resultfuture of micro hydro developments in the country wouldneed a manufacturer to provide turbines and parts with newdesign

Figure 1 shows some MHP areas These areas are mainlyin the Western and South-Western part of the country andthey are characterized by high mean annual rainfall rangingfrom 300mm to over 900mm For many of these sitesa Pelton turbine is the only option This is due to highermountains providing higher heads and seasonal variation inflow rates appropriate for the choice of Pelton turbines forhydro power projects in the country [4ndash6]

Depending on water flow and design Pelton wheelsoperate best with heads from 15 meters to 1800 metersalthough there is no theoretical limit In this turbine water

HindawiInternational Journal of Rotating MachineryVolume 2017 Article ID 3030217 17 pageshttpsdoiorg10115520173030217

2 International Journal of Rotating Machinery

Mean annualWater surplus

More than 900ＧＧ

700 to 900500 to 700

300 to 500100 to 300Less than 100ＧＧ

Figure 1 Distribution of MHP potential sites in Ethiopia [4]

is brought down through the penstock pipe to a nozzle andit comes out into the turbine casing The jet is then directedat a wheel or runner which has a number of buckets aroundits edge The force of the jet on this wheel makes it turn andgives the output power [7ndash9] However investigation revealsthat there is no company or institution engaged in supplyingthis micro Pelton turbine locally in the country As a resultthe necessity and the possibilities to design and manufacturePelton turbines locally are increasingMore often thematerialand the skilled labour as well as technical staff are availablebut what is missing is the information and knows-how [4 6]

More precisely in the new context where harvestingsmall hydro potentials can become economically viablethere is also a need to provide solutions to reduce thedesign cycle time and cost for Pelton runners It is knownthat with increasing demand the performance analysis ofturbine such as efficiency and dynamic behavior is also animportant aspect to analyze its suitability under differentoperating conditions [7] Additionally it is used by theturbine producer to guarantee the hydraulic performance ofa turbine to the customer However it is known that designof Pelton turbine is mainly conducted from know-how andextensive experimental testing which provide an empiricalunderstanding of factors that are important to turbine designBut in todayrsquos highly competitive market of turbine theperformance is often difficult to determine in the short termwith this traditional practice Therefore the incorporation ofcomputational fluid dynamics (CFD) in the design of microhydro turbines appears to be necessary in order to improvetheir efficiency and cost-effectiveness beyond the traditionaldesign practices [7 10ndash12]

The main topic of investigations by the CFD method hasfocused on the interactions between the jet and the rotatingbuckets as well as the relative flows within the buckets Theseare flows that are so far not easily accessible by experimental

measurements [11] CFD simulations are therefore likelyconsidered as an availableway for investigating complex flowsin Pelton turbines provided that they are reliable and able toreveal the possibility of improving the system efficiency andreducing the manufacturing cost In addition CFD providedeeper understanding of the flow mechanisms that governperformance The most detailed CFD analysis of rotatingPelton turbine was done by Perrig et al [13 14] by consideringfive buckets and the computed results were compared withexperimental results at best efficiency point (BEP)

As explained by Zhang [7] in Pelton turbine bookhydraulic design of a Pelton turbine the related practicalexperiences have thus always played a major role besidesapplying general design rules Even the optimum bucketnumber and the size of a Pelton wheel for instance weredetermined only by experience ormodel tests without relyingon any hydro mechanical background The main reasonsfor this were the complex flow conditions in both thehigh-speed jet and the unsteady interaction between thehigh-speed jet and the rotating Pelton buckets [7 11] Butnowadays the largest amount of publications on modelingof Pelton turbines uses commercial code ANSYS CFX [710 14] The capability of solving complex impulse turbinerelated problems that include multiphase flow with freesurfaces has been demonstrated by a number of studies andis becoming increasingly significant [10ndash18] However largecomputational cost of the simulations is also the main factorwhy there is a lack of publications on CFD usage for Peltonturbines [11] As a result various authors made differentsimplifying assumptions in order to reduce this cost as muchas possible and make Pelton simulation for performancepredictions possible Most CFD simulations reviewed in theliteratureswere assuming symmetry in the flow as simplifyingassumption and therefore theymodel only half of a runner ora bucket Because of the periodic behavior assumption themajority of simulations used also only a fraction of a runnerwith the number of buckets in the section modeled being 23 5 7 or even 10 [11] Many authors used only 3 consecutivebuckets where the torque wasmeasured only on the bucket inthe middle This torque measured on a single middle bucketwas then used to construct the torque on the runner assumingthat every bucket would undergo identical loading [10 11]The first bucket was required to produce the back-splashingwater that impacts the middle bucket The third bucket wasrequired to realistically cut the jet when it is impacting thesecond bucket Even though it was shown that it is possible tomodel the complete runner this could be seen as unnecessaryusage of computational resources For instance using thesame computational resources and a reduced complexitysimulation with only 3 buckets would allow simulations withbetter discretized grids (therefore improving accuracy) oranalyzing more operating points or design variations andenable the optimization of Pelton turbine (see [11 13 14])

So far few investigators have only reported diverse valuesof maximum efficiencies as shown in Table 1 Because ofcommerciality of the turbine many of the investigatorsnormalized their results in their publications Most papersreport that the shape of the efficiency curve is well capturedwhile actual differences between measured and numerically

International Journal of Rotating Machinery 3

Table 1 Some Pelton turbine studies and maximum efficiency levels attained

Investigators Net head (m) Flow rate(m3sec)

Runner speed(rpm) PCD (mm) Maximum

efficiency Panthee et al [10] 539 005 600 400 825Panagiotopoulos et al[19] 100 135 of BEP 1000 400 867

Solemslie and Dahlhaug[20] 70 mdash mdash 513 7775

Pudasaini et al [21] 8085 009218 600 490 8771

Table 2 Proposed site data for MHP development [22]

Region Zone Wereda Kebel Rivername Head (m) Flow rate

(Ls)

Oromia Wshowa Tokikutay MelkeyHera Indris gt50 140

predicted efficiency remain unreported An exception is [1019ndash21] where predicted efficiency was quite close to themeasurements Fewer still go deeper into the design andperformance analysis of the turbine

Due to the natural limitations concerning publication ofresults concerning turbines from commercial companies oneof the goals of this research paper has been to design andsimulate using a Pelton turbine and compare the obtainedresult with the reference from Table 1 The results in Table 1may have also depended on the laboratory settings andother controls of design parameters the results still indicateroom for further performance improvement Even thoughthis is a well-established turbine technology there are manyunanswered questions regarding design and optimizationThus further development is still relevant today As a mainfeature previous studies have mainly focused on experimen-tal studies of turbine efficiency as a function of differentgeometrical parameters of the buckets No paper that consistsof design analysismodeling numerical performance analysisof rotating Pelton turbine runner and its comparison withexperimental data to reduce the size of the turbine hasbeen published as far as we know Therefore a design studythat takes into account the links between the size of therunner and the flow field characteristics is neededThis paperaddresses this issue for one of the selected potential sites(Indris River) in Ethiopia to meet the requirements of theenergy demands The design process consists of sequentialstages parametric design of turbine and CFD simulationwith the baseline design and a smaller size of the turbine fromthe baseline design The result of this study will be an inputto the optimization of the runner for future study In thisway a study was carried on Pelton turbine runner specificallydesigned and the result of this research was compared withthat of Table 1 (published results) In the second part of thisarticle optimization of the geometry of this turbine localmanufacturing of the optimal geometry and testing of thisturbine in the lab and finally comparison of the resultsobtainedwill be presentedThe result of this researchwill alsoensure availability of documented procedure by contributingknowledge for designing micro hydro Pelton turbine in the

country Most importantly a general awareness and technicalunderstanding of successful micro hydro turbine technologywill be developed and fostered at the local and regional levelsso that rural electrification projects can be implementedeffectively

2 Method and Methodology

21 Problem Description After surveying different villages inthe South-West District of Ethiopia we narrowed our choicesdown to one Melkey Herra Village It is a rural communityKeble roughly 149 kilometers from Addis Ababa and is wellrenowned for tourism Its geographical coordinates are 08∘ 5110158404010158401015840North and 37∘ 451015840 1010158401015840 East which does not have the accessto electricity The selected water resource for hydroelectricgeneration is ldquoIndris Riverrdquo for the communities living in thevillage called ldquoMelkey Herrardquo [22] The micro hydroelectricproject is a main priority to the community Due to the recentcrises of electricity in the community it is utmost need for theutilization of micro hydropower The data (Table 2) has beenfound from primary and secondary data collection

22 Steps Involved in Design of the Turbine To start the initialdesign calculations will be conducted to size turbine partsThe theory behind these is mainly taken from the ldquoMicroHydro Pelton Turbine Manual by Thake [6]rdquo Differentassumptions are made in the design process using designguides and literature

221 Calculation of the Net Head (119867119899) The net head at thenozzle exits can be expressed by the following formula [6]

119867119899 = 119867119892 minus 119867119897 (1)where 119867119892 is the gross head and 119867119897 is total head losses dueto the open channel trash rack intake penstock and gate orvalve These losses approximately equal 5 of gross head [6]This makes the net head available at the end of penstock as50m minus 25m = 475m

222 Selection of Turbine For the proposed site data head50m and flow rate 140 litersec combination (from Table 2)


Table 3 Calculation summary to determine the turbine speed (119873) and PCD

Name Symbol Unit ValueNumber of jets 119899jet mdash 1 2 3 4Jet diameter 119889jet mm 770 544 444 385Runner PCD PCD m 699667 494740 403953 349834Available PCD PCD mm 700 500 425 350Turbine speed 119873 rpm 371 520 611 742Gear ratio 119883 mdash 404 289 245 202

Output shaft power200 Ｅ７

Pelton20 Ｅ７

10 Ｅ７5 Ｅ７

1 Ｅ７

50 Ｅ７ndash100 Ｅ７

100７Propeller

Crossflow

Flow (Ls)

Net

hea

d (m

) 100

10

1000

110010 10001

Figure 2 Application ranges for different types of turbine [6]

principally a choice was necessary between Pelton and crossflow situations as shown in Figure 2 The figure shows theapproximate application ranges of turbines for micro hydroTherefore this chart can be used for selection of the turbinetype The area highlighted in solid line shows an indicativerange of operation for the Pelton runner used in this researchpaper

223 Calculation of Jet Diameter (119889119869119890119905) The pressure at thebottom of the penstock creates a jet of water with velocity119881jet

119881jet = 119870119873radic2119892119867119899 (2)

where 119881jet is jet velocity (ms) 119870119873 is nozzle velocity coeffi-cient (normally around 095 to 099) and 119867119899 is net head atthe nozzle The flow rate (119876) is then given by this velocitymultiplied by the cross-sectional area of the jets

119876 = 119860 jet times 119881jet times 119899jet= Π1198892jet4 sdot 119881jet sdot 119899jet

(3)

where 119899jet is number of jets and 119889jet is diameter of jets (m)Combining (2) and (3) and using an average value of 097

for119870119873 then solving for 119889jet becomes

119889jet = 05411986714119899 sdot radic 119876119899jet (4)

The next step in the turbine design process is to determinethe pitch circle diameter (PCD) of the turbine

PCD

Nozzle

Pelton runner

P

UＤＮ

Figure 3 Diagram of a Pelton runner showing PCD [6]

224 Calculation of the Runner Circle Diameter (PCD)Figure 3 shows a schematic of a Pelton runner with a pitchcircle diameter119863 (=2119877) rotating at angular velocity 120596119901

Beginning with the derived formula to determine theturbine speed which can be expressed as

212058711987360 sdot 1198632 = 119909 sdot 119881jet (5)

where (119863) or PCD is pitch circle diameter (m) and 119909 is ratioof runner velocity to jet velocity (119909 = 046 is used to producethe maximum power out of the turbine) [6] 119873 is rotationalvelocity of runner (rpm) Substituting for 119881jet from (2) andusing 119909 = 046 (2) becomes

119863 = 377 times radic119867119899119873 (6)

A spreadsheet is prepared as shown in Table 3 to deter-mine the turbine speed (119873) and PCD

From Table 3 all the gear ratios are possible with beltdrives From the result in Table 3 runner pitch diameters(119863) of 350mm and 425mm with 4-jet and 3-jet turbinerespectively have smaller pitch diameter However for aturbine of these powers making is very complex and needsconsiderable expertise so these are probably not an option[6] The single jet solution is possible but a 700mm PCDrunner makes a very big turbine The best solution is the500mm 2-jet turbine Therefore we can take the PCD to be500mm in our design analysis To estimate the final systempower output efficiency values for the nozzles turbine andgenerator can be assumedThake [6] provides reasonable val-ues for each Table 4 shows the values of assumed efficiencyin this research

The equations used to determine the different designparameters of wheel are collected in Table 5


Part Section D-D

Section A-A

Section B-B

Partial view on C

AA

B

B

C

D

D

REF

Add material to giverounded edge

Flat areas

340

140

R100

R100

R100

160

380

20 150∘

150∘ ref

120

19

R69 spherical

R69 spherical

50

114

70

150∘ ref

527∘

50∘

110

R1 min

900∘

Notch fromsplitter tipto centre of back

All dimensions in PCD

Bucket symmetrical about centreline

Spherical radius continuesinto notch area

Figure 4 A scalable Pelton bucket All dimensions are in of PCD [6]

Table 4 Pelton turbine partsrsquo assumed efficiency [6]

Part Symbol Assumedefficiency

Penstock 120578119901 095Manifold 120578119898 098Nozzle 120578119899 094Runner 120578119903 08Drive 120578119889 1Generator 120578119892 08Overall efficiency 120578119900 056

225 Detail Bucket Geometry Design Figure 4 shows thedimensions of the bucket as percentage values of the PCD ofthe turbine Like the basic bucket model changing the PCDvalue within the model allows it to be scaled [6]The physicaldimensions of the bucket for the selected site data based onempirical relations for 500mm PCD are shown in Table 6which is used in this report for modeling of the bucket

A basic stem for machining used for bolting or clampingthe buckets to the hub is shown in Figure 5 Bolted bucketsare an ideal solution for this research and are chosen asdiscussed in [6]

From all the above calculated parameters in Table 6and some standard parameters using Figures 4 and 5 the

16

R15

35

10∘ 20∘

Figure 5 A basic bucket stem design for bolted fixing All dimen-sions are in PCD [6]

modeling of the bucket is done using CATIA V5 softwareas shown in Figure 6(a) The bucket design was specified bydefining the outline of the bucket using the dimensions givenin Figures 4 and 5

The basic bucket model was adapted to form an entirebucket by the use of patterning Two-disc plate was used to


Table 5 Basic design calculation summary of Pelton turbine

Descriptions Data Unit Design guidelines Thake 2000 [6]119867-net turbine 465 mm H-net turbine =119867-nettimesmanifold efficiency119870119873 097 mdash Ranges (between 095ndash099)119881-jet 296 ms Velocity of the jet (for 119899jet = 2)119889 jet 544 mm Diameter of the jet (for 119899jet = 2) 119889 jet = 011 times PCD119909(119880119881-jet) 046 mdash For maximum power output (blade speedV-jet) ratioBucket speed 136 ms 119880 = 119909 sdot 119881jet = 046 times 296119873 1500 Rpm Standard generator RPM119873-119903 1170 Rpm Runaway speed = 18 turbine optimum speed120578 056 Total system efficiency119875 3657 kW Estimated electrical power = 120588119892119867-net times 119876 times 1205780119875-turbine 512 kW Turbine mechanical power = 120588gH-net turbine times 119876 times 120578119903

Table 6 Physical baseline bucket dimensions result for the selected site data

Parameters formula [6] Calculation Dimensionsresult UnitHeight of bucket ℎ = 034D ℎ = 034 times 500 170 mmCavity length ℎ1 = 56D ℎ1 = (0056) times 500 28 mmLength to impact point ℎ2 = 0114D ℎ2 = 0114 times 500 57 mmWidth of bucket opening 119886 = 014D 119886 = 014 times 500 56 mmBucket thickness 1199051 = 0002D 1199051 = 0002 times 500 1 mmApproximate number of buckets 119885 119885 = 1198632119889 + 15 18Depth of the bucket 119905 = 0121D 119905 = 0121 times 500 605 mmWidth of the bucket 119887 = 038D 119887 = 038 times 500 190 mm

xyz

(a) (b)

Figure 6 Solid model of Pelton turbine for the selected site data (a) bucket and (b) 3D view of the runner right

mount the buckets circularly as shown in Figure 6(b) Thediscs were to sandwich the buckets into place

3 Computational Analysis

For the selected Melkey Herrarsquos micro hydro power sitePelton turbine was the most suitable hence chosen for ournumerical performance analysisThemain dimensions of theturbine examined here correspond to this ideal plant Thenumerical techniques created during this section included

many numerical and physical assumptions to simplify theproblem This was necessary because accurate modeling ofimpulse turbines (Pelton in this case) that include complexphenomena like free surface flow multifluid interactionrotating frame of reference and unsteady time dependentflow is a challenge from a computational cost point of view[10ndash18]

31 Physical Assumptions and Scaling Down The computa-tional domain was created removing the features that were


Table 7 Turbine geometry and setup values for prototype and model

Parameters Symbol Unit Prototypesrsquovalues

Selected modeloperating condition

Flow rate 119876 Ltss 140 2084278Head 119867 m 475 1334275PCD 119863 mm 500 265Bucket width 119861 mm 190 1007 gt 80mmPower 119875 KW 512 214Number ofbuckets 119885 18 18

(a)

Rotating domain

Stationary domain

000

200

00

100

00

400

00

(mm)

300

00 00

025

005

0

010

0

(m)

007

5

Nozzle

Half buckets

(b)

Figure 7 Domain geometries stationary (a) and assembly of the rotating and stationary domain (b)

assumed to have no or minor effect when comparing therunner designs as follows The following are some of thesimplifying assumptions made in the analysis

No Casing Modeling the Pelton turbine without casingsimilar methods can be found in the literatures [10 11]

Symmetry To reduce computational cost the buckets nozzleand water-jet are cut in half at the symmetry axis [10 11]

Single Jet Modeling of only the single jet operation was foundin most of the publications reviewed in Section 1 [10 11]No Hub The flow will not be interacting with any other partof the runner except for the bucket Hence there is no needto include the hub into the CFD model as suggested in theliteratures [10 11 13]

Periodic Torque Three buckets are enough to recreate thecomplete runner torque and are used also in this research[10 11]

ldquoSimilituderdquo Similitude in a general sense is the indicationof a known relationship between a model and a prototypeEquation (7) represents head coefficient flow coefficient andpower coefficient for model studies [10] In order to achievesimilarity between model and prototype behavior all thecorresponding terms must be equated between model and

prototype So the model is presumed to have the same valuesof speed ratio flow ratio and specific speed

( 11986711986321198732 )prototype = ( 11986711986321198732 )model

( 1198761198731198633 )prototype = ( 1198751198731198633 )model

( 11987511986351198733 )prototype = ( 11987511986351198733 )model

(7)

Scaling Down Scaling down of the prototype is also impor-tant to reduce the time consumption and to ease the com-putational processing in normal computers On the basisof the above considerations the scaling factor of 053 wasused to meet the minimum bucket width standard for modeltesting and the Reynolds number also needs to be greaterthan 2 times 106 This is based on the international standardIEC 60193 of the International Electrotechnical Commissionwhich applies to laboratory testing of model turbines [10 23]In this standard the factor greater than 028 was found tosatisfy IEC 60193 criteria for Pelton turbines

Table 7 shows the values for prototype andmodel with thesame speed of 520 rpm

32 Computational Domain Creation Figure 7 depicts thecompleted CAD drawings of the rotating and stationary


Middle bucket Bottom bucket

Top bucket

XZ

Y

(a)

000

0

005

0

010

0

(m)

XZ

XZ

Y

(b)

Figure 8 Meshed rotating (a) and stationary domain (b) sizing and inflations were applied

domain which is modeled separately and assembled here toshow their relative initial positions Stationary domain con-tains half a cylinder for the inlet and a ring to accommodatean interface between the two domains

Imagine that the rotating domain in Figure 7 is alignedwith the stationary domainWhen the rotating domain leavesthis position another identical domain is introduced at thetop (the same geometry) Thus one achieves a continuoussimulation of a runner [11]

33 Meshing Figure 8 shows both stationary and rotatingdomains meshed as they are imported into CFX-Pre Assuggested in the literature [10 19] unstructured tetrahedralelements were used for the rotating domain meshing becauseof more complex geometry to be captured by the meshand also to allow automatic meshing for all the upcominggeometrymodifications In order to determine theminimumgrid size or mesh resolution required to resolve the boundarylayer and the mean flow features a grid independence studywas conducted This allows minimization of errors anduncertainties in the predicted results for example the runnerpower output or the efficiency Therefore grid convergenceanalysis has been carried out considering power output (inthis study bymonitoring torque) as a parameter of significantinterestThe results of grid independence study are presentedin Section 36

34 Physical Setup with ANSYS Preprocessing In this sectionthe essentials of the ANSYS Pre setup are presented

Analysis Type In each ldquoFlow Analysisrdquo in ANSYS Pre thereis a tab called ldquoAnalysis Typerdquo This is where one defineswhether or not the simulation is transient or steady-statecontrol simulation time and time steps In this case thetransient optionwas chosen Time steps are interval forwhichCFX solver calculates flow parameters in transient analysisThe time step was 120 total time which corresponds to0001714 sec to capture 20 time frames per rotation

Multiphase Model The flow through the penstock pipe ishaving only single phase for the fluid As the water-jet comes

out of the nozzle it is directly freed to the atmosphere andthe effect of free water-jet will come into picture This flowpasses through runner buckets and it will be a free surfaceflow This free surface flow glides through internal surface ofthe buckets and themomentum transfer takes placeThe flowleaving the runner bucket will be converted into dispersedwater droplets as the fluid leaves contact from the bucketsThis way the flow through the Pelton turbine is multiphasein nature in agreement with the literatures [10 11 13 14] Tocapture the flow accurately homogenous multiphase analysisis performed in this research

Volume Fraction of Water As suggested by the literature [5]the volume fraction of water should change from 0 to 1 Ineach control cell the volume fractions of the water and airsum to 1 120572119908 + 120572119892 = 1 Then 120572119908 = 0 denotes cells filledwith air while 120572119908 = 1 denotes cells filled with water and0 lt 120572119894 lt 1 denotes that the cell contains an interfacebetween the water and air In the beginning of the simulationboth domains are full of air with 0ms velocity Thereforethe given initial conditions are 0ms velocity and 0 Pa forrelative pressure Initial water volume fraction is 0 and initialair volume fraction is 1

Turbulence Model Shear Stress Turbulence (SST) model isable to capture turbulent scales in flow in high shear stressregions [10 11] So SST turbulencemodel is chosen for furthersimulations

Domain Interface The interface type between the stationaryand rotating domainswas Fluid-Fluid [10 11] Interfacemodelfor this type was General Connection and the TransientRotor Stator option was selected for Frame ChangeMixingModel Pitch ratio wasmaintained to value 1 between domaininterfaces by maintaining equal area in interface region Toapply a rotation to the rotating domain domain motion inthe rotating domain was set to rotating and angular velocitywas defined by the expression ldquoOmegardquo In this case theangular velocity is negative because the domain was modeledto rotate in the negative rotation direction about the 119911-axisThis method is also found in the literatures [10 11 14]


Table 8 Expressions defined in ANSYS Pre for the baseline design [5 11]

Name Expression DescriptionGravity 982 [msminus2] Acceleration due to gravityHead 1334 [m] Model head based on scalingTurbine radius 1325 [mm] Model turbine radius based on scalingInlet velocity (2 times gravity times head)05 [ms] Water velocity at the nozzle inletOmega Inlet velocity(2 times turbine radius) [rads] Angular velocity rotation in the negative direction is selectedTorque middle bucket wall Torque zMiddel Bucket Wall The entire middle bucket is selectedTotal time ((120 times pi)180)Omega Total simulation running time

Jet inlet (water inlet)Jet wall

Air inlet

openingStationary

Rotating opening

X

Z

Y

X

Z

Y0045 00900(m)

(a)

Symmetry

Rotating opening

Interference betweenrotating and stationary domain

XZ

Y0045 00900(m)

(b)

Figure 9 Boundaries applied on the domains

Boundary Condition in Rotating Domain This section con-tains a list of boundaries and their conditions No boundaryfor outlet is defined in the rotating domain Rather openingtype boundary condition has been defined The bucketsurface is defined by wall type boundary condition and aninterface type boundary condition at interface between therotating and stationary domain All other remaining bound-aries are defined as opening type since it is unpredictableabout the actual outlet and flow pattern of fluid throughthe runner An overview of the boundary conditions can befound in Figure 9

Solver Control and OutputThe chosen advection scheme wasHigh Resolution according to the CFXModeling GuideThisgives a good compromise between robustness and accuracySecond-Order Backward Euler option was selected for theTransient Scheme as it is generally recommended for mosttransient runs in CFX [5 10 11 13 14]

Monitor Points Themain output of the simulation is the totaltorque on the middle bucket A monitor for the expressionldquoTorque onMiddle Bucket Wallrdquo was added which logged the

torque and made it possible to monitor the torque during thesimulation The calculated torque data on the middle bucketwas extracted from the simulation using an inbuilt torquefunction applied to the Named Selections created for theregions for the middle bucket This function is then plottedas a Monitor Point while the simulation runs allowing thecalculated torque at each time step to be exported

Expressions Defining expressions is a good way of streamlin-ing a CFD case The expressions in Table 8 are used in thesetup This way of defining expressions can be also found inthe literatures [5 11]

35 Result and Discussion In general rule a small runneris cheaper to manufacture than the larger one It takes lessmaterial to cast it and the housing and associated componentsalso can be smaller For this reason consequences of reducingPCD (=400mm) from the baseline design (PCD = 500mm)are evaluated and results are compared with those publishedby Panthee et al [10] and Panagiotopoulos et al [19]respectively The geometrical characteristics of their Peltonturbine model used for their study correspond to a Pelton


Water velocity in Stn framestreamline 1

(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001


(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001

Figure 10 Flow visualization of the baseline design side views and face views (PCD = 500mm)


(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001


(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001

Figure 11 Flow distribution of the runner water velocity in Stn frame side views and face views (PCD = 500mm)

turbine installed in Khimti Hydropower in Nepal [10] andtheNational Technical University of Athens [19] respectivelyThe PCD of the model runner for both power plants was400mm and the axis is horizontal with two injectors

Next a visualization of the flow in the turbine buckets forthis study can be seen in Figure 10

As seen in Figures 10 and 11 only very small amount ofldquoleakedrdquo water is present next to the bottom bucket with lowjet velocityThese visualizations give good information aboutthe flow pattern The streamlines that came from the nozzleentered into the runner hitting the buckets and dividing thejet into three portions (Figures 10 and 11) First the portionfrom the bottom of the jet touched the outside and inside ofthe top bucket that is close to the nozzle The second portionof the jet was the one from the middle which hit the nextmiddle bucket Finally the rest portion of the jet crossed intothe latter bucket On the face and side view on Figure 10 onecan observe the part of the flow escaping from the cutout ofthe bucket as well as the lateral sheet flow

It can be observed on Figure 12 that the maximumpressure point in red corresponds to the PCD of the bottombucket and the tip of the middle bucket which is aligned withthe axis of the impinging jet Similar finding is observed inthe literature [10]

As seen in Figure 13 when the PCD is reduced to 400mma large amount of water does not leave the buckets causingsevere backwash on the backside of the bucket which variesfrom certain sound value at the place of impingement tothe reduced values as water goes outward (Figure 13(b))However there is a small amount of the flow that leavesthrough the cutout with high velocity without being utilized(cutout leakage)This phenomenon has to be reduced duringthe optimization stage

The water is unevenly distributed across the buckets andthere are several local accumulations of cells with a highvolume fraction of water most visible in the bottom bucketin Figure 14 This volume of fraction of water will vary withtime as the buckets rotate This occurs when the portion of


Pressurecontour 2

(Pa)minus2655e + 004minus1889e + 004minus1123e + 004minus3577e + 0034080e + 0031174e + 0041939e + 0042705e + 0043471e + 0044236e + 0045002e + 004

Pressurecontour 2


0

001

5

003

006

0

(m)

004

5 0

002

004

008

0

(m)

006

0

X

Z

Y

X

Z

Y

X

Z

Y

X

ZY

Figure 12 Pressure contours on the bucket (PCD = 500mm)

the jet is going to leave out completely from the bottombucketand completely enters the next top and consequential bucketsThe red and blue regions show respectively water and air inthe computational domain In a more complex situation theatmosphere also exerts pressure on the surface (water-vaporinterface) [24]

Looking at Figures 13(b) and 14 it is clear that as thewater starts entering into the top bucket the inner surfaceof the middle and bottom bucket will still be having somewater volume fraction inside it It means that for a particularinstance of time and runner rotation more than one ofthe runner buckets are having water volume fraction Theamount of the water flow touching the runner bucket sidesand back surface of the bucket (backwash) is also visibleThiswater fraction at the back side and side surface of the bucketwill impart some force to the buckets and if this fraction ishigh then the intensity of force on the bucket will be higherand it will reduce the strength of the buckets [11 13 14]Another effect of this is that the water is acting as a brake onthe runner rather than helping it turn and this gives a seriousloss of power These energy losses occur with jet entering thebucket and providing some amount of counter-torque as theouter side of the bucket hits by the surface of the jet

The pressure distribution in the bucket was due to impactof high jet This pressure distribution applied on the bucketagain varies with the time due to the rotation of the runner Itwas found that the pressure peaks are obtained at bucket tipand PCD of the runnerThe pressure peak in bucket tip is dueto flow disturbance when jet strikes bucket tip It is obvious to

obtain the pressure peak at the runner PCD since the Peltonrunners are designed such that it would convert most of thehydraulic energy to mechanical energy when the jet strikesthe runner PCD Result showed high pressure with the valueof 3559times 104 Pa for the first top and the secondmiddle bucketat somedegree of rotation of the runner as shown in Figure 15This pressure value is lower than the previous value whenPCD = 500mm (Figure 12) This might indicate that there isenergy loss in the runner

The images in Figure 15 are taken of the right buckethalf then it is mirrored here to ease the comparison throughsymmetryThenext stepwill be focused on future simulationsregarding the study of the hydraulic efficiency a betterapproximation of the numerical torque

The hydrodynamic torque and the hydraulic efficiency ofthe runner are computed after completing the evaluation ofa jet-bucket interaction flow starting from the moment ofimpingement (jet cut in) until the evacuation of the bucket(jet cutout) [11] The calculations are then continued for theparticles of the oncoming frames until all particles of a frameimpinge on the next coming bucket (jet cut) As can beobserved in Figure 15 the shape of the torque curve is alsosimilar to the previous studies by different authors [10 19] butthe irregularity of the curve in this area was attributed due tothe Coanda effect and the impact of the back flow which cre-ates counter-torque on the bucket andmakes it slightly differ-ent from the previous studies [5 11 19] Some indicative pic-tures from the turbine examined here show how the energytransfer occurred in a single bucket as illustrated in Figure 16


Cutout leakage Back wash

XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)

Water velocity in Stn frameisosurface 1

(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)



Water volume fractioncontour 1

1282e minus 0131000e minus 0012000e minus 0013000e minus 0014000e minus 0015000e minus 0016000e minus 0017000e minus 0018000e minus 0019000e minus 0011000e + 000



Figure 14 Volume fraction of water for reference bucket design at a particular time step (PCD = 400mm)

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Figure 15 Pressure distribution at some degree of rotation of reference bucket design (PCD = 400mm)

At the start (cut in) a counter-torque can also be observedcaused by the interaction of the jet with the back surface of thebucket this value is larger for PCD = 400mm comparing tothe baseline design (Figure 16) Just afterwards the torque isincreasing asmorewater interacts with the inner surface untilthe full jet interacts with the bucket to produce themaximumtorqueThe maximum torque produce by the baseline design(500mm) is larger than that of a reduced PCD (400mm)Theresult in Figure 16 shows also that smaller turbine is fasterthan the larger one which is true

Next the total curves of the complex unsteady flow inthe bucket for the seven buckets analyzed can be acquiredwith the aid of time history views like the ones in Figures17 and 18 The total torque curve is shifted by the singleblade passage phase for the whole range of total torquevalues and summed to give the total torque acting on theturbine shaft In this research paper the torque generatedby the middle bucket is replicated over time to determinetotal torque generated by Pelton turbine This is done byassuming that at stable conditions every bucket is producingidentical torque periodically The replication was done tillthe summation graph gave steady values which occurs after

Jet cut in

Full jet

Jet cut out

Counter torque001 002 003 0040

Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ

Baseline design (０＄ = 500ＧＧ)

Figure 16 Torque generated by middle bucket versus time

three buckets covered by the water sheets at 003 sec of therotation of the runner The plot obtained was due to half


Table 9 Mesh dependent test analyzed for PCD = 500mm

Mesh type M1 M2 M3 M4 M5 M6 M7 M8Total number elements 294952 520687 2011665 2239650 2398044 2861243 3955723 5050204Calculated total torque (Nm) minus3093 minus3220 minus3432 minus3450 minus3469 minus3492 minus3502 minus3525Standard torque (Nm) minus3506 minus3506 minus3506 minus3506 minus3506 minus3506 minus3506 minus3506Torque error percent () 118 82 21 16 11 04 01 05


Mesh type M1 M2 M3 M4 M5 M6 M7 M8Total numberElements 128251 128546 130961 2321026 3019180 4052422 4771226 6855793Calculated totaltorque (Nm) minus1813 minus1815 minus1829 minus2184 minus2215 minus2227 minus2237 minus2241Standard torque(Nm) minus2805 minus2805 minus2805 minus2805 minus2805 minus2805 minus2805 minus2805Torque errorpercent () 354 353 348 221 210 206 202 201

minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)

Bucket 1Bucket 2Bucket 3


Bucket 7Total torque onthe runner

Figure 17 Dynamic runner and bucket torque over time for (PCD= 500mm)




001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)


nozzle and the maximum torque on the runner at a time isgiven by peak value multiplied by 4 as there are two nozzlesin each unit This runner torque has been taken for poweroutput calculations by taking the average value from 003 to005 sec of the runner rotation Methods of calculating thepower output from a single bucket torque readings similar to

those described above are quite common and can be found inthe literature [10ndash12]

To calculate the efficiency power input has to be calcu-lated as well which for a complete turbine is calculated usingtwo variables describing the flow conditions the net pressurehead and the flow rate [11]

119875input = 120588119892119876119867net119875out = 2 times Π times 119873 times 11987960 (8)

Therefore (hydraulic) runner efficiency in this model wascalculated using (9) as follows

120578 = 119875output119875input (9)

The next validation phase is to compare efficiency of thismodel to the published results by Panthee et al [10] andPanagiotopoulos et al [19] This will be done after checkingthe accuracy of the model in agreement with the literature[10 19]

36 Mesh Independency Study and Model Validation Meshor grid independent study is done in order to get a solutionthat does not vary significantly even when we refine ourmesh further Eight different mesh sizes were tested with aneffective head of 475m for two different cases The meshsize on the rotating domain is controlled by element sizeThe relevance was increased for finer mesh Afterwards theorthogonal quality of the mesh has been checked and it wasin an acceptable range (015ndash100) for each mesh developedEach mesh was also created with the same physical setupand boundary conditions During the simulations resultsobtained were directly dependent on the accuracy in qualityof mesh And it was performed while analyzing the torquevariation by developing the SST turbulence model

Tables 9 and 10 indicate the grid information the calcu-lated torque the standard torque and the resulting modeled


Table 11 Validation and performance prediction of Pelton runner

Parameters Unit Baseline design testcases Off- design test cases

Published resultby Panthee et al

[10]

Published result byPanagiotopoulos et al

[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP

PCD mm 500 500 500 400 400 400 400 400Runner speed Rpm 520 520 520 650 600 1000 600 1000Number of buckets mdash 18 18 18 18 22 22 22 22Model efficiency 788 835 846 626 661 716 825 867

runner efficiency for two different cases namely the baselinedesign (PCD = 500mm) and the reduced size (PCD =400mm) respectively

The standard torque was calculated with the powerobtained from power coefficient and the angular velocity ofrunner for comparison One can observe that from the resultin Tables 9 and 10 a finer mesh will give a solution of alittle higher accuracy than required but at the expense ofcomputational power and time About 39 million elementswere required to obtain mesh independent result for PCD =500mm (Table 9) Similarly for the PCD = 400mm turbinea total number of 68 million mesh elements were requiredto obtain mesh independent results for the torque output(Table 10) A solution was considered grid independent forless than 03 difference in the torque output between threedifferent consecutivemesh sizes It appears that no significantenhancement is to be expected from a further refinementof the mesh As seen from the results a relative error of201 between the CFD and the analytical data was foundfor turbine with PCD = 400mm and 01 relative error forthe baseline turbine (PCD = 500mm) at the design-pointoperating condition (119876 = 014m3s and 119867 = 475m)Hence high value of relative torque error indicates that thereare losses in the reduced size of the turbine influencingthe efficiency characteristics The torque variation curves ofthe runner obtained using different density meshes are alsopresented in Figures 19 and 20

Table 11 shows the performance prediction and compari-son of the model results with two published results

The computational analysis results presented in Table 11showed that the performance of the baselinersquos turbine designwas very good since the relative error is only 04 at thedesign operating conditions Torque value from mesh (M7)resulted in 788 of model runner efficiency for PCD =500mm (baseline design) The postprocessing visualization(Figures 10 and 11) was able to qualitatively show that thereason for the better performance for the case of baselinedesign may be explained by less cutout leakage and a moreoptimal bucket design for its intended use As presented inTable 11 the model hydraulic efficiencies for reduced sizeof the turbine (PCD = 400mm) for mesh (M8) were only626 661 and 7164 It can be observed that fromthe results of the different cases analyzed these hydraulicefficiencies were remarkably lower than that of the baseline

002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)

Mesh dependency test for ０＄ = 500ＧＧ

M1M2M3

M4M5M6

M7M8

Figure 19 Total torque variations for different mesh sizes for PCD= 500mm


minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8


design Moreover it can be observed that for a reduced flowrate and an increase in number of buckets equal to 005m3s22 respectively more water was catched by the inner surfaceof the bucketsThis could explainwhy the predicted efficiencyincreases rapidly for volume flow less than the design flow


rateThe lower efficiency of themodel at off-design condition(PCD = 400mm) is mainly due to a little backsplash (thebreaking effect) on the bucket and the missing jet velocity(leakage flow rate) because of a nonoptimized bucket designAs this phenomenon highlighted before the qualitative viewsof Figures 13ndash15 are reasonable for the lower efficiencies in theoff-design cases Thus the goal was to compare flow visual-ization at these two conditions using image postprocessingin order to explain the difference in runner performance Anexplanation for the discrepancy is that a decrease in PCDfrom the baseline design (PCD = 500mm) to PCD= 400mmwould lead to high hydraulic losses even though it will resultin less value of manufacturing cost It is important to notethat the bucket shape used in the baseline design (as shownin Figure 4) in this paper is based on JeremyThake 2000 book[6] In this book it is suggested that ldquothe design jet diameter is11 of PCDrdquowhichwill give a PCDof approximately 500mmTherefore if we optimizechange the shape of this bucketfor each case analyzed above the optimum results presentedin both published results above and the reduced size of theturbine (PCD = 400mm) might be different from this studyFor future work the design optimization of this turbinebucket will be made by keeping the PCD to be 400mm tolower the manufacturing cost and improve efficiency of therunner CFD results by Zidonis and Aggidis [25] also showthat less number of buckets were required to increase thehydraulic efficiencyTherefore as the final step it was decidedto change the length depth and angular position (jet-bucketinteraction) and alter the surface close to the lip and redefinethe shape of the lip curve to reduce the leakage intern toreduce the energy loss

4 Conclusion

The next-generation turbine designs for small-scale hydro-power systems seek higher efficiency and low manufacturingcosts The (size of Pelton turbine) PCD is an importantparameter to lower themanufacturing cost of a Pelton turbinerunner However no consistent guidance based on numericalresearch data is available in the public domain This studyprovides a guideline for selecting designing modeling andperformance analysis of a micro hydro Pelton turbine andprovides an example of how the size of turbine (PCD) canaffect the efficiency of the turbine

The paper describes also the methods used for CFD anal-ysis of scaled model Pelton turbine which is ideally designedfor Melkey Herra Village hydropower plant using ANSYSCFX software The bucket model was designed according tothe baseline design or calculated parameters The time andcost in CFD analysis of Pelton turbine are also reduced byselecting 3 buckets to predict the flow behavior of completeturbine One of the objectives was to understand how the tur-bine performancewill changewhen the flowfield is perturbedby reducing the size of turbine for a given operating condition(ie flow rate and head) Results obtained from the baselinedesign (PCD = 500mm) have been successfully comparedto that of the reduced size (PCD = 400mm) of the turbineThe results of the two turbine designs at the design flowrate and head of turbine are as follows one turbine (PCD =

400mm) has amaximum efficiency of 626 and the baselinedesign turbine (PCD= 500mm) has amaximum efficiency of788 The flow visualization study of this research providesinsights into the reasons for efficiency as well as guidance forimproving the efficiency The low efficiency in the reducedsize of the turbine ismainly caused by a large amount of waterleaving the bucket through the lip and hence transferringclose to zero of its energy to the shaft The problem wastherefore the choice of the runner PCD that could givethe best advantages in terms of efficiency on the wholeplantrsquos operational field For the purpose of validation andperformance characterization two Pelton turbines reportedin the literature were consideredThe first turbine has PCD =400mm a maximum efficiency of 825 which was studiedby Panthee et al 2014 for Khimti Hydropower in Nepal[10] The second turbine has also the same PCD (=400mm)but with a maximum efficiency of 867 which was studiedby Panagiotopoulos et al 2015 [19] using a reference casecorresponding to a Pelton turbine installed in the LHT at theNational Technical University of AthensThese were essentialfor the purpose of computational validation and performancecharacterization

The design optimization production and experimentaltesting of a model runner based on this design may also berealized in the next part of this paper Based on the resultobtained this study planned a modification on the baselinedesign and will consist of the following new designs beingtested

(i) Changing the length depth angular position (Jet-bucket interaction) and number of the buckets whilekeeping all other parameters constant

(ii) Altering the surface close to the lip and redefining theshape of the lip curve to reduce the leakage

Based on the results presented in this study there areopportunities for improving the maximum efficiency aswell as reducing manufacturing cost of Pelton turbines ifthe design is prescribed using the above criteria followedby high-fidelity computational simulations It would thenno longer be necessary to start the design and numericalsimulation each time from scratch

A natural extension of this paper would be also to validatethe model for other selected sites Achieving such a goalwould be a great step towards improving the understandingof the micro hydro power development and making tools forvalidating CFD results so that the benefits of this technologycan be brought to rural populations

Abbreviations

CFD Computational fluid dynamicsCFX CFD code by ANSYSSST Shear stress transportVOF Volume of fluidMHP Micro hydro powerMHT Micro hydro turbineMWIE Ministry of Water Irrigation and EnergyBEF Best efficiency point


Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This paper was funded by Ministry of Water Irrigation andEnergy The authors would like to thank Ministry of WaterIrrigation and Energy Office for the fund and for all informa-tion and data provided to accomplish the research work

References

[1] Energy Situation httpsenergypediainfowikiEthiopia[2] A Dalelo Rural Electrification in Ethiopia opportunities and

bottlenecks Addis Ababa University College of Education[3] World Small Hydropower Development Report 2013ndash The

Need for Further Resource Assessments L Esser InternationalCenter on Small Hydro Power Division of Multilateral Devel-opment Hangzhou Ethiopia

[4] SMelessaw ldquoEthiopiarsquos SmallHydro EnergyMarket-GiZndashtargetmarket analysis-hydro ethiopiardquo httpwwwgerman-energy-solutionsdeenwwwgtzdeprojektentwicklungsprogram

[5] L F Barstad CFD Analysis of a Pelton Turbine [Master thesis]Norwegian University of Science and Technology 2012

[6] JThakeTheMicro-Hydro Pelton TurbineManual DesignMan-ufacture and Installation for Small-Scale Hydro-Power ITDGpublishing London UK 2000

[7] Z Zhang Pelton turbines book published by Springer Naturethe registered company is Springer International PublishingAG Switzerland 2016

[8] MHPG Series ldquoHarnessingWater Power on a Small Scalerdquo Vol9 (Micro Pelton Turbines) Published by SKAT Swiss Center forAppropriate Technology 1991

[9] A Harvey Micro hydro design manual a guide to small scalewater power schemes

[10] A Panthee B Thapa and H P Neopane ldquoCFD Analysis ofpelton runnerrdquo International Journal of Scientific and ResearchPublications (IJSRP) vol 4 no 8 2014

[11] A Zidonis A Panagiotopoulos G A Aggidis J S Anag-nostopoulos and D E Papantonis ldquoParametric optimisationof two Pelton turbine runner designs using CFDrdquo Journal ofHydrodynamics vol 27 no 3 pp 840ndash847 2015

[12] J D Anderson Computational Fluid Dynamics The Basics withApplications McGraw-Hill New York NY USA 1995

[13] A PerrigHydrodynamics of the free surface low in Pelton turbinebuckets [Ph D Thesis] Ecole polytechnique fed 2007

[14] A Perrig F Avellan J-L Kueny M Farhat and E ParkinsonldquoFlow in a Pelton turbine bucket numerical and experimentalinvestigationsrdquo Journal of Fluids Engineering vol 128 no 2 pp350ndash358 2006

[15] Y X Xiao T Cui Z W Wang and Z G Yan ldquoNumerical sim-ulation of unsteady free surface flow and dynamic performancefor a Pelton turbinerdquo inProceedings of the 26th IAHRSymposiumon Hydraulic Machinery and Systems chn August 2012

[16] M Eisenring Micro Pelton turbines St Gallen SwitzerlandSwiss Center for Appropriate Technology 1991

[17] B Janetzky H Ruprecht C Keck C Scharer and E A GodeldquoNumerical simulation of the flow in a Pelton bucketrdquo inProceedings of the in IAHR pp 276ndash283 1998

[18] J S Anagnostopoulos and D E Papantonis ldquoA fast Lagrangiansimulation method for flow analysis and runner design inPelton turbinesrdquo Journal of Hydrodynamics B vol 24 no 6 pp930ndash941 2012

[19] A Panagiotopoulos A Zidonis G A Aggidis J S Anagnos-topoulos and D E Papantonis ldquoFlow Modeling in Pelton Tur-bines by an Accurate Eulerian and a Fast Lagrangian EvaluationMethodrdquo International Journal of Rotating Machinery vol 2015Article ID 679576 2015

[20] BW Solemslie andO G Dahlhaug ldquoA reference Pelton turbinedesignrdquo in Proceedings of the IAHR 26thIAHR Symposiumon Hydraulic Machinery and Systems IOP Conf Earth andEnvironmental Science Beijing China August 2012

[21] S Pudasaini H P Neopane Amod P et al ldquoComputationalFluid Dynamics (CFD) analysis of Pelton runner of KhimtiHydro-power Project of Nepalrdquo in Rentech Symposium Com-pendium vol 4 September 2014

[22] N Tilahun W Bogale F Bekele and E Dribssa ldquoFeasibilitystudy for power generation using off- grid energy systemfrom micro hydro-PV-diesel generator-battery for rural area ofEthiopia The case of Melkey Hera village Western EthiopiardquoAIMS Energy vol 5 no 4 pp 667ndash690 2017

[23] Hydraulic Turbines Storage pumps and pump turbines- Modelacceptance tests (IEC 60193) 1999

[24] F M White and I Coreld Viscous Fluid Flow vol 3 McGraw-Hill New York NY USA 2006

[25] A Zidonis and G A Aggidis ldquoPelton turbine Identifying theoptimum number of buckets using CFDrdquo Journal of Hydrody-namics vol 28 no 1 pp 75ndash83 2016

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Mean annualWater surplus

More than 900ＧＧ

700 to 900500 to 700

300 to 500100 to 300Less than 100ＧＧ

Figure 1 Distribution of MHP potential sites in Ethiopia [4]

is brought down through the penstock pipe to a nozzle andit comes out into the turbine casing The jet is then directedat a wheel or runner which has a number of buckets aroundits edge The force of the jet on this wheel makes it turn andgives the output power [7ndash9] However investigation revealsthat there is no company or institution engaged in supplyingthis micro Pelton turbine locally in the country As a resultthe necessity and the possibilities to design and manufacturePelton turbines locally are increasingMore often thematerialand the skilled labour as well as technical staff are availablebut what is missing is the information and knows-how [4 6]

More precisely in the new context where harvestingsmall hydro potentials can become economically viablethere is also a need to provide solutions to reduce thedesign cycle time and cost for Pelton runners It is knownthat with increasing demand the performance analysis ofturbine such as efficiency and dynamic behavior is also animportant aspect to analyze its suitability under differentoperating conditions [7] Additionally it is used by theturbine producer to guarantee the hydraulic performance ofa turbine to the customer However it is known that designof Pelton turbine is mainly conducted from know-how andextensive experimental testing which provide an empiricalunderstanding of factors that are important to turbine designBut in todayrsquos highly competitive market of turbine theperformance is often difficult to determine in the short termwith this traditional practice Therefore the incorporation ofcomputational fluid dynamics (CFD) in the design of microhydro turbines appears to be necessary in order to improvetheir efficiency and cost-effectiveness beyond the traditionaldesign practices [7 10ndash12]

The main topic of investigations by the CFD method hasfocused on the interactions between the jet and the rotatingbuckets as well as the relative flows within the buckets Theseare flows that are so far not easily accessible by experimental

measurements [11] CFD simulations are therefore likelyconsidered as an availableway for investigating complex flowsin Pelton turbines provided that they are reliable and able toreveal the possibility of improving the system efficiency andreducing the manufacturing cost In addition CFD providedeeper understanding of the flow mechanisms that governperformance The most detailed CFD analysis of rotatingPelton turbine was done by Perrig et al [13 14] by consideringfive buckets and the computed results were compared withexperimental results at best efficiency point (BEP)

As explained by Zhang [7] in Pelton turbine bookhydraulic design of a Pelton turbine the related practicalexperiences have thus always played a major role besidesapplying general design rules Even the optimum bucketnumber and the size of a Pelton wheel for instance weredetermined only by experience ormodel tests without relyingon any hydro mechanical background The main reasonsfor this were the complex flow conditions in both thehigh-speed jet and the unsteady interaction between thehigh-speed jet and the rotating Pelton buckets [7 11] Butnowadays the largest amount of publications on modelingof Pelton turbines uses commercial code ANSYS CFX [710 14] The capability of solving complex impulse turbinerelated problems that include multiphase flow with freesurfaces has been demonstrated by a number of studies andis becoming increasingly significant [10ndash18] However largecomputational cost of the simulations is also the main factorwhy there is a lack of publications on CFD usage for Peltonturbines [11] As a result various authors made differentsimplifying assumptions in order to reduce this cost as muchas possible and make Pelton simulation for performancepredictions possible Most CFD simulations reviewed in theliteratureswere assuming symmetry in the flow as simplifyingassumption and therefore theymodel only half of a runner ora bucket Because of the periodic behavior assumption themajority of simulations used also only a fraction of a runnerwith the number of buckets in the section modeled being 23 5 7 or even 10 [11] Many authors used only 3 consecutivebuckets where the torque wasmeasured only on the bucket inthe middle This torque measured on a single middle bucketwas then used to construct the torque on the runner assumingthat every bucket would undergo identical loading [10 11]The first bucket was required to produce the back-splashingwater that impacts the middle bucket The third bucket wasrequired to realistically cut the jet when it is impacting thesecond bucket Even though it was shown that it is possible tomodel the complete runner this could be seen as unnecessaryusage of computational resources For instance using thesame computational resources and a reduced complexitysimulation with only 3 buckets would allow simulations withbetter discretized grids (therefore improving accuracy) oranalyzing more operating points or design variations andenable the optimization of Pelton turbine (see [11 13 14])

So far few investigators have only reported diverse valuesof maximum efficiencies as shown in Table 1 Because ofcommerciality of the turbine many of the investigatorsnormalized their results in their publications Most papersreport that the shape of the efficiency curve is well capturedwhile actual differences between measured and numerically







Pudasaini et al [21] 8085 009218 600 490 8771



(Ls)















Pelton20 Ｅ７

10 Ｅ７5 Ｅ７

1 Ｅ７


100７Propeller

Crossflow

Flow (Ls)

Net

hea

d (m

) 100

10

1000

110010 10001




119881jet = 119870119873radic2119892119867119899 (2)



(3)





PCD

Nozzle

Pelton runner

P

UＤＮ




212058711987360 sdot 1198632 = 119909 sdot 119881jet (5)


119863 = 377 times radic119867119899119873 (6)





Part Section D-D

Section A-A

Section B-B

Partial view on C

AA

B

B

C

D

D

REF


Flat areas

340

140

R100

R100

R100

160

380

20 150∘

150∘ ref

120

19

R69 spherical

R69 spherical

50

114

70

150∘ ref

527∘

50∘

110

R1 min

900∘












16

R15

35

10∘ 20∘









xyz

(a) (b)












(a)

Rotating domain

Stationary domain

000

200

00

100

00

400

00

(mm)

300

00 00

025

005

0

010

0

(m)

007

5

Nozzle

Half buckets

(b)









( 11986711986321198732 )prototype = ( 11986711986321198732 )model

( 1198761198731198633 )prototype = ( 1198751198731198633 )model

( 11987511986351198733 )prototype = ( 11987511986351198733 )model

(7)






Top bucket

XZ

Y

(a)

000

0

005

0

010

0

(m)

XZ

XZ

Y

(b)
















Air inlet

openingStationary

Rotating opening

X

Z

Y

X

Z

Y0045 00900(m)

(a)

Symmetry

Rotating opening


XZ

Y0045 00900(m)

(b)










(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001


(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001



(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001


(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001









Pressurecontour 2


Pressurecontour 2


0

001

5

003

006

0

(m)

004

5 0

002

004

008

0

(m)

006

0

X

Z

Y

X

Z

Y

X

Z

Y

X

ZY










XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)








Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Pudasaini et al [21] 8085 009218 600 490 8771



(Ls)















Pelton20 Ｅ７

10 Ｅ７5 Ｅ７

1 Ｅ７


100７Propeller

Crossflow

Flow (Ls)

Net

hea

d (m

) 100

10

1000

110010 10001




119881jet = 119870119873radic2119892119867119899 (2)



(3)





PCD

Nozzle

Pelton runner

P

UＤＮ




212058711987360 sdot 1198632 = 119909 sdot 119881jet (5)


119863 = 377 times radic119867119899119873 (6)





Part Section D-D

Section A-A

Section B-B

Partial view on C

AA

B

B

C

D

D

REF


Flat areas

340

140

R100

R100

R100

160

380

20 150∘

150∘ ref

120

19

R69 spherical

R69 spherical

50

114

70

150∘ ref

527∘

50∘

110

R1 min

900∘












16

R15

35

10∘ 20∘









xyz

(a) (b)












(a)

Rotating domain

Stationary domain

000

200

00

100

00

400

00

(mm)

300

00 00

025

005

0

010

0

(m)

007

5

Nozzle

Half buckets

(b)









( 11986711986321198732 )prototype = ( 11986711986321198732 )model

( 1198761198731198633 )prototype = ( 1198751198731198633 )model

( 11987511986351198733 )prototype = ( 11987511986351198733 )model

(7)






Top bucket

XZ

Y

(a)

000

0

005

0

010

0

(m)

XZ

XZ

Y

(b)
















Air inlet

openingStationary

Rotating opening

X

Z

Y

X

Z

Y0045 00900(m)

(a)

Symmetry

Rotating opening


XZ

Y0045 00900(m)

(b)










(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001


(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001



(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001


(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001









Pressurecontour 2


Pressurecontour 2


0

001

5

003

006

0

(m)

004

5 0

002

004

008

0

(m)

006

0

X

Z

Y

X

Z

Y

X

Z

Y

X

ZY










XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)








Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Pelton20 Ｅ７

10 Ｅ７5 Ｅ７

1 Ｅ７


100７Propeller

Crossflow

Flow (Ls)

Net

hea

d (m

) 100

10

1000

110010 10001




119881jet = 119870119873radic2119892119867119899 (2)



(3)





PCD

Nozzle

Pelton runner

P

UＤＮ




212058711987360 sdot 1198632 = 119909 sdot 119881jet (5)


119863 = 377 times radic119867119899119873 (6)





Part Section D-D

Section A-A

Section B-B

Partial view on C

AA

B

B

C

D

D

REF


Flat areas

340

140

R100

R100

R100

160

380

20 150∘

150∘ ref

120

19

R69 spherical

R69 spherical

50

114

70

150∘ ref

527∘

50∘

110

R1 min

900∘












16

R15

35

10∘ 20∘









xyz

(a) (b)












(a)

Rotating domain

Stationary domain

000

200

00

100

00

400

00

(mm)

300

00 00

025

005

0

010

0

(m)

007

5

Nozzle

Half buckets

(b)









( 11986711986321198732 )prototype = ( 11986711986321198732 )model

( 1198761198731198633 )prototype = ( 1198751198731198633 )model

( 11987511986351198733 )prototype = ( 11987511986351198733 )model

(7)






Top bucket

XZ

Y

(a)

000

0

005

0

010

0

(m)

XZ

XZ

Y

(b)
















Air inlet

openingStationary

Rotating opening

X

Z

Y

X

Z

Y0045 00900(m)

(a)

Symmetry

Rotating opening


XZ

Y0045 00900(m)

(b)










(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001


(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001



(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001


(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001









Pressurecontour 2


Pressurecontour 2


0

001

5

003

006

0

(m)

004

5 0

002

004

008

0

(m)

006

0

X

Z

Y

X

Z

Y

X

Z

Y

X

ZY










XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)








Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Part Section D-D

Section A-A

Section B-B

Partial view on C

AA

B

B

C

D

D

REF


Flat areas

340

140

R100

R100

R100

160

380

20 150∘

150∘ ref

120

19

R69 spherical

R69 spherical

50

114

70

150∘ ref

527∘

50∘

110

R1 min

900∘












16

R15

35

10∘ 20∘









xyz

(a) (b)












(a)

Rotating domain

Stationary domain

000

200

00

100

00

400

00

(mm)

300

00 00

025

005

0

010

0

(m)

007

5

Nozzle

Half buckets

(b)









( 11986711986321198732 )prototype = ( 11986711986321198732 )model

( 1198761198731198633 )prototype = ( 1198751198731198633 )model

( 11987511986351198733 )prototype = ( 11987511986351198733 )model

(7)






Top bucket

XZ

Y

(a)

000

0

005

0

010

0

(m)

XZ

XZ

Y

(b)
















Air inlet

openingStationary

Rotating opening

X

Z

Y

X

Z

Y0045 00900(m)

(a)

Symmetry

Rotating opening


XZ

Y0045 00900(m)

(b)










(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001


(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001



(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001


(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001









Pressurecontour 2


Pressurecontour 2


0

001

5

003

006

0

(m)

004

5 0

002

004

008

0

(m)

006

0

X

Z

Y

X

Z

Y

X

Z

Y

X

ZY










XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)








Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














xyz

(a) (b)












(a)

Rotating domain

Stationary domain

000

200

00

100

00

400

00

(mm)

300

00 00

025

005

0

010

0

(m)

007

5

Nozzle

Half buckets

(b)









( 11986711986321198732 )prototype = ( 11986711986321198732 )model

( 1198761198731198633 )prototype = ( 1198751198731198633 )model

( 11987511986351198733 )prototype = ( 11987511986351198733 )model

(7)






Top bucket

XZ

Y

(a)

000

0

005

0

010

0

(m)

XZ

XZ

Y

(b)
















Air inlet

openingStationary

Rotating opening

X

Z

Y

X

Z

Y0045 00900(m)

(a)

Symmetry

Rotating opening


XZ

Y0045 00900(m)

(b)










(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001


(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001



(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001


(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001









Pressurecontour 2


Pressurecontour 2


0

001

5

003

006

0

(m)

004

5 0

002

004

008

0

(m)

006

0

X

Z

Y

X

Z

Y

X

Z

Y

X

ZY










XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)








Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














(a)

Rotating domain

Stationary domain

000

200

00

100

00

400

00

(mm)

300

00 00

025

005

0

010

0

(m)

007

5

Nozzle

Half buckets

(b)









( 11986711986321198732 )prototype = ( 11986711986321198732 )model

( 1198761198731198633 )prototype = ( 1198751198731198633 )model

( 11987511986351198733 )prototype = ( 11987511986351198733 )model

(7)






Top bucket

XZ

Y

(a)

000

0

005

0

010

0

(m)

XZ

XZ

Y

(b)
















Air inlet

openingStationary

Rotating opening

X

Z

Y

X

Z

Y0045 00900(m)

(a)

Symmetry

Rotating opening


XZ

Y0045 00900(m)

(b)










(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001


(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001



(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001


(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001









Pressurecontour 2


Pressurecontour 2


0

001

5

003

006

0

(m)

004

5 0

002

004

008

0

(m)

006

0

X

Z

Y

X

Z

Y

X

Z

Y

X

ZY










XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)








Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Top bucket

XZ

Y

(a)

000

0

005

0

010

0

(m)

XZ

XZ

Y

(b)
















Air inlet

openingStationary

Rotating opening

X

Z

Y

X

Z

Y0045 00900(m)

(a)

Symmetry

Rotating opening


XZ

Y0045 00900(m)

(b)










(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001


(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001



(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001


(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001









Pressurecontour 2


Pressurecontour 2


0

001

5

003

006

0

(m)

004

5 0

002

004

008

0

(m)

006

0

X

Z

Y

X

Z

Y

X

Z

Y

X

ZY










XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)








Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Air inlet

openingStationary

Rotating opening

X

Z

Y

X

Z

Y0045 00900(m)

(a)

Symmetry

Rotating opening


XZ

Y0045 00900(m)

(b)










(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001


(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001



(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001


(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001









Pressurecontour 2


Pressurecontour 2


0

001

5

003

006

0

(m)

004

5 0

002

004

008

0

(m)

006

0

X

Z

Y

X

Z

Y

X

Z

Y

X

ZY










XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)








Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001


(ＧＭminus1)

3617e + 000

7423e + 000

1123e + 001

1503e + 001

1884e + 001



(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001


(ＧＭminus1)

8028e + 000

1058e + 001

1312e + 001

1567e + 001

1822e + 001









Pressurecontour 2


Pressurecontour 2


0

001

5

003

006

0

(m)

004

5 0

002

004

008

0

(m)

006

0

X

Z

Y

X

Z

Y

X

Z

Y

X

ZY










XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)








Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Pressurecontour 2


Pressurecontour 2


0

001

5

003

006

0

(m)

004

5 0

002

004

008

0

(m)

006

0

X

Z

Y

X

Z

Y

X

Z

Y

X

ZY










XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)








Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











XZ

YX

Z

Y

X

Z

Y

0050 01000(m)

0050 0100 0150 02000(m)

010000500(m)


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001


(ＧＭminus1)

9084e + 000

5051e + 000

1019e + 000

1312e + 001

1715e + 001

(a)

Back wash

X

Z

YX

ZY

X

ZY

0050 01000(m)

0100 0200015000500(m)

0050 01000(m)


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus


(ＧＭminus1)

9587e + 000

5028e + 000

1415e + 001

1870e + 001

4701e 001minus

(b)








Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004

Pressurecontour 2

(Pa)

3559e + 004

2789e + 004

2019e + 004

1250e + 004

4800e + 003

minus4138e + 004

minus3368e + 004

minus2599e + 004

minus2896e + 003

minus1829e + 004

minus1059e + 004




Jet cut in

Full jet

Jet cut out


Time (sec)

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2

02

Torq

ue (N

m)

０＄ = 400ＧＧ









minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














minus35

minus30

minus25

minus20

minus15

minus10

minus5

05

Torq

ue (N

m) 001 002 003 004 0050

Time (sec)








001 002 003 004 0050Time (sec)

minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)







120578 = 119875output119875input (9)








[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













[10]


[19]Head m 475 539 100 475 539 100 539 100

Flow rate m3s 014 005 135BEP 014 005 135

BEP 005 135 BEP






002 004 0060Time (sec)

minus40

minus30

minus20

minus10

0

10

Torq

ue (N

m)


M1M2M3

M4M5M6

M7M8



minus25

minus20

minus15

minus10

minus5

0

5

Torq

ue (N

m)

001 002 003 004 0050Time (sec)

M1M2M3

M4M5M6

M7M8





4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











4 Conclusion









Abbreviations





Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









design, modeling, and cfd analysis of a micro hydro pelton ...design, modeling, and cfd analysis of...

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