PELTONTURBINE

Impulseturbine

Therelativeproportionofenergytransferobtainedbythechangeinstaticheadandbythechangeindynamicheadisoneoftheimportantfactorsy g y pforclassifyingfluidmachines.

Foranaxialflowimpulsemachine.Foranimpulsemachine,therotorcanbemadeopen,thatis,thevelocityV1 can, p , , y 1representanopenjetoffluidflowingthroughtherotor,whichneedsnocasing.Averysimpleexampleofanimpulsemachineisapaddlewheelrotatedbytheimpingementofwaterfromastationarynozzle

Degreeofreaction=0

Themachineforwhichthechangeinstaticheadintherotoriszeroisk i l hiknownasimpulsemachine.

INTRODUCTIONINTRODUCTION

Named after the designer Mr A Pelton inNamedafterthedesignerMr.A.PeltoninCaliforniaat1810

Impulse turbine as there is no pressure drop Impulseturbine asthereisnopressuredropacrossthebucketsS i bl f hi h h d f b 100 500 Suitableforhighheadsofabout100500m

Requirescomparativelylessquantityofwater

SCHEMATIC DIAGRAMSCHEMATICDIAGRAM

WORKINGWORKING Watersuppliedisfromahighheadthroughalongconduitcalledpenstock.

Thewaterisacceleratedinnozzle andtheheadisconverted into velocity and discharges at high speed inconvertedintovelocityanddischargesathighspeedintheformofajetatatmosphericpressure

Thejetstrikesbuckets attachedtotherimofarotatingwheel (runner)wheel(runner)

Impactofwateronbucketsproduceaforcewhichcausesthewheeltorotatebysupplyingatorqueonh h ftheshaft

waterdischargedatrelativelylowspeedfallsintolowerreservoirortailrace

NOZZLEASSEMBLY

NOZZLEASSEMBLY PowerproducedbyturbineproportionaltoQxH

whereQ:VolumeflowrateH:effectivehead

SinceHcannotbevariedeasily,Q(crosssectionalareaxvelocityofflowisvaried)

Forwheelspeedtobemaintainedconstant,jetvelocityisnotvaried.

Crosssectionalareaisvariedusingaspearvalve Spearvalveisactuatedtoandfroasperthepowerdemand

Deflector Sometimes,needarisesforimmediateclosureofnozzle.

Ifflowisreducedsuddenly,highbackpressurewaveswillbegeneratedongpenstockpipes

Deflector alters the jet trajectory Deflectoraltersthejettrajectory

RUNNER WITH BUCKETSRUNNERWITHBUCKETS

Undercuts are provided so that the jet bye passes the inclined bladesUndercuts are provided so that the jet bye-passes the inclined blades which are obstructing the jet to strike the blade which is vertical in position

RUNNERWITHBUCKETS Usually more than 15 buckets Usuallymorethan15buckets Eachbucketissplitverticallyintotwopartsbyasplitterthathasasharpedgeatthecentrep g

Strikingjetofwaterisdividedintotwopartsbythesplitter

eachpartofjetflowssidewaysroundthesmoothinnersurfaceofthebucketandleavesitwitharelativevelocity almost opposite in direction of the original jetvelocityalmostoppositeindirectionoftheoriginaljet

Notchattheedgeofouterrimofeachbucketensuresalossfreeentryofthejetintothebuckets.

Bucketofpeltonturbine

RUNNERWITHBUCKETS Maximumchangeinmomentumisobtainedwhenthejetis180

But angle is restricted to 165 so that the fluid leaving Butangleisrestrictedto165 sothatthefluidleavingonebucketdoesnotstrikebackthesucceedingbucket

Bucketsaremadeofspecialbronze steelalloyswithp yNickel,Chromiumorstainlesssteel.

Bucketsareproperlypolishedforsmoothchangeindi ti d th f ti f l k tdirectionandtheformationoflowpressurepocketscausedduetoerosionareavoided

Buckets can be bolted construction( for large turbines)Bucketscanbeboltedconstruction(forlargeturbines)orofsinglecast

CASING

Preventssplashingofwater Guideswatertoflowthroughthetailrace Provides housing and support to the thrustProvideshousingandsupporttothethrustbearingsandshaft

Since the buckets are symmetrical side or Sincethebucketsaresymmetrical,sideoraxialthrustsproducedbywaterineachhalfisbalancedbalanced

Providessafetyagainstaccidents

ANALYSIS

Velocityofwaterjet,

1 2vV C gH=where,

vC =0.95to0.99

Histhenetheadavailableatthenozzleexit

Coefficientofvelocity

214

Q d V=Rateofdischarge, distheleastdiameterofthejet;variesfrom20to30 variesfrom30to45

All fluid is assumed to be striking the bucket at radius r( pitch circle radius)=D/2Allfluidisassumedtobestrikingthebucketatradiusr(pitchcircleradius)=D/2

60DNu =Peripheralvelocityisgivenby60

WhereNisthespeedofthewheelinrevolutionsperminute

2 1r rV KV= WhereKislessthanunityRelativevelocities 2 1r r yForceexertedbythefluidjetinthedirectionofrotationis

1 2( )x w wF Q V V= + (DirectionofVw2 isoppositetoVw1)

Powerproducedbythewheel

( )P Q V V u= +1 2( )w wP Q V V u= +Inputiskineticenergy.Sohydraulicefficiency,

( )Q V V u +1 221

12

( )w wh

Q V V uQV

+= =

1 cos (1 cos )KV u K = +2 2 1 1cos cos [( ) cos ]w r rV V u KV u K V u u = = =

Wehave

121

2 (1 cos )( )hu K V u

V = +

1

ForagivenvalueofV1,efficiencyismaximumwhen

0 (2 4 )d V u = = 10 (2 4 )V udu = =

1

2Vu =2

max1 cos

2K +=

Andmaximumefficiency

Efficiencyisbetween85and90% Power loss occur due toPowerlossoccurdueto

Frictioninbearing Frictionbetweenwheelandatmosphere

L i l Lossinnozzle

u=V1 iscalledrunawayspeed,speedatnoload Volumetric efficiencyVolumetricefficiency

Q Qv

Q QQ

=

Sincesomewatermaysliptotailracewithoutdoingusefulworkefficiencyspeedratio

Q1.Apeltonturbineproduces25MWwhilerunningat750rpmunder an effective head of 1770m. Calculate (i) least diameterunderaneffectiveheadof1770m.Calculate(i)leastdiameterofthejet(ii)meandiameteroftherunner(iii)numberofbuckets:

Letthecoefficientofvelocitybe0.98.Theabsolutevelocityofwater jet will then bewaterjetwillthenbe

1 2 0.98 2 9.81 1770 182.63 /vV C gH m s= = =Themaximumpossibleoutputfromtheturbineis.QgHp pAssuminganoverallefficiencyequalto0.85,thegivenoutput

Qg625 10 0.85watts QgH =

Thevolumeflowrate,6

35

25 10 1.694 /Q m s= =50.85 10 9.81 1770Q

Since 214

Q d V= 4

wheredisthediameterofthejet,

4 4 1 694Q

1

4 4 1.694 10.87182.63

Qd cmV

= = =h i ffi i i b i d d ithemaximumefficiencyisobtainedatspeedratio,

0.462

ugH

=Therefore,themeanspeed

0.46 2u gH=

0.46 186.360DNu = =

and

60

therefore 0.46 186.3 60 2.18750

D m = =750

the ratio D/d is called the jet ratio and is an importantparameter in the design and selection of Pelton turbine. Theparameter in the design and selection of Pelton turbine. Thenumber of buckets in any Pelton wheel is fixed by theconsideration that the buckets do not frequently interfere withthe path of incoming ater jet If the n mber of b ckets isthe path of incoming water jet. If the number of buckets issmall, they would be widely spaced and a part of the water jetmay not strike a bucket. If the buckets are closely spaced, thepath of water jet will get distributed by the incoming buckets.Dr. Taygun of Zurich (Austria) has suggested an empiricalrelation for obtaining the number of buckets. According to him,relation for obtaining the number of buckets. According to him,the number of buckets

2.180 5 15 0 5 15 25Dz = + = + 0.5 15 0.5 15 250.1089

zd

= + = +

Q2.Apeltonwheelproduces15MWunderaheadof400mwhenrunning at a speed of 500rpm. If the diameter of the jet is notrunningataspeedof500rpm.Ifthediameterofthejetisnottoexceedonetenthofthewheeldiameter,calculatethenumberanddiameterofthejets,diameterofthewheelandquantity of flow Assume overall efficiency =0 88 Cv=0 98 andquantityofflow.Assumeoverallefficiency=0.88,Cv=0.98andspeedratio=0.46

Theoverallefficiencyis0.88andtherefore,thepowerthatcouldhavebeendeveloped,

6

0

15 10QgH =

615 10 23

15 10 4.344 /0.88 10 9.81 400

Q m s= = Thevelocityofthejet,

31 2 0.98 2 9.81 400 86.817 /vV C gH m s= = =

Peripheralspeedofwheel,

0.46 2 40.75 /u gH m s= =Wheeldiameter,

60 40.75 60 1.56500

uD mN = = =

fThejetratioshouldnotexceed10themaximumdiameterofthejetis0.156m

and2

1 . .4Q d V no of jets=

and,

Noofjets 2 21

4 4 4.344 2.18(0.156) 86.817

Qd V

= = = Or3jets

Jetdiameterd=1

4 4 4.344 0.1457 145.73 3 86.817Q m mmV

= = =

Specificspeedalsoindicatesnumberofjets

/4 34.2N PN = =5/4 34.2sN H

Quiz

The mean blade speed in a Pelton turbine is 14 m/s. The rate of flow of water supplied by the jet under a head ospp y j450 m is 800 L/s. If the jet is deflected by the blades at an angle of 165o and the friction factor at the blade is 0.9, find the theoretical power output and hydraulic efficiency of thethe theoretical power output and hydraulic efficiency of the turbine.

Hint: the blade speed is not optimumAdditonal question

Compare the current efficiency with the optimum condition and discuss the physical reason for change in efficiency

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